on positivity of line bundles on enriques surfaces we study linear systems on enriques surfaces we prove rationality of seshadri constants of ample line bundles on enriques surfaces and provide lower bounds on these numbers we show the nonexistence of k very ample line bundles on enriques surfaces of degree 4k 4 for k 1 thus answering an old question of ballico and sommese introduction in this note we answer a question posed by ballico and sommese 1 see also terakawa 14 concerning the existence of k very ample line bundles of degree 4k 4 on enriques surfaces we show that such line bundles exist if and only if k 0 and that in fact the degree of a k very ample line bundle on an enriques surface is subject to a much more restrictive bound theorem 2 4 this has strong consequences for the local positivity of line bundles on enriques surfaces we address this questions in section 3 in particular we show that seshadri constants of ample line bundles on enriques surfaces are always rational 1 auxiliary material and notation the basic reference for this paper is the monograph 6 by cossec and dolgachev here we briefly recall properties of enriques surfaces needed for our considerations first of all an enriques surface is a surface y of kodaira dimension zero with no differential forms in particular ho ky 0 and the canonical bundle ky is a 2torsion element in pico y i e 2ky oy to alleviate notation it is convenient to use the following convention in the sequel we make frequent use of vanishing theorems and statements on adjoint line bundles since the canonical divisor ky is numerically trivial the adjoint line bundle ky l has the same numerical properties as l in particular if l is nef and big ample then so is ky l by the nakai moishezon criterion so in order to get vanishing statements for l we apply vanishing theorems to ky l and use the fact that 2ky is trivial in the sequel we do so without comment and hope to cause no confusion this way received by the editors june 1 2000 2000 mathematics subject classification primary 14j28 secondary 14c20 14e25

vector bundles of rank 2 and linear systems on algebraic surfaces let s be a smooth complex algebraic surface and let l be a divisor on s it is well known that the linear system il ksi where ks is the canonical divisor plays an important role in understanding the geometry of s several authors see for example 8 11 studied various properties of this system our paper treats the same subject but the point of view is different from the works mentioned above the philosophy underlying our approach is almost classical points on s more generally effective 0 cycles in special position with respect to il ksi see definition below contain information about the geometry of s this point of view was recently revived in 5 also 10 in fact this paper contains the technique of going from the effective 0 cycle z in special position with respect to il ksi to the geometry of s for the sake of completeness we give a definition and state a theorem which can be found in 5 10

the gonality and the clifford index of curves on a toric surface abstract we determine the gonality and the clifford index for curves on a compact smooth toric surface moreover it is shown that their gonality is computed by pencils on the ambient surface from the geometrical viewpoint this means that the gonality can be read off from the lattice polygon associated to the curve

the generic green lazarsfeld secant conjecture using lattice theory on special k3 surfaces calculations on moduli stacks of pointed curves and voisin s proof of green s conjecture on syzygies of canonical curves we prove the prym green conjecture on the naturality of the resolution of a general prym canonical curve of odd genus as well as many cases of the green lazarsfeld secant conjecture on syzygies of non special line bundles on general curves

shape control of vibrating simply supported rectangular plates we determine the optimum location of a given rectangular piezoceramic pzt actuator that will require the minimum voltage to annul the deflections of a simply supported rectangular linear elastic plate vibrating near one of its fundamental frequencies keeping the location of the centroid and the shape of the pzt fixed we ascertain the voltage required as a function of the length of its diagonal to nullify the deflections of the plate

koszul homology and syzygies of veronese subalgebras a graded k algebra r has property np if it is generated in degree 1 has relations in degree 2 and the syzygies of order p on the relations are linear the green lazarsfeld index of r is the largest p such that it satisfies the property np our main results assert that under a mild assumption on the base field the cth veronese subring of a polynomial ring has green lazarsfeld index c 1 the same conclusion also holds for an arbitrary standard graded algebra provided c gg 0

green s conjecture for curves on rational surfaces with an anticanonical pencil green s conjecture is proved for smooth curves c lying on a rational surface s with an anticanonical pencil under some mild hypotheses on the line bundle l mathcal o s c constancy of clifford dimension clifford index and gonality of curves in the linear system vert l vert is also obtained

cyclic coverings and higher order embeddings of algebraic varieties in the present paper we study higher order embeddings in the context of cyclic coverings analyzing the positivity of the line bundle downstairs and its relationship with the branch divisor we provide criteria for its pull back to define an embedding of given order we show that the obtained criteria are sharp finally we apply them to various sometimes seemingly unrelated problems in algebraic geometry

projection pursuit density estimation abstract the projection pursuit methodology is applied to the multivariate density estimation problem the resulting nonparametric procedure is often less biased than the kernel and near neighbor methods in addition graphical information is produced that can be used to help gain geometric insight into the multivariate data distribution

coevolutionary approaches to structural optimization the numerical results on the shape control of laminated plates with piezoelectric actuators demonstrate that even if the plate is unconstrained the piezoelectrically induced in plane stresses may signie cantly affect the mechanical behavior of the plate therefore for the case of combined in phase and out of phase piezoelectric actuation accurate modeling of composite plates with piezoelectric elements should account for the stress stiffening effects the importance of the stress stiffness effect depends on the magnitude of the in phase actuation and geometric arrangement of the piezoelectric actuators boundary conditions geometry of the problem and material properties the ability of controlling the plate stiffness has potentially interesting applications in smart structures for example piezoelectric actuationsystemsmay be designed to tune the vibrationfrequencies of composite plates also the problem of buckling control of composite plates with piezoelectric elements can be properly modeled using the present formulation

investigating the performance of alternate regression weights by studying all possible criteria in regression models with a fixed set of predictors we describe methods for assessing all possible criteria i e dependent variables and subsets of criteria for regression models with a fixed set of predictors x where x is an n 1 vector of independent variables our methods build upon the geometry of regression coefficients hereafter called regression weights in n dimensional space for a full rank predictor correlation matrix rxx of order n and for regression models with constant r2 coefficient of determination the ols weight vectors for all possible criteria terminate on the surface of an n dimensional ellipsoid the population performance of alternate regression weights such as equal weights correlation weights or rounded weights can be modeled as a function of the cartesian coordinates of the ellipsoid these geometrical notions can be easily extended to assess the sampling performance of alternate regression weights in models with either fixed or random predictors and for models with any value of r2 to illustrate these ideas we describe algorithms and r r development core team 2009 code for 1 generating points that are uniformly distributed on the surface of an n dimensional ellipsoid 2 populating the set of regression weight vectors that define an elliptical arc in n and 3 populating the set of regression vectors that have constant cosine with a target vector in n each algorithm is illustrated with real data the examples demonstrate the usefulness of studying all possible criteria when evaluating alternate regression weights in regression models with a fixed set of predictors

on the projective normality of line bundles of extremal degree we propose a new method using deformation theory to study the maximal rank conjecture for line bundles of extremal degree which can be viewed as the first case to test the conjecture we prove that maximal rank conjecture holds by our new method

generation of k jets on toric varieties the notion of a k convex delta support function for a toric variety x delta is introduced a criterion for a line bundle l to generate k jets on x is given in terms of the k convexity of the delta support function psi l equivalently l is proved to be k jet ample if and only if the restriction to each invariant curve has degree at least k

a variant of the acceptance rejection method for computer generation of random variables abstract a variant of the common acceptance rejection method for generating random variables guarantees that steps are not repeated this approach affords considerable flexibility in tailoring the method efficiently to the specified density an algorithm for generating cauchy random variables illustrates the use of this approach

generalized hybrid method for fuzzy multiobjective optimization of engineering systems a generalized hybrid approach is presented for the multiobjective optimization of engineering systems in the presence of objectives and constraints that are partly fuzzy and partly crisp the methodology is based on both fuzzy set and dempster shafer theories to capture the features of incomplete imprecise uncertain or vague information that is often present in real world engineering systems the original partly fuzzy multiobjective optimization problem is first defuzzified into a crisp generalized multiobjective optimization problem using fuzzy set theory the resulting multiobjective problem is then transformed into an equivalent single objective optimization problem using a modified dempster shafer theory the computational details of the approach are illustrated with a structural design example

on the vanishing of higher syzygies of curves ii we verify green s conjecture for a generic k gonal curve of genus g for g geq k k 1 2