eigenvalue assignment by minimal state feedback gain in lti multivariable systems in this article an improved method for eigenvalue assignment via state feedback in the linear time invariant multivariable systems is proposed this method is based on elementary similarity operations and involves mainly utilisation of vector companion forms and thus is very simple and easy to implement on a digital computer in addition to the controllable systems the proposed method can be applied for the stabilisable ones and also systems with linearly dependent inputs moreover two types of state feedback gain matrices can be achieved by this method 1 the numerical one which is unique and 2 the parametric one in which its parameters are determined in order to achieve a gain matrix with minimum frobenius norm the numerical examples are presented to demonstrate the advantages of the proposed method

deformations of quasi homogeneous surface singularities let a a be a finitely generated normal graded domain over e so that i 0 v spec a has an isolated singularity we say v is a quasi homogeneous singularity or admits a good ie action or is defined by weighted homogeneous polynomials we are concerned with two questions about the deformations of v there are two natural notions of equisingular deformation of v first one has deformations of weight 0 that is one perturbs the defining equations of vby terms of weight at least as big to make a good notion out of this dock sang rim observed one is really deforming a and the weight filtration ij where ij ai

koszul divisors on moduli spaces of curves given a moduli space how can one construct the best in the sense of higher dimensional algebraic geometry effective divisor on it we show that at least in the case of the moduli space of curves the answer is provided by the koszul divisor defined in terms of the syzygies of the parameterized objects in this paper we find a formula for the slopes of all koszul divisors on overline cal m g in particular we obtain the first infinite series of counterexamples to the harris morrison slope conjecture and we prove the maximal rank conjecture in the case when the brill noether number of the corresponding linear series equals 0 we also find shorter proofs for the formulas of the class of the brill noether and gieseker petri divisors finally we improve most of logan s results on the kodaira dimension of the moduli spaces overline cal m g n of pointed stable curves

application of a fractional step method to incompressible navier stokes equations a numerical method for computing three dimensional time dependent incompressible flows is presented the method is based on a fractional step or time splitting scheme in conjunction with the approximate factorization technique it is shown that the use of velocity boundary conditions for the intermediate velocity field can lead to inconsistent numerical solutions appropriate boundary conditions for the intermediate velocity field are derived and tested numerical solutions for flows inside a driven cavity and over a backward facing step are presented and compared with experimental data and other numerical results

a new non overlapping concept to improve the hybrid particle level set method in multi phase fluid flows a novel non overlapping concept is augmented to the hybrid particle level set hpls method to improve its accuracy and suitability for the modelling of multi phase fluid flows the concept addresses shortcomings in the reseeding algorithm which maintains resolution of the surface at runtime these shortcomings result in the misplacement of newly seeded particles in the opposite signed domain and necessitate a restriction on the distance that a particle can escape without deletion which reduces the effectiveness of the method the non overlapping concept judges the suitability of potential new particles based on information already contained within the particle representation of the surface by preventing the misplacement of particles it is possible to significantly relax the distance restriction thereby increasing the accuracy of the hpls method in multi phase flows to demonstrate its robustness and efficiency the concept is examined with a number of challenging test cases including both level set only simulations and two phase fluid flows a novel non overlapping concept is augmented to the hybrid particle level set hpls method to improve its accuracy and suitability for the modelling of multi phase fluid flows we first diagnose the key flaws in existing particle level set methods that may result in the misplacement of newly seeded particles in the opposite signed domain the non overlapping concept effectively prevents the misplacement of particles during reseeding operations and thereby relaxes the common restriction placed on escaped particles the concept is examined with a number of challenging test cases including both the level set only simulations and the two phase fluid flows

sharp interface immersed boundary level set method for wave body interactions a sharp interface cartesian grid method for the large eddy simulation of two phase turbulent flows interacting with moving bodies is presented the overall approach uses a sharp interface immersed boundary formulation and a level set ghost fluid method for solid fluid and fluid fluid interface treatments respectively a four step fractional step method is used for velocity pressure coupling and a lagrangian dynamic smagorinsky subgrid scale model is adopted for large eddy simulations a simple contact angle boundary condition treatment that conforms to the immersed boundary formulation is developed a variety of test cases of different scales ranging from bubble dynamics water entry and exit landslide generated waves to ship hydrodynamics are performed for validation extensions for high reynolds number ship flows using wall layer models are also considered

robust eigenstructure assignment in geometric control theory in this paper we employ the rosenbrock system matrix pencil for the computation of output nulling subspaces of linear time invariant systems which appear in the solution of a large number of control and estimation problems we also consider the problem of finding friends of these output nulling subspaces i e the feedback matrices that render such subspaces invariant with respect to the closed loop map and output nulling with respect to the output map and which at the same time deliver a robust closed loop eigenstructure we show that the methods presented in this paper offer considerably more robust eigenstructure assignment than the other commonly used methods and algorithms

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

on the projective normality of double coverings over a rational surface abstract we study the projective normality of a minimal surface x which is a ramified double covering over a rational surface s with dim k s 1 in particular horikawa surfaces the minimal surfaces of general type with k x 2 2 p g x 4 are of this type up to resolution of singularities let be the covering map from x to s we show that the z 2 invariant adjoint divisors k x r a are normally generated where the integer r 3 and a is an ample divisor on s

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

a geometric effective nullstellensatz the purpose of this paper is to present a geometric theorem which clarifies and extends in several directions work of brownawell kollar and others on the effective nullstellensatz specifically we work on an arbitrary smooth complex projective variety x with the previous classical results corresponding to the case when x is projective space in this setting we prove a local effective nullstellensatz for ideal sheaves and a corresponding global division theorem for adjoint type bundles we also make explicit the connection with the intersection theory of fulton and macpherson finally constructions involving products of prime ideals that appear in earlier work are replaced by geometrically more natural conditions involving orders of vanishing along subvarieties much of the previous activity in this area has been algebraic in nature and seems perhaps not well known in detail among geometers therefore we have felt it worthwhile to include here a rather extended introduction we start with an overview of the questions and earlier work on them then we present the set up and statement of our main theorem we conclude with a series of examples which can be read before the general result of what it yields in special cases

secant varieties and birational geometry we show how to use information about the equations defining secant varieties to smooth projective varieties in order to construct a natural collection of birational transformations these were first constructed as flips in the case of curves by m thaddeus via geometric invariant theory and the first flip in the sequence was constructed by the author for varieties of arbitrary dimension in an earlier paper we expose the finer structure of a second flip again for varieties of arbitrary dimension we also prove a result on the cubic generation of the secant variety and give some conjectures on the behavior of equations defining the higher secant varieties

singularities and syzygies of secant varieties of nonsingular projective curves in recent years the equations defining secant varieties and their syzygies have attracted considerable attention the purpose of the present paper is to conduct a thorough study on secant varieties of curves by settling several conjectures and revealing interaction between singularities and syzygies the main results assert that if the degree of the embedding line bundle of a nonsingular curve of genus g is greater than 2g 2k p for nonnegative integers k and p then the k th secant variety of the curve has normal du bois singularities is arithmetically cohen macaulay and satisfies the property n k 2 p in addition the singularities of the secant varieties are further classified according to the genus of the curve and the castelnuovo mumford regularities are also obtained as well as one of the main technical ingredients we establish a vanishing theorem on the cartesian products of the curve which may have independent interests and may find applications elsewhere

a unified method for optimal arbitrary pole placement abstract we consider the classic problem of pole placement by state feedback we offer an eigenstructure assignment algorithm to obtain a novel parametric form for the pole placing feedback matrix that can deliver any set of desired closed loop eigenvalues with any desired multiplicities this parametric formula is then exploited to introduce an unconstrained nonlinear optimisation algorithm to obtain a feedback matrix that delivers the desired pole placement with optimal robustness and minimum gain lastly we compare the performance of our method against several others from the recent literature

on syzygies of non complete embedding of projective varieties let x be a non degenerate not necessarily linearly normal projective variety in mathbb p r recently the generalization of property np to non linearly normal projective varieties have been considered and its algebraic and geometric properties are studied extensively one of the generalizations is the property nd p for the saturated ideal ix eisenbud et al in compos math 141 1460 1478 2005 and the other is the property n p s for the graded module of the twisted global sections of mathcal o x 1 kwak and park in j reine angew math 582 87 105 2005 in this paper we are interested in the algebraic and geometric meaning of properties n p s for every p 0 and the syzygetic behaviors of isomorphic projections and hyperplane sections of a given variety with property n p s

a castelnuovo mumford regularity bound for scrolls abstract let x p r be a scroll of codimension e and degree d over a smooth projective curve of genus g the purpose of this paper is to prove a linear castelnuovo mumford regularity bound that reg x d e 1 g e 1 this bound works over an algebraically closed field of arbitrary characteristic

a second order projection method for the incompressible navier stokes equations in this paper we describe a second order projection method for the time dependent incom pressible navier stokes equations as in the original projection method developed by chorin we first solve diffusion convection equations to predict intermediate velocities which are then projected onto the space of divergence free vector fields by introducing more coupling between the diffusion onvection step and the projection step we obtain a temporal discretiza tion that is second order accurate our treatment of the diffusion convection step uses a specialized higher order godunov method for differencing the nonlinear convective terms that provides a robust treatment of these terms at high reynolds number the godunov procedure is second order accurate for smooth flow and remains stable for discontinuous initial data even in the zero viscosity limit we approximate the projection directly using a galerkin procedure that uses a local basis for discretely divergence free vector fields numerical results are presented validating the convergence properties of the method we also apply the method to doubly periodic shear layers to assess the performance of the method on more difficult

parametric time optimal control of linear discrete time systems by state feedback part 2 irregular kronecker invariants in an earlier paper part 1 a parametric state feedback time optimal control law was devised for the regular kronecker invariants on the basis of parametrization of the vector companion form the present paper describes a straight forward technique for obtaining the parametric feedback matrix by exploiting the parametric vector companion forms in the case of irregular kronecker invariants hidden properties of vector companion forms are also given which result in entirely different and interesting techniques for parametrization of the control law an illustrative example is presented

regular article a pde based fast local level set method we develop a fast method to localize the level set method of osher and sethian 1988 j comput phys 79 12 and address two important issues that are intrinsic to the level set method a how to extend a quantity that is given only on the interface to a neighborhood of the interface b how to reset the level set function to be a signed distance function to the interface efficiently without appreciably moving the interface this fast local level set method reduces the computational effort by one order of magnitude works in as much generality as the original one and is conceptually simple and easy to implement our approach differs from previous related works in that we extract all the information needed from the level set function or functions in multiphase flow and do not need to find explicitly the location of the interface in the space domain the complexity of our method to do tasks such as extension and distance reinitialization is o n where n is the number of points in space not o n log n as in works by sethian 1996 proc nat acad sci 93 1591 and helmsen and co workers 1996 spie microlithography ix p 253 this complexity estimation is also valid for quite general geometrically based front motion for our localized method

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

on pole structure assignment in linear systems the problem of pole structure assignment psa by state feedback in implicit linear and uncontrollable systems is discussed in the article it is shown that the problem is solvable if the system is regularisable then necessary and sufficient conditions for characteristic polynomial assignment are established in the case of psa invariant polynomials assignment just necessary conditions have been obtained but it turns out that these conditions are also sufficient in some special cases this happens for example when the system does not possess any non proper controllability indexes a possible application of the achieved results to modelling a constrained movement of a robot arm is outlined too

minimal resolutions chow forms and ulrich bundles on k3 surfaces the minimal resolution conjecture mrc for points on a projective varietyx p predicts that the minimal graded free resolution of a general set x of points is as simple as the geometry of x allows originally the most studied case has been that when x p see epsw the general form of the mrc for subvarieties x p was formulated in mus and fmp the betti diagram of a large enough set x consisting of general points is obtained from the betti diagram of x by adding two rows indexed by u 1 and u where u is an integer depending on all differences bi 1 u 1 bi u are known and depend on the hilbert polynomial px and i u and see fmp the minimal resolution conjecture for general points on x predicts that

on syzygies of calabi yau varieties and varieties of general type abstract we establish projective normality property n p and effective very ampleness for line bundles on a calabi yau variety as well as for pluricanonical bundles of a variety of general type we also prove a result on the degrees of generators of canonical rings under the condition that the image of the canonical map has minimal degree

parametric state feedback design of linear distributed parameter systems the parametric approach for the design of state feedback controllers has been formulated so far only for linear lumped parameter systems it yields an explicit parametric expression for the state feedback gain given the closed loop eigenvalues and the set of corresponding parameter vectors this contribution presents a parameterisation of state feedback controllers for linear distributed parameter systems with scalar state and distributed control by introducing the closed loop eigenvalues and the parameter vectors as design parameters an explicit expression for the state feedback is obtained in contrast to the pure eigenvalue assignment the parameterisation allows the assignment not only of the closed loop eigenvalues but also of the closed loop eigenfunctions the usefulness of the proposed parametric approach is demonstrated by decoupling the transfer behaviour of a mimo diffusion system with respect to its dominant modes

parameterizations of the state feedback controllers for linear multivariable systems abstract a general framework is constructed upon which an explicit parametric formula can be derived for state feedback controllers containing all the possible combination of parameters the relation between the parameters is nonlinear in general and therefore many different constraint may be imposed by the designer to obtain desired performance criteria a couple of illustrative examples are presented

robust and minimum norm pole assignment with periodic state feedback a computational approach is proposed to solve the minimum norm or robust pole assignment problem for linear periodic discrete time systems the proposed approach uses a periodic sylvester equation based parametrization of the periodic pole assignment problem and exploits the nonuniqueness of the problem by imposing conditions on the norm of the resulting periodic state feedback or on the condition numbers of the periodic eigenvector matrices of the closed loop system the solution method relies on using gradient search methods on suitably defined cost functions explicit expressions of the gradients of cost functions are derived and the efficient evaluation of the cost functions and gradients is discussed numerical examples illustrate the effectiveness of the proposed approach

most odd degree hyperelliptic curves have only one rational point consider the smooth projective models c of curves y 2 f x with f x 2 z x monic and separable of degree 2g 1 we prove that for g 3 a positive fraction of these have only one rational point the point at innity we prove a lower bound on this fraction that tends to 1 as g 1 finally we show that c q can be algorithmically computed for such a fraction of the curves the method can be summarized as follows using p adic analysis and an idea of mccallum we develop a reformulation of chabauty s method that shows that certain computable conditions imply c q 1 on the other hand using further p adic analysis the theory of arithmetic surfaces a new result on torsion points on hyperelliptic curves and crucially the bhargava gross theorems on the average number and equidistribution of nonzero 2 selmer group elements we prove that these conditions are often satised for p 2

static output feedback pole placement via a trust region approach this technical note presents two closely related algorithms for the problem of pole placement via static output feedback the algorithms are based on two different trust region methods and utilize the derivatives of the closed loop poles extensive numerical experiments show the effectiveness of the algorithms in practice though convergence to a solution is not guaranteed for either algorithm while desired poles must be distinct strategies for dealing with repeated poles are also presented

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

curves and symmetric spaces ii let sym 3 c p k sym 3 k sym 3 k k p 13 a 1 a a det a be the veronese embedding of the space of symmetric matrices of degree 3 where a is the cofactor matrix of a the closure spg 3 6 of this image is a 6 dimensional homogeneous variety of the symplectic group sp 3 a canonical curve c 16 c p 8 of genus 9 over a perfect field k is isomorphic to a complete linear section of this projective variety spg 3 6 c p 13 unless c k k k being the algebraic closure is a covering of degree at most 5 of the projective line we prove this by means of linear systems of higher rank

level set methods an overview and some recent results the level set method was devised by s osher and j a sethian 1988 j comput phys 79 12 49 as a simple and versatile method for computing and analyzing the motion of an interface in two or three dimensions bounds a possibly multiply connected region the goal is to compute and analyze the subsequent motion of under a velocity field v this velocity can depend on position time the geometry of the interface and the external physics the interface is captured for later time as the zero level set of a smooth at least lipschitz continuous function x t i e t x x t 0 is positive inside negative outside and is zero on t topological merging and breaking are well defined and easily performed in this review article we discuss recent variants and extensions including the motion of curves in three dimensions the dynamic surface extension method fast methods for steady state problems diffusion generated motion and the variational level set approach we also give a user s guide to the level set dictionary and technology and couple the method to a wide variety of problems involving external physics such as compressible and incompressible possibly reacting flow stefan problems kinetic crystal growth epitaxial growth of thin films vortex dominated flows and extensions to multiphase motion we conclude with a discussion of applications to computer vision and image processing

robust pole assignment in linear state feedback numerical methods are described for determining robust or well conditioned solutions to the problem of pole assignment by state feedback the solutions obtained are such that the sensitivity of the assigned poles to perturbations in the system and gain matrices is minimized it is shown that for these solutions upper bounds on the norm of the feedback matrix and on the transient response are also minimized and a lower bound on the stability margin is maximized a measure is derived which indicates the optimal conditioning that may be expected for a particular system with a given set of closed loop poles and hence the suitability of the given poles for assignment

moduli of theta characteristics via nikulin surfaces we study moduli spaces of k3 surfaces endowed with a nikulin involution and their image in the moduli space r g of prym curves of genus g we observe a striking analogy with mukai s well known work on ordinary k3 surfaces many of mukai s results have a very precise prym nikulin analogue for instance a general prym curve from r g is a section of a nikulin surface if and only if g 7 and g 6 furthermore r 7 has the structure of a fibre space over the corresponding moduli space of polarized nikulin surfaces we then use these results to study the geometry of the moduli space s g of even spin curves with special emphasis on the transition case of s 8 which is a 21 dimensional calabi yau variety

on parametric state feedback design an explicit parametric expression for the controller gain matrix in linear state variable feedback is derived it involves both the case where the set of closed loop eigenvalues does not include any open loop eigenvalue and the case where the two eigenvalue sets have elements in common some advantages of this new explicit parameterization of the controller gain matrix are illustrated by two numerical examples

a new algorithm for an eigenvalue assignment problem from singular control theory in this paper a new numerical algorithm for an eigenvalue assignment problem which arises from a singular system control is developed the algorithm is based on orthogonal row column compressions which can be implemented in a numerically reliable way

mathematica implementation of output feedback pole assignment for uncertain systems via symbolic algebra this paper presents the application of symbolic algebra techniques to the mathematica implementation of a set of output feedback pole assignment algorithms for systems characterized by parametric uncertainty for multivariable systems there may be more than one feedback matrix solution leading to the same closed loop poles based on the same algorithm used thus over parameterized solutions are sought by generalizing the existing algorithms with extra degrees of freedom retained in the symbolic variables the general parametric form of output feedback compensators is developed in terms of the uncertain parameters and symbols representing the extra degrees of freedom the implementation of three output feedback pole assignment techniques is presented with the theory briefly introduced and examples illustrating the effectiveness of the algorithms described

hilbert functions of cox rings of del pezzo surfaces to study syzygies of the cox rings of del pezzo surfaces we calculate important syzygetic invariants such as the hilbert functions the green lazarsfeld indices the projective dimensions and the castelnuovo mumford regularities using these computations as well as the natural multigrading structures by the picard groups of del pezzo surfaces and weyl group actions on picard lattices we determine the betti diagrams of the cox rings of del pezzo surfaces of degree at most four

moduli of roots of line bundles on curves we treat the problem of completing the moduli space for roots of line bundles on curves special attention is devoted to higher spin curves within the universal picard scheme two new different constructions both using line bundles on nodal curves as boundary points are carried out and compared with pre existing ones

an efficient interface preserving level set redistancing algorithm and its application to interfacial incompressible fluid flow in sussman smereka and osher j comp phys 94 1994 pp 146 159 a numerical scheme was presented for computing incompressible air water flows using the level set method crucial to the above method was a new iteration method for maintaining the level set function as the signed distance from the zero level set in this paper we implement a constraint along with higher order difference schemes in order to make the iteration method more accurate and efficient accuracy is measured in terms of the new computed signed distance function and the original level set function having the same zero level set we apply our redistancing scheme to incompressible flows with noticeably better resolved results at reduced cost we validate our results with experiment and theory we show that our distance level set scheme with the added constraint competes well with available interface tracking schemes for basic advection of an interface we perform basic accuracy checks and more stringent tests involving complicated interfacial structures as with all level set schemes our method is easy to implement

an improved particle correction procedure for the particle level set method the particle level set method d enright r fedkiw j ferziger i mitchell a hybrid particle level set method for improved interface capturing j comput phys 183 2002 83 116 can substantially improve the mass conservation property of the level set method by using lagrangian marker particles to correct the level set function in the under resolved regions in this study the limitations of the particle level set method due to the errors introduced in the particle correction process are analyzed and an improved particle correction procedure is developed based on a new interface reconstruction scheme moreover the zero level set is anchored as the level set functions are reinitialized hence the additional particle correction after the level set reinitialization is avoided with this new scheme a well defined zero level set can be obtained and the disturbances to the interface are significantly reduced consequently the particle reseeding operation will barely result in the loss of interface characteristics and can be applied as frequently as necessary to demonstrate the accuracy and robustness of the proposed method two extreme particle reseeding strategies one without reseeding and the other with reseeding every time step are applied in several benchmark advection tests and the results are compared with each other three interfacial flow cases a 2d surface tension driven oscillating droplet a 2d gas bubble rising in a quiescent liquid and a 3d drop impact onto a liquid pool are simulated to illustrate the advantages of the current method over the level set and the original particle level set methods with regard to the smoothness of geometric properties and mass conservation in real physical applications

a continuum method for modeling surface tension abstract a new method for modeling surface tension effects on fluid motion has been developed interfaces between fluids of different properties or colors are represented as transition regions of finite thickness across which the color variable varies continuously at each point in the transition region a force density is defined which is proportional to the curvature of the surface of constant color at that point it is normalized so that the conventional description of surface tension on an interface is recovered when the ratio of local transition region thickness to local radius of curvature approaches zero the continuum method eliminates the need for interface reconstruction simplifies the calculation of surface tension enables accurate modeling of two and three dimensional fluid flows driven by surface forces and does not impose any modeling restrictions on the number complexity or dynamic evolution of fluid interfaces having surface tension computational results for two dimensional flows are given to illustrate the properties of the method

analysis on some infinite modules inner projection and applications a projective scheme x is called quadratic if x is scheme theoretically cut out by homogeneous equations of degree 2 furthermore we say that x satisfies property n2 p if it is quadratic and the quadratic ideal has only linear syzygies up to the first p th steps in the present paper we compare the linear syzygies of the inner projections with those of x and obtain a theorem on embedded linear syzygies as one of our main results this is the natural projection analogue of restricting linear syzygies in the linear section case as an immediate corollary we show that the inner projections of x satisfy property n2 p 1 for any reduced scheme x with property n2 p moreover we also obtain the neccessary lower bound codimx p p p 1 2 which is sharp on the number of quadrics vanishing on x in order to satisfy n2 p and show that the arithmetic depths of inner projections are equal to that of the quadratic scheme x these results admit an interesting syzygetic rigidity theorem on property n2 p which leads the classifications of extremal and next to extremal cases for these results we develop the elimination mapping cone theorem for infinitely generated graded modules and improve the partial elimination ideal theory initiated by m green this new method allows us to treat a wider class of projective schemes which cannot be covered by the koszul cohomology techniques because these are not projectively normal in general

pole assignment with improved control performance by means of periodic feedback this technical note is concerned with the pole placement of continuous time linear time invariant lti systems by means of lq suboptimal periodic feedback it is well known that there exist infinitely many generalized sampled data hold functions gshf for any controllable lti system to place the modes of its discrete time equivalent model at prescribed locations among all such gshfs this technical note aims to find the one which also minimizes a given lq performance index to this end the gshf being sought is written as the sum of a particular gshf and a homogeneous one the particular gshf can be readily obtained using the conventional pole placement techniques the homogeneous gshf on the other hand is expressed as a linear combination of a finite number of functions such as polynomials sinusoidals etc the problem of finding the optimal coefficients of this linear combination is then formulated as a linear matrix inequality lmi optimization the procedure is illustrated by a numerical example

on pole placement via eigenstructure assignment approach this note comes back to the hard problem of pole placement by static output feedback let a triplet of matrices a b c be given with n state variables m inputs and p ouputs find a matrix k such that the spectrum of a bkc equals a specified set when mp m p a simple noniterative technique based upon the notion of eigenstructure that in most cases assigns m p roots is proposed it therefore enables the designer to assign the whole of the desired spectrum when m p n mp

syzygies of torsion bundles and the geometry of the level l modular variety over overline mathcal m _ g we formulate and in some cases prove three statements concerning the purity or more generally the naturality of the resolution of various modules one can attach to a generic curve of genus g and a torsion point of l in its jacobian these statements can be viewed an analogues of green s conjecture and we verify them computationally for bounded genus we then compute the cohomology class of the corresponding non vanishing locus in the moduli space mathcal r g ell of twisted level l curves of genus g and use this to derive results about the birational geometry of mathcal r g ell for instance we prove that mathcal r g 3 is a variety of general type when g 11 and the kodaira dimension of mathcal r 11 3 is greater than or equal to 19 in the last section we explain probabilistically the unexpected failure of the prym green conjecture in genus 8 and level 2

a coupled level set and volume of fluid method for computing 3d and axisymmetric incompressible two phase flows we present a coupled level set volume of fluid clsvof method for computing 3d and axisymmetric incompressible two phase flows this method combines some of the advantages of the volume of fluid method with the level set method to obtain a method which is generally superior to either method alone we present direct comparisons between computations made with the clsvof method and computations made with the level set method the volume of fluid method and the boundary integral method we also compare our computations to the exact solution for an oscillating ellipse due to lamb and experimental results obtained for a rising gas bubble in liquid obtained by hnat and buckmaster our computational examples focus on flows in which surface tension forces and changes in topology are dominant features of the flow

a hybrid level set volume constraint method for incompressible two phase flow a second order hybrid level set volume constraint method hlsvc for numerically simulating deforming boundaries is presented we combine the hlsvc interface advection algorithm with a two phase flow solver in order to numerically capture deforming bubbles and drops whose actual volume s fluctuate about fixed target volume s three novel developments are described 1 a new method for enforcing a volume constraint in which the number of bubbles and drops can change due to merging or splitting 2 a new second order semi lagrangian narrow band level set reinitialization algorithm and 3 validation of a two phase flow numerical method by comparison with linear stability analysis results for a co flowing liquid jet in gas the new interface capturing method is tested on benchmark problems in which the velocity is prescribed passive advection of interfaces and in which the velocity is determined by the incompressible navier stokes equations for two phase flow the error in interface position when using the hybrid level set volume constraint method is reported for many benchmark problems in polar coordinates cylindrical coordinates and on an adaptive grid in which one criteria of adaptivity is the magnitude of the interface curvature

a front tracking method for the computations of multiphase flow direct numerical simulations of multiphase flows using a front tracking method are presented the method is based on writing one set of governing equations for the whole computational domain and treating the different phases as one fluid with variable material properties interfacial terms are accounted for by adding the appropriate sources as functions at the boundary separating the phases the unsteady navier stokes equations are solved by a conventional finite volume method on a fixed structured grid and the interface or front is tracked explicitly by connected marker points interfacial source terms such as surface tension are computed on the front and transferred to the fixed grid advection of fluid properties such as density is done by following the motion of the front the method has been implemented for fully three dimensional flows as well as for two dimensional and axisymmetric ones first the method is described for the flow of two or more isothermal phases the representation of the moving interface and its dynamic restructuring as well as the transfer of information between the moving front and the fixed grid are discussed applications and extensions of the method to homogeneous bubbly flows atomization flows with variable surface tension solidification and boiling are then presented

level structures on abelian varieties kodaira dimensions and lang s conjecture abstract assuming lang s conjecture we prove that for a prime p number field k and positive integer g there is an integer r such that no principally polarized abelian variety a k has full level p r structure to this end we use a result of zuo to prove that for each closed subvariety x in the moduli space a g of principally polarized abelian varieties of dimension g there exists a level m x such that the irreducible components of the preimage of x in a g m are of general type for m m x

smooth varieties of almost minimal degree abstract in this article we study non linearly normal smooth projective varieties x p r of deg x codim x p r 2 we first give geometric characterizations for x theorem 1 1 indeed x is the image of an isomorphic projection of smooth varieties x p r 1 of minimal degree also if x is not the veronese surface then there exists a smooth rational normal scroll y p r which contains x as a divisor linearly equivalent to h 2 f where h is the hyperplane section of y and f is a fiber of the projection morphism y p 1 by using these characterizations 1 we determine all the possible types of y from the type of x theorem 1 2 and 2 we investigate the relation between the betti diagram of x and the type of y theorem 1 3 in particular we clarify the relation between the number of generators of the homogeneous ideal of x and the type of y as an application we construct non linearly normal examples where the converse to theorem 1 1 in d eisenbud m green k hulek s popescu restriction linear syzygies algebra and geometry compos math 141 2005 1460 1478 fails to hold remark 2

pole assignment by state transition graph the pole assignment problem is considered using the graph representation of a matrix the parametrization of controllers which have a specified characteristic polynomial is given a simple algorithm based on graphs is presented and two examples are given

a hybrid particle level set method for improved interface capturing in this paper we propose a new numerical method for improving the mass conservation properties of the level set method when the interface is passively advected in a flow field our method uses lagrangian marker particles to rebuild the level set in regions which are underresolved this is often the case for flows undergoing stretching and tearing the overall method maintains a smooth geometrical description of the interface and the implementation simplicity characteristic of the level set method our method compares favorably with volume of fluid methods in the conservation of mass and purely lagrangian schemes for interface resolution the method is presented in three spatial dimensions