the lack of polynomial stability to mixtures with frictional dissipation abstract we consider the system modeling a mixture of n materials with frictional damping we show that the corresponding semigroup is exponentially stable if and only if the imaginary axis is contained in the resolvent set of the infinitesimal generator in particular this implies the lack of polynomial stability to the corresponding semigroup

novel gramians for linear semistable systems in this paper the notions of pseudo gramians are introduced for linear time invariant semistable systems which allow multiple semisimple poles at the origin the proposed gramians are the generalizations of standard gramian matrices defined for asymptotically stable systems and they can be computed by a set of lyapunov equations furthermore it is shown that the controllability and observability of a semistable system are indicated by the ranks of the pseudo gramians and the controllability and observability energy functions are also characterized using the pseudo gramians additionally the h2 norm and h norm of a semistable system are analyzed and then the results are used for the model reduction of semistable systems finally the effectiveness of the methods is illustrated by an example of a gene regulation network

distributed control of spatially invariant systems we consider distributed parameter systems where the underlying dynamics are spatially invariant and where the controls and measurements are spatially distributed these systems arise in many applications such as the control of vehicular platoons flow control microelectromechanical systems mems smart structures and systems described by partial differential equations with constant coefficients and distributed controls and measurements for fully actuated distributed control problems involving quadratic criteria such as linear quadratic regulator lqr h sub 2 and h sub spl infin optimal controllers can be obtained by solving a parameterized family of standard finite dimensional problems we show that optimal controllers have an inherent degree of decentralization and this provides a practical distributed controller architecture we also prove a general result that applies to partially distributed control and a variety of performance criteria stating that optimal controllers inherit the spatial invariance structure of the plant connections of this work to that on systems over rings and systems with dynamical symmetries are discussed

finite time semistability and consensus for nonlinear dynamical networks this paper focuses on semistability and finite time stability analysis and synthesis of systems having a continuum of equilibria semistability is the property whereby the solutions of a dynamical system converge to lyapunov stable equilibrium points determined by the system initial conditions in this paper we merge the theories of semistability and finite time stability to develop a rigorous framework for finite time semistability in particular finite time semistability for a continuum of equilibria of continuous autonomous systems is established continuity of the settling time function as well as lyapunov and converse lyapunov theorems for semistability are also developed in addition necessary and sufficient conditions for finite time semistability of homogeneous systems are addressed by exploiting the fact that a homogeneous system is finite time semistable if and only if it is semistable and has a negative degree of homogeneity unlike previous work on homogeneous systems our results involve homogeneity with respect to semistable dynamics and require us to adopt a geometric description of homogeneity finally we use these results to develop a general framework for designing semistable protocols in dynamical networks for achieving coordination tasks in finite time

thermal creep of a rarefied gas on the basis of non linear korteweg theory the study of thermal transpiration more commonly called thermal creep is accomplished by use of korteweg s theory of capillarity incorporation of this theory into the balance laws of continuum mechanics allows resolution of boundary value problems via solutions to systems of ordinary differential equations the problem was originally considered by maxwell in his classic 1879 paper maxwell phil trans roy soc london 170 231 256 1879 in that paper maxwell derived what is now called the burnett higher order contribution to the cauchy stress but was not able to solve his newly derived system of partial differential equations in this paper the authors note that a more appropriate higher order contribution to the cauchy stress follows from korteweg s 1901 theory korteweg arch neerl sci exactes nat ser ii 6 1 24 1901 the appropriateness of korteweg s theory is based on the exact summation of the chapman enskog expansion given by gorban and karlin the resulting balance laws are solved exactly qualitatively and numerically and the results are qualitatively similar to the numerical and exact results given by aoki et al loyalka et al and struchtrup et al

velocity boundary condition at solid walls in rarefied gas calculations maxwell s famous slip boundary condition is often misapplied in current rarefied gas flow calculations e g in hypersonics microfluidics for simulations of gas flows over curved or moving surfaces this means crucial physics can be lost we give examples of such cases we also propose a higher order boundary condition based on maxwell s general equation and the constitutive relations derived by burnett unlike many other higher order slip conditions these are applicable to any form of surface geometry it is shown that these maxwell burnett boundary conditions are in reasonable agreement with the limited experimental data available for poiseuille flow and can also predict sone s thermal stress slip flow a phenomenon which cannot be captured by conventional slip boundary conditions

extension of a second order velocity slip temperature jump boundary condition to simulate high speed micro nanoflows abstract in the current work for the first time we extend the application of a second order slip jump equations introduced by karniadakis et al for the simulation of high speed high knudsen k n number flows over a nano scale flat plate and a micro scale cylinder the ns equations subject to a second order slip jump boundary conditions are solved using the petrov galerkin finite element discretization we compare our numerical solution for flow and thermal field with the solution of the dsmc and generalized hydrodynamic gh techniques as well as a recently developed slip jump boundary condition i e paterson equation current results demonstrate the suitable accuracy of the employed boundary conditions for different set of test cases our numerical solutions are obtained with much less numerical costs compared to alternative boundary conditions

tauberian theorems and stability of one parameter semigroups the main result is the following stability theorem let t t t tzo be a bounded co semigroup on a reflexive space x denote by a the generator of t and by a a the spectrum of a if a a n ir is countable and no eigenvalue of a lies on the imaginary axis then limt boo t t x o for all x e x

perturbation of strongly and polynomially stable riesz spectral operators abstract in this paper we consider bounded and relatively bounded finite rank perturbations of a riesz spectral operator generating a polynomially stable semigroup of linear operators on a hilbert space we concentrate on a commonly encountered situation where the spectrum of the unperturbed operator is contained in the open left half plane of the complex plane and approaches the imaginary axis asymptotically we present conditions on the perturbing operator such that the spectrum of the perturbed operator is contained in the open left half plane of the complex plane and additional conditions for the strong and polynomial stabilities of the perturbed semigroup we consider two applications of the perturbation results in the first example we apply the results to the perturbation of a polynomially stabilized one dimensional wave equation in the second example we consider the perturbation of a closed loop system consisting of a distributed parameter system and an observer based feedback controller solving the robust output regulation problem related to an infinite dimensional signal generator

semistability finite time stability differential inclusions and discontinuous dynamical systems having a continuum of equilibria this paper focuses on semistability and finite time semistability for discontinuous dynamical systems having a continuum of equilibria semistability is the property whereby the solutions of a dynamical system converge to lyapunov stable equilibrium points determined by the system initial conditions in this paper we extend the theory of semistability to discontinuous autonomous dynamical systems in particular lyapunov based tests for semistability and finite time semistability for autonomous differential inclusions are established

decay of solutions for a mixture of thermoelastic one dimensional solids we study a pde system modeling thermomechanical deformations for a mixture of thermoelastic solids in particular we investigate the asymptotic behavior of the solutions first we identify conditions on the constitutive coefficients to guarantee that the imaginary axis is contained in the resolvent subsequently we find the necessary and sufficient conditions to guarantee the exponential decay of solutions when the decay is not of exponential type we prove that the solutions decay polynomially and we find the optimal polynomial decay rate

strong asymptotic stability of linear dynamical systems in banach spaces abstract in this paper we investigate the strong asymptotic stability of linear dynamical systems in banach spaces let a be the infinitesimal generator of a c0 semigroup et a of bounded linear operators in a banach space x we first show that if et a is a c0 isometric group then there exists at least one pure imaginary i a the spectrum of a and if et a is only a c0 isometric semigroup but not a group then r a the residual spectrum of a for all c with re a is uniformly bounded and re a then et a is strongly asymptotically stable i e et a x 0 as t for all x x conversely if et a is strongly asymptotically stable then it is uniformly bounded and re 0 for all a and any pure imaginary can be only a continuous spectral point of a finally we consider the c0 semigroup et a b associated with linear elastic systems with damping b aw 0 in a hilbert space h where a b is the closure of a b formula a very general result with regard to strong asymptotic stability of the semigroup et a b is obtained

galois points for plane curves and cremona transformations abstract we study the relation between galois points for plane curves and cremona transformations first we prove that a galois point is preserved by a standard quadratic transformation then we define a certain minimality for a pair of a plane curve and a galois point so that we study defining equations of plane curves with a galois point

field theory for function fields of plane quartic curves abstract let c be a smooth plane quartic curve over a field k and k c be a rational function field of c we develop a field theory for k c in the following method let p be the projection from c to a line l with a center p p 2 the p induces an extension field k c k p 1 where k p 1 is a maximal rational subfield in this paper we study the extension k c k p 1 from several points of view for example we consider the following questions when is the extension k c k p 1 galois what is the galois closure of k c k p 1

internal model theory for distributed parameter systems in this paper we consider robust output regulation of distributed parameter systems and the internal model principle the main purpose is to generalize the internal model principle by francis and wonham for infinite dimensional systems and clarify the relationships between different generalizations of the internal model we also construct a signal generator capable of generating infinite dimensional polynomially increasing signals

consistent lattice boltzmann modeling of low speed isothermal flows at finite knudsen numbers in slip flow regime ii application to curved boundaries gaseous flows inside microfluidic devices often fall in the slip flow regime according to this theoretical description the navier stokes model remains applicable in bulk while at solid walls a slip velocity boundary model shall be considered physically it is well established that to properly account for the wall curvature the wall slip velocity must be determined by the shear stress rather than the normal component of the velocity derivative alone as commonly applied to planar surfaces it follows that the numerical transcription of this type of boundary condition is generally a challenging task for standard computational fluid dynamics cfd techniques this paper aims to show that the realization of the slip velocity condition on arbitrarily shaped boundaries can be accomplished in a natural way with the lattice boltzmann method lbm to substantiate this conclusion this work undertakes the following three studies first we examine the conditions under which the generic reflection type boundary rules used by lbm become consistent models for the slip velocity boundary condition this effort makes use of the second order chapman enskog expansion method where we address both planar and curved boundaries the analysis also clarifies the capabilities and limitations behind the considered reflection type slip schemes second we revisit the family of parabolic accurate lbm slip boundary schemes originally formulated in phys rev e 96 013311 2017 2470 004510 1103 physreve 96 013311 on the basis of the multireflection framework and discuss their characteristics when operating on curved boundaries as well as the limitations of other less accurate lbm slip boundary formulations such as the linearly accurate slip schemes and the widely popular kinetic based boundary schemes in addition we also discuss the numerical stability of the parabolic slip schemes previously developed providing an heuristic strategy to improve their stable range of operation third we evaluate the performance of the several slip boundary schemes debated in this paper the numerical tests correspond to two classical 2d benchmark flow problems of slip over non planar solid surfaces namely i the velocity profile of the cylindrical couette flow and ii the permeability of a slow rarefied gas over a periodic array of circular cylindrical obstacles the obtained numerical results confirm the competitiveness of the lbm when equipped with slip boundary schemes of parabolic accuracy as cfd tool to simulate slippage phenomena over arbitrarily non planar surfaces indeed although operating on a simple uniform mesh discretization the lbm yields a similar or even superior level of accuracy compared to state of the art fem simulations conducted on hardworking body fitted meshes this conclusion establishes the lbm as a very appealing cfd technique for simulating microfluidic flows in the slip flow regime a result that deserves further exploration in future studies

rational curve with galois point and extendable galois automorphism abstract let g be the galois group of a galois point for a plane curve c an element of g induces a birational transformation of c we study if it can be extended to a projective or birational transformation of the plane in the course of the study we give the defining equation of a rational curve with the galois point furthermore we introduce a special birational transformation in order to make the defining equation into a simpler form

stability analysis of discontinuous dynamical systems determined by semigroups we present lyapunov stability results for discontinuous dynamical systems dds determined by linear and nonlinear semigroups defined on banach space dds of the type considered herein arise in the modeling of a variety of finite and infinite dimensional systems including certain classes of hybrid systems discrete event systems switched systems systems subjected to impulse effects and the like we apply our results in the analysis of several important specific classes of dds

on the multidimensional gas kinetic bgk scheme this paper concerns the performance difference among the multidimensional md gas kinetic bgk scheme the corresponding quasi one dimensional q1d extension and the directional splitting ds scheme with kinetic boundary conditions the md scheme includes tangential slopes in the flux calculation which are absent in a q1d or ds method in spite of taking more computational time the md scheme is found to be able to capture the characteristics of rarefied flow having a boundary with curvature or a nonuniform temperature such as the inverted velocity distribution in rarefied cylindrical couette flow and the weak flow field induced by the temperature gradient of a body where the q1d fails the md scheme can also yield clearly better results in high speed microchannel flow and power law fluid flow between concentric rotating cylinders when compared with direct simulation monte carlo studies and analytic solutions in the low reynolds number flow around a naca0012 airfoil case the md scheme and the q1d method predict wall heat flux distribution with obvious difference the ds method predicts results nearly identical to those from q1d in these steady flow cases except that it can hardly give reasonable solutions in power law fluid case with viscous exponential factor away from unity correct prediction of the stress and the wall temperature gradient is considered responsible for this better performance in simulations of the scalar convection diffusion equation it is found that the inclusion of tangential slopes in the flux computation can clearly improve the temporal accuracy of the scheme in this case the ds scheme also shows good performance the present study suggests caution in adopting of the q1d extension or ds method in multidimensional flow when it is sensitive to the accuracy of stress or wall variable gradient calculations it is better to use the md scheme for high performance simulation

stability for dynamical systems with first integrals a topological criterion this paper provides a new criterion for stability of equilibrium points of topological flows in the presence of first integrals the result generalizes a well known criterion for stability of such systems obtained by means of liapunov theory

singular plane curves with infinitely many galois points for a plane curve c we call a point p p2 a galois point with respect to c if the point projection from p induces a galois extension of function fields we give an example of a singular plane curve having infinitely many inner and outer galois points we also classify plane curves whose general points are inner galois points before our results known examples in the theory of galois points have only finitely many galois points except trivial cases

polynomial stability of the rao nakra beam with a single internal viscous damping abstract in this paper we consider the stability of the rao nakra sandwich beam equation with various boundary conditions which consists of two wave equations for the longitudinal displacements of the top and bottom layers and one euler bernoulli beam equation for the transversal displacement polynomial stability of certain orders are obtained when there is only one viscous damping acting either on the beam equation or one of the wave equations for a few special cases optimal orders are confirmed we also study the synchronization of the model with viscous damping on the transversal displacement our results reveal that the order of the polynomial decay rate is sensitive to various boundary conditions and to the damping locations

nontangency based lyapunov tests for convergence and stability in systems having a continuum of equilibria this paper focuses on the stability analysis of systems having a continuum of equilibria two notions that are of particular relevance to such systems are convergence and semistability convergence is the property whereby every solution converges to a limit point that may depend on the initial condition semistability is the additional requirement that all solutions converge to limit points that are lyapunov stable we give new lyapunov function based results for convergence and semistability of nonlinear systems these results do not make assumptions of sign definiteness on the lyapunov function instead our results use a novel condition based on nontangency between the vector field and invariant or negatively invariant subsets of the level or sublevel sets of the lyapunov function or its derivative and represent extensions of previously known stability results involving semidefinite lyapunov functions to illustrate our results we deduce convergence and semistability of the kinetics of the michaelis menten chemical reaction and the closed loop dynamics of a scalar system under a universal adaptive stabilizing feedback controller

single node second order boundary schemes for the lattice boltzmann method abstract based on our recently developed maxwell iteration for the lattice boltzmann method we propose a class of single node boundary schemes for dirichlet boundary conditions of the navier stokes equations the schemes all have second order accuracy for both straight and curved boundaries the accuracy and stability of two specific schemes are examined through several numerical experiments the results validate the second order accuracy and show that a boundary scheme with a convex combination of distribution functions has better stability

stabilizability of coupled wave equations in parallel under various boundary conditions stability of the wave equations coupled in parallel suspension system is investigated for free and fixed boundary conditions by energy dissipation boundary controller s to this end the exponential stability criterion and rouche s theorems are used the former is utilized for uniformly exponentially decaying systems and the latter otherwise the results are characterized by the rate of convergence of the solutions and the system parameters for the stated boundary conditions

galois points for smooth hypersurfaces abstract let v be a smooth hypersurface in p n 1 we consider a projection of v from p p n 1 to a hyperplane h this projection induces an extension of fields k v k h which does not depend on the choice of h we study the structures of this extension and the hypersurfaces together the point p is called a galois point if the extension is galois we show estimates of the number of the galois points and some rules of their distributions especially we give the defining equation of v with maximal number of galois points

semistability theory for spatially distributed systems abstract the concepts of semistability and exponential semistability are well developed for finite dimensional systems with nonisolated equilibrium points where asymptotic or exponential stability is not possible definitions of semistability and exponential semistability have recently been formulated for networks with time delays this paper further extends the semistability theory to continuous and discrete spatially distributed systems this requires the definition of the notions of exact and approximate semicontrollability and semiobservability and discrete approximate semicontrollability and semiobservability also introduced is the property of weak semistability necessary and sufficient conditions are given for exponential semistability and weak semistability and sufficient conditions are given for semistability

a birational embedding of an algebraic curve into a projective plane with two galois points abstract a criterion for the existence of a birational embedding of an algebraic curve into a projective plane with two galois points is presented several novel examples of plane curves with two inner galois points as an application are described

galois points on singular plane quartic curves abstract we study the structure of function fields of plane curves following our method developed in k miura h yoshihara field theory for function fields of plane quartic curves j algebra 226 2000 283 294 especially we study galois points on singular plane quartic curves and determine the number of galois points on them furthermore we give concrete defining equations when the curve has a galois point

spectrum and stability for elastic systems with global or local kelvin voigt damping in this paper we study the mathematical properties of a variational second order evolution equation which includes the equations modelling vibrations of the euler bernoulli and rayleigh beams with the global or local kelvin voigt k v damping in particular our results describe the semigroup setting the strong asymptotic stability and exponential stability of the semigroup the analyticity of the semigroup as well as characteristics of the spectrum of the semigroup generator under various conditions on the damping we also give an example to show that the energy of a vibrating string does not decay exponentially when the k v damping is distributed only on a subinterval which has one end coincident with one end of the string

spectral conditions for stability of one parameter semigroups abstract let s t t 0 be a c 0 semigroup on a banach space y with generator b and t t t 0 be a bounded c 0 semigroup on a banach space x with generator a suppose that b i r is countable p a i r is empty and that there is a bounded linear operator c y x with dense range which intertwines the two semigroups then t t x x 0 as t for each x in x this generalises results of w arendt and the author yu i lyubich and v quoc phong and falun huang

distributed control design for spatially interconnected systems this paper deals with analysis synthesis and implementation of distributed controllers designed for spatially interconnected systems we develop a state space framework for posing problems of this type and focus on systems whose model is spatially discrete in this paper analysis and synthesis results are developed for this class of systems using the l sub 2 induced norm as the performance criterion the results are stated in terms of linear matrix inequalities and are thus readily amenable to computation a special implementation of the resulting controllers is presented which is particularly attractive for distributed operation of the controller several examples are provided to further illustrate the application of the results

function field theory of plane curves by dual curves we study the structure of function fields of plane curves following our method developed previously k miura and h yoshihara 2000 j algebra226 283 294 let k be the function field of a smooth plane curve c of degree d 4 and let kp be a maximal rational subfield of k for p p2 we study the field extension k kp from a geometrical viewpoint especially we give a sufficient condition that the galois group of the galois closure of k kp becomes a full symmetric group

on the stability of spatially distributed systems in this note a sufficient condition is derived for the stability of a spatially invariant distributed dynamical system based on the geometrical structure of the null space of a matrix polynomial this condition is less conservative than the available computationally feasible criteria moreover using the idea of parameter dependent linear matrix inequalities a necessary and sufficient condition is obtained both of these two conditions are expressed by lmis while the necessity of the latter is lost if the degree of the related matrix polynomials is small its conservativeness can be sequentially reduced

stabilization of a joint leg beam system with boundary damping abstract in this paper we study a model for combined axial and transverse motions of two euler bernoulli beams connected through two legs to a joint we prove that the joint leg beam system is polynomially stable but not exponentially stable with linear control of velocity feedback

families of galois closure curves for plane quintic curves abstract in yoshihara 2003 14 yoshihara studied a family of curves of genus ten over a smooth plane quartic curve which is called a family of galois closure curves and determined the types of singular fibers in this paper we consider similar problem for a smooth quintic plane curve consequently we obtain smooth projective minimal surfaces of general type with c 1 2 2 c 2

indirect stabilization of weakly coupled kirchhoff plate and wave equations with frictional damping abstract we investigate the indirect stabilization of a weakly coupled system consisting of a kirchhoff plate equation involving free boundary conditions and the wave equation with dirichlet boundary conditions in a bounded domain the distributed damping is frictional and appears in one of the equations only first we consider the case where the damping occurs in the wave equation and using the frequency domain method combined with an interpolation inequality we derive a polynomial decay estimate for the associated semigroup afterwards we consider the case where the frictional damping occurs in the kirchhoff plate equation and we use the same technique to derive a polynomial decay estimate for the underlying semigroup that latter polynomial decay estimate is similar to the one obtained earlier by different authors in the case of a coupling between a frictionally damped euler bernoulli plate equation and an undamped wave equation which is quite surprising since the operator defining the damping in the kirchhoff plate equation is compact

riccati equations for strongly stabilizable bounded linear systems we obtain necessary and sufficient conditions for the existence of strongly stabilizing solutions to riccati equations for infinite dimensional systems that are strongly but not exponentially stabilizable we apply the theory to derive a riccati criterion for the existence of j spectral factorizations and illustrate it by proving the strict positive real and bounded real lemmas for a class of strongly stable systems with collocated actuators and sensors

inertia theorems for operator lyapunov inequalities we study operator lyapunov inequalities and equations for which the in1nitesimal generator is not necessarily stable but it satis1es the spectrum decomposition assumption and it has at most 1nitely many unstable eigenvalues moreover the input or output operators are not necessarily bounded but are admissible we prove an inertia result under mild conditions we show that the number ofunstable eigenvalues ofthe generator is less than or equal to the number ofnegative eigenvalues ofthe self adjoint solution ofthe operator lyapunov inequality c 2001 elsevier science b v all rights reserved

qualitative theory of compartmental systems dynamic models of many processes in the biological and physical sciences which depend on local mass balance conditions give rise to systems of ordinary differential equations many nonlinear that are called compartmental systems in this paper the authors define compartmental systems specify their relations to other nonnegative systems and discuss examples of applications the authors review the qualitative results on linear and nonlinear compartmental systems including their relation to cooperative systems they review the results for linear compartmental systems and then integrate and expand the results on nonlinear compartmental systems providing a framework for unifying them under a few general theorems in the course of that they complete the solution of a problem posed by bellman and show that closed nonlinear autonomous n compartment systems can show the full gamut of possible behaviors of systems of odes finally to provide additional structure to this study the authors show how to partiti