parabolic partial differential equations with discrete state dependent delay classical solutions and solution manifold abstract classical solutions to pdes with discrete state dependent delay are studied we prove the well posedness in a set x f which is analogous to the solution manifold used for ordinary differential equations with state dependent delay we prove that the evolution operators are c 1 smooth on the solution manifold

the dimensional reduction approach for 2d non prismatic beam modelling a solution based on hellinger reissner principle abstract the present paper considers a non prismatic beam i e a beam with a cross section varying along the beam axis in particular we derive and discuss a model of a 2d linear elastic non prismatic beam and the corresponding finite element to derive the beam model we use the so called dimensional reduction approach from a suitable weak formulation of the 2d linear elastic problem we introduce a variable cross section approximation and perform a cross section integration the satisfaction of the boundary equilibrium on lateral surfaces is crucial in determining the model accuracy since it leads to consider correct stress distribution and coupling terms i e equation terms that allow to model the interaction between axial stretch and bending therefore we assume as a starting point the hellinger reissner functional in a formulation that privileges the satisfaction of equilibrium equations and we use a cross section approximation that exactly enforces the boundary equilibrium the obtained beam model is governed by linear ordinary differential equations odes with non constant coefficients for which an analytical solution cannot be found in general as a consequence starting from the beam model we develop the corresponding beam finite element approximation numerical results show that the proposed beam model and the corresponding finite element are capable to correctly predict displacement and stress distributions in non trivial cases like tapered and arch shaped beams

picard fuchs equations for relative periods and abel jacobi map for calabi yau hypersurfaces we study the variation of relative cohomology for a pair consisting of a smooth projective hypersurface and an algebraic subvariety in it we construct an inhomogeneous picard fuchs equation by applying a picard fuchs operator to the holomorphic top form on a calabi yau hypersurface in toric variety and deriving a general formula for the d exact form on one side of the equation we also derive a double residue formula giving a purely algebraic way to compute the inhomogeneous picard fuchs equations for the abel jacobi map which has played an important role in the recent study of d branes by morrison and walcher using the variation formalism we prove that the relative periods of toric b branes on calabi yau hypersurface satisfy the enhanced gkz hypergeometric system proposed in physics literature by alim hecht mayr and mertens and discuss the relations between several works in the recent study of open string mirror symmetry we also give the general solutions to the enhanced hypergeometric system

an isogeometric collocation approach for bernoulli euler beams and kirchhoff plates abstract in this paper iga collocation methods are for the first time introduced for the solution of thin structural problems described by the bernoulli euler beam and kirchhoff plate models in particular a precise description of the proposed methods of the relevant implementation details and of the strategy to efficiently deal with different combinations of boundary conditions is given finally several numerical experiments confirm that the proposed formulations represent an efficient and geometrically flexible tool for the simulation of thin structures

locking free isogeometric collocation methods for spatial timoshenko rods in this work we present the application of isogeometric collocation techniques to the solution of spatial timoshenko rods the strong form equations of the problem are presented in both displacement based and mixed formulations and are discretized via nurbs based isogeometric collocation several numerical experiments are reported to test the accuracy and efficiency of the considered methods as well as their applicability to problems of practical interest in particular it is shown that mixed collocation schemes are locking free independently of the choice of the polynomial degrees for the unknown fields such an important property is also analytically proven

superstability and rigorous asymptotics in singularly perturbed state dependent delay differential equations abstract we study the singularly perturbed state dependent delay differential equation e x t x t k x t r r r x t 1 x t which is a special case of the equation e x t g x t x t r r r x t one knows that for every sufficiently small e 0 eq possesses at least one so called slowly oscillating periodic solution and moreover the graph of every such solution approaches a specific sawtooth like shape as e 0 in this paper we obtain higher order asymptotics of the sawtooth including the location of the minimum and maximum of the solution with the form of the solution near these turning points and as well an asymptotic formula for the period using these and other asymptotic formulas we further show that the solution enjoys the property of superstability namely the nontrivial characteristic multipliers are of size o e for small e this stability property implies that this solution is unique among all slowly oscillating periodic solutions again for small e

effective superpotentials for compact d5 brane calabi yau geometries for compact calabi yau geometries with d5 branes we study n 1 effective superpotentials depending on both open and closed string fields we develop methods to derive the open closed picard fuchs differential equations which control d5 brane deformations as well as complex structure deformations of the compact calabi yau space their solutions encode the flat open closed coordinates and the effective superpotential for two explicit examples of compact d5 brane calabi yau hypersurface geometries we apply our techniques and express the calculated superpotentials in terms of flat open closed coordinates by evaluating these superpotentials at their critical points we reproduce the domain wall tensions that have recently appeared in the literature finally we extract orbifold disk invariants from the superpotentials which up to overall numerical normalizations correspond to orbifold disk gromov witten invariants in the mirror geometry

dynamics of second order in time evolution equations with state dependent delay abstract we deal with a class of second order in time nonlinear evolution equations with state dependent delay this class covers several important pde models arising in the theory of nonlinear plates we first prove well posedness in a certain space of functions which are c 1 in time in contrast with the first order models with discrete state dependent delay this result does not require any compatibility conditions the solutions constructed generate a dynamical system in a c 1 type space over delay time interval our main result shows that this dynamical system possesses compact global and exponential attractors of finite fractal dimension to obtain this result we adapt the recently developed method of quasi stability estimates

merging homoclinic solutions due to state dependent delay abstract for 2 5 2 the linear differential equation x t x t 1 with constant time lag is unstable and hyperbolic for sufficiently close to 5 2 we construct a state dependent delay d u 0 2 on an open set in the space c 1 2 0 with d u 1 for close to 0 so that the nonlinear equation x t x t d u x t has a one parameter family of entire solutions c r r r r r u which are homoclinic to zero and merge in finite time at some t y 0 c r t c 0 t for r r u and t t y this complements earlier results on complicated solution behaviour caused by state dependent delay and shows that there exist delay functionals for which certain transversality and regularity conditions along homoclinic solutions are violated

a periodic solution of a differential equation with state dependent delay we study a differential equation for delayed negative feedback which models a situation where the delay depends on the present state and becomes effective in the future the main result is existence of a periodic solution in case the equilibrium is linearly unstable the proof employs the ejective fixed point principle on a compact convex set k0 c h 0 r of lipschitz continuous functions and uses that the equation generates a smooth semiflow on an infinite dimensional submanifold of the space c1 h 0 r

a differential equation with state dependent delay from cell population biology we analyze a differential equation describing the maturation of a stem cell population with a state dependent delay which is implicitly defined via the solution of an ode we elaborate smoothness conditions for the model ingredients in particular vital rates that guarantee the existence of a local semiflow and allow to specify the linear variational equation the proofs are based on theoretical results of hartung et al combined with implicit function arguments in infinite dimensions moreover we elaborate a criterion for global existence for differential equations with state dependent delay to prove the result we adapt a theorem by hale and lunel to the c1 topology and use a result on metric spaces from diekmann et al

differentiability of solutions with respect to parameters in neutral differential equations with state dependent delays in this paper we consider a class of nonlinear neutral differential equations with state dependent delays in both the neutral and the retarded terms we study well posedness and continuous dependence issues and differentiability of the parameter map with respect to the initial function and other possibly infinite dimensional parameters in a pointwise sense and also in the c norm

free vibration and wave propagation analysis of uniform and tapered rotating beams using spectrally formulated finite elements this paper presents a formulation of an approximate spectral element for uniform and tapered rotating euler bernoulli beams the formulation takes into account the varying centrifugal force mass and bending stiffness the dynamic stiffness matrix is constructed using the weak form of the governing differential equation in the frequency domain where two different interpolating functions for the transverse displacement are used for the element formulation both free vibration and wave propagation analysis is performed using the formulated elements the studies show that the formulated element predicts results that compare well with the solution available in the literature at a fraction of the computational effort in addition for wave propagation analysis the element shows superior convergence

stability of periodic solutions of state dependent delay differential equations abstract we consider a class of autonomous delay differential equations z t f z t which includes equations of the form z t g z t z t r 1 z t r n r i r i z t for 1 i n with state dependent delays r i z t 0 the functions g and r i satisfy appropriate smoothness conditions we assume there exists a periodic solution z x t which is linearly asymptotically stable namely with all nontrivial characteristic multipliers satisfying 1 we prove that the appropriate nonlinear stability properties hold for x t namely that this solution is asymptotically orbitally stable with asymptotic phase and enjoys an exponential rate of attraction given in terms of the leading nontrivial characteristic multiplier a principal difficulty which distinguishes the analysis of equations such as from ones with constant delays is that even with g and r i smooth the associated function f is not smooth in function space techniques of hartung krisztin walther and wu are employed to resolve these issues

partial differential equations with discrete and distributed state dependent delays this work is an attempt to treat partial differential equations with discrete concentrated state dependent delay the main idea is to approximate the discrete delay term by a sequence of distributed delay terms all with state dependent delays we study local existence and long time asymptotic behavior of solutions and prove that the model with distributed delay has a global attractor while the one with discrete delay possesses the trajectory attractor

isogeometric collocation methods for cosserat rods and rod structures abstract we present a novel method for the mechanical simulation of slender elastic spatial rods and rod structures subject to large deformation and rotation we develop an isogeometric collocation method for the geometrically exact nonlinear cosserat rod theory the rod centerlines are represented as spatial nurbs curves and cross section orientations are parameterized in terms of unit quaternions as 4 dimensional nurbs curves within the isogeometric framework the strong forms of the equilibrium equations of forces and moments of the discretized cosserat model are collocated leading to an efficient method for higher order discretizations for rod structures consisting of multiple connected rods we introduce a formulation with rigid quasi g 1 coupling it is based on the strong enforcement of continuity of displacement and change of cross section orientation at interfaces we also develop a mixed isogeometric formulation which is based on an independent discretization of internal forces and moments and alleviates shear locking for thin rods the novel rod simulation methods are verified by numerical convergence studies further computational examples include realistic applications with large deformations and rotations as well as a large scale rod structure with several hundreds of coupled rods and complex buckling behavior

existence results for fractional neutral integro differential equations with state dependent delay in this paper we study the existence of mild solutions for a class of abstract fractional neutral integro differential equations with state dependent delay the results are obtained by using the leray schauder alternative fixed point theorem an example is provided to illustrate the main results

kodaira spencer theory of gravity and exact results for quantum string amplitudes we develop techniques to compute higher loop string amplitudes for twistedn 2 theories with 3 i e the critical case an important ingredient is the discovery of an anomaly at every genus in decoupling of brst trivial states captured to all orders by a master anomaly equation in a particular realization of then 2 theories the resulting string field theory is equivalent to a topological theory in six dimensions the kodaira spencer theory which may be viewed as the closed string analog of the chern simons theory using the mirror map this leads to computation of the number of holomorphic curves of higher genus curves in calabi yau manifolds it is shown that topological amplitudes can also be reinterpreted as computing corrections to superpotential terms appearing in the effective 4d theory resulting from compactification of standard 10d superstrings on the correspondingn 2 theory relations withc 1 strings are also pointed out

on differentiability of solutions with respect to parameters in state dependent delay equations in this paper we study differentiability of solutions with respect to parameters in state dependent delay equations in particular we give sufficient conditions for differentiability of solutions in thew1 pnorm 1 p in establishing our main results we make use of a version of the uniform contraction principle for quasi banach spaces

global stability and wavefronts in a cooperation model with state dependent time delay abstract this article deals with a diffusive cooperative model with state dependent delay which is assumed to be an increasing function of the population density with lower and upper bounds for the cooperative dde system the positivity and boundedness of solutions are firstly given using the comparison principle of the state dependent delay equations obtained the stability criterion of model is analyzed both from local and global points of view when the diffusion is properly introduced the existence of traveling waves is obtained by constructing a pair of upper lower solutions and schauder s fixed point theorem calculating the minimum wave speed shows that the wave is slowed down by the state dependent delay finally the traveling wavefront solutions for large wave speed are also discussed and the fronts appear to be all monotone regardless of the state dependent time delay this is an interesting property since many findings are frequently reported that delay causes a loss of monotonicity with the front developing a prominent hump in some other delay models

a necessary and sufficient condition for well posedness of initial value problems of retarded functional differential equations abstract we introduce the retarded functional differential equations rfdes with general delay structure to treat various delay differential equations ddes in a unified way and to clarify the delay structure in those dynamics we are interested in the question as to which space of histories is suitable for the dynamics of each dde and investigate the well posedness of the initial value problems ivps of the rfdes a main theorem is that the ivp is well posed for any admissible history functional if and only if the semigroup determined by the trivial rfde x 0 is continuous we clarify the meaning of the hale kato axiom hale kato 12 by applying this result to rfdes with infinite delay we also apply the result to ddes with unbounded time and state dependent delays

semigroup properties and the crandall liggett approximation for a class of differential equations with state dependent delays abstract we present an approach for the resolution of a class of differential equations with state dependent delays by the theory of strongly continuous nonlinear semigroups we show that this class determines a strongly continuous semigroup in a closed subset of c 0 1 we characterize the infinitesimal generator of this semigroup through its domain finally an approximation of the crandall liggett type for the semigroup is obtained in a dense subset of c as far as we know this approach is new in the context of state dependent delay equations while it is classical in the case of constant delay differential equations

isogeometric collocation methods for the reissner mindlin plate problem abstract within the general framework of isogeometric methods collocation schemes have been recently proposed as a viable and promising low cost alternative to standard isogeometric galerkin approaches in this paper isogeometric collocation methods for the numerical approximation of reissner mindlin plate problems are proposed for the first time locking free primal and mixed formulations are herein considered and the potential of isogeometric collocation as a geometrically flexible and computationally efficient simulation tool for shear deformable plates is shown through the solution of several numerical tests

non linear partial differential equations with discrete state dependent delays in a metric space we investigate a class of non linear partial differential equations with discrete state dependent delays the existence and uniqueness of strong solutions for initial functions from a banach space are proved to get the well posed initial value problem we restrict our study to a smaller metric space construct the dynamical system and prove the existence of a compact global attractor

single variable formulations and isogeometric discretizations for shear deformable beams abstract we present numerical formulations of timoshenko beams with only one unknown the bending displacement and it is shown that all variables of the beam problem can be expressed in terms of it and its derivatives we develop strong and weak forms of the problem the strong form of the problem involves the fourth derivative of the bending displacement whereas the symmetric weak form involves somewhat surprisingly third and second derivatives based on these we develop isogeometric collocation and galerkin formulations that are completely locking free and involve only half the degrees of freedom compared to standard timoshenko beam formulations several numerical tests are presented to demonstrate the performance of the proposed formulations

global hopf bifurcation for differential equations with state dependent delay abstract we develop a global hopf bifurcation theory for a system of functional differential equations with state dependent delay the theory is based on an application of the homotopy invariance of s 1 equivariant degree using the formal linearization of the system at a stationary state our results show that under a set of mild conditions the information about the characteristic equation of the formal linearization with frozen delay can be utilized to detect the local hopf bifurcation and to describe the global continuation of periodic solutions for such a system with state dependent delay

remodeling the b model we propose a complete new formalism to compute unambiguously b model open and closed amplitudes in local calabi yau geometries including the mirrors of toric manifolds the formalism is based on the recursive solution of matrix models recently proposed by eynard and orantin the resulting amplitudes are non perturbative in both the closed and the open moduli the formalism can then be used to study stringy phase transitions in the open closed moduli space at large radius this formalism may be seen as a mirror formalism to the topological vertex but it is also valid in other phases in the moduli space we develop the formalism in general and provide an extensive number of checks including a test at the orbifold point of ap fibrations where the amplitudes compute the t hooft expansion of vevs of wilson loops in chern simons theory on lens spaces we also use our formalism to predict the disk amplitude for the orbifold mathbb c 3 mathbb z 3

a note on computations of the d brane superpotential we develop some computational methods for the integrals over the 3 chains on the compact calabi yau 3 folds that play a prominent role in the analysis of the topological b model in the context of the open mirror symmetry we discuss such 3 chain integrals in two approaches in the first approach we provide an algorithm to obtain the inhomogeneous picard fuchs equations in the second approach we discuss the analytic continuation of the period integral to compute the 3 chain integral directly the latter direct integration method is applicable for both on shell and off shell formalisms

connections between morse sets for delay differential equations on etudie la dynamique globale de l equation differentielle a retard scalaire x t f x t x t 1 avec des conditions appropriees sur f

isogeometric analysis for nonlinear planar kirchhoff rods weighted residual formulation and collocation of the strong form abstract high order shape functions used in isogeometric analysis allow the direct solution not only to the weighted residual formulation of the strong form opening the door to new integration schemes e g reduced gauss lobatto quadrature integration at superconvergent sites but also to collocation approaches e g using greville or superconvergent collocation points the goal of the present work is to compare these different methods through the application to the planar kirchhoff rod a fourth order rotation free formulation used to model slender beams under large deformations robustness of the geometrically nonlinear solution is improved using the mixed integration point mip newton a method that combines the advantages of displacement and mixed formulations based on the observations of the convergence plots convergence order estimates are provided for each discretization method advantages and weaknesses in terms of robustness and computation cost are also discussed for a set of benchmarks

opening mirror symmetry on the quintic aided by mirror symmetry we determine the number of holomorphic disks ending on the real lagrangian in the quintic threefold we hypothesize that the tension of the domainwall between the two vacua on the brane which is the generating function for the open gromov witten invariants satisfies a certain extension of the picard fuchs differential equation governing periods of the mirror quintic we verify consistency of the monodromies under analytic continuation of the superpotential over the entire moduli space we further check the conjecture by reproducing the first few instanton numbers by a localization computation directly in the a model and verifying ooguri vafa integrality this is the first exact result on open string mirror symmetry for a compact calabi yau manifold

on state dependent delay partial neutral functional integro differential equations in this paper the existence of mild solutions for a class of abstract neutral integro differential equations with state dependent delay is studied

positive periodic solution of second order neutral functional differential equations abstract in this paper we consider two types of second order neutral functional differential equations by choosing available operators and applying krasnoselskii s fixed point theorem we obtain sufficient conditions for the existence of periodic solutions to such equations

existence of periodic solutions for delay differential equations with state dependent delay abstract in this paper we study the existence of periodic solutions of a delay differential equation with delay depending indirectly on the state a fixed point problem related to a poincare operator is constructed and solved using an ejective fixed point theorem

the solution manifold and c1 smoothness for differential equations with state dependent delay abstract let h 0 u c 1 h 0 r n open and f u r n continuously differentiable if f satisfies two mild additional smoothness conditions then the set x u 0 f is a c1 submanifold of codimension n in c 1 h 0 r n the maximal solutions x of the initial value problems x t f x t x 0 x define a continuous semiflow f on x and all operators f t are continuously differentiable their derivatives d2f t are given in the usual way by solutions v to the variational equation along x with segments vt in the tangent spaces tf t x the additional conditions on f are motivated by properties of differential equations with state dependent delay and are verified for an example

metastable periodic patterns in singularly perturbed state dependent delayed equations abstract we consider the scalar delayed differential equation x t x t f x t r where 0 r r x 1 r x and f represents either a monotone positive feedback d f d x 0 or a monotone negative feedback d f d x 0 plus some other hypotheses when the delay is a constant i e r x 1 this equation can support metastable rapidly oscillating solutions that are transients whose duration is of order exp c for some c 0 in this paper combining analytic and numerical techniques we investigate whether this metastable behavior persists when the delay r x depends non trivially on the state variable x more precisely we proceed in three steps first we explore theoretically and numerically the existence of branches of rapid periodic solutions for these equations then to predict conditions for metastability we introduce transition layer equations that depict the asymptotic shape of transient oscillations when tends to zero and finally these predictions are validated by numerical simulations numerical explorations are also performed for other scalings of with our conclusions are i when 0 0 there are no metastable transients ii when 0 0 and 0 is finite for monotone negative feedback the metastable oscillations exist irrespective of choices of f and r iii for monotone positive feedback they require that the feedback f and the delay r satisfy extra conditions such as f being an odd function and the delay r x an even function one novel result is that state dependent delays may lead to metastable dynamics in equations that cannot support such regimes when the delay is constant

global bifurcation of periodic solutions to some autonomous differential delay equations we are concerned with slowly oscillating periodic solutions of the parametrized differential delay equation x xdot t email protected x t 1 l 0 where is an odd continuous and nonlinear function satisfying email protected x 0 for all x 0 due to the oddness of we can identify odd harmonic periodic solutions having the period t with other solutions of the periods 2t t 2 from this observation and a result of nussbaum we obtain the existence of periodic solutions with a period close to 2 moreover we can reach conclusions about a secondary bifurcation of periodic solutions we present a combination of a galerkin scheme with a continuation method which yields a feasable numerical procedure for the effective computation and continuation of periodic solutions we report the results of an extensive case study for the nonlinearities x x 1 x p p 1 for p 8 we show many different continua of periodic solutions which are either disjoint or bifurcating from continua of periodic solutions that contain a higher symmetry for p 1 and l p 2 it is known that periodic solutions are unique we discuss two homotopies linking the cases p 8 and p 1 which exhibit very different transitions from multiplicity to uniqueness of solutions

boundary layer phenomena for differential delay equations with state dependent time lags i in this paper we begin a study of the differential delay equation mathtype mtef 2 1 feaafiart1ev1aaatcvaufebsjuyzl2yd9gzlbvynv2caerbulwbln hiov2dgi1btfmbaexatlxbi9gbaerbd9wdylwzybitldharqqtubsr 4rnchbgeagqivu0je9sqqrpepc0xbbl8f4rqqrffpeea0jc9yq jc9 vqaqpepm0xbba9pwe9q8fs0 yqaqpepae9pg0firpeps0he9vr0 vr 0 vqpwqaaeaabigaciaacaqabeaadaqaaqaaaoqaaiabew7aljqadi hagaqbaiaacicacawg0bgaaiykaiabg2da9iabgkhitiaadihacagg oagaamidaiaacmcacqghrawkcawgmbgaaiikaiaadihacaggoagaam idaiabgkhitiaadkhacaggpagaaiykaiaacycacaqggagaaeiiaiaa dkhacqgh9aqpcawgybgaaiikaiaadihacaggoagaamidaiaacmcaca ggpaaaaa 5192 varepsilon x t x t f x t r r r x t we prove the existence of periodic solutions for 0 0 where 0 is an optimal positive number we investigate regularity and monotonicity properties of solutions x t which are defined for all t and of associated functions like t t r x t we begin the development of a poincare bendixson theory and phase plane analysis for such equations in a companion paper these results will be used to investigate the limiting profile and corresponding boundary layer phenomena for periodic solutions as approaches zero

morse decompositions for delay differential equations abstract the attractor for the scalar delay differential equation x t f x t x t 1 is shown to possess a morse decomposition under the hypothesis of a negative feedback condition in the delay term using this decomposition we prove results on the asymptotic rate of oscillation of solutions of the initial value problem existence of both slowly and rapidly oscillating periodic solutions is also proved

smoothness of semiflows for parabolic partial differential equations with state dependent delay in this paper the smoothness properties of semiflows on c1 solution submanifold of a parabolic partial differential equations with state dependent delay are investigated the problem is formulated as an abstract ordinary retarded functional differential equation of the form du t dt au t f ut with a continuously differentiable map g from an open subset u of the space c1 h 0 l2 where a is the infinitesimal generator of a compact c0 semigroup the present study is continuation of a previous work 14 that highlights the classical solutions and c1 smoothness of solution manifold here we further prove the continuous differentiability of the semiflow we finally verify all hypotheses by a biological example which describes a stage structured diffusive model where the delay which is the time taken from birth to maturity is assumed as a function of a immature species population

mixed stress displacement isogeometric collocation for nearly incompressible elasticity and elastoplasticity abstract we propose a mixed stress displacement isogeometric collocation method for nearly incompressible elastic materials and for materials exhibiting von mises plasticity the discretization is based on isogeometric analysis iga with non uniform rational b splines nurbs as basis functions as compared to conventional iga galerkin formulations isogeometric collocation methods offer a high potential of computational cost reduction for higher order discretizations as they eliminate the need for quadrature in the proposed mixed formulation both stress and displacement fields are approximated as primary variables with the aim of treating volumetric locking and instability issues which occur in displacement based isogeometric collocation for nearly incompressible elasticity and von mises plasticity the performance of the proposed approach is demonstrated by several numerical examples

differential equations with locally bounded delay abstract for differential delay equations of the general form x t g x t which include equations with unbounded finite state dependent delays we construct semiflows of continuously differentiable solution operators on suitable banach manifolds and provide local stable and unstable manifolds at equilibria examples occur in feedback systems with delays caused by signal transmission

topological strings and almost modular forms the b model topological string theory on a calabi yau threefold x has a symmetry group generated by monodromies of the periods of x this acts on the topological string wave function in a natural way governed by the quantum mechanics of the phase space h3 x we show that depending on the choice of polarization the genus g topological string amplitude is either a holomorphic quasi modular form or an almost holomorphic modular form of weight 0 under moreover at each genus certain combinations of genus g amplitudes are both modular and holomorphic we illustrate this for the local calabi yau manifolds giving rise to seiberg witten gauge theories in four dimensions and local ip2 and ip1 ip1 as a byproduct we also obtain a simple way of relating the topological string amplitudes near different points in the moduli space which we use to give predictions for gromov witten invariants of the orbifold mathbb c 3 mathbb z 3

differential equations with discrete state dependent delay uniqueness and well posedness in the space of continuous functions abstract partial differential equations with discrete concentrated state dependent delays in the space of continuous functions are investigated in general the corresponding initial value problem is not well posed so we find an additional assumption on the state dependent delay function to guarantee the well posedness for the constructed dynamical system we study the long time asymptotic behavior and prove the existence of a compact global attractor

a non local pde model for population dynamics with state selective delay local theory and global attractors we propose a non local pde model for the evolution of a single species population that involves delayed feedback where the delay such as the maturation time in the delayed birth rate is selective and the selection depends on the status of the system this delay selection in contrast with the usual state dependent delay widely used in ordinary delay differential equation ensures the lipschitz continuity of the nonlinear functional in the classical phase space we also develop the local theory and the existence and upper semi continuity of the global attractor with respect to parameters

polynomial invariants for torus knots and topological strings we make a precision test of a recently proposed conjecture relating chern simons gauge theory to topological string theory on the resolution of the conifold first we develop a systematic procedure to extract string amplitudes from vacuum expectation values vevs of wilson loops in chern simons gauge theory and then we evaluate these vevs in arbitrary irreducible representations of su n for torus knots we find complete agreement with the predictions derived from the target space interpretation of the string amplitudes we also show that the structure of the free energy of topological open string theory gives further constraints on the chern simons vevs our work provides strong evidence towards an interpretation of knot polynomial invariants as generating functions associated to enumerative problems

boundedness global existence and continuous dependence for nonlinear dynamical systems describing physiologically structured populations abstract the paper is aimed as a contribution to the general theory of nonlinear infinite dimensional dynamical systems describing interacting physiologically structured populations we carry out continuation of local solutions to maximal solutions in a functional analytic setting for maximal solutions we establish global existence via exponential boundedness and by a contraction argument adapted to derive uniform existence time moreover within the setting of dual banach spaces we derive results on continuous dependence with respect to time and initial state to achieve generality the paper is organized top down in the way that we first treat abstract nonlinear dynamical systems under very few but rather strong hypotheses and thereafter work our way down towards verifiable assumptions in terms of more basic biological modelling ingredients that guarantee that the high level hypotheses hold

the topological vertex we construct a cubic field theory which provides all genus amplitudes of the topological a model for all non compact toric calabi yau threefolds the topology of a given feynman diagram encodes the topology of a fixed calabi yau with schwinger parameters playing the role of kahler classes of the threefold we interpret this result as an operatorial computation of the amplitudes in the b model mirror which is the quantum kodaira spencer theory the only degree of freedom of this theory is an unconventional chiral scalar on a riemann surface in this setup we identify the b branes on the mirror riemann surface as fermions related to the chiral boson by bosonization

existence of solutions for a mixed type differential equation with state dependence abstract in this paper we study a general n dimensional mixed type differential equation with state dependence many known works give the existence of solutions with the so called return condition in this paper without requiring the return condition we prove a non local existence of solutions by using a technique of compactification and the dependence of the maximum of functions on the size of their domains we apply our result to differential equations with iterates

c1 α strict solutions and wellposedness of abstract differential equations with state dependent delay abstract we study the existence and uniqueness of c 1 strict solutions for a general class of abstract differential equations with state dependent delay we also study the local well posedness of this type of problems on subspaces of c 1 p 0 x some examples involving partial differential equations are presented

existence uniqueness and approximate controllability of abstract differential equations with state dependent delay abstract we study the approximate controllability of a general class of first order abstract control differential problems with state dependent delay to this end we establish and prove several new results on local and global existence and uniqueness of mild and strict solutions for abstract differential equations with state dependent delay in the last section some examples are presented

a condition on delay for differential equations with discrete state dependent delay abstract parabolic differential equations with discrete state dependent delay are studied the approach based on an additional condition on the delay function introduced in a v rezounenko differential equations with discrete state dependent delay uniqueness and well posedness in the space of continuous functions nonlinear anal 70 11 2009 3978 3986 is developed we propose and study an analogue of the condition which is sufficient for the well posedness of the corresponding initial value problem on the whole space of continuous functions c the dynamical system is constructed in c and the existence of a compact global attractor is proved

systems of differential delay equations floquet multipliers and discrete lyapunov functions abstract we define a discrete integer valued lyapunov function v for cyclic nearest neighbor systems of differential delay equations possessing a feedback condition this extends analogous definitions for cyclic systems of ode s and for scalar differential delay equations we relate the values of v to the real parts of the floquet multipliers for such linear periodic systems and thereby prove all floquet subspaces are at most two dimensional

on the application of isogeometric finite volume method in numerical analysis of wet steam flow through turbine cascades abstract the isogeometric finite volume analysis is utilized in this research to numerically simulate the two dimensional viscous wet steam flow between stationary cascades of a steam turbine for the first time in this approach the analysis suitable computational mesh with curved boundaries is generated for the fluid flow by employing a non uniform rational b spline nurbs surface that describes the cascade geometry and the governing equations are then discretized by the nurbs representation thanks to smooth and accurate geometry representation of the nurbs formulation the employed isogeometric framework not only resolves issues concerning the conventional mesh generation techniques of the finite volume method in steam turbine problems but also as validated against well established experiments significantly improves the accuracy of the numerical solution in addition the shock location in the cascade is predicted and tracked with a sufficient accuracy

slowly oscillating periodic solutions of autonomous state dependent delay equations more than a dozen years since the peak of activity on the question of the existence of periodic slowly oscillating solutions of autonomous delay differential equations following the early work of jones l wright 2 and grafton 3 the work of nussbaum 4 51 is to be specially noted for providing several new fixed point results and a global bifurcation theorem which are particularly useful for proving the existence of periodic solutions other important works include those of hadeler and tomiuk 6 kaplan and yorke 7 chow 8 chow and hale 9 alt lo 111 and walther 12 131 see hale s book 14 for an overview to the best of our knowledge only nussbaum 5 and alt 1 l considered the question of the existence of periodic solutions of autonomous state dependent delay differential equations nussbaum considered a special equation 0 3 below in 5 but did not prove a general result alt 1 l considered more complicated integral threshold type state dependent delays which have arisen in various models in epidemiology and structured population models alt obtained a theorem for a general class of state dependent equations on which we comment below the lack of results on periodic solutions for state dependent equations is probably explained by the fact that it is not clear what kinds of state dependent delays are interesting or natural and on a lack of compelling examples of such equations arising from plausible mathematical models however some recent papers of belair and mackey 15 and belair 16 contain some interesting state dependent delay equations arising in economics and population biology state dependent delays of threshold type arise naturally in structured population models see lo 111 the motivation for this paper stems from consideration of the innocent looking equation x t kx t r x t 0 1 where r x is bell shaped e g r x 01 emxz 1 01 0 i 01 5 1 if k 7r 2 and r o 1 then the zero solution of 0 1 is unstable a formal linearization would yield z t kz t 1 which is known to be unstable for

periodic solutions for differential equations with state dependent delay and positive feedback existence of a nontrivial periodic orbit and a homoclinic orbit connecting 0 to the periodic orbit is shown for the differential equation x t x t f x t r r r x t with state dependent delay and positive feedback here 0 f and r are smooth real functions with r 0 1 and f 0

linearized stability for a class of neutral functional differential equations with state dependent delays abstract in this paper we formulate a stability theorem by means of linearization around a trivial solution in the case of autonomous neutral functional differential equations with state dependent delays we prove that if the trivial solution of the linearized equation is exponentially stable then the trivial solution of the nonlinear equation is exponentially stable as well as an application of the main result explicit stability conditions are given

existence of solutions for neutral integro differential equations with state dependent delay in this paper we study the existence and regularity of solutions for a neutral functional integro differential equation with state dependent delay in banach space the mild solutions are investigated by sadovskii fixed point theorem under compactness condition for the resolvent operator and the theory of fractional power and a norm are also used in the discussion since the nonlinear terms of the system involve spacial derivatives the strict solutions are obtained under holder continuity condition hence this work extends and develops the existed results on this topic in the end an example is provided to illustrate the application of the obtained results

non prismatic beams a simple and effective timoshenko like model abstract the present paper discusses simple compatibility equilibrium and constitutive equations for a non prismatic planar beam specifically the proposed model is based on standard timoshenko kinematics i e planar cross section remain planar in consequence of a deformation but can rotate with respect to the beam center line an initial discussion of a 2d elastic problem highlights that the boundary equilibrium deeply influences the cross section stress distribution and all unknown fields are represented with respect to global cartesian coordinates a simple beam model i e a set of ordinary differential equations odes is derived describing accurately the effects of non prismatic geometry on the beam behavior and motivating equation s terms with both physical and mathematical arguments finally several analytical and numerical solutions are compared with results existing in literature the main conclusions can be summarized as follows i the stress distribution within the cross section is not trivial as in prismatic beams in particular the shear stress distribution depends on all generalized stresses and on the beam geometry ii the derivation of simplified constitutive relations highlights a strong dependence of each generalized deformation on all the generalized stresses iii axial and shear bending problems are strictly coupled iv the beam model is naturally expressed as an explicit system of six first order odes v the odes solution can be obtained through the iterative integration of the right hand side term of each equation vi the proposed simple model predicts the real behavior of non prismatic beams with a good accuracy reasonable for the most of practical applications

effects of parameterization and knot placement techniques on primal and mixed isogeometric collocation formulations of spatial shear deformable beams with varying curvature and torsion abstract we present a displacement based and a mixed isogeometric collocation iga c formulation for free form three dimensional shear deformable beams with high and rapidly varying curvature and torsion when such complex shapes are concerned the approach used to build the iga geometric model becomes relevant although iga c has been so far successfully applied to a wide range of problems the effects that different parameterization and knot placement techniques may have on the accuracy of collocation based formulations is still an unexplored field to fill this gap primal and mixed formulations are used combining two parameterization methods chord length and equally spaced with two knot placement techniques uniformly spaced and de boor with respect to the space varying frenet local frame we derive the strong form of the governing equations in a compact form through the definition of two matrix operators conveniently used to perform first and second order derivatives of the vector fields involved in the formulations this approach is very efficient and easy to implement within a collocation based scheme several challenging numerical experiments allow to test the different considered parameterizations and knot placement techniques revealing in particular that with the primal formulation an equally spaced parameterization is definitively the most recommended choice and it should always be used with an approximation degree of at least p 6 although some caution must be adopted when very high jacobians and small curvatures occur the same holds for the mixed formulation with the difference that p 4 is enough to yield accurate results

existence and controllability results for second order impulsive stochastic evolution systems with state dependent delay in this paper we discuss a kind of impulsive second order stochastic evolution systems with state dependent delay in a real separable hilbert space the results concerning the existence and controllability of mild solutions have been addressed by means of the fixed point techniques some sufficient conditions are formulated as well as an application involving partial differential equation with impulses is presented

avoiding shear locking for the timoshenko beam problem via isogeometric collocation methods in this work we study isogeometric collocation methods for the timoshenko beam problem considering both mixed and displacement based formulations in particular we show that locking free solutions are obtained for mixed methods independently on the approximation degrees selected for the unknown fields moreover several numerical tests are provided in order to support our theoretical results and to show the good behavior and the flexibility of isogeometric collocation methods in this context

non prismatic timoshenko like beam model the present paper combines an effective beam theory with a simple and accurate numerical technique opening the door to the prediction of the structural behavior of planar beams characterized by a continuous variation of the cross section geometry that in general deeply influences the stress distribution and therefore leads to non trivial constitutive relations accounting for these peculiar aspects the beam theory is described by a mixed formulation of the problem represented by six linear ordinary differential equations odes with non constant coefficients depending on both the cross section displacements and the internal forces due to the odes complexity the solution can be typically computed only numerically also for relatively simple geometries loads and boundary conditions however the use of classical numerical tools for this problem like a six field mixed finite element approach might entail several issues e g shear locking ill conditioned matrices etc conversely the recently proposed isogeometric collocation method consisting of the direct discretization of the odes in strong form and using the higher continuity properties typical of spline shape functions allows an equal order approximation of all unknown fields without affecting the stability of the solution this makes such an approach simple robust efficient and particularly suitable for solving the system of odes governing the non prismatic beam problem several numerical experiments confirm that the proposed mixed isogeometric collocation method is actually cost effective and able to attain high accuracy

on abstract differential equations with state dependent non local conditions abstract in this paper we introduce the concept of state dependent nonlocal condition and study the existence and uniqueness of solution for a general class of abstract differential equations with state dependent delay subject to this class of conditions in this type of problem the nonlocal condition can be dependent on times or time intervals determined by the unknown solution some examples on partial differential equations with state dependent delay arising in population dynamics are presented

boundary layer phenomena for differential delay equations with state dependent time lags iii in this paper we begin a study of the differential delay equation varepsilon x t x t f x t r r r x t

abstract algebraic delay differential systems and age structured population dynamics abstract we consider the abstract algebraic delay differential system x t a x t f x t a t a t h x t a t here a is a linear operator on d a x satisfying the hille yosida conditions x t d a x and a t r n where x is a real banach space with a global lipschitz condition on f and an appropriate hypothesis on the function h we show that the corresponding initial value problem gives rise to a continuous semiflow in a subset of the space of continuous functions we establish the positivity of the x component and give some examples arising from age structured population dynamics the examples come from situations where the age of maturity of an individual at a given time is determined by whether or not the resource concentration density which depends on the immature population reaches a prescribed threshold within that time

computing genus zero twisted gromov witten invariants twisted gromov witten invariants are intersection numbers in moduli spaces of stable maps to a manifold or orbifold x which depend in addition on a vector bundle over x and an invertible multiplicative characteristic class special cases are closely related to local gromov witten invariants of the bundle and to genus zero one point invariants of complete intersections in x we develop tools for computing genus zero twisted gromov witten invariants of orbifolds and apply them to several examples we prove a quantum lefschetz theorem that expresses genus zero one point gromov witten invariants of a complete intersection in terms of those of the ambient orbifold x we determine the genus zero gromov witten potential of the type a surface singularity c2 zn we also compute some genus zero invariants of c3 z3 verifying predictions of aganagic bouchard and klemm 3 in a self contained appendix we determine the relationship between the quantum cohomology of the an surface singularity and that of its crepant resolution thereby proving the crepant resolution conjectures of ruan and of bryan and graber 12 in this case

principle of linearized stability and instability for parabolic partial differential equations with state dependent delay abstract in this paper the stability properties of a parabolic partial differential equation with state dependent delay are investigated by the heuristic approach the previous works 1 2 obtained a continuously differentiable semiflow with continuously differentiable solution operators defined by the classical solutions and resolved the problem of linearization for this equation here we clarify the relation between the spectral properties of the linearization of the semiflow at a stationary solution and the strong continuous semigroup defined by the solutions of the linearization of this equation and consider the local stable and unstable invariant manifolds of the semiflow at a stationary solution by a biological application we finally verify all hypotheses for an age structured diffusive model with state dependent delay and consider its stability behavior

stability and hopf bifurcation for a cell population model with state dependent delay we propose a mathematical model describing the dynamics of a hematopoietic stem cell population the method of characteristics reduces the age structured model to a system of differential equations with a state dependent delay a detailed stability analysis is performed a sufficient condition for the global asymptotic stability of the trivial steady state is obtained using a lyapunov razumikhin function a unique positive steady state is shown to appear through a transcritical bifurcation of the trivial steady state the analysis of the positive steady state behavior through the study of a first order exponential polynomial characteristic equation concludes the existence of a hopf bifurcation and gives criteria for stability switches a numerical analysis confirms the results and stresses the role of each parameter involved in the system on the stability of the positive steady state

convergence of solutions for an equation with state dependent delay abstract a result of smith and thieme shows that if a semiflow is strongly order preserving then a typical orbit converges to the set of equilibria for the equation with state dependent delay t x t f x t r x t where 0 and f and r are smooth real functions with f 0 0 and f 0 we construct a semiflow which is monotone but not strongly order preserving we prove a convergence result under a monotonicity condition different from the strong order preserving property and apply it to the above equation to obtain generic convergence

the poincare bendixson theorem for a class of delay equations with state dependent delay and monotonic feedback abstract we consider the real valued differential equation x t f x t x t d x t with state dependent delay where f is strictly monotonic in its second argument we describe a class of such equations for which a version of the poincare bendixson theorem holds

isogeometric collocation for kirchhoff love plates and shells abstract with the emergence of isogeometric analysis iga the galerkin rotation free discretization of kirchhoff love shells is facilitated enabling more efficient thin shell structural analysis high order shape functions used in iga also allow the collocation of partial differential equations avoiding the time consuming numerical integration of the galerkin technique the goal of the present work is to apply this method to nurbs based isogeometric kirchhoff love plates and shells under the assumption of small deformations since kirchhoff love plate theory yields a fourth order formulation two boundary conditions are required at each location on the contour generating some conflicts at the corners where there are more equations than needed to remedy this overdetermination we provide priority and averaging rules that cover all the possible combinations of adjacent edge boundary conditions i e the clamped simply supported symmetric and free supports greville and alternative superconvergent points are used for nurbs basis of even and odd degrees respectively for square circular and annular flat plates convergence orders are found to be in agreement with a priori error estimates the proposed isogeometric collocation method is then validated and benchmarked against a galerkin implementation by studying a set of problems involving kirchhoff love shells

d branes categories and n 1 supersymmetry we show that boundary conditions in topological open string theory on calabi yau cy manifolds are objects in the derived category of coherent sheaves as foreseen in the homological mirror symmetry proposal of kontsevich together with conformal field theory considerations this leads to a precise criterion determining the supersymmetry preserving branes at any point in cy moduli space completing the proposal of ii stability