the absolutely continuous spectrum of discrete canonical systems has absolutely continuous spectrum of a certain multiplicity then there is a corresponding number of linearly independent solutions y which are bounded in a weak sense

semiclassical analysis of low lying eigenvalues iv the flea on the elephant abstract the two lowest eigenvalues e 0 e 1 of a symmetric double well tunnelling problem 2 v as are considered and they are compared to the two lowest eigenvalues e 0 e 1 of 2 v w where w is supported away from the well bottoms of v we determine the leading exponential splitting of various differences of the four numbers e 0 e 1 e 0 e 1 related problems are discussed

semiclassical analysis of low lying eigenvalues ii tunneling we discuss the leading asymptotics of eigenvalue splittings of 2 x2v in the limit as x o and where v is a non negative potential with several zeros for example if eo x e1 x are the two lowest eigenvalues in a situation where v has precisely two zeros a and b related by a symmetry then limx x lin e1 x eo x is given as the distance from a to b in a certain riemann metric

a new approach to inverse spectral theory i fundamental formalism we present a new approach distinct from gelfand levitan to the the orem of borg marchenko that the m function equivalently spectral measure for a finite interval or half line schrodinger operator determines the poten tial our approach is an analog of the continued fraction approach for the moment problem we prove there is a representation for the m function m 2 r b

krein type theorems and ordered structure for cauchy de branges spaces abstract we extend some results of m g krein to the class of entire functions which can be represented as ratios of discrete cauchy transforms in the plane as an application we obtain new versions of de branges ordering theorem for nearly invariant subspaces in a class of hilbert spaces of entire functions examples illustrating sharpness of the obtained results are given we also discuss applications to spectral theory of rank one perturbations of normal operators

a comparison of hybrid and quadratic upstream differencing in high reynolds number elliptic flows abstract numerical computations have been performed of various two dimensional elliptic flows at high reynolds number with a view to assessing the relative merits of the widely used hybrid i e upwind central interpolation and the recently proposed quadratic upstream interpolation of leonard known as quick the latter scheme possesses less intrinsic stability than hybrid differencing by selectively evaluating some of the convective elements at a previous iteration level however satisfactorily rapid convergence has been obtained it is concluded from the flows tested that the extra computational effort per node required for quick over the hybrid difference scheme is more than repaid by the greater numerical accuracy that results

i simple pulsatile flow in an artery with a constriction abstract a smooth isolated axisymmetric occlusion in a straight vascular tube is a tractable problem for pulsatile flow calculations via finite difference approximations to the navier stokes equation steady flow depends on the reynolds number and two geometric parameters which describe the stenosis the mere addition of a simple harmonic to the mean flow adds two more parameters one is the reduced frequency or stokes number and the other e the ratio of unsteady to steady flux after describing steady stenosis flow examples the dynamic patterns of pulsatile flow are illustrated indicating the inadequacy of basing hypotheses of atherosclerosis on mean steady flow

schrodinger operators and de branges spaces abstract we present an approach to de branges s theory of hilbert spaces of entire functions that emphasizes the connections to the spectral theory of differential operators the theory is used to discuss the spectral representation of one dimensional schrodinger operators and to solve the inverse spectral problem

on the linear damped wave equation abstract in this work we estimate the spectrum of the linear damped wave semigroup under homogeneous dirichlet boundary conditions by using the principal eigenvalue of an elliptic operator related to the equation our estimate is optimal for real eigenvalues then we analyze the behavior of the estimate as the damping amplitude grows to infinity when the damping changes of sign we extend a result of freitas 5 to show that the semigroup possesses at least two real eigenvalues greater than one if the amplitude is sufficiently large in particular the trivial state is unstable in strong contrast with the sign definited case finally we characterize the limiting behavior of the real eigenpairs which originate the inestability of the trivial state this analysis is based upon the behavior of the principal eigenpair of a singular perturbation problem at the singular limit our theory is of interest by itself and it has many applications to reaction diffusion systems c f for instance 6

asymptotic behaviour of principal eigenvalues for a class of cooperative systems this paper analyzes the asymptotic behaviour as of the principal eigenvalue of the cooperative operator l l1 a x b cl2 d x in a bounded smooth domain of rn n 1 under homogeneous dirichlet boundary conditions on where a 0 d 0 and b x 0 c x 0 for all x precisely our main result establishes that if int a d 1 0 consists of two components 0 1 and 0 2 then lim 1 l mini 1 2 1 l 0 0 i where for any d and r 1 l d stands for the principal eigenvalue of l in d moreover if we denote by the principal eigenfunction associated to l normalized so that 2 2 1 and for instance 1 l 0 0 1 1 l 0 0 2 then the limit lim is well defined in h01 h01 0 in 0 1 and 0 1 provides us with the principal eigenfunction of l 0 0 1 this is a rather striking result for as according to it the principal eigenfunction must approximate zero as if a d 0 in spite of the cooperative structure of the operator

universal bounds on spectral measures of one dimensional schrodinger operators let h d2 dx2 v x be a schrodinger operator on l2 0 with spectral measure and suppose that the potential v is known on an initial interval 0 n we show that this information yields strong restrictions on i for intervals i r more precisely we prove upper and lower bounds on i the upper bound is finite for any i that is bounded above and the lower bound is positive if the interior of i contains at least two eigenvalues of the operator on l2 0 n these results are developments of classical work of chebyshev and markov on orthogonal polynomials

on a variable coefficient korteweg de vries model in fluid filled elastic tubes in this paper we investigate a variable coefficient korteweg de vries vckdv model in arterial mechanics a new lax pair of the vckdv model is constructed based on which the b cklund transformation solitonic and some other solutions of the vckdv model are obtained with symbolic computation the influence of the variable coefficients on solitonic propagation is investigated based on the solitonic solution which has the following three aspects i the coefficient of the nonlinear term affects the solitonic amplitude ii the coefficient of the dispersive term controls the solitonic velocity and propagation trace iii the coefficient of the dissipative term acts on both the solitonic amplitude and the velocity we also analyze the variations of velocity and pressure of blood flow along the scaled axial coordinate after the static deformation in the vicinity of stenosis

finite element simulation of pulsatile flow through arterial stenosis the problem of blood flow through a stenosis is solved using the incompressible navier stokes equations in a rigid circular tube presenting a partial occlusion calculations are based on a galerkin finite element method the time marching scheme employs a predictor corrector technique using a variable time step results are obtained for steady and physiological pulsatile flows computational experiments analyse the effect of varying the degree of stenosis the stricture length the reynolds number and womersley number the method gives results which agree well with previous computations for steady flows and experimental findings for steady and pulsatile flows

a contribution on the effects of inlet conditions when modelling stenoses using sudden expansions abstract using three diameter ratios and up to four inlet velocity profiles the laminar flow in axisymmetric sudden expansions is investigated numerically for inlet reynolds numbers of 250 or lower the vortex reattachment length is found to be a linear function of the reynolds number regardless of either the diameter ratio or inlet velocity profile however the inlet velocity profile plays an important role in contributing to a non linear relationship between the vortex length as a function of the expansion step height the wall shear stress distribution in the larger pipe is found to depend strongly upon the diameter ratio inlet velocity profile and reynolds number

the asymptotic form of the titchmarsh weyl m function associated with a second order differential equation with locally integrable coefficient on deduit un developpement asymptotique pour la m fonction de titchmarsh weyl associee a l equation differentielle lineaire d ordre 2 y qy y sur 0 dans le cas ou la seule restriction sur la fonction a valeur reelle q est q l 1 0 e pour e 0

numerical investigation of the non newtonian blood flow in a bifurcation model with a non planar branch the pulsatile flow of non newtonian fluid in a bifurcation model with a non planar daughter branch is investigated numerically by using the carreau yasuda model to take into account the shear thinning behavior of the analog blood fluid the objective of this study is to deal with the influence of the non newtonian property of fluid and of out of plane curvature in the non planar daughter vessel on wall shear stress wss oscillatory shear index osi and flow phenomena during the pulse cycle the non newtonian property in the daughter vessels induces a flattened axial velocity profile due to its shear thinning behavior the non planarity deflects flow from the inner wall of the vessel to the outer wall and changes the distribution of wss along the vessel in particular in systole phase downstream of the bifurcation the velocity profiles are shifted toward the flow divider and low wss and high shear stress temporal oscillations characterized by osi occur on the outer wall region of the daughter vessels close to the bifurcation secondary motions become stronger with the addition of the out of plane curvature induced by the bending of the vessel and the secondary flow patterns swirl along the non planar daughter vessel a significant difference between the non newtonian and the newtonian pulsatile flow is revealed during the pulse cycle however reasonable agreement between the non newtonian and the rescaled newtonian flow is found calculated results for the pulsatile flow support the view that the non planarity of blood vessels and the non newtonian properties of blood are an important factor in hemodynamics and may play a significant role in vascular biology and pathophysiology

sum rules and spectral measures of schrodinger operators with l 2 potentials necessary and sufficient conditions are presented for a positive measure to be the spectral measure of a half line schrodinger operator with square integrable potential

on the potentialities of 3d 1d coupled models in hemodynamics simulations this work comprises a step towards the quantitative and qualitative analysis of coupled local and global hemodynamics phenomena in the arterial system the aim of this work is to present some numerical examples to put in evidence the importance of the use of 3d 1d coupled models in hemodynamics problems when carrying out simulations of rather complex situations accordingly some cases for which classical modeling cannot be applied are identified and solved the results obtained here allow us to assess some interrelations between local pointwise quantities defined at the level of the 3d model and global mean quantities defined at the level of the 1d model

a consistently formulated quick scheme for fast and stable convergence using finite volume iterative calculation procedures abstract previous applications of quick for the discretization of convective transport terms in finite volume calculation procedures have failed to employ a rigorous and systematic approach for consistently deriving this finite difference scheme instead earlier formulations have been established numerically by trial and error the new formulation for quick presented here is obtained by requiring that it satisfy four rules that guarantee physically realistic numerical solutions having overall balance careful testing performed for the wall driven square enclosure flow configuration shows that the consistently derived version of quick is more stable and converges faster than any of the formulations previously employed this testing includes the relative evaluation of boundary conditions approximated by second and third order finite difference schemes as well as calculations performed at higher reynolds numbers than previously reported

on the location of the weyl circles the paper deals with explicit estimates concerning certain circles in the complex plane which were associated with sturm liouville problems by h weyl by the use of riccati equations instead of linear integral equations improvements are obtained for results of everitt and halvorsen concerning the behaviour of the titchmarsh weyl m coefficient

the calculation of some laminar flows using various discretisation schemes abstract for various laminar two dimensional flows the upwind hybrid and the quadratic finite difference schemes are evaluated the upwind and hybrid schemes are used in their normal forms the quadratic formulation leonard s quick scheme has in the past been found to be less stable than these two other schemes because it can on occasion generate both negative and positive influence coefficients two new forms of the quadratic formulation both of which always generate positive influence coefficients are presented for a uniform grid distribution and tested by reference to the results obtained from the upwind and hybrid schemes and data from other sources these two new schemes are found to be stable although one form seems to be sensitive to the size of the finite difference grid furthermore the solutions obtained using these new formulations are equal to or better than those obtained using the upwind and or the hybrid schemes it is concluded that these new formulations require further validation and to this end these new formulations are provided in a form that is easy to install into existing computer codes

multiblock hybrid grid finite volume method to solve flow in irregular geometries in this work a finite volume based finite element method is suitably developed for solving incompressible flow and heat transfer on collocated hybrid grid topologies the method is generally applicable to arbitrarily shaped elements and orientations and thus challenges the potential to unify many of the different grid topologies into a single formulation the key point in this formulation is the correct estimation of the convective and diffusive fluxes at the cell faces using a novel physical influence scheme this scheme remarkably enhances the achieved solution accuracy it is shown that the extended formulation is robust enough to treat any combination of multiblock meshes with dual element shape employments in this regard the solution domain is broken up into a number of different multiblock arrangements in which each block is filled with only one type of finite element shape the combined grid can decrease the computational time and memory requirements and increase the numerical accuracy the results of the extended formulation are validated against different benchmark and other solutions the current results are in excellent agreement with the other solutions without exhibiting any disturbances around the block boundaries

the m functions of discrete schrodinger operators are sparse compared to those for jacobi operators abstract we explore the sparsity of weyl titchmarsh m functions of discrete schrodinger operators due to this the set of their m functions cannot be dense on the set of those for jacobi operators all this reveals why an inverse spectral theory for discrete schrodinger operators via their spectral measures should be difficult to obtain the result de branges theory of canonical systems is applied to work on them instead of weyl titchmarsh m functions

an assessment of flow oriented schemes for reducing false diffusion un facteur limitatif important dans la modelisation precise des problemes d ecoulement est la representation numerique des termes de convection dans les equations de navier stokes revue des differentes methodes d approximation des termes de convection pour reduire les erreurs de fausse diffusion dans le contexte des methodes de differences finies et de volumes finis

on the spectral characterization of entire operators with deficiency indices 1 1 abstract for entire operators and entire operators in the generalized sense we provide characterizations based on the spectra of their selfadjoint extensions in order to obtain these spectral characterizations we discuss the representation of a simple regular closed symmetric operator with deficiency indices 1 1 as a multiplication operator in a certain de branges space

the effect of unsteadiness on the flow through stenoses and bifurcations abstract this paper is concerned with the influence of a stenosis or a bifurcation on the flow through a tube in particular the effect of unsteadiness is investigated using simple pulsatile and physiological type flows fig 1 the experimental investigations reported herein are concerned with velocity measurements and flow visualizations these measurements performed in a 60 bifurcation have permitted the reconstruction of the three dimensional velocity profiles the importance of the secondary flow in the branching is analyzed for various values of the flow parameters results of tests show a strong influence of unsteadiness on flow characteristics and then on hemodynamic factors one conclusion is the following if hemodynamic factors play an important role in the problems of atheroselerosis then for macrocirculation studies it is necessary to take into account unsteadiness and in particular the actual shape of the flow time forcing function

inverse scattering on matrices with boundary conditions we describe inverse scattering for the matrix schrodinger operator with general self adjoint boundary conditions at the origin using the marchenko equation our approach allows the recovery of the potential as well as the boundary conditions it is easily specialized to inverse scattering on star shaped graphs with boundary conditions at the node

semiclassical analysis of general second order elliptic operators on bounded domains in this work we ascertain the semiclassical behavior of the fundamental energy and the ground state of an arbitrary second order elliptic operator not necessarily selfadjoint on a bounded domain our analysis provides us with substantial improvements of many previous results found in the context of quantum mechanics for c perturbations of the laplacian

the periodic principal eigenvalues with applications to the nonlocal dispersal logistic equation abstract in this paper we study the nonlocal dispersal equation u t r n j x y u y t d y u u a x t u p in 0 u x t 0 in r n 0 u x 0 u 0 x in where r n is a bounded domain and p 1 are constants the dispersal kernel j is nonnegative the function a c r is nonnegative and t periodic in t but a x t has temporal or spatial degeneracies a x t vanishes we first study the periodic nonlocal eigenvalue problems with parameter and establish the asymptotic behavior of principal eigenvalues when the parameter is large we find that the spatial degeneracy of a x t always guarantees a principal eigenfunction then we consider the dynamical behavior of the equation if a x t has temporal or spatial degeneracies our results indicate that only the temporal degeneracy can not cause a change of the dynamical behavior but the spatial degeneracy always causes fundamental changes whether or not the temporal degeneracy appears

three dimensional simulation of steady flow past a partial stenosis abstract the steady non uniform viscous flow past a partial stenosis in a circular vessel has been calculated numerically by a modified mac sola method the stenosis is represented by a half ring of nearly square cross section steady flows at reynolds numbers of 25 and 150 were generated by using the time dependent equations of motion and calculating until the solutions became convergent velocity field depictions indicate the occurrence of a small upstream and a large downstream separation zone at the stenosis pressure and shear distributions at various radial and angular positions show significant changes in these kinetic variables near the stenosis strong secondary flow development and decay are exemplified by changes in the vorticity component in the axial direction a change in the nature of this vorticity occurs as the stenosis is passed the size length of the separation zone near the vessel wall as determined by numerical calculation is confirmed by experimental observations at a reynolds number of 149

inverse spectral theory for one dimensional schrodinger operators the a function we link recently developed approaches to the inverse spectral problem due to simon and myself respectively we obtain a description of the set of simon s a functions in terms of a positivity condition this condition also characterizes the solubility of simon s fundamental equation

remling s theorem on canonical systems in this paper we extend the remling s theorem on canonical systems that the limit points of the hamiltonian under the shift map are reflectionless on the support of the absolutely continuous part of the spectral measure of a canonical system

a power law model of blood flow through a tapered overlapping stenosed artery a mathematical model of non newtonian blood flow through a tapered stenotic artery is considered the non newtonian model chosen is characterized by the generalized power law model incorporating the effect of tapering due to the pulsatile nature of blood flow the flow is assumed to be unsteady laminar two dimensional and axisymmetric the governing equations of motion in terms of the viscous shear stress in the cylindrical coordinate system are solved numerically using a finite difference scheme numerical results obtained for the positive taper angle show that the blood flow characteristics such as the axial velocity profiles flow rate and wall shear stress have lower values while the resistive impedances have higher values than the newtonian model

the class of n entire operators we introduce a classification of simple regular closed symmetric operators with deficiency indices 1 1 according to a geometric criterion that extends the classical notions of entire operators and entire operators in the generalized sense due to m g krein we show that these classes of operators have several distinctive properties some of them related to the spectra of their canonical self adjoint extensions in particular we provide necessary and sufficient conditions on the spectra of two canonical self adjoint extensions of an operator for it to belong to one of our classes our discussion is based on some recent results in the theory of de branges spaces

a new approach to inverse spectral theory ii general real potentials and the connection to the spectral measure we continue the study of the a amplitude associated to a half line schrodinger operator d 2 dx 2 q in l 2 0 b b a is related to the weyl titchmarsh m function via m k 2 k a 0 a e 2 k d o e 2 k for all 0 we discuss five issues here first we extend the theory to general q in l 1 0 for all a including q s which are limit circle at infinity second we prove the following relation between the a amplitude and the spectral measure p a 2 1 2 sin 2 dp since the integral is divergent this formula has to be properly interpreted third we provide a laplace transform representation for m without error term in the case b fourth we discuss m functions associated to other boundary conditions than the dirichlet boundary conditions associated to the principal weyl titchmarsh m function finally we discuss some examples where one can compute a exactly

irreducible compact operators the purpose of the present paper is to show that a positive compact ideal irreducible operator t in a banach lattice of dimension greater than one has spectral radius r t 0 i e t is not quasi nilpotent it was shown in 6 that there exist positive irreducible operators which are quasi nilpotent and the question under what conditions a positive irreducible operator t satisfies r t 0 has been studied extensively see e g 6 and 7 sect v 6 in particular we mention the ando krieger theorem see e g 9 theorem 136 9 which states that a positive irreducible kernel operator t in a banach function space has r t 0 recently in 8 some special situations are discussed in which a compact positive irreducible operator has a strictly positive spectral radius let l be a real or complex banach lattice by 2 we denote the banach space of all bounded linear operators in l as usual we write s t in l whenever su tu for all o uel given 0 t l the closed ideal j in l is called t invariant if t j j and t is called ideal irreducible if the only closed t invariant ideals are 0 and l see 7 iii 8 for the general theory of banach lattices and positive operators we refer to the books 7 and 9 in the proof of the main result of the paper we will use some properties of the center of a banach lattice we recall some elementary facts let l be a real banach lattice the center z l of l is the subspace of 5 l consisting of all operators z for which there exists 0 2 ir such that f l 2 f for all f l the center has the structure of a vector lattice with nl v n2 u n l u v n2u and ozla zz u lu a nzu for all o u l and all l n2ez l moreover z l is a commutative algebra with respect to composition as multiplication and the identity operator i in l is a strong unit i e for any rc z l there exists 0 2eir such that zi 2i see 9 chap 20 note that if l c k for some compact hausdorff space k then z l can be identified with c k acting on itself by multiplication if l is a dedekind complete banach lattice and 0 u v in l then it is an easy consequence of the freudenthal spectral theorem 4 theorem 40 2 that there exists n z l such that zcv u and o n i however in an arbitrary banach lattice such a 7z need not exist as is shown by the banach lattice l c 0 1 the next lemma shows that under rather mild conditions we can

pulsatile flow of non newtonian fluids through arterial stenoses the problem of blood flow through stenoses is solved using the incompressible generalized newtonian model the herschel bulkley bingham and power law fluids are incorporated the geometry corresponds to a rigid circular tube with a partial occlusion calculations are performed by a galerkin finite element method for the pulsatile case a predictor corrector time marching scheme is used with an adaptive time step results are obtained for steady and pulsatile physiological flows computations show that the memory effects taken into account in the model affect deeply the flow compared with newtonian reference case the disturbances are stronger by their vorticity intensity and persist after the geometrical obstacle this is especially true for severe stenoses

connectedness of the isospectral manifold for one dimensional half line schrodinger operators let v0be a real valued function on 0 and v l1 0 r for all r 0 so that h v0 frac d 2 dx 2 v0in l2 0 with u 0 0 boundary conditions has discrete spectrum bounded from below let m v0 be the set of vso that h v and h v0 have the same spectrum we prove that m v0 is connected

the effects of transport on the maximum principle abstract we study the qualitative effects of the transport terms on the maximum principle for a family of one dimensional linear second order boundary value problems we mainly focus on sign changing transport functions denoted by b x there is a huge difference between the cases when b is non increasing or non decreasing it turns out that when b is non increasing the maximum principle holds when the amplitude of b is sufficiently large whereas it fails to be true if b is non decreasing

second order upwind differencing in a recirculating flow in this study we have investigated the accuracy and stability of the second order upwind differencing scheme originally suggested by price et al and recently used by several others the solution algorithm employed is based on a coupled solution of the nonlinear finite difference equations by the multigrid technique calculations have been made of the driven cavity flow for several reynolds numbers and finite difference grids we observe that in comparison with the hybrid differencing the second order upwind differencing is somewhat more accurate but that it is not monotonically accurate with mesh refinement also the convergence of the solution algorithm deteriorates with the use of the second order upwind differencing nomenclature a finite difference coefficient c convective flux d diffusive flux d cavity depth f right hand side of the equation l f i restriction prolongation operator p pressure r residual in the solution re reynolds number uw d v s source term u ar direction velocity uw top wall u velocity d direction velocity x y coordinate directions e error tolerance t smoothing factor v fluid kinematic viscosity p fluid density general transport variable

canonical systems with discrete spectrum abstract we study spectral properties of two dimensional canonical systems y t z j h t y t t a b where the hamiltonian h is locally integrable on a b positive semidefinite and weyl s limit point case takes place at b we answer the following questions explicitly in terms of h is the spectrum of the associated selfadjoint operator discrete if it is discrete what is its asymptotic distribution here asymptotic distribution means summability and limit superior conditions relative to comparison functions growing sufficiently fast making an analogy with complex analysis this corresponds to convergence class and type w r t proximate orders having order larger than 1 it is a surprising fact that these properties depend only on the diagonal entries of h in 1968 l de branges posed the following question as a fundamental problem which hamiltonians are the structure hamiltonian of some de branges space we give a complete and explicit answer

bounds for eigenfunctions of the laplacian on compact riemannian manifolds suppose that is an eigenfunction of with eigenvalue 0 it is proved that c1 n 14 2 where n is the dimension of m and c1 depends only upon a bound for the absolute value of the sectional curvature of m and a lower bound for the injectivity radius of m it is then shown that if m admits an isometric circle action and the metric is generic one has exceptional sequences of eigenfunctions satisfying the complementary bounds k c2 n 18k 2

the maximum principle and the existence of principal eigenvalues for some linear weighted boundary value problems abstract in this work we deal with the problem of the existence and uniqueness of principal eigenvalues for some linear weighted boundary value problems associated to a general second order uniformly elliptic operator for a large class of sign definited weights we characterize whether the boundary value problem admits a principal eigenvalue or not

density of schrodinger weyl titchmarsh m functions on herglotz functions abstract we show that the herglotz functions that arise as weyl titchmarsh m functions of one dimensional schrodinger operators are dense in the space of all herglotz functions with respect to uniform convergence on compact subsets of the upper half plane this result is obtained as an application of de branges theory of canonical systems

the sine _ beta operator we show that text sine beta the bulk limit of the gaussian beta ensembles is the spectrum of a self adjoint random differential operator begin aligned f mapsto 2 r t 1 left begin array cc 0 tfrac d dt tfrac d dt 0 end array right f qquad f 0 1 rightarrow mathbb r 2 end aligned where r t is the positive definite matrix representation of hyperbolic brownian motion with variance 4 beta in logarithmic time the result connects the montgomery dyson conjecture about the text sine 2 process and the non trivial zeros of the riemann zeta function the hilbert polya conjecture and de brange s attempt to prove the riemann hypothesis we identify the brownian carousel as the sturm liouville phase function of this operator

solvability of a class of integro differential equations and connections to one dimensional inverse problems abstract a new approach to one dimensional inverse problem was recently introduced by barry simon we continue the study on an intermediate object a which satisfies a nonlinear integro differential equation we prove local solvability of this a equation and find a necessary condition for global solvability some exact solutions are presented

oversampling and aliasing in de branges spaces arising from bessel operators abstract we show that a class of de branges spaces generated by means of generalized fourier transforms associated with perturbed bessel differential equations has the properties of oversampling and aliasing

mathematical modelling of pulsatile flow of casson s fluid in arterial stenosis the effects of non newtonian nature of blood and pulsatility on flow through a stenosed artery have been investigated it is of interest to note that the thickness of the viscous flow region changes with axial distance an important result is that the mean and steady flow rates decrease as the yield stress increases the critical value of the yield stress at which the flow rate behaviour changes from one type to another has been determined another important result of pulsatility is the mean resistance to flow is greater than its steady flow value whereas the mean value of the wall shear for pulsatile blood flow is equal to steady wall shear stress the velocity profiles and associated physiological characteristics involved in the analysis have been determined many standard results regarding casson and newtonian fluids flow uniform and steady flow in an artery can be obtained in the present analysis as the special cases

a stable and accurate convective modelling procedure based on quadratic upstream interpolation a convective modelling procedure is presented which avoids the stability problems of central differencing while remaining free of the inaccuracies of numerical diffusion associated with upstream differencing for combined convection and diffusion the number of operations at each grid point is comparable to that of standard upstream pluscentral differencing however highly accurate solutions can be obtained with a grid spacing much larger than that required by conventional methods for comparable accuracy with obvious practical advantaged in terms of both speed and storage the algorithm is based on a conservative control volume formulation with cell wall values of each field variable written in terms of a quadratic interpolation using in any one coordinate direction the two adjacent nodal values together with the value at the next upstream node this results in a convective differencing scheme with greater formal accuracy than central differencing while retaining the basic stable convective sensitivity property of upstream weighted schemes the consistent treatment of diffusion terms is equivalent to central differencing with careful modelling numerical boundary conditions are not troublesome some idealized problems are studied showing the practical advantages of the method over other schemes in comparison with exact solutions an application to a complex unsteady two dimensional flow is briefly discussed

on db spaces with nondensely defined multiplication operator and the existence of zero free functions abstract in this work we consider de branges spaces where the multiplication operator by the independent variable is not densely defined first we study the canonical selfadjoint extensions of the multiplication operator as a family of rank one perturbations from the viewpoint of the theory of de branges spaces then on the basis of the obtained results we provide new necessary and sufficient conditions for a real zero free function to lie in a de branges space

properties of the principal eigenvalues of a general class of non classical mixed boundary value problems in this paper we characterize the existence of principal eigenvalues for a general class of linear weighted second order elliptic boundary value problems subject to a very general class of mixed boundary conditions our theory is a substantial extension of the classical theory by p hess and t kato 1980 comm partial differential equations5 999 1030 in obtaining our main results we must give a number of new results on the continuous dependence of the principal eigenvalue of a second order linear elliptic boundary value problem with respect to the underlying domain and the boundary condition itself these auxiliary results complement and in some sense complete the theory of d daners and e n dancer 1997 j differential equations138 86 132 the main technical tool used throughout this paper is a very recent characterization of the strong maximum principle in terms of the existence of a positive strict supersolution due to h amann and j lopez gomez 1998 j differential equations146 336 374