the steady state collision of two compressible subsonic perfect flows abstract this paper is devoted to the mathematical theory for the steady state collision of two compressible subsonic irrotational flows issuing from two infinitely long nozzles we established the existence uniqueness and asymptotic behavior of the subsonic collision flow with a smooth interface for the steady euler system in an important physical regime more precisely there exists a critical value if the summation of the incoming mass fluxes in the inlets of the nozzles is less than the critical value then there exists a unique smooth subsonic compressible collision flow and furthermore there exists a smooth interface which separates the two non miscible compressible subsonic flows in particular a key observation is that the location of the interface can be determined uniquely by the incoming mass fluxes in the inlets of the nozzles finally we showed some monotonic relationship between the location of the interface and the incoming mass fluxes

a degenerate elliptic problem from subsonic sonic flows in general nozzles abstract this paper deals with two dimensional subsonic sonic potential flows in general nozzles which is governed by a free boundary problem of a quasilinear degenerate elliptic equation for a large class of nozzles it is shown that if the variation rate of the cross section of the nozzle is suitably small there exists a unique subsonic sonic flows in the nozzle such that the sonic curve intersects the upper wall at a fixed point and the velocity of the flow is along the normal direction at the inlet and the sonic curve furthermore the sonic curve of this flow is a free boundary where the flow is singular in the sense that the speed is only holder continuous and the acceleration blows up at the sonic state

stability of supersonic contact discontinuity for two dimensional steady compressible euler flows in a finite nozzle abstract in this paper we study the stability of supersonic contact discontinuity for the two dimensional steady compressible euler flows in a finitely long nozzle of varying cross sections we formulate the problem as an initial boundary value problem with the contact discontinuity as a free boundary to deal with the free boundary value problem we employ the lagrangian transformation to straighten the contact discontinuity and then the free boundary value problem becomes a fixed boundary value problem we develop an iteration scheme and establish some novel estimates of solutions for the first order of hyperbolic equations on a cornered domain finally by using the inverse lagrangian transformation and under the assumption that the incoming flows and the nozzle walls are smooth perturbations of the background state we prove that the original free boundary problem admits a unique weak solution which is a small perturbation of the background state and the solution consists of two smooth supersonic flows separated by a smooth contact discontinuity

continuous subsonic sonic flows in a general nozzle abstract this paper concerns continuous subsonic sonic potential flows in a two dimensional finite nozzle with a general upper wall and a straight lower wall we give a class of nozzles where continuous subsonic sonic flows may exist consider a continuous subsonic sonic flow in such a nozzle after rescaling the upper wall in a small scale it is shown that for a given inlet and a fixed point at the upper wall there exists uniquely a continuous subsonic sonic flow whose velocity vector is along the normal direction at the inlet and the sonic curve which satisfies the slip conditions on the nozzle walls and whose sonic curve intersects the upper wall at the fixed point furthermore the sonic curve of this flow is a free boundary where the flow is singular in the sense that the speed is only c 1 2 holder continuous and the acceleration blows up at the sonic state as the scale tends to zero the precise convergent rate of the continuous subsonic sonic flow converging to the sonic state is also determined

subsonic non isentropic euler flows with large vorticity in axisymmetric nozzles abstract in this paper we investigate the effects of vorticity for smooth subsonic non isentropic euler flows in infinitely long axisymmetric nozzles it is a sequel to b duan and z luo 2013 13 on non isentropic euler system in 13 the authors obtained the unique existence of a smooth subsonic solution with restriction on the smallness of bernoulli s function in the upstream the smallness assumption is sufficient to prevent the appearance of singularity however it leads that the vorticity is also small the purpose of this paper is to remove such restriction on the smallness of the vorticity

parametric integer linear programming a synthesis of branch and bound with cutting planes abstract a branch and bound algorithm is designed to solve the general integer linear programming problem with parametric right hand sides the right hand sides have the form b d where b and d are comformable vectors d consists of nonnegative constants and varies from zero to one the method consists of first determining all possible right hand side integer constants and appending this set of integer constants to the initial tableau to form an expanded problem with a finite number of family members the implicit enumeration method gives a lower bound on the integer solutions the branch and bound method is used with fathoming tests which allow one family member possibly to fathom other family members a cutting plane option applies a finite number of cuts to each node before branching in addition the cutting plane method is invoked whenever some members are feasible at a node and others are infeasible the branching and cutting process is repeated until the entire family of problem has been solved

parametric uncapacitated facility location we consider the parametric uncapacitated facility location problem uflp where the demand of each customer is allowed to vary over a certain interval despite the value of parametric analysis no such efforts are found for the uflp that mainly seems to be due to the fact that parametric analysis usually requires the computation of a number of uflp s with heavy computational burden in this paper we will show that the special structure of the uflp provides a nice property for its parametric version based on which an efficient branch and bound procedure for the parametric analysis is developed

two dimensional subsonic euler flows past a wall or a symmetric body the existence and uniqueness of two dimensional steady compressible euler flows past a wall or a symmetric body are established more precisely given positive convex horizontal velocity in the upstream there exists a critical value rho rm cr such that if the incoming density in the upstream is larger than rho rm cr then there exists a subsonic flow past a wall furthermore rho rm cr is critical in the sense that there is no such subsonic flow if the density of the incoming flow is less than rho rm cr the subsonic flows possess large vorticity and positive horizontal velocity above the wall except at the corner points on the boundary moreover the existence and uniqueness of a two dimensional subsonic euler flow past a symmetric body are also obtained when the incoming velocity field is a general small perturbation of a constant velocity field and the density of the incoming flow is larger than a critical value the asymptotic behavior of the flows is obtained with the aid of some integral estimates for the difference between the velocity field and its far field states

on two dimensional sonic subsonic flow a compensated compactness framework is established for sonic subsonic approximate solutions to the two dimensional euler equations for steady irrotational flows that may contain stagnation points only crude estimates are required for establishing compactness it follows that the set of subsonic irrotational solutions to the euler equations is compact thus flows with sonic points over an obstacle such as an airfoil may be realized as limits of sequences of strictly subsonic flows furthermore sonic subsonic flows may be constructed from approximate solutions the compactness framework is then extended to self similar solutions of the euler equations for unsteady irrotational flows

phragmen lindelof principles on algebraic varieties from several results in recent years starting with h6rmander s characterization of the constant coefficient partial differential equations p d u f that have a real analytic solution u for every real analytic function f it has become clear that certain properties of the partial differential operator p d are equivalent to estimates of phragmen lindelof type for plurisubharmonic functions on the algebraic variety

the algebraic surfaces on which the classical phragmen lindelof theorem holds let v be an algebraic variety in open image in new window we say that v satisfies the strong phragmen lindelof property spl or that the classical phragmen lindelof theorem holds on v if the following is true there exists a positive constant a such that each plurisubharmonic function u on v which is bounded above by z o z on v and by 0 on the real points in v already is bounded by a im z for algebraic varieties v of pure dimension k we derive necessary conditions on v to satisfy spl and we characterize the curves and surfaces in open image in new window which satisfy spl several examples illustrate how these results can be applied

the geometry of analytic varieties satisfying the local phragmen lindelof condition and a geometric characterization of the partial differential operators that are surjective on ℝ the local phragmen lindelof condition for analytic subvarieties of c n at real points plays a crucial role in complex analysis and in the theory of constant coefficient partial differential operators as hormander has shown here necessary geometric conditions for this phragmen lindelof condition are derived they are shown to be sufficient in the case of curves in arbitrary dimension and of surfaces in c 3 the latter result leads to a geometric characterization of those constant coefficient partial differential operators which are surjective on the space of all real analytic functions on r 4

steady subsonic ideal flows through an infinitely long nozzle with large vorticity in this paper the existence uniqueness and far field behavior of a class of subsonic flows with large vorticity for the steady euler equations in infinitely long nozzles are established more precisely for any given convex horizontal velocity of incoming flow in the upstream there exists a critical value mcr if the mass flux is larger than mcr then there exists a unique smooth subsonic euler flow through the infinitely long nozzle this well posedness result is proved by a new observation for the method developed in xie and xin siam j math anal 42 751 784 2010 to deal with the euler system furthermore the optimal convergence rates of the subsonic flows at far fields are obtained via the maximum principle and an elaborate choice of the comparison functions

on a degenerate free boundary problem and continuous subsonic sonic flows in a convergent nozzle this paper concerns the well posedness of a boundary value problem for a quasilinear second order elliptic equation which is degenerate on a free boundary such problems arise when studying continuous subsonic sonic flows in a convergent nozzle with straight solid walls it is shown that for a given inlet being a perturbation of an arc centered at the vertex of the nozzle and a given incoming mass flux belonging to an open interval depending only on the adiabatic exponent and the length of the arc there is a unique continuous subsonic sonic flow from the given inlet with the angle of the velocity orthogonal to the inlet and the given incoming mass flux furthermore the sonic curve of this continuous subsonic sonic flow is a free boundary where the flow is singular in the sense that while the speed is c1 2 holder continuous at the sonic state the acceleration blows up at the sonic state

the value function of an integer program we consider integer programs in which the objective function and constraint matrix are fixed while the right hand side varies the value function gives for each feasible right hand side the criterion value of the optimal solution we provide a precise characterization of the closed form expression for any value function

three dimensional steady subsonic euler flows in bounded nozzles abstract the existence and uniqueness of three dimensional steady subsonic euler flows in rectangular nozzles were obtained when prescribing normal component of momentum at both the entrance and exit if in addition the normal component of the voriticity and the variation of bernoulli s function at the entrance are both zero then there exists a unique subsonic potential flow when the magnitude of the normal component of the momentum is less than a critical number as the magnitude of the normal component of the momentum approaches the critical number the associated flows converge to a subsonic sonic flow furthermore when the normal component of vorticity and the variation of bernoulli function are both small the existence and uniqueness of subsonic euler flows with non zero vorticity are established the proof of these results is based on a new formulation for the euler system a priori estimate for nonlinear elliptic equations with nonlinear boundary conditions detailed study for a linear div curl system and delicate estimate for the transport equations

algebraic varieties on which the classical phragmen lindelof estimates hold for plurisubharmonic functions algebraic varieties v are investigated on which the natural analogue of the classical phragmen lindelof principle for plurisubharmonic functions holds for a homogeneous polynomial p in three variables it is shown that its graph has this property if and only if p has real coefficients no elliptic factors is locally hyperbolic in all real characteristics and the localizations in these characteristics are square free the last condition is shown to be necessary in any dimension

parameterisation algorithms for the integer linear programs in binary variables abstract in this paper we consider the integer programmiing problem minimize z x c x subject to ax b x binary roodman appended the objective function z x to the body of the constraints and presented a modified version of the balas additive algorithm by which each fathomed partial solution is attributed to the constraint which caused the fathoming exploiting this information he conducted a ranging analysis i e calculating bounds on the values of the parameters which leave the original optimal solution unchanged and b parameter change analysis i e determining new optimal solutions if any for revised values of the parameters outside the ranging bounds we extend roodman s results and construct parametric functions of the following form let be any parameter of c or b or a and replace by then holding every other parameter of the program fixed and varying in the set of real numbers we construct the parametric function z which matches non overlapping intervals of with optimal solutions this replaces by exact bounds in the linear programming sense the bounds underestimated by roodman s ranging analysis it also determines optimal solutions for any values of rather than for a revised set of values finally some results of computational experience are presented

a contraction algorithm for the multiparametric integer linear programming problem we designed and implemented an algorithm to solve the continuos right hand side multiparametric integer linear programming ilp problem that is to solve a family of ilp problems in which the problems are related by having identical objective and matrix coefficients our algorithm works by choosing an appropiate finite sequence of nonparametric mixed integer linear programming milp problems in order to obtain a complete multiparametrical analysis the algorithm may be implemented by using any software capable of solving milp problems

existence and optimal convergence rates of multi dimensional subsonic potential flows through an infinitely long nozzle with an obstacle inside in this paper the well posedness and optimal convergence rates of subsonic irrotational flows through a three dimensional infinitely long nozzle with a smooth obstacle inside are established more precisely the global existence and uniqueness of the uniformly subsonic flow are obtained via variational formulation as long as the incoming mass flux is less than a critical value furthermore with the aid of delicate choice of weight functions we prove the optimal convergence rates of the flow at far fields via weighted energy estimates and nash moser iteration

optimal gevrey classes for the existence of solution operators for linear partial differential operators in three variables abstract for a constant coefficient linear partial differential operator acting on all infinitely differentiable functions or ultradifferentiable functions of beurling type on euclidean 3 space the existence of a continuous linear solution operator is investigated it is shown that there is an optimal weight in the sense that a solution operator exists for a weight if and only if o provided that such an operator exists for at least one weight furthermore the optimal class is either a gevrey class of rational exponent or the class of all infinitely differentiable functions