extensions of frechet ϵ subdifferential calculus and applications abstract in this paper we establish some calculus rules for the limiting frechet subdifferentials of marginal functions and composite functions necessary conditions for approximate solutions of a constrained optimization problem are derived

high lewis number combustion wavefronts a perturbative melnikov analysis the wavefronts associated with a one dimensional combustion model with arrhenius kinetics and no heat loss are analyzed within the high lewis number perturbative limit this situation in which fuel diffusivity is small in comparison to that of heat is appropriate for highly dense fluids a formula for the wavespeed is established by a nonstandard application of melnikov s method and slow manifold theory from dynamical systems and compared to numerical results a simple characterization of the wavespeed correction is obtained it is proportional to the ratio between the exothermicity parameter and the lewis number the perturbation method developed herein is also applicable to more general coupled reaction diffusion equations with strongly differing diffusivities the stability of the wavefronts is also tested using a numerical evans function method

second order necessary conditions for nonlinear optimization problems in banach spaces and their application to an optimal control problem we study second order necessary conditions for nonlinear optimization problems with equality and set constraints in banach spaces the necessary conditions are given in the primal form and the dual form by the use of second order neustadt derivative moreover we apply the necessary conditions to an optimal control problem without state constraints

differentiability of relations and differential stability of perturbed optimization problems several new concepts of differentiability of multifunctions are introduced special attention is paid to relations given by perturbed inequalities applications are given to the study of the value or marginal function of a perturbed nonlinear program

on scalar and vector l stable functions abstract the notion of a scalar function that is l stable at a point is introduced in d bedna ik k pastor on second order conditions in unconstrained optimization math program ser a 113 2008 283 298 in the present paper a characterization of the l stable functions is obtained further the notion of an l stable function is generalized from scalar to vector functions in an application optimality conditions for constrained vector problems with l stable data are established

a large deviations principle for the maki thompson rumour model abstract we consider the stochastic model for the propagation of a rumour within a population which was formulated by maki and thompson 20 sudbury 22 established that as the population size tends to infinity the proportion of the population never hearing the rumour converges in probability to 0 2032 watson 23 later derived the asymptotic normality of a suitably scaled version of this proportion we prove a corresponding large deviations principle with an explicit formula for the rate function

average complexity of moore s and hopcroft s algorithms in this paper we prove that for the uniform distribution on complete deterministic automata the average time complexity of moore s state minimization algorithm is o nloglogn where n is the number of states in the input automata and the number of letters in the alphabet is fixed then an unusual family of implementations of hopcroft s algorithm is characterized for which the algorithm will be proved to be always faster than moore s algorithm finally we present experimental results on the usual implementations of hopcroft s algorithm

on second order optimality conditions in constrained multiobjective optimization abstract in this paper we study a multiobjective optimization problem with inequality constraints on finite dimensional spaces a second order necessary condition for local weak efficiency is proved under strict differentiability assumptions we also establish a second order sufficient condition for local firm efficiency of order 2 under l stability assumptions in this way we generalize some corresponding results obtained by p q khanh and n d tuan and by the authors

a hitchhiker s guide to descriptional complexity through analytic combinatorics nowadays increasing attention is being given to the study of the descriptional complexity in the average case although the underlying theory for such a study seems intimidating one can obtain interesting results in this area without too much effort in this gentle introduction we take the reader on a journey through the basic analytical tools of that theory giving some illustrative examples using regular expressions additionally new asymptotic average case results for several e nfa constructions are presented in a unified framework it turns out that asymptotically and in the average case the complexity gap between the several constructions is significantly larger than in the worst case furthermore one of the e nfa constructions approaches the corresponding e free nfa construction asymptotically and on average

stability and instability of solitary waves of the fifth order kdv equation a numerical framework abstract the spectral problem associated with the linearization about solitary waves of the generalized fifth order kdv equation is formulated in terms of the evans function a complex analytic function whose zeros correspond to eigenvalues a numerical framework based on a fast robust shooting algorithm on exterior algebra spaces is introduced the complete algorithm has several new features including a rigorous numerical algorithm for choosing starting values a new method for numerical analytic continuation of starting vectors the role of the grassmannian g 2 c 5 in choosing the numerical integrator and the role of the hodge star operator for relating 2 c 5 and 3 c 5 and deducing a range of numerically computable forms for the evans function the algorithm is illustrated by computing the stability and instability of solitary waves of the fifth order kdv equation with polynomial nonlinearity

necessary and sufficient optimality conditions for a class of nonsmooth minimization problems the purpose of this paper is to derive in a unified way second order necessary and sufficient optimality criteria for four types of nonsmooth minimization problems thediscrete minimax problem thediscrete l1 approximation the minimization of theexact penalty function and the minimization of theclassical exterior penalty function our results correct and supplement conditions obtained by various authors in recent papers

second order optimality conditions for problems with c1 data abstract in this paper we obtain second order optimality conditions of karush kuhn tucker type and fritz john one for a problem with inequality constraints and a set constraint in nonsmooth settings using second order directional derivatives in the necessary conditions we suppose that the objective function and the active constraints are continuously differentiable but their gradients are not necessarily locally lipschitz in the sufficient conditions for a global minimum x we assume that the objective function is differentiable at x and second order pseudoconvex at x a notion introduced by the authors i ginchev v i ivanov higher order pseudoconvex functions in i v konnov d t luc a m rubinov eds generalized convexity and related topics in lecture notes in econom and math systems vol 583 springer 2007 pp 247 264 the constraints are both differentiable and quasiconvex at x in the sufficient conditions for an isolated local minimum of order two we suppose that the problem belongs to the class c 1 1 we show that they do not hold for c 1 problems which are not c 1 1 ones at last a new notion parabolic local minimum is defined and it is applied to extend the sufficient conditions for an isolated local minimum from problems with c 1 1 data to problems with c 1 one

on the average state and transition complexity of finite languages we investigate the average case state and transition complexity of deterministic and nondeterministic finite automata when choosing a finite language of a certain size n uniformly at random from all finite languages of that particular size here size means that all words of the language are either of length n or of length at most n it is shown that almost all deterministic finite automata accepting finite languages over a binary input alphabet have state complexity q 2 nn while nondeterministic finite automata are shown to perform better namely the nondeterministic state complexity is in q 2 n interestingly in both cases the aforementioned bounds are asymptotically like in the worst case however the nondeterministic transition complexity is shown to be again q 2 nn the case of unary finite languages is also considered moreover we develop a framework that allows us to investigate the average case complexity of operations like e g union intersection complementation and reversal on finite languages in this setup

optimality conditions for irregular inequality constrained problems we consider feasible sets given by conic constraints where the cone defining the constraints is convex with nonempty interior we study the case where the feasible set is not assumed to be regular in the classical sense of robinson and obtain a constructive description of the tangent cone under a certain new second order regularity condition this condition contains classical regularity as a special case while being weaker when constraints are twice differentiable assuming that the cone defining the constraints is finitely generated we also derive a special form of primal dual optimality conditions for the corresponding constrained optimization problem our results subsume optimality conditions for both the classical regular and second order regular cases while still being meaningful in the more general setting in the sense that the multiplier associated with the objective function is nonzero

second order conditions in c 1 1 constrained vector optimization we consider the constrained vector optimization problem minc f x g x k where f n m and g n p are c1 1 functions and c m and k p are closed convex cones with nonempty interiors two type of solutions are important for our considerations namely w minimizers weakly efficient points and i minimizers isolated minimizers we formulate and prove in terms of the dini directional derivative second order necessary conditions for a point x0 to be a w minimizer and second order sufficient conditions for x0 to be an i minimizer of order two we discuss the reversal of the sufficient conditions under suitable constraint qualifications of kuhn tucker type the obtained results improve the ones in liu neittaanmaki k i ek 21

second order necessary conditions for optimality in nonsmooth nonlinear programming the notion of a second order directional derivative introduced by ben tal and zowe and a generalization of this notion by penot are used to state new second order necessary optimality conditions for a nonsmooth nonlinear programming problem with a finite number of inequality and equality constraints

numerical testing of the stability of viscous shock waves a new theoretical evans function condition is used as the basis of a numerical test of viscous shock wave stability accuracy of the method is demonstrated through comparison against exact solutions a convergence study and evaluation of approximate error equations robustness is demonstrated by applying the method to waves for which no current analytic results apply highly nonlinear waves from the cubic model and strong shocks from gas dynamics an interesting aspect of the analysis is the need to incorporate features from the analytic evans function theory for purposes of numerical stability for example we find it necessary for numerical accuracy to solve odes on the space of wedge products

instability of the hocking stewartson pulse and its implications for three dimensional poiseuille flow the linear stability problem for the hocking stewartson pulse obtained by linearizing the complex ginzburg landau cgl equation is formulated in terms of the evans function a complex analytic function whose zeros correspond to stability exponents a numerical algorithm based on the compound matrix method is developed for computing the evans function using values in the cgl equation associated with spanwise modulation of plane poiseuille flow we show that the hocking stewartson pulse associated with points along the neutral curve is always linearly unstable due to a real positive eigenvalue implications for the spanwise structure of nonlinear poiseuille problem between parallel plates are also discussed

topological properties of the approximate subdifferential abstract the approximate subdifferential introduced by mordukhovich has attracted much attention in recent works on nonsmooth optimization potential advantages over other concepts of subdifferentiability might be related to its nonconvexity this is motivation to study some topological properties more in detail as the main result it is shown that any weakly compact subset of any hilbert space may be obtained as the kuratowski painleve limit of approximate subdifferentials from a one parametric family of lipschitzian functions sharper characterizations are possible for strongly compact subsets as a consequence in any hilbert space the approximate subdifferential of a suitable lipschitzian function may be homeomorphic both in the strong and weak topology to the cantor set further results relate the approximate subdifferential to specific topological types to the one dimensional case which is extraordinary in some sense and to the value function of a c 1 optimization problem

the state complexity of random dfas the state complexity of a deterministic finite state automaton dfa is the number of states in its minimal equivalent dfa we study the state complexity of random n state dfas over a k symbol alphabet drawn uniformly from the set n n k 2 n of all such automata we show that with high probability the latter is k n o n log n for a certain explicit constant k

first and second order optimality conditions for nonsmooth vector optimization using set valued directional derivatives we investigate a nonsmooth vector optimization problem with a feasible set defined by a generalized inequality constraint an equality constraint and a set constraint both necessary and sufficient optimality conditions of first and second order for weak solutions and firm solutions are established in terms of fritz john lagrange multiplier rules using set valued directional derivatives and tangent cones and second order tangent sets we impose steadiness and strict differentiability for first and second order necessary conditions respectively stability and l stability for first and second order sufficient conditions respectively the obtained results improve or include some recent known ones several illustrative examples are also provided

second order optimality conditions based on parabolic second order tangent sets in this paper we discuss second order optimality conditions in optimization problems subject to abstract constraints our analysis is based on various concepts of second order tangent sets and parametric duality we introduce a condition called second order regularity under which there is no gap between the corresponding second order necessary and second order sufficient conditions we show that the second order regularity condition always holds in the case of semidefinite programming

on second order fritz john type optimality conditions in nonsmooth multiobjective programming we study a multiobjective optimization program with a feasible set defined by equality constraints and a generalized inequality constraint we suppose that the functions involved are frechet differentiable and their frechet derivatives are continuous or stable at the point considered we provide necessary second order optimality conditions and also sufficient conditions via a fritz john type lagrange multiplier rule and a set valued second order directional derivative in such a way that our sufficient conditions are close to the necessary conditions some consequences are obtained for parabolic directionally differentiable functions and c1 1 functions in this last case expressed by means of the second order clarke subdifferential some illustrative examples are also given

on second order conditions in unconstrained optimization the main purpose of this paper is to establish the second order nonsmooth sufficient unconstrained optimality condition for so called l stable at some point functions and in this way to generalize some previous results in this direction we provide the comparisons with other results by examples

strict efficiency in vector optimization the notion of strict minimum of order m for real optimization problems is extended to vector optimization its properties and characterization are studied in the case of finite dimensional spaces multiobjective problems also the notion of super strict efficiency is introduced for multiobjective problems and it is proved that in the scalar case all of them coincide necessary conditions for strict minimality and for super strict minimality of order m are provided for multiobjective problems with an arbitrary feasible set when the objective function is frechet differentiable necessary and sufficient conditions are established for the case m 1 resulting in the situation that the strict efficiency and super strict efficiency notions coincide

variational analysis of a composite function a formula for the lower second order epi derivative an exact formula is established for the lower second order epi derivative of a function of the form g f x where f is a smooth map from one banach space into another and g is a convex function generally not everywhere finite unconstrained minimization of such functions typically arise as an equivalent in one or another sense reduction form for many important classes of constrained optimization problems the formula is further applied to study epi differentiability of the max function x max q x q q

gasless combustion fronts with heat loss for a model of gasless combustion with heat loss we use geometric singular perturbation theory to show existence of traveling combustion fronts we show that the fronts are nonlinearly stable in an appropriate sense if an evans function criterion which can be verified numerically is satisfied for a solid reactant and exothermicity parameter that is not too large we verify numerically that the criterion is satisfied

uniform random generation of decomposable structures using floating point arithmetic the em recursive method formalized by nijenhuis and wilf cite niwi78 and systematized by flajolet van cutsem and zimmermann cite flziva94 is extended here to floating point arithmetic the resulting adz method enables one to generate decomposable data structures both labelled or unlabelled uniformly at random in expected o n 1 epsilon time and space after a preprocessing phase of o n 2 epsilon time which reduces to o n 1 epsilon for context free grammars

second order optimality conditions with the envelope like effect for nonsmooth vector optimization in infinite dimensions abstract second order necessary conditions and sufficient conditions with the envelope like effect for optimality in nonsmooth vector optimization are established we use approximations as generalized derivatives imposing strict differentiability for necessary conditions and differentiability for sufficient conditions and avoiding continuous differentiability convexity conditions are not imposed explicitly the results make it clear when the envelope like effect occurs and improve or include several recent existing ones examples are provided to show advantages of our theorems over some known ones in the literature

enumeration and generation with a string automata representation the representation of combinatorial objects is decisive for the feasibility of several enumerative tasks in this work we present a unique string representation for complete initially connected deterministic automata icdfas with n states over an alphabet of k symbols for these strings we give a regular expression and show how they are adequate for exact and random generation allow an alternative way for enumeration and lead to an upper bound for the number of icdfas the exact generation algorithm can be used to partition the set of icdfas in order to parallelize the counting of minimal automata and thus of regular languages a uniform random generator for icdfas is presented that uses a table of pre calculated values based on the same table an optimal coding for icdfas is obtained

second order optimality conditions with the envelope like effect in nonsmooth multiobjective mathematical programming ii optimality conditions second order necessary conditions and sufficient conditions with the envelope like effect for optimality in nonsmooth multiobjective mathematical programming are established we use set valued second order directional derivatives and impose strict differentiability for necessary conditions and l stability for sufficient conditions avoiding continuous differentiability the results improve and sharpen several recent existing ones examples are provided to show advantages of our theorems over some known ones in the literature in part i we consider l stability and second order set valued directional derivatives of vector functions part ii is devoted to second order necessary optimality conditions and sufficient ones

the theory of 2 regularity for mappings with lipschitzian derivatives and its applications to optimality conditions we study local structure of a nonlinear mapping near points where standard regularity and or smoothness assumptions need not be satisfied we introduce a new concept of 2 regularity a certain kind of second order regularity for a once differentiable mapping whose derivative is lipschitz continuous under this 2 regularity condition we obtain the representation theorem and the covering theorem i e stability with respect to right hand side perturbations under assumptions that are weaker than those previously employed in the literature for results of this type these results are further used to derive a constructive description of the tangent cone to a set defined by 2 regular equality constraints and optimality conditions for related optimization problems the class of mappings introduced and studied in the paper appears to be a convenient tool for treating complementarity structures by means of an appropriate equation based reformulation optimality conditions for mathematical programs with equivalently reformulated complementarity constraints are also discussed

enumeration and random generation of accessible automata we present a bijection between the set a n of deterministic and accessible automata with n states on a k letters alphabet and some diagrams which can themselves be represented as partitions of a set of kn 1 elements into n non empty subsets this combinatorial construction shows that the asymptotic order of the cardinality of a n is related to the stirling number knn our bijective approach also yields an efficient random sampler for the uniform distribution of automata with n states its complexity is o n 3 2 using the framework of boltzmann samplers

second order optimality conditions with the envelope like effect in nonsmooth multiobjective mathematical programming i l stability and set valued directional derivatives abstract second order necessary conditions and sufficient conditions with the envelope like effect for optimality in nonsmooth multiobjective mathematical programming are established we use set valued second order directional derivatives and impose strict differentiability for necessary conditions and l stability for sufficient conditions avoiding continuous differentiability the results improve and sharpen several recent existing ones examples are provided to show advantages of our theorems over some known ones in the literature in part i we consider l stability and second order set valued directional derivatives of vector functions part ii is devoted to second order necessary optimality conditions and sufficient ones

stability of the travelling wave solution of the fitzhugh nagumo system on demontre la stabilite relative au systeme complet d equations aux derivees partielles de ces ondes de propagation

the orr sommerfeld equation on a manifold the most effective and widely used methods for integrating the orr sommerfeld equation by shooting are the continuous orthogonalization method and the compound matrix method in this paper we consider this problem from a differential geometric point of view a new definition of orthogonalization is presented restriction of the orr sommerfeld to a complex stiefel manifold and this definition leads to a new formulation of continuous orthogonalization which differs in a precise and interesting geometric way from existing orthogonalization routines present orthogonalization methods based on davey9s algorithm are shown to have a different differential geometric interpretation restriction of the orr sommerfeld equation to a complex grassmanian manifold this leads us to introduce the concept of a grassmanian integrator which preserves linear independence and not necessarily orthogonality using properties of grassmanian manifolds and their tangent spaces a new grassmanian integrator is introduced that generalizes davey9s algorithm furthermore it is shown that the compound matrix method is a dual grassmanian integrator it uses plucker coordinates for integrating on a grassmanian manifold and this characterization suggests a new algorithm for constructing the compound matrices extension of the differential geometric framework to general systems of linear ordinary differential equations is also discussed

parametric random generation of deterministic tree automata uniform random generators deliver a simple empirical means to estimate the average complexity of an algorithm we present a general rejection algorithm that generates sequential letter to letter transducers up to isomorphism we also propose an original parametric random generation algorithm to produce sequential letter to letter transducers with a fixed number of transitions we tailor this general scheme to randomly generate deterministic tree walking automata and deterministic top down tree automata we apply our implementation of the generator to the estimation of the average complexity of a deterministic tree walking automata to nondeterministic top down tree automata construction we also implemented

second order conditions for optimization problems with constraints using a projective approach new necessary conditions and new sufficient conditions for optimization problems with explicit or implicit constraints are examined they are compared to previous ones a particular emphasis is given to mathematical programming problems with non polyhedral constraints this case occurs in particular when the constraints are defined in functional spaces

optimality conditions in mathematical programming and composite optimization new second order optimality conditions for mathematical programming problems and for the minimization of composite functions are presented they are derived from a general second order fermat s rule for the minimization of a function over an arbitrary subset of a banach space the necessary conditions are more accurate than the recent results of kawasaki 1988 and cominetti 1989 but more importantly in the finite dimensional case they are twinned with sufficient conditions which differ by the replacement of an inequality by a strict inequality we point out the equivalence of the mathematical programming problem with the problem of minimizing a composite function our conditions are especially important when one deals with functional constraints when the cone defining the constraints is polyhedral we recover the classical conditions of ben tal zowe 1982 and cominetti 1990

stability of gasless combustion fronts in one dimensional solids for gasless combustion in a one dimensional solid we show a type of nonlinear stability of the physical combustion front if a perturbation of the front is small in both a spatially uniform norm and an exponentially weighted norm then the perturbation stays small in the spatially uniform norm and decays in the exponentially weighted norm provided the linearized operator has no eigenvalues in the right half plane other than zero using the evans function we show that the zero eigenvalue must be simple factors that complicate the analysis are 1 the linearized operator is not sectorial and 2 the linearized operator has good spectral properties only when the weighted norm is used but then the nonlinear term is not lipschitz the result is nevertheless physically natural to prove it we first show that when the weighted norm is used the semigroup generated by the linearized operator decays on a subspace complementary to the operator s kernel by showing that it is a compact perturbation of the semigroup generated by a more easily analyzed triangular operator we then use this result to help establish that solutions stay small in the spatially uniform norm which in turn helps establish nonlinear convergence in the weighted norm

a calculus for the random generation of labelled combinatorial structures a systematic approach to the random generation of labelled combinatorial objects is presented it applies to structures that are decomposable i e formally specifiable by grammars involving set sequence and cycle constructions a general strategy is developed for solving the random generation problem with two closely related types of methods for structures of size n the boustrophedonic algorithms exhibit a worst case behaviour of the form o n log n the sequential algorithms have worst case o n2 while offering good potential for optimizations in the average case the complexity model is in terms of arithmetic operations and both methods appeal to precomputed numerical table of linear size that can be computed in time o n2 a companion calculus permits systematically to compute the average case cost of the sequential generation algorithm associated to a given specification using optimizations dictated by the cost calculus several random generation algorithms of the sequential type are developed most of them have expected complexity 1 2n log n and are thus only slightly superlinear the approach is exemplified by the random generation of a number of classical combinatorial structures including cayley trees hierarchies the cycle decomposition of permutations binary trees functional graphs surjections and set partitions

sampling different kinds of acyclic automata using markov chains we propose algorithms that use markov chain techniques to generate acyclic automata uniformly at random we first consider deterministic accessible and acyclic automata then focus on the class of minimal acyclic automata in each case we explain how to define random local transformations that describe an ergodic and symmetric markov chain the distribution of the automaton obtained after t random steps in this markov chain tends to the uniform distribution as t tends to infinity

nonsmooth optimum problems with constraints this paper develops second order necessary conditions for nonsmooth infinite dimensional optimization problems with banach space valued equality and real valued inequality constraints another constraint in the form of a closed convex set is also present the objective function is the maximum over a parameter of functions f t z that are lipschitz in z and upper semicontinuous in t the inequality constraints g s z depend on a parameter s the technique we use is a generalization of that of dubovitskii and milyutin the second order conditions obtained here are in terms of a certain function sigma that disappears when the parameters and a certain set that derives from the given convex set are absent the presence of the function sigma and that set is due to the envelope like effect discovered by kawasaki

l stable functions are continuous abstract it has been shown that l stability of the function at some point implies continuity near the point then the previous second order optimality condition introduced by the authors can be stated under weak assumptions

first and second order sufficient conditions for strict minimality in nonsmooth vector optimization abstract in this paper we present first and second order sufficient conditions for strict local minima of orders 1 and 2 to vector optimization problems with an arbitrary feasible set and a twice directionally differentiable objective function with this aim the notion of support function to a vector problem is introduced in such a way that the scalar case and the multiobjective case in particular are contained the obtained results extend the multiobjective ones to this case moreover specializing to a feasible set defined by equality inequality and set constraints first and second order sufficient conditions by means of lagrange multiplier rules are established

approximations and metric regularity in mathematical programming in banach space this paper establishes verifiable conditions ensuring the important notion of metric regularity for general nondifferentiable programming problems in banach spaces these conditions are used to obtain lagrange kuhn tucker multipliers for minimization problems with infinitely many inequality and equality constraints

second order necessary and sufficient conditions for convex composite ndo in convex composite ndo one studies the problem of minimizing functions of the formf h f whereh m is a finite valued convex function andf n m is continuously differentiable this problem model has a wide range of application in mathematical programming since many important problem classes can be cast within its framework e g convex inclusions minimax problems and penalty methods for constrained optimization in the present work we extend the second order theory developed by a d ioffe in 11 12 13 for the case in whichh is sublinear to arbitrary finite valued convex functionsh moreover a discussion of the second order regularity conditions is given that illuminates their essentially geometric nature

second order optimality conditions using approximations for nonsmooth vector optimization problems under inclusion constraints abstract second order necessary conditions and sufficient conditions for optimality in nonsmooth vector optimization problems with inclusion constraints are established we use approximations as generalized derivatives and avoid even continuity assumptions convexity conditions are not imposed explicitly not all approximations in use are required to be bounded the results improve or include several recent existing ones examples are provided to show that our theorems are easily applied in situations where several known results do not work

combustion waves in hydraulically resistant porous media in a special parameter regime abstract in this paper we study the stability of fronts in a reduction of a well known pde system that is used to model the combustion in hydraulically resistant porous media more precisely we consider the original pde system under the assumption that one of the parameters of the model the lewis number is chosen in a specific way and with initial conditions of a specific form for a class of initial conditions then the number of unknown functions is reduced from three to two for the reduced system the existence of combustion fronts follows from the existence results for the original system the stability of these fronts is studied here by a combination of energy estimates and numerical evans function computations and nonlinear analysis when applicable we then lift the restriction on the initial conditions and show that the stability results obtained for the reduced system extend to the fronts in the full system considered for that specific value of the lewis number the fronts that we investigate are proved to be either absolutely unstable or convectively unstable on the nonlinear level

numerical exterior algebra and the compound matrix method the compound matrix method which was first proposed for numerically integrating systems of differential equations in hydrodynamic stability on k 2 3 dimensional subspaces of mathbb c n by using compound matrices as coordinates is reformulated in a coordinate free way using exterior algebra spaces bigwedge k mathbb c n