radial symmetry of positive solutions in nonlinear polyharmonic dirichlet problems we extend the symmetry result of gidas ni nirenberg to semilinear polyharmonic dirichlet problems in the unit ball in the proof we develop a new variant of the method of moving planes relying on fine estimates for the green function of the polyharmonic operator we also consider minimizers for subcritical higher order sobolev embeddings for embeddings into weighted spaces with a radially symmetric weight function we show that the minimizers are at least axially symmetric this result is sharp since we exhibit examples of minimizers which do not have full radial symmetry

a non autonomous seirs model with general incidence rate for a non autonomous seirs model with general incidence that admits kuniya and nakata 2012 as a very particular case we obtain conditions for extinction and strong persistence of the infectives our conditions are computed for several particular settings and extend the hypothesis of several proposed non autonomous models additionally we show that our conditions are robust in the sense that they persist under small perturbations of the parameters in some suitable family we also present some simulations that illustrate our results

the full automorphism group of a cyclic p gonal surface if p is prime a compact riemann surface x of genus g 2 is called cyclic p gonal if it admits a cyclic group of automorphisms cp of order p such that the quotient space x cp has genus 0 if in addition cp is not normal in the full automorphism a then we call x a non normal p gonal surface in the following we classify all non normal p gonal surfaces

asymptotically autonomous semiflows chain recurrence and lyapunov functions from the work of c conley it is known that the omega limit set of a precompact orbit of an autonomous semiflow is a chain recurrent set here we improve a result of l markus by showing that the omega limit set of a solution of an asymptotically autonomous semiflow is a chain recurrent set relative to the limiting autonomous semiflow in the special case that there is a lyapunov function for the limiting semiflow sufficient conditions are given for an omega limit set of the asymptotically autonomous semiflow to be contained in a level set of the lyapunov function

boundary blow up solutions to elliptic systems of competitive type abstract we consider the elliptic system u u p v q v u r v s in where p s 1 q r 0 and r n is a smooth bounded domain subject to different types of dirichlet boundary conditions f u v i u v and sf u v on where 0 under several hypotheses on the parameters p q r s we show existence and nonexistence of positive solutions uniqueness and nonuniqueness we further provide the exact asymptotic behaviour of the solutions and their normal derivatives near some more general related problems are also studied

well defined steady state response does not imply cics abstract systems for which each constant input gives rise to a unique globally attracting equilibrium are considered a counterexample is provided to show that inputs which are only asymptotically constant may not result in states converging to equilibria failure of the converging input converging state or cics property

components of moduli spaces of spin curves with the expected codimension we prove a conjecture of gavril farkas claiming that for all integers r ge 2 and g ge left begin array c r 2 2 end array right there exists a component of the locus mathcal s r g of spin curves with a theta characteristic l such that h 0 l ge r 1 and h 0 l equiv r 1 text mod 2 which has codimension left begin array c r 1 2 end array right inside the moduli space mathcal s g of spin curves of genus g

a remark on uniqueness of large solutions for elliptic systems of competitive type abstract we prove that the semilinear system u a x u p v q v b x u r v s in a smooth bounded domain r n has a unique positive solution with the boundary condition u v on provided that p s 1 q r 0 and p 1 s 1 q r 0 the main novelty is imposing a growth on the possibly singular weights a x b x near rather than requiring them to have a precise asymptotic behavior

some asymptotic theory for the bootstrap efron s bootstrap method of distribution approximation is shown to be asymptotically valid in a large number of situations including t statistics the empirical and quantile processes and von mises functionals some counter examples are also given to show that the approximation does not always succeed

gaussian maps gieseker petri loci and large theta characteristics for an integer g 1 we consider the moduli space sg of smooth spin curves parametrizing pairs c l where c is a smooth curve of genus g and l is a thetacharacteristic that is a line bundle on c such that l2 kc it has been known classically that the natural map sg mg is finite of degree 2 2g and that sg is a disjoint union of two components seven g and s odd g corresponding to even and odd theta characteristics a geometrically meaningful compactification sg of sg has been constructed by cornalba by means of stable spin curves of genus g cf c the space sg and more generally the moduli spaces s 1 r g n of stable n pointed r spin curves of genus g parametrizing pointed curves with r roots of the canonical bundle have attracted a lot of attention in recent

a remark on the existence of entire positive solutions for a class of semilinear elliptic systems abstract under the simple conditions on f and g we show that entire positive radial solutions exist for the semilinear elliptic system u p x f v v q x g u x r n n 3 where the functions p q 0 0 are continuous

entire solutions for a class of variational problems involving the biharmonic operator and rellich potentials abstract we study existence multiplicity and qualitative properties of entire solutions for a noncompact problem related to second order interpolation inequalities with weights more precisely we deal with the following family of equations 2 u x 4 u x u q 2 u in r n where n 5 q 2 n q n 4 2 and r is smaller than the rellich constant

on the canonical rings of covers of surfaces of minimal degree let s be a regular surface of general type with at worst canonical singularities and with basepoint free canonical system let x be its canonical image it is well known that x must be a canonical surface or a minimal degree surface the main result of the authors completely describes the number and degree of the generators of the canonical ring of s in the second case more concretely if r deg x and n is the degree of the canonical map then 1 if n 2 and r 1 the canonical ring is generated in degree 1 plus one generator in degree 4 2 in the other cases the canonical ring is generated in degree 1 plus r n 2 generators in degree 2 and r 1 generators in degree 3 this result together with previous results of ciliberto and green describes when the canonical ring of s is generated in degree less than or equal to 2 x is not a surface of minimal degree other than the plane and in this last case n 6 2 the authors also construct a series of non trivial examples of the theorem and prove that some expected ones do not exist finally the authors apply their results to calabi yau threefolds obtaining analogous results the key point here is that for a calabi yau threefold the general member of a big and base point free linear system is a surface of general type

effects of a degeneracy in the competition model part i classical and generalized steady state solutions abstract we study the competition model where the coefficient functions are strictly positive over the underlying spatial region except b x which vanishes in a nontrivial subdomain of and is positive in the rest of we show that there exists a critical number such that if then the model behaves similarly to the well studied classical competition model where all the coefficient functions are positive constants but when new phenomena occur our results demonstrate the fact that heterogeneous environmental effects on population models are not only quantitative but can be qualitative as well in part i here we mainly study two kinds of steady state solutions which determine the dynamics of the model one consists of finite functions while the other consists of generalized functions which satisfy u v 0 on the part of the domain that b x vanishes but are positive and finite on the rest of the domain and are determined by certain boundary blow up systems the research is continued in part ii where these two kinds of steady state solutions will be used to determine the dynamics of the model

existence and boundary blow up rates of solutions for boundary blow up elliptic systems abstract in this paper we study some elliptic systems with boundary blow up conditions in a smooth bounded domain by constructing the suitable upper and lower solutions we discuss the existence and global estimate of the positive solution furthermore the boundary blow up rates of the positive solution are also partly discussed

blow up oscillating solutions to some nonlinear fourth order differential equations abstract we give strong theoretical and numerical evidence that solutions to some nonlinear fourth order ordinary differential equations blow up in finite time with infinitely many wild oscillations we exhibit an explicit example where this phenomenon occurs we discuss possible applications to biharmonic partial differential equations and to the suspension bridges model in particular we give a possible new explanation of the collapse of bridges

maximal order of automorphisms of trigonal riemann surfaces in this paper we find the maximal order of an automorphism of a trigonal riemann surface of genus g g 5 we find that this order is smaller for generic than for cyclic trigonal riemann surfaces showing that generic trigonal surfaces have less symmetry than cyclic trigonal surfaces finally we prove that the maximal order is attained for infinitely many genera in both the cyclic and the generic case

pullback permanence in a non autonomous competitive lotka volterra model abstract the goal of this work is to study in some detail the asymptotic behaviour of a non autonomous lotka volterra model both in the conventional sense as t and in the pullback sense starting a fixed initial condition further and further back in time the non autonomous terms in our model are chosen such that one species will eventually die out ruling out any conventional type of permanence in contrast we introduce the notion of pullback permanence and show that this property is enjoyed by our model this is not just a mathematical artifice but rather shows that if we come across an ecology that has been evolving for a very long time we still expect that both species are represented and their numbers are bounded below even if the final fate of one of them is less happy the main tools in the paper are the theory of attractors for non autonomous differential equations the sub supersolution method and the spectral theory for linear elliptic equations

an elliptic system with bifurcation parameters on the boundary conditions in this paper we consider the elliptic system u a x upvq v b x urvs in a smooth bounded domain with boundary conditions u u v v on here and are regarded as parameters and p s 1 q r 0 verify p 1 s 1 qr we consider the case where a x 0 in and a x is allowed to vanish in an interior subdomain 0 while b x 0 in our main results include existence of nonnegative nontrivial solutions in the range 0 0 where 1 is characterized by means of an eigenvalue problem and the uniqueness of such solutions we also study their asymptotic behavior in all possible cases as both 0 as 1 for fixed respectively for fixed and when both in case 1

global asymptotic behavior of a chemostat model with discrete delays this paper studies the global asymptotic behavior of an exploitative competition model between n species in a chemostat the model incorporates discrete time delays to describe the delay in the conversion of nutrient consumed to viable biomass and hence includes delays simultaneously in variables of nutrient and species concentrations in the case where only two species are engaged in competition it is shown that competitive exclusion holds for any monotone growth response functions sufficient conditions are also obtained for the model to exhibit competitive exclusion in the n species case in regard to the delay effects on the qualitative outcome of competition it is demonstrated that when the delays are relatively small the predictions of the model are identical with the predictions given by corresponding models without time delays however including large delays in the model may alter the predicted outcome of competition the techniques used also work when different removal rates are permitted an

the picard group of the moduli space of r spin riemann surfaces abstract an r spin riemann surface is a riemann surface equipped with a choice of r th root of the co tangent bundle we give a careful construction of the moduli space orbifold of r spin riemann surfaces and explain how to establish a madsen weiss theorem for it this allows us to prove the mumford conjecture for these moduli spaces but more interestingly allows us to compute their algebraic picard groups for g 10 or g 9 in the 2 spin case we give a complete description of these picard groups in terms of explicitly constructed line bundles

better bootstrap confidence intervals abstract we consider the problem of setting approximate confidence intervals for a single parameter in a multiparameter family the standard approximate intervals based on maximum likelihood theory can be quite misleading in practice tricks based on transformations bias corrections and so forth are often used to improve their accuracy the bootstrap confidence intervals discussed in this article automatically incorporate such tricks without requiring the statistician to think them through for each new application at the price of a considerable increase in computational effort the new intervals incorporate an improvement over previously suggested methods which results in second order correctness in a wide variety of problems in addition to parametric families bootstrap intervals are also developed for nonparametric situations

optimal uniqueness theorems and exact blow up rates of large solutions in this paper we prove some optimal uniqueness results for large solutions of a canonical class of semilinear equations under minimal regularity conditions on the weight function in front of the non linearity and combine these results with the localization method introduced in lopez gomez the boundary blow up rate of large solutions j differential equations 195 2003 25 45 to prove that any large solution l of u a x up p 1 a 0 must satisfy limx x0l x fx0 dist x i0 pp 1p 1p 1p 1p 1foreachx0 where fx0 t t 0sfx01p 1 p 1p 1ds i0 limt 0fx0 t fx0 t fx0 t 2 and fx0 is any smooth extension of the boundary normal section of a at x0 i e fx0 t a x0 tnx0 t 0 t 0 subsequently nx0 stands for the outward unit normal at x0 therefore the theory can be extended to cover the general case when fx0 l1p 1

half canonical series on algebraic curves preprint enviat per a la seva publicacio en una revista cientifica transactions of the american mathematical society vol 302 no 1 1987 pp 99 115 https www jstor org stable 2000899

bootstrap method for measuring accuracy of probabilistic choice models abstract probabilistic choice models that include choice attributes are increasingly being utilized by decision makers particularly in the business area the output of these models are point estimates of the coefficients of the choice attributes and rate of correct prediction accuracy measures of these point estimates are either based upon the asymptotic properties of the estimation procedures or are not provided this paper indicates that bootstrap is a method by which the assumption of asymptotic properties can be empirically validated for a given model and can provide measures of accuracy on point estimates where currently no such measure exists the empirical application of bootstrap to a real world data set indicates that decision makers will have considerably more information about their problem than is currently provided in the point estimates of the choice model managerial strategy and actions taken based upon the additional information may be quite different from actions suggested by the point estimates alone

groups of automorphisms of cyclic trigonal riemann surfaces abstract we give the list of all groups g acting as a group of automorphisms of some cyclic trigonal compact riemann surface x of genus g 5 and containing the trigonality automorphism group an abstract group g may act in different ways producing coverings x x g with different ramification type the list of all such different ramification types is also given

general uniqueness results and variation speed for blow up solutions of elliptic equations let omega be a smooth bounded domain in r n we prove general uniqueness results for equations of the form delta u au b x f u in omega subject to u infty on partial omega our uniqueness theorem is established in a setting involving karamata s theory on regularly varying functions which is used to relate the blow up behavior of u x with f u and b x where b equiv 0 on partial omega and a certain ratio involving b is bounded near partial omega a key step in our proof of uniqueness uses a modification of an iteration technique due to safonov

existence and asymptotic behavior of positive blow up solutions for semilinear elliptic coupled system in this article we study the existence and the boundary behavior of positive blow up solutions for the semilinear elliptic coupled system our arguments are based on the subsupersolution method and the karamata regular variation theory in this article we study the existence and the boundary behavior of positive blow up solutions for the semilinear elliptic coupled system our arguments are based on the subsupersolution method and the karamata regular variation theory

nondegeneracy and uniqueness for boundary blow up elliptic problems abstract in this paper we use for the first time linearization techniques to deal with boundary blow up elliptic problems after introducing a convenient functional setting we show that the problem u a x u p g x u in with u on has a unique positive solution for large enough and determine its asymptotic behavior as here p 1 a x is a continuous function which can be singular near and g x u is a perturbation term with potential growth near zero and infinity we also consider more general problems obtained by replacing u p by e u or a logistic type function f u

classification of radial solutions for semilinear elliptic systems with nonlinear gradient terms abstract we are concerned with the classification of positive radial solutions for the system u v p v f u where p 0 and f c 1 0 is a nondecreasing function such that f t 0 for all t 0 we show that in the case where the system is posed in the whole space r n such solutions exist if and only if 1 0 s f t d t p 2 p 1 d s this is the counterpart of the keller osserman condition for the case of single semilinear equation similar optimal conditions are derived in case where the system is posed in a ball of r n if f t t q q 1 using dynamical system techniques we are able to describe the behaviour of solutions at infinity in case where the system is posed in the whole r n or around the boundary in case of a ball

on the bootstrap and confidence intervals we derive an explicit formula for the first term in an unconditional edgeworth type expansion of coverage probability for the nonparametric bootstrap technique applied to a very broad class of studentized statistics the class includes sample mean k sample mean sample correlation coefficient maximum likelihood estimators expressible as functions of vector means etc we suggest that the bootstrap is really an empiric one term edgeworth inversion with the bootstrap simulations implicitly estimating the first term in an edgeworth expansion this view of the bootstrap is reinforced by our discussion of the iterated bootstrap which inverts an edgeworth expansion to arbitrary order by simulating simulations

multiple solutions of a critical polyharmonic equation we prove that for n 2m the equation mu u 4m n 2mu on rn has a sequence of nodal finite energy solutions which is unbounded in dm 2 rn this generalizes a classical result of weiyue ding for m 1

pullback attractors and extremal complete trajectories for non autonomous reaction diffusion problems abstract we analyse the dynamics of the non autonomous nonlinear reaction diffusion equation u t u f t x u subject to appropriate boundary conditions proving the existence of two bounding complete trajectories one maximal and one minimal our main assumption is that the nonlinear term satisfies a bound of the form f t x u u c t x u 2 d t x u where the linear evolution operator associated with c t x is exponentially stable as an important step in our argument we give a detailed analysis of the exponential stability properties of the evolution operator for the non autonomous linear problem u t u c t x u between different l p spaces

a construction of non kahler calabi yau manifolds and new solutions to the strominger system abstract we propose a new construction of compact non kahler calabi yau manifolds with balanced metrics and study the strominger system on them in particular we obtain explicit solutions to the strominger system with degeneracies on g t 4 where g is an immersed minimal surface of genus g 3 in flat t 3

expanding the asymptotic explosive boundary behavior of large solutions to a semilinear elliptic equation the main goal of this paper is to study the asymptotic expansion near the boundary of the large solutions of the equation delta u lambda u m f in omega where lambda 0 m 1 f is an element of c omega f 0 and omega is an open bounded set of r n n 1 with boundary smooth enough roughly speaking we show that the number of explosive terms in the asymptotic boundary expansion of the solution is finite but it goes to infinity as in goes to 1 we prove that the expansion consists in two eventual geometrical and non geometrical parts separated by a term independent on the geometry of partial derivative omega but dependent on the diffusion for low explosive sources the non geometrical part does not exist all coefficients depend on the diffusion and the geometry of the domain by means of well known properties of the distance function dist x partial derivative omega for high explosive sources the preliminary coefficients relative to the non geometrical part are independent on omega and the diffusion finally the geometrical part does not exist for very high explosive sources consists in two eventual geometrical and non geometrical parts separated by a term independent on the geometry of partial omega but dependent on the diffusion for low explosive sources the non geometrical part does not exist all coefficients depend on the diffusion and the geometry of the domain by means of well known properties of the distance function rm dist x partial omega dist x for high explosive sources the preliminary coefficients relative to the non geometrical part are independent on omega and the diffusion finally the geometrical part does not exist for very high explosive sources

subcanonical points on projective curves and triply periodic minimal surfaces in the euclidean space a point p in c on a smooth complex projective curve of genus g ge 3 is subcanonical if the divisor 2g 2 p is canonical the subcanonical locus mathcal g g subset mathcal m g 1 described by pairs c p as above has dimension 2g 1 and consists of three irreducible components apart from the hyperelliptic component mathcal g g mathrm hyp the other components mathcal g g mathrm odd and mathcal g g mathrm even depend on the parity of h 0 c g 1 p and their general points satisfy h 0 c g 1 p 1 and 2 respectively in this paper we study the subloci mathcal g g r of pairs c p in mathcal g g such that h 0 c g 1 p ge r 1 and h 0 left c g 1 p right equiv r 1 mathrm mod 2 in particular we provide a lower bound on their dimension and we prove its sharpness for r le 3 as an application we further give an existence result for triply periodic minimal surfaces immersed in the 3 dimensional euclidean space completing a previous result of the second author

topological classification of conformal actions on cyclic p gonal riemann surfaces abstract a compact riemann surface x of genus g 1 which can be realized as a p sheeted covering of the riemann sphere for some prime p is called p gonal if there is an automorphism of order p on x which permutes the sheets we call x cyclic p gonal here we classify conformal actions on cyclic p gonal riemann surfaces of genus g p 1 2 up to topological conjugacy and determine which of them can be maximal

theoretical comparison of bootstrap confidence intervals we develop a unified framework within which many commonly used bootstrap critical points and confidence intervals may be discussed and compared in all seven different bootstrap methods are examined each being usable in both parametric and nonparametric contexts emphasis is on the way in which the methods cope with first and second order departures from normality percentile t and accelerated bias correction emerge as the most promising of existing techniques certain other methods are shown to lead to serious errors in coverage and position of critical point an alternative approach based on shortest bootstrap confidence intervals is developed we also make several more technical contributions in particular we confirm efron s conjecture that accelerated bias correction is second order correct in a variety of multivariate circumstances and give a simple interpretation of the acceleration constant

liouville type theorems for polyharmonic equations in mathbb r n and in mathbb r n_ by using the moving plane method combined with integral inequalities and hardy s inequality some new liouville type theorems for semilinear polyharmonic equations in mathbb r n and in mathbb r n are proved

oscillatory radial solutions for subcritical biharmonic equations it is well known that the biharmonic equation 2u u u p 1 with p 1 has positive solutions on rn if and only if the growth of the nonlinearity is critical or supercritical we close a gap in the existing literature by proving the existence and uniqueness up to scaling and symmetry of oscillatory radial solutions on rn in the subcritical case analyzing the nodal properties of these solutions we also obtain precise information about sign changing large radial solutions and radial solutions of the dirichlet problem on a ball

radial solutions of a polyharmonic equation with power nonlinearity abstract we classify the regular radial solutions of the equation m u u u p 1 with m a positive integer and p 1 any such solution u is uniquely determined by the center values of u and its iterated laplacians up to order m 1 that is by the center point u 0 u 0 m 1 u 0 most solutions have finite exit radius that is they are unbounded and defined on open balls of finite radius are eventually monotonic with respect to the radial variable and diverge to or the center points of these solutions form two open half spaces in r m separated by an m 1 dimensional manifold m solutions with center points on m are either global or they have finite exit radius and oscillate about 0 with unbounded amplitude our results yield precise information regarding the existence multiplicity and nature of large radial solutions of m u u u p 1 on a ball of given radius

an information theoretic two stage two decision rule choice model abstract recent articles in choice modeling advocate two stage decision processes in which the decision maker uses the first stage to screen down the number of feasible alternatives and the second stage to make a final choice a key question in the analysis of two stage decision processes is whether the probabilities estimated in the first stage strongly influence the final second stage probabilities or is the first stage used only to reduce the number of alternatives this question has not been addressed in the literature primarily because the second stage model is generally a sinusoidal simultaneous compensatory model such as logit probit tobit using maximum likelihood estimation mle which cannot directly incorporate first stage probability estimates as the dependent variable this paper formulates a minimum discrimination information mdi approach to intertwine the two stages of a decision process the mdi methodology discussed in this paper is capable of using proportions directly as input for estimation of the simultaneous compensatory models which makes it potentially useful for a variety of other applications for a wide class of models the mdi estimates exist and the mdi estimate of logit model is unique the performance of the mdi method is compared with the mle in a monte carlo simulation and in application to a real world data set for the real world data set analyzed the first stage probabilities appear to strongly influence the final choice probabilities

asymptotic behavior of large radial solutions of a polyharmonic equation with superlinear growth this paper concerns the blow up behavior of large radial solutions of polyharmonic equations with power nonlinearities and positive radial weights specifically we consider radially symmetric solutions of mu c x u p on an annulus x rn x with 0 and 0 that diverge to infinity as x here n m n p 1 and c is a positive continuous function on the interval letting r qc r q for r with q 2m p 1 q q q 1 q 2m 1 1 p 1 and c c 1 p 1 we show that as x the ratio u x x remains between positive constants that depend only on m and p extending well known results for the second order problem we prove in the fourth order case that u x x 1 as x and obtain precise asymptotic expansions if c is sufficiently smooth at in certain higher order cases we find solutions for which the ratio u x x does not converge but oscillates about 1 with non vanishing amplitude

effects of a degeneracy in the competition model part ii perturbation and dynamical behaviour this is the second part of our study on the competition model where the coefficient functions are strictly positive over the underlying spatial region except b x which vanishes in a nontrivial subdomain of and is positive in the rest of in part i we mainly discussed the existence of two kinds of steady state solutions of this system namely the classical steady states and the generalized steady states here we use these solutions to determine the dynamics of the model we do this with the help of the perturbed model where b x is replaced by b x e which itself is a classical competition model this approach also reveals the interesting relationship between the steady state solutions both classical and generalized of the above system and that of the perturbed system

plane models for riemann surfaces admitting certain half canonical linear series ii for r 2 closed riemann surfaces of genus 3r 2 admitting two simple half canonical linear series gr 1 h r i are characterized by the existence of certain plane models of degree 2r 3 where the linear series are apparent the plane curves have r 2 3 fold singularities one 2r 1 fold singularity q and two other double points typically tacnodes whose tangents pass through q the lines through q cut out a g4 which is unique the case where the g4 is the set of orbits of a noncycic group of automorphisms of order four is characterized by the existence of 3r 3 pairs of half canonical linear series of dimension r 1 where the sum of the two linear series in any pair is linearly equivalent to g3rr h3r p

min max level estimate for a singular quasilinear polyharmonic equation in r2m abstract using the framework first presented by ruf and sani we give a proof of an adams type inequality which can be applied to the functional j u 1 2 r 2 m m u 2 0 m 1 a x u 2 d x r 2 m f x u x d x r 2 m h u d x under two kinds of assumptions on the nonlinearity we estimate the min max level of the functional as an application a multiplicity result for the related singular quasilinear elliptic equation is proved

the boundary blow up rate of large solutions abstract in this paper we ascertain the blow up rate of the large solutions of a class of sublinear elliptic boundary value problems with a weight function in front of the nonlinearity that vanishes on the boundary of the underlying domain at different rates according to the point of the boundary x all previous results in the literature assumed the decay rate of the underlying weight function to be the same at any point of this hypothesis substantially simplified the mathematical analysis of the problem as it allowed constructing global sub and supersolutions in an open neighborhood of obtaining general results requires localizing at each particular point of the boundary making particularly involved the mathematical analysis of the problem

large solutions for an elliptic system of competitive type existence uniqueness and asymptotic behavior abstract this paper deals with the existence uniqueness and asymptotic behavior of boundary blow up solutions for an elliptic system of competitive type where the weight functions a x b x vanish on the boundary of the underlying domain at different rates according to the point of the boundary the proof relies on subsolutions and supersolutions and the localization method

asymptotic behavior of large solution for boundary blowup problems with non linear gradient terms let email protected r n n 3 be a bounded domain with smooth boundary we show the asymptotic behavior of boundary blowup solutions to non linear elliptic equation du u q b x f u in w subject to the singular boundary condition u x as dist x email protected 0 f is c varying at our analysis is based on the karamata regular variation theory combined with the method of lower and supper solution

dynamics of a periodically pulsed bio reactor model abstract global attractivity and uniform persistence are established for both single species growth and two species competition in a periodically pulsed bio reactor model in terms of principal eigenvalues of the periodic parabolic eigenvalue problem by appealing to the theories of monotone discrete dynamical systems abstract persistence asymptotically periodic semiflows and perturbation of global attractors

theta characteristics on algebraic curves the theory of theta characteristics is developed algebraically so that it may be applied to possibly singular and or reducible algebraic curves the configuration of theta characteristics on a curve is described in terms of its singularities with applications to the geometry of plane quartic curves and the problem of appolonius some results on gorenstein local rings are appended 0 introduction the theory of theta characteristics has been studied from different points of view and often inadvertently cf for example the 19th century literature on bitangents to smooth plane quartic curves e g 4 and 10 until recently however virtually all treatments of theta characteristics per se involved the transcendental theory of the theta function associated to a compact riemann surface then in 1971 mumford in 8 gave a completely algebraic treatment of the subject formulating the main results and proving them without reference to the transcendental theory this in turn suggested that theta characteristics could be studied in a more general context for example on possibly singular and or reducible algebraic curves in this paper we undertake such an analysis in 1 following mumford we establish some of the basic facts about theta characteristics algebraically so as to apply to more general curves in fact 1 10 i and 1 13 in their present generality are due to mumford while he assumes throughout 8 that his curve x is smooth his proof seems to apply as given the argument for 1 13 here is somewhat different in order to make the proof more elementary and selfcontained one bonus is the result 1 11 on the subvariety of the moduli space 9thg consisting of curves with large semicanonical linear series this fact seemingly can be proved only via the algebraic set up in 2 we investigate the number and configuration of odd and even theta characteristics on a singular curve the results are expressed in the two main theorems 2 12 and 2 22 giving a more or less complete answer to these questions in terms of the singularities of the curve interestingly a recurrent motif in these arguments is one introduced by mumford in 8 the behavior of the maximal isotropic subspaces for a nondegenerate quadratic form on an even dimensional vector space here the mainspring of theorems 1 13 2 12 and 2 22 is assertion 1 4 below that the sum of the dimensions of the pairwise intersections of any three such subspaces is congruent to n mod 2 received by the editors july 11 1980 and in revised form october 22 1981 1980 mathematics subject classification primary 14h99 14h30 secondary 14h20 14h40 14k25 research partially supported by nsf grant mcs78 04008 aol dl 982 american mathematical society 0002 9947 8 1 0000 0371 10 25