scaling theory for gelling systems work in progress abstract gelation as it arises in the kinetic equations describing irreversible aggregation the so called smoluchowski equations is briefly reviewed the scaling theory near the gel point immediately before the transition is presented the equations presented earlier for the scaling function and the exponent are cast in a form more amenable to numerical study an algorithm to solve them is described and applied to the kernels of the form k x y x y x y a theory for the behaviour immediately after the gel transition is also presented and is found to be verified in one special exactly solved case product kernel with power law initial conditions

equivariant cohomology fock space and loop groups equivariant de rham cohomology is extended to the infinite dimensional setting of a loop subgroup acting on a loop group using hida supersymmetric fock space for the weil algebra and malliavin test forms on the loop group the mathai quillen isomorphism in the brst formalism of kalkman is defined so that the equivalence of various models of the equivariant de rham cohomology can be established

extended sufficient semilocal convergence for the secant method we establish new sufficient convergence conditions for the secant method to a locally unique solution of a nonlinear equation in a banach space using our new concept of recurrent functions and combining lipschitz and center lipschitz conditions on the divided difference operator we obtain a new semilocal convergence analysis of the secant method moreover our sufficient convergence conditions expand the applicability of the secant method in cases not covered before dennis 1971 9 hernandez et al 2005 8 laasonen 1969 15 ortega and rheinboldt 1970 11 potra 1982 5 potra 1985 7 schmidt 1978 18 yamamoto 1987 12 wolfe 1978 19 numerical examples are also provided in this study

renormalization of gauge invariant operators and anomalies in yang mills theory a long standing conjecture on the structure of renormalized gauge invariant integrated operators of arbitrary dimension in yang mills theory is established the general solution of the consistency condition for anomalies with sources included is also derived this is achieved by computing explicitly the cohomology of the full unrestricted becchi rouet stora tyutin operator in the space of local polynomial functionals with ghost number equal to zero or one the argument does not use power counting and is purely cohomological it relies crucially on standard properties of the antifeld formalism

structure of higher spin gauge interactions in a previous paper higher spin gauge field theory was formulated in an abstract way essentially only keeping enough machinery to discuss gauge invariance of an action the approach could be thought of as providing an interface or syntax toward an implementation or semantics yet to be constructed the structure then revealed turned out to be that of a strongly homotopy lie algebra in the present paper the framework will be connected to more conventional field theoretic concepts the fock complex vertex operator implementation of the interactions in the brst bv formulation of the theory will be elaborated the relation between the vertex order expansion and homological perturbation theory will be clarified a formal nonobstruction argument is reviewed the syntactically derived sh lie algebra structure is semantically mapped to the fock complex implementation and it is shown that the equations governing the higher order vertices are reproduced global symmetries and subsidiary conditions are discu

geometric quantization of the brst charge in the first half of this paper sects 1 4 we generalise the standard geometric quantization procedure to symplectic supermanifolds in the second half sects 5 6 we apply this to two examples that exhibit classical brst symmetry i e we quantize the brst charge and the ghost number more precisely in the first example we consider the reduced symplectic manifold obtained by symplectic reduction from a free group action with ad equivariant moment map in the second example we consider a foliated configuration space whose cotangent bundle admits the construction of a brst charge associated to this foliation we show that the classical brst symmetry can be described in terms of a hamiltonian supergroup action on the extended phase space and that geometric quantization gives us a super unitary representation of this supergroup finally we point out how these results are related to reduction at the quantum level as compared with the reduction at the classical level

convergence of a finite volume scheme for coagulation fragmentation equations this paper is devoted to the analysis of a numerical scheme for the coagulation and fragmentation equation a time explicit finite volume scheme is developed based on a conservative formulation of the equation it is shown to converge under a stability condition on the time step while a first order rate of convergence is established and an explicit error estimate is given finally several numerical simulations are performed to investigate the gelation phenomenon and the long time behavior of the solution

on the application of substochastic semigroup theory to fragmentation models with mass loss a linear integro differential equation modelling multiple fragmentation with inherent mass loss is investigated by means of substochastic semigroup theory the existence of a semigroup is established and under natural conditions on certain coefficients the generator of this semigroup is identified this yields in particular a validation of the formal mass loss rate equation for the model

improving the domain of starting points for secant like methods abstract from the simplified secant method and a family of secant like methods we construct a family of predictor corrector iterative methods for solving a nonlinear equation in banach spaces

ostrowski type methods for solving systems of nonlinear equations abstract four generalized algorithms builded up from ostrowski s method for solving systems of nonlinear equations are written and analyzed a development of an inverse first order divided difference operator for functions of several variables is presented as well as a direct computation of the local order of convergence for these variants of ostrowski s method furthermore a sequence that approximates the order of convergence is generated for the examples and it confirms in a numerical way that the order of the methods is well deduced

analytic fragmentation semigroups and continuous coagulation fragmentation equations with unbounded rates abstract in this paper we show that continuous fragmentation operators are sectorial for a large range of physically relevant fragmentation rates and use this fact to prove classical solvability of the combined coagulation fragmentation equation with unbounded coagulation kernels

on a class of continuous coagulation fragmentation equations abstract a model for the dynamics of a system of particles undergoing simultaneously coalescence and breakup is considered each particle being assumed to be fully identified by its size existence of solutions to the corresponding evolution integral partial differential equation is shown for product type coagulation kernels with a weak fragmentation the failure of density conservation or gelation is also investigated in some particular cases

an sp 2 covariant version of generalized canonical quantization of dynamical systems with linearly dependent constraints an sp 2 covariant version of the method of generalized canonical quantization of dynamical systems with linearly dependent first class constraints is proposed the existence theorem for solutions of generating equations of a gauge algebra is proved and the natural arbitrariness in these solutions is described the scheme proposed is shown to be equivalent to the standard version of generalized canonical quantization

secant like methods for solving nonlinear integral equations of the hammerstein type we consider a one parametric family of secant type iterations for solving nonlinear equations in banach spaces we establish a semilocal convergence result for these iterations by means of a technique based on a new system of recurrence relations this result is then applied to obtain existence and uniqueness results for nonlinear integral equations of the hammerstein type we also present a numerical example where the solution of a particular hammerstein integral equation is approximated by different secant type methods

weak solutions to the continuous coagulation equation with multiple fragmentation the existence of weak solutions to the continuous coagulation equation with multiple fragmentation is shown for a class of unbounded coagulation and fragmentation kernels the fragmentation kernel having possibly a singularity at the origin this result extends previous ones where either boundedness of the coagulation kernel or no singularity at the origin for the fragmentation kernel was assumed

the brs method and geometric quantization some examples we recall the method of quantization of constraints as outlined by kostant and sternberg we discuss various examples to test compatibility between geometric quantization and this procedure in almost all cases reduction and quantization commute

on the local convergence of a family of two step iterative methods for solving nonlinear equations a local convergence analysis for a generalized family of two step secant like methods with frozen operator for solving nonlinear equations is presented unifying earlier methods such as secant s newton chebyshev like steffensen and other new variants the family of iterative schemes is built up where a profound and clear study of the computational efficiency is also carried out numerical examples and an application using multiple precision and a stopping criterion are implemented without using any known root finally a study comparing the order efficiency and elapsed time of the methods suggested supports the theoretical results claimed

numerical simulation of the smoluchowski coagulation equation in this paper we develop a numerical scheme for the smoluchowski coagulation equation which relies on a conservative formulation and a finite volume approach several numerical simulations are performed to test the validity of the scheme and the expected behavior of the model in particular the gelation phenomenon and the long time behavior of the solution are numerically studied

fedosov deformation quantization as a brst theory the relationship is established between the fedosov deformation quantization of a general symplectic manifold and the bfv brst quantization of constrained dynamical systems the original symplectic manifold is presented as a second class constrained surface in the fibre bundle which is a certain modification of a usual cotangent bundle equipped with a natural symplectic structure the second class system is converted into the first class one by continuation of the constraints into the extended manifold being a direct sum of and the tangent bundle t this extended manifold is equipped with a nontrivial poisson bracket which naturally involves two basic ingredients of fedosov geometry the symplectic structure and the symplectic connection the constructed first class constrained theory being equivalent to the original symplectic manifold is quantized through the bfv brst procedure the existence theorem is proven for the quantum brst charge and the quantum brst invariant observables the adjoint action of the quantum brst charge is identified with the abelian fedosov connection while any observable being proven to be a unique brst invariant continuation for the values defined in the original symplectic manifold is identified with the fedosov flat section of the weyl bundle the fedosov fibrewise star multiplication is thus recognized as a conventional product of the quantum brst invariant observables

characteristic cohomology of p form gauge theories the characteristic cohomologyh k char d for an arbitrary set of freep form gauge fields is explicitly worked out in all form degreesk n 1 wheren is the spacetime dimension it is shown that this cohomology is finite dimensional and completely generated by the forms dual to the field strengths the gauge invariant characteristic cohomology is also computed the results are extended to interactingp form gauge theories with gauge invariant interactions implications for the brst cohomology are mentioned

convergence analysis of sectional methods for solving breakage population balance equations ii the cell average technique this work presents the convergence of the cell average technique kumar et al in powder technol 179 205 228 2007 for solving breakage population balance equation similarly to our paper kumar and warnecke numerische math 2008 of this series we study convergence on four different types of meshes a second order convergence is proved for uniform locally uniform and non uniform smooth meshes finally the scheme is analyzed on random mesh and it is found that the scheme is only first order accurate nevertheless we obtain for locally uniform as well as for random mesh one order higher accuracy than the fixed pivot technique discussed by the authors in the first paper all mathematical observations of convergence analysis are also validated numerically and numerical results are compared with the results of the first part

the antifield koszul tate complex of reducible noether identities a generic degenerate lagrangian system of even and odd fields is examined in algebraic terms of the grassmann graded variational bicomplex its euler lagrange operator obeys noether identities which need not be independent but satisfy first stage noether identities and so on we show that if a certain necessary and sufficient condition holds one can associate to a degenerate lagrangian system the exact koszul tate complex with the boundary operator whose nilpotency condition restarts all its noether and higher stage noether identities this complex provides a sufficient analysis of the degeneracy of a lagrangian system for the purpose of its bv quantization

homological perturbation theory and the algebraic structure of the antifield antibracket formalism for gauge theories the algebraic structure of the antifield antibracket formalism for both reducible and irreducible gauge theories is clarified this is done by using the methods of homological perturbation theory hpt a crucial ingredient of the construction is the koszul tate complex associated with the stationary surface of the classical extremals the koszul tate differential acts on the antifields and is graded by the antighost number it provides a resolution of the algebraa of functions defined on the stationary surface namely it is acyclic except at degree zero where its homology group reduces toa acyclicity only holds because of the introduction of the ghosts of ghosts and provides an alternative criterion for what is meant by a proper solution of the master equation the existence of the brst symmetry follows from the techniques of hpt the classical lagrangian brst cohomology is completely worked out and shown to be isomorphic with the cohomology of the exterior derivative along the gauge orbits on the stationary surface the algebraic structure of the formalism is identical with the structure of the hamiltonian brst construction the role played there by the constraint surface is played here by the stationary surface only elementary quantum questions general properties of the measure are addressed

new semilocal and local convergence analysis for the secant method we present a new convergence analysis for the secant method in order to approximate a locally unique solution of a nonlinear equation in a banach space our idea uses lipschitz and center lipschitz instead of just lipschitz conditions in the convergence analysis the new convergence analysis leads to more precise error bounds and to a better information on the location of the solution than the corresponding ones in earlier studies such as 2 6 9 11 14 15 17 20 22 26 numerical examples validating the theoretical results are also provided in this study

a topological characterization of classical brst cohomology the recent identification of classical brst cohomology with the vertical cohomology of a certain fibration is used to compute it in terms of the classical observables and the topology of the gauge orbits when the gauge orbits are compact and orientable a duality theorem is exhibited

on the convergence of newton s method for a class of nonsmooth operators we provide an analog of the newton kantorovich theorem for a certain class of nonsmooth operators this class includes smooth operators as well as nonsmooth reformulations of variational inequalities it turns out that under weaker hypotheses we can provide under the same computational cost over earlier works s m robinson newton s method for a class of nonsmooth functions set valued anal 2 1994 291 305 a semilocal convergence analysis with the following advantages finer error bounds on the distances involved and a more precise information on the location of the solution in the local case not examined in s m robinson newton s method for a class of nonsmooth functions set valued anal 2 1994 291 305 we can show how to enlarge the radius of convergence and also obtain finer error estimates numerical examples are also provided to show that in the semilocal case our results can apply where others s m robinson newton s method for a class of nonsmooth functions set valued anal 2 1994 291 305 fail whereas in the local case we can obtain a larger radius of convergence than before s m robinson newton s method for a class of nonsmooth functions set valued anal 2 1994 291 305

brst cohomology and phase space reduction in deformation quantization in this article we consider quantum phase space reduction when zero is a regular value of the momentum map by analogy with the classical case we define the brst cohomology in the framework of deformation quantization we compute the quantum brst cohomology in terms of a quantum chevalley eilenberg cohomology of the lie algebra on the constraint surface to prove this result we construct an explicit chain homotopy both in the classical and quantum case which is constructed out of a prolongation of functions on the constraint surface we have observed the phenomenon that the quantum brst cohomology cannot always be used for quantum reduction because generally its zero part is no longer a deformation of the space of all smooth functions on the reduced phase space but in case the group action is sufficiently nice e g proper which is the case for all compact lie group actions it is shown for a strongly invariant star product that the brst procedure always induces a star product on the reduced phase space in a rather explicit and natural way simple examples and counterexamples are discussed

classical brst cohomology and invariant functions on constraint manifolds i given a manifoldm and a submanifoldc together with a lie groupg acting onm and leavingc invariant it is shown how the algebra ofg invariant functions onc can be described in terms of cohomology whenc is defined as the common zero level of an irreducible set of g covariant constraints the construction is independent of any additional structures such as e g a symplectic structure onm and therefore it provides a natural framework for a unified description of brst cohomology both for lagrangian and hamiltonian systems finally it is discussed how one can in various typical situations replace invariance under an infinite dimensional gauge group by invariance under a suitable finite dimensional lie group this is a necessary prerequisite for handling brst cohomology for such systems within a completely finite dimensional setting

on the convergence of broyden s method in hilbert spaces abstract in this paper we present a new semilocal convergence analysis for an inverse free broyden s method in a hilbert space setting in the analysis we apply our new idea of recurrent functions concepts of divided differences of order one and lipschitz center lipschitz conditions on the operator involved our analysis extends the applicability of broyden s method in cases not covered before finally we give an example to illustrate the main result in this paper

spacetime locality of the brst formalism the spacetime locality of the brst formalism is investigated the analysis covers gauge theories with either closed or open algebras and is undertaken in the explicit context of the antifield formulation of the brst theory under appropriate conditions the homology of the koszul tate differential modulo the spacetime exterior derivative is shown to be trivial in the space of non integrated densities with positive antighost and pure ghost numbers as a result i the solution of the master equation can be taken to be a local functional ii the gauge fixed action is also a local functional provided one takes the gauge fixing fermion to be a local functional as well and iii the brst transformation is local

becchi rouet stora tyutin formalism and zero locus reduction in the becchi rouet stora tyutin brst quantization of gauge theories the zero locus zq of the brst differential q carries an anti bracket whose parity is opposite to that of the fundamental bracket observables of the brst theory are in a 1 1 correspondence with casimir functions of the bracket on zq for any constrained dynamical system with the phase space n0 and the constraint surface we prove its equivalence to the constrained system on the bfv extended phase space with the constraint surface given by zq reduction to the zero locus of the differential gives rise to relations between bracket operations and differentials arising in different complexes the gerstenhaber schouten berezin kirillov and sklyanin brackets the equation ensuring the existence of a nilpotent vector field on the reduced manifold can be the classical yang baxter equation we also generalize our constructions to the bi qp manifolds which from the brst theory viewpoint correspond to the brst anti brst symmetric quantiza

newton like methods for the computation of fixed points abstract the celebrated banach fixed point theorem provides conditions which assure that the method of successive substitution is convergent the convergence however may take place very slowly so that it may be desirable to use a newton like method for the computation of the fixed point if newton s method itself is applied one ignores the additional information that the problem arises from a frixed point problem with a contraction mapping in the present note some variants of newton s method are discussed which make use of this contraction information it turns out that the convergence of newton s method can be accelerated without any relevant additional computational labour

a pseudospectral method for hammerstein equations abstract this paper considers hammerstein equations formula and presents a pseudospectral method for solving them numerically the method is applied to approximate the solution not to the equation in its original form but rather to an equivalent equation z t g t y t the function z is approximated by a polynomial z n of degree n with coefficients determined by collocation at the legendre gauss lobatto nodes we define the desire approximation to y by formula and establish that under suitable conditions lim n y n t y t uniformly in t advantages of the proposed method compared with existing methods in the literature are discussed an illustrative example is included to show the accuracy of the proposed method

existence uniqueness and cohomology of the classical brst charge with ghosts of ghosts a complete canonical formulation of the brst theory of systems with redundant gauge symmetries is presented these systems includep form gauge fields the superparticle and the superstring we first define the koszul tate differential and explicitly show how the introduction of the momenta conjugate to the ghosts of ghosts makes it acyclic the global existence of the brst generator is then demonstrated and the brst charge is proved to be unique up to canonical transformations in the extended phase space which includes the ghosts finally the brst cohomology in classical mechanics is investigated and shown to be equal to the cohomology of the exterior derivative along the gauge orbits as in the irreducible case this is done by re expressing the exterior algebra along the gauge orbits as a free differential algebra containing generators of higher degree which are identified with the ghosts of ghosts the quantum cohomology is not dealt with

brst cohomology for certain reducible topological symmetries in this paper two different definitions of the brst complex are connected we obtain the brst complex of topological quantum field theories leading to equivariant cohomology from the standard definition of the classical brst complex leading to lie algebra cohomology provided that we include ghosts for ghosts hereby we use a finite dimensional model with a semi direct product action ofh diffm on a configuration spacem whereh is a compact lie group representing the gauge symmetry in this model

quantum dynamics on super groups constraints and the brst supergroup the smallest supergroup b k containing among its generators those of a constraint group k the brst charge and the corresponding ghost and antighost operators is constructed the supergroup b k can be enlarged to include the ordinary dynamical variables of the unconstrained physical system in a group approach to quantization b k generalizes the ordinary u 1 phase invariance of wave functions in particular this mechanism reproduces the essential features of the brst quantization when k is diff s1 the critical values of string theory are those for which the space of polarized functions on the enlarged brst supergroup is not irreducible

dynamics and local convergence of a family of derivative free iterative processes abstract in this paper we establish the construction of a family of free derivative of point to point iterative processes with quadratic convergence from two known data in each previous iteration besides we study the accessibility of this family by means of the basins of attraction and the convergence balls we provide a local convergence analysis for the family of iterative processes free of derivatives when the operator f is not necessarily frechet differentiable the sufficient convergence conditions are weaker and more flexible than in earlier studies an application is provided involving mixed hammerstein nonlinear integral equation with application in real world problems finally we show also a dynamical study and the convergence regions of some members of the family

hamiltonian brst anti brst theory the hamiltonian brst anti brst theory is developed in the general case of arbitrary reducible first class systems this is done by extending the methods of homological perturbation theory originally based on the use of a single resolution to the case of a biresolution the brst and the anti brst generators are shown to exist the respective links with the ordinary brst formulation and with thesp 2 covariant formalism are also established

a technique to choose the most efficient method between secant method and some variants abstract a few variants of the secant method for solving nonlinear equations are analyzed and studied in order to compute the local order of convergence of these iterative methods a development of the inverse operator of the first order divided differences of a function of several variables in two points is presented using a direct symbolic computation the computational efficiency and the approximated computational order of convergence are introduced and computed choosing the most efficient method among the presented ones furthermore we give a technique in order to estimate the computational cost of any iterative method and this measure allows us to choose the most efficient among them

from the discrete to the continuous coagulation fragmentation equations the connection between the discrete and the continuous coagulation fragmentation models is investigated a weak stability principle relying on a priori estimates and weak compactness in l 1 is developed for the continuous model we approximate the continuous model by a sequence of discrete models and writing the discrete models as modified continuous ones we prove the convergence of the latter towards the former with the help of the above mentioned stability principle another application of this stability principle is the convergence of an explicit time and size discretization of the continuous coagulation fragmentation model

numerical simulation and convergence analysis of a finite volume scheme for solving general breakage population balance equations this paper presents a finite volume scheme fvs for solving general breakage population balance equations bpbes in particular the number density based bpbe is transformed to the form of a mass conservation law then it becomes easy to apply the well known fvss that have an important property of mass conservation following kumar and warnecke for fixed pivot fp method 16 and cell average technique cat 15 the stability and the convergence analysis of the semi discretized fvs are studied unlike the cat and the fp method the fvs is second order consistent independently of the type of meshes we also observe that fvs gives second order convergence rate on four different types of uniform and non uniform meshes with non decreasing behavior of mesh width nevertheless one order better accuracy than the fp method is achieved on locally uniform meshes it is also noticed that on non uniform random meshes the fvs shows one order and two orders higher accuracy than the cat and the fp method respectively the mathematical results of convergence analysis are validated numerically by taking three test problems the numerical simulations are also compared with the results obtained by the cat and the fp method

existence of gelling solutions for coagulation fragmentation equations we study the smoluchowski coagulation fragmentation equation which is an infinite set of non linear ordinary differential equations describing the evolution of a mono disperse system of particles in a well stirred solution approximating the solutions of the smoluchowski equations by a sequence of finite markov chains we investigate the qualitative behavior of the solutions we determine a device on the finite chains which can detect the gelation phenomena the density dropping phenomena it shows how the gelation phenomena are reflected on the sequence of finite markov chains using this device we determine various types of gelation kernels and get the bounds of gelation times

brst cohomology in classical mechanics the classical non quantum cohomology of the becchi rouet stora tyutin brst symmetry in phase space is defined and worked out no group action for the gauge transformations is assumed the results cover therefore the general case of an open algebra and are valid off shell each cohomology class contains all brst invariant functions with fixed ghost number an integer which differ from each other by a brst variation if the ghost number is negative there is only the trivial class whose elements are equivalent to zero if the ghost number is positive or zero there is a bijective correspondence between the brst classes and those of the exterior derivative along the gauge orbits these gauge orbits lie in the phase space surface on which the gauge generators are constrained to vanish the brst invariant functions of ghost numberp are then related to closedp forms along the orbits the addition of a brst variation corresponds to the addition of an exact form some comments about the quantum case are included the physical meaning of the classes with ghost number greater than zero is not discussed

the discrete coagulation fragmentation equations existence uniqueness and density conservation the discrete coagulation fragmentation equation describes the kinetics of cluster growth in which clusters can coagulate via binary interactions to form larger clusters or fragment to form smaller ones these models have many applications in pure and applied science ranging from cluster formation in galaxies to the kinetics of phase transformations in binary alloys our results relate to existence uniqueness density conservation and continuous dependence and they generalise the corresponding results in ref 2 for the becker doring equations for which the processes are restricted to clusters gaining or shedding one particle examples are given which illustrate the role of the assumptions on the kinetic coefficients and show the rich set of analytic phenomena supported by the general discrete coagulation fragmentation equations

asymptotic behaviour of solutions to the generalized becker doring equations for general initial data we prove the following asymptotic behaviour for solutions to the generalized becker doring system for general initial data under a detailed balance assumption and in situations where density is conserved in time there is a critical density s such that solutions with an initial density s converge strongly to the equilibrium with density and solutions with initial density s converge in a weak sense to the equilibrium with density s this extends the previous knowledge that this behaviour happens under more restrictive conditions on the initial data the main tool is a new estimate on the tail of solutions with density below the critical density

generalized classical brst cohomology and reduction of poisson manifolds in this paper we formulate a generalization of the classical brst construction which applies to the case of the reduction of a poisson manifold by a submanifold in the case of symplectic reduction our procedure generalizes the usual classical brst construction which only applies to symplectic reduction of a symplectic manifold by a coisotropic submanifold i e the case of reducible first class constraints in particular our procedure yields a method to deal with second class constraints we construct the brst complex and compute its cohomology brst cohomology vanishes for negative dimension and is isomorphic as a poisson algebra to the algebra of smooth functions on the reduced poisson manifold in zero dimension we then show that in the general case of reduction of poisson manifolds brst cohomology cannot be identified with the cohomology of vertical differential forms

algebraic structure of the brst symmetry an explicit construction of the brst symmetry is presented in the hamiltonian approach the construction is based on the splitting homotopy and the transference problem

a new collocation type method for hammerstein integral equations on presente une methode du type de collocation pour la resolution numerique des equations integrales d hammerstein on etablit la convergence de l approximation desiree vers la solution exacte

the generalized koszul differential in the brst quantization a new geometrical structure is proposed for a differential complex of the koszul type the generators of the complex are structured on more levels and new graduations are used a generalized differential that can be split in many pieces acts on the generators the first two items are identified with the koszul operators from the sp 2 brst quantization this result suggests the possibility of the implementation of a symmetry bigger than sp 2 the third order koszul differential is effectively constructed as an application of this construction the brst charges and the extended hamiltonian suitable for the sp 3 brst quantization of a first rank gauge theory are presented

optimizing the applicability of a theorem by f potra for newton like methods abstract we present a new sufficient semilocal convergence conditions for newton like methods in order to approximate a locally unique solution of an equation in a banach space setting thi s way we expand the applicability of these methods in cases not covered in other studies such as dennis 1971 12 ezquerro et al 2000 2010 13 14 kornstaedt 1975 18 potra and ptak 1984 24 potra 1985 1979 1982 1981 1984 23 25 26 27 28 proinov 2010 29 schmidt 1978 31 or yamamoto 1987 32 the advantages of our approach also include a tighter convergence analysis under the same computational cost applications where the older convergence criteria are not satisfied but the new convergence criteria are satisfied are also given in this study

expanding the applicability of the secant method under weaker conditions abstract we present a new semilocal convergence analysis for secant method in order to approximate a locally unique solution of a nonlinear equation in a banach space setting our analysis includes the computation of the bounds on the limit points of the majorizing sequences involved under the same computational cost on the parameters involved our convergence criteria are weaker and the error bounds more precise than in earlier studies such as amat and busquier 2003 amat et al in press argyros and hilout 2012 argyros et al 2014 argyros and magrenan 2014 2015 dennis 1971 ezquerro et al 2000 ortega and rheinboldt 1970 potra and ptak 1984 schmidt 1978 numerical examples are also presented to illustrate the theoretical results obtained in this study

a cohomological approach to the batalin lavrov tyutin covariant quantization of irreducible gauge theory the anti brst transformation for an arbitrary irreducible gauge invariant action is implemented in the usual batalin vilkovisky bv approach this is done without duplicating the gauge symmetries but rather by duplicating all fields and antifields of the theory in this way the sp 2 covariant quantization can be accomplished in the standard bv approach and its equivalence with the batalin lavrov tyutin blt approach is proved by a special gauge fixing procedure

on steffensen s method on banach spaces we present a modification of steffensen s method as a predictor corrector iterative method so that we can use steffensen s method to approximate a solution of a nonlinear equation in banach spaces from the same starting points from which newton s method converges we study the semilocal convergence of the predictor corrector method by using the majorant principle we illustrate the method with an application to a discrete problem

semilocal convergence of secant like methods for differentiable and nondifferentiable operator equations abstract from well known secant like methods we observe that we can construct a new family of secant like methods that includes the secant method and kurchatov s method we analyse the local orders of convergence and the efficiencies of the methods of the family and study the semilocal convergence for differentiable and nondifferentiable operators finally we apply our results to conservative problems

scaling theory for systems with instantaneous gelation partial results we study a system of kinetic equations describing irreversible aggregation the so called smoluchowski equations for a peculiar case in which even starting from initial conditions for which only a monomer is present at arbitrarily small times an infinite cluster appears and causes the total mass of the system to decrease this phenomenon known as instantaneous gelation is known to arise in cases where the reaction rates between large clusters increase strongly as the cluster size goes to infinity we resolve two puzzles linked to this behaviour first from general results it is well known that a power law behaviour must form instantly at large masses for arbitrarily small times we show that the small time behaviour can be analysed for these systems but this must be done in an essentially different manner than in the regular case the correct treatment provides a mechanism for the instantaneous appearance of a power law tail at large masses in the aggregate size distribution we additionally show that instantaneous gelation is connected to the presence of an essential singularity in the solution and also show how from the numerical study of the formal power series describing the solution the nature of the singularity can be guessed and the time dependence of the mass scale for the onset of the power law behaviour conjectured

the continuous coagulation equation with multiple fragmentation abstract we present a proof of the existence of solutions to the continuous coagulation equation with multiple fragmentation whenever the kernels satisfy certain growth conditions the proof relies on weak l 1 compactness methods applied to suitably chosen approximating equations the question of uniqueness is also considered

a steffensen type method of two steps in banach spaces with applications this paper is devoted to the analysis of a steffensen type of two steps with order of convergence at least three the main advantage of this method is that it does not need to evaluate any frechet derivative or any bilinear operator the method includes extra parameters in the divided difference in order to ensure a good approximation to the first derivative in each iteration we prove using recurrence relations a semilocal convergence result in banach spaces and do a detailed study of the domain of parameters associated to this result finally some numerical results including differentiable and nondifferentiable operators are presented special attention is paid in the approximation of solutions of boundary problems using the multiple shooting method and in the approximation of a nonlinear model related with image processing

equivariant brst quantization and reducible symmetries working from first principles quantization of a class of hamiltonian systems with reducible symmetry is carried out by constructing first the appropriate reduced phase space and then the brst cohomology the constraints of this system correspond to a first class set for a group g and a second class set for a subgroup h the brst operator constructed is equivariant with respect to h using algebraic techniques analogous to those of equivariant de rham theory the brst operator is shown to correspond to that obtained by bv quantization of a class of systems with reducible symmetry the ghosts for ghosts correspond to the even degree two generators in the cartan model of equivariant cohomology as an example of the methods developed a topological model is described whose brst quantization relates to the equivariant cohomology of a manifold under a circle action

on the local convergence of fast two step newton like methods for solving nonlinear equations a local convergence analysis is presented for a fast two step newton like method tsnlm for solving nonlinear equations in a banach space setting the tsnlm unifies earlier methods such as newton s secant newton like chebyshev secant chebyshev newton steffensen stirling s and other single or multistep methods numerical examples and a comparative study of these methods validating our theoretical results are also given in the concluding section of this paper

global strict solutions to continuous coagulation fragmentation equations with strong fragmentation in this paper we give an elementary proof of the unique global in time solvability of the coagulation multiple fragmentation equation with polynomially bounded fragmentation and particle production rates and a bounded coagulation rate the proof relies on a new result concerning domain invariance for the fragmentation semigroup which is based on a simple monotonicity argument

geometric brst quantization i prequantization this is the first part of a two part paper dedicated to the definition of brst quantization in the framework of geometric quantization after recognizing prequantization as a manifestation of the poisson module structure of the sections of the prequantum line bundle we define brst prequantization and show that it is the homological analog of the symplectic reduction of prequantum data we define a prequantum brst cohomology theory and interpret it in terms of geometric objects we then show that all poisson structures correspond under homological reduction this allows to prove in the brst context that prequantization and reduction commute

constraints in hamiltonian time dependent mechanics the key point of the study of constraints in hamiltonian time dependent mechanics lies in the fact that a poisson structure does not provide dynamic equations and a poisson bracket of constraints with a hamiltonian is ill defined we describe hamiltonian dynamics in terms of hamiltonian forms and connections on the vertical cotangent bundle v q r seen as a momentum phase space a poisson bracket v on v q is induced by the canonical poisson bracket t on the cotangent bundle t q with v an algebra of first and second class time dependent constraints is described but we use the pull back of the evolution equation onto t x and the bracket t in order to extend the constraint algorithm to time dependent constraints the case of lagrangian constraints of a degenerate almost regular lagrangian is studied in detail one can assign to this lagrangian l a set of hamiltonian forms which are not necessarily degenerate such that any solution of the corresponding hamilton equations which lives in the lag

on the quantization of reducible gauge systems reducible gauge theories with constraints linear in the momenta are quantized the equivalence of the reduced phase space quantization dirac quantization and brst quantization is established provided one transforms appropriately the dirac wave functions under changes of representation of the constraint surface and of the reducibility functions the ghosts of ghosts are found to play a crucial role in the equivalence proof