on james and jordan von neumann constants of lorentz sequence spaces the nonsquare or james constant j x and the jordan von neumann constant cnj x are computed for two dimensional lorentz sequence spaces d 2 w q in the case where 2 q the jordan von neumann constant is also calculated in the case where 1 q 2

on the borel summability of planar perturbation series transition to minkowski space in recent years t hooft and rivasseau proved the borel summability of planar asymptotically free massive theories in euclidean space the corresponding borel sums in minkowski space are shown to exist as linear functionals if the euclidean counterparts are bounded polynomially in momentum space and fulfill certain analyticity conditions both can be verified in massive planar wrong sign 44 using rivasseau s approach the functionals alternatively are densely defined and unbounded on anlp space or bounded on the whole of a banach space with a more restrictive norm

on some geometric parameters in banach spaces abstract let x be a normed linear space and s x x x x 1 be the unit sphere of x let 0 2 0 1 x 0 0 and j x sup x y x y x and y s x be the modulus of convexity the modulus of smoothness and the modulus of squareness of x respectively let e x sup x y 2 x y 2 x y s x in this paper we proved some sufficient conditions on x j x e x and w x sup 0 lim inf n x n x lim inf n x n x where the supremum is taken over all the weakly null sequence x n in x and all the elements x of x for the uniform normal structure

renormalization theory in four dimensional scalar fields i we present a renormalization group approach to the renormalization theory of 44 using techniques that have been introduced and used in previous papers and that lead to very simple methods to bound the coefficients of the effective potential and of the schwinger functions the main aim of this paper is to show how one can in this way obtain then bounds

local existence of the borel transform in euclidean φ 4 4 we bound rigorously the large order behaviour of 44 euclidean perturbative quantum field theory as the simplest example of renormalizable but non super renormalizable theory the needed methods are developed to take into account the structure of renormalization which plays a crucial role in the estimates as a main thorem it is shown that the schwinger functions at ordern are bounded byknn which implies a finite radius of convergence for the borel transform of the perturbation series

on the large order behavior of φ44 we continue the rigorous study of the large order behavior of the perturbation series for the 4 model in 4 dimensions started in 1 in this paper we prove a result announced in 1 we show that the exact radius of convergence of the borel transform of the renormalized perturbation series for 44 is greater than or equal to the expected value given by the position of the first renormalon 2 this result holds for any vector 2 2 model withn components and makes use of the lipatov bound of 1 this result is based on a partial resummation of counterterms similar to the one of 3 but in a phase space analysis of the renormalized series

a note on jordan von neumann constant and james constant abstract let x be a non trivial banach space l maligranda conjectured c nj x 1 j x 2 4 for james constant j x and von neumann jordan constant c nj x of x satit saejung gave a proof of it in 2006 in this note we show that the last step in satit saejung s proof is not valid using his proof the result should be c nj x 1 j x 2 4 j x 4 2 j x 2 2 4 on the other hand we give a new proof of c nj x 1 j x 2 4 as an application we give a relation between j x and j l p x

fixed point property of direct sums abstract for a uniformly convex space z we show that z direct sums x 1 x n z of banach spaces x 1 x n with r a x i 1 a for some a 0 1 have the fixed point property for nonexpansive mappings as a direct consequence the result holds for all direct sums with being strictly convex the same result is extended to all direct sums x y of spaces x and y with property m whenever 1 the permanence of properties that are sufficient for the fixed point property are obtained for z direct sums and then for direct sums such properties include the properties r x 2 wnus c nj a x 2 ukk and nuc

non squareness properties of orlicz lorentz sequence spaces abstract in this paper criteria for non squareness properties non squareness local uniform non squareness and uniform non squareness of orlicz lorentz sequence spaces and of their n dimensional subspaces n n 2 as well as of the subspaces a of all order continuous elements in are given since degenerate orlicz functions and degenerate weight sequences are also admitted these investigations concern the most possible wide class of orlicz lorentz sequence spaces finally as immediate consequences criteria for all non squareness properties of orlicz sequence spaces which complete the results of sundaresan 1966 53 hudzik 1985 23 hudzik 1985 24 are deduced it is worth recalling that uniform non squareness is an important property because it implies super reflexivity as well as the fixed point property see james 1964 31 james 1972 33 and garcia falset et al 2006 19

a simple inequality for the von neumann jordan and james constants of a banach space abstract let c nj x and j x be the von neumann jordan and james constants of a banach space x respectively we shall show that c nj x j x where equality holds if and only if x is not uniformly non square this answers affirmatively to the question in a recent paper by alonso et al j alonso p martin p l papini wheeling around von neumann jordan constant in banach spaces studia math 188 2008 135 150 this inequality looks quite simple and covers all the preceding results in particular this is much stronger than maligranda s conjecture c nj x j x 2 4 1

on some geometric properties of generalized orlicz lorentz function spaces in this article we continue investigations concerning generalized orlicz lorentz function spaces initiated in the papers foralewski 2011 29 30 cf also foralewski 2008 27 28 first it is shown that modular is orthogonally subadditive next monotonicity properties are considered in order to get sufficient conditions for uniform monotonicity of the space a strong condition of 2 type and the notion of regularity of the generated musielak orlicz function are introduced finally criteria for non squareness of are presented

another look at cesaro sequence spaces abstract we consider the cesaro sequence space ces p as a closed subspace of the infinite l p sum of finite dimensional spaces we easily obtain many known results for example ces p has property of rolewicz uniform opial property and weak uniform normal structure we also consider some generalized cesaro sequence spaces finally we compute the von neumann jordan and james constants of the two dimensional cesaro sequence space ces p 2 when 1 p 2

uniform convexity of ψ direct sums of banach spaces abstract let x and y be banach spaces and a continuous convex function on the unit interval 0 1 satisfying certain conditions let x y be the direct sum of x and y equipped with the associated norm with we show that x y is uniformly convex if and only if x y are uniformly convex and is strictly convex as a corollary we obtain that the l p q direct sum x p q y 1 q p not p q 1 nor is uniformly convex if and only if x y are where l p q is the lorentz sequence space these results extend the well known fact for the l p sum x p y 1 some other examples are also presented

the strong coupling expansion and the ultra local approximation in field theory abstract we first discuss the strong coupling expansion in 4 d theory and quantum electrodynamics in a d dimensional euclidean space in a formal representation for the schwinger functional we treat the gaussian part of the action as a perturbation with respect to the remaining terms in this way we develop a perturbative expansion around the ultra local model where fields defined at different points of euclidean space are decoupled we examine the singularities of the strong coupling perturbative expansion analysing the analytic structure of the zero dimensional generating functions in the coupling constant complex planes we also discuss the ultra local generating functional in a non polynomial model in field theory defined by the following interaction lagrangian density l ii g 1 g 2 g 1 cosh g 2 x 1 finally we use the strong coupling perturbative expansion to compute the renormalized vacuum energy of the strongly coupled 4 d theory assuming that the scalar field is defined in a region bounded by two parallel hyperplanes where we are imposing dirichlet dirichlet boundary conditions

geometric mean and triangles inscribed in a semicircle in banach spaces we consider the triangles with vertices x x and y where x y are points on the unit sphere of a normed space using the geometric means of the variable lengths of the sides of these triangles we define two geometric constants for banach spaces these constants are closely related to the modulus of convexity of the space under consideration and they seem to represent a useful tool to estimate the exact values of the james and jordan von neumann constants of some banach spaces

a note on geometrical properties of banach spaces using ψ direct sums abstract let x be a banach space and a continuous convex function on 0 1 satisfying certain conditions let x x be the direct sum of x in this note we characterize the strict convexity uniform convexity and uniformly non squareness of banach spaces using direct sums which extends the well known characterization of these spaces

non squareness properties of orlicz spaces equipped with the p amemiya norm abstract this paper is a continuation of the studies from cui et al 2008 7 and cui et al 2009 12 non squareness uniform non squareness locally uniform non squareness of orlicz spaces equipped with the p amemiya norm are studied criteria for these three properties in the orlicz spaces l p are given in the most general case of orlicz function and for all 1 p

absolute norms on cn abstract in this paper we study the absolute normalized norms on c n we show that the set of all absolute normalized norms on c n is in one to one correspondence with the set n of all continuous convex functions on n with some suitable conditions where n s1 sn 1 r n 1 s1 s2 sn 1 1 si 0 1 i n 1 as some applications we show that an absolute norm on c n is strictly convex if and only if the corresponding function on n is strictly convex further we consider the von neumann jordan constant of c n with an absolute normalized norm

borel summability of the 1 n expansion for then vector o n non linear σ models we construct an analytic interpolation in 1 n for then vector o n non linear models withn component fields on a lattice this interpolation valid at sufficiently high temperatures extends over a large domain in the complex plane containing the half plane re 1 n 0 we use this result to show that the 1 n expansion of the free energy density and of the correlation functions is borel summable in the thermodynamic limit and at high temperature

construction of a non trivial planar field theory with ultraviolet stable fixed point we study a 4 4 planar euclidean quantum field theory with propagator 1 p 2 2 0 with the help of the tree expansion of gallavotti and nicolo 1 this non renormalizable theory is shown to have a non trivial ultraviolet stable fixed point at negative coupling constant the vicinity of the fixed point is discussed

extremal structure of the set of absolute norms on r2 and the von neumann jordan constant abstract the set of all absolute normalized norms on r 2 denoted by an 2 and the set of all convex functions on 0 1 satisfying max 1 t t t 1 for t 0 1 denoted by 2 are identified by a one to one correspondence t 1 t t for t 0 1 the set an 2 has a convex structure which is isomorphic to that of 2 in this paper we determine the set of all extreme points of an 2 by considering the set 2 moreover we will give the von neumann jordan constant of r 2 when is an extreme point of an 2

on the local borel transform of perturbation theory we prove existence of the local borel transform for the perturbative series of massive varphi 4 4 theory as compared to previous proofs in the literature the present bounds are much sharper as regards the dependence on external momenta they are explicit in the number of external legs and they are obtained quite simply through a judiciously chosen induction hypothesis applied to the wegner wilson polchinski flow equations we pay attention not to generate an astronomically large numerical constant for the inverse radius of convergence of the borel transform

complex strict convexity of absolute norms on cn and direct sums of banach spaces abstract we show that an absolute normalized norm on c 2 is complex strictly convex if and only if the associated convex function on 0 1 satisfies t max 1 t t for all 0 t 1 using this result we characterize when the direct sum x y of the complex banach spaces x and y is complex strictly convex and complex uniformly convex a characterization of complex strict convexity of c n for n 2 equipped with an absolute normalized norm is also given

some properties concerning milman s moduli abstract in this paper some properties concerning milman s moduli j t x and s t x including equivalent representations upper and lower bounds as well as relationship between some geometric properties and these two moduli are studied in addition some sufficient conditions for the fixed point property are presented

the lipatov argument for φ 3 4 perturbation theory we extend to 3 4 the work of s breen on the leading behavior at large order of 2 4 perturbation theory using a phase space expansion to obtain new estimates on the high energy behavior of 3 4 feynman graphs and a rigorous semiclassical expansion we prove that the radius of convergence of the borel transform of the pertubative series for 3 4 euclidean field theory is the one computed by the lipatov method

some inequalities concerning the james constant in banach spaces abstract let a 2 x be the constant introduced by baronti casini and papini this paper discusses the constant a 2 x and states an estimate a 2 x 1 j x 1 in terms of the james constant the estimate enables us to improve an inequality between the james and von neumann jordan constants

dimensional regularization and renormalization of qed we give an space definition of dimensional regularization suited to the tree expansion method of renormalization we apply the dimensionally regularized tree expansion to qed obtaining sharp bounds on the size of a renormalized graph subtractions are made with the lagrangian counterterms of the tree expansion not by minimal subtraction techniques and so do not entail a knowledge of the meromorphic structure of a graph as a function of dimension this renormalization procedure respects the ward identities and the counterterms required are gauge invariant

isosystolic inequalities and the topological expansion for random surface and matrix models using the isosystolic inequalities on riemann surfaces we prove that for many random surface or matrix models the radius of convergence of the perturbative series at fixed genus is independent of the genus this result applies for instance to the dynamically triangulated random surface model in any dimension or to many matrix models with regular propagators in the superrenormalizable domain for instance 3 in dimensiond 6 lambda phi 4 sqrt lambda phi 3 in dimensiond 4 and various otherp 2 models in particular all those containing an odd power of we hope that this result is a first step towards a more rigorous understanding of the genus dependence of surface models or of quantum gravity coupled with matter fields

renormalization in the complete mellin representation of feynman amplitudes the feynman amplitudes are renormalized in the formalism of the cm representation this mellin barnes type integral representation previously introduced for the study of asymptotic behaviours is shown to have the following interesting property in contrast with the usual subtraction procedures the renormalization leaves the cm integrand unchanged and only results into translations of the integration path the explicit cm representation of the renormalized amplitudes is given in addition the dimensional regularization and the extension to spinor amplitudes are sketched

perturbation theory and non renormalizable scalar fields we study how to set up systematic summation rules that could permit us to interpret the divergent expressions arising in the perturbation theory of p d when one does not allow any renormalization besides the usual coupling constants mass and wave function renormalizations

on a new geometric constant related to the von neumann jordan constant abstract the von neumann jordan constant c nj x is computed for x being l 2 l 1 and l l 1 space by introducing a new geometric constant x t these partly give an answer to an open question posed by kato et al some basic properties of this new coefficient are investigated moreover we obtain a new class of banach spaces with uniform normal structure

a renormalization group proof of perturbative renormalizability this paper presents a proof of bounds on the renormalized perturbation expansion of the euclidean 4 4 theory its aim is partly pedagogical by combining the insights and techniques of numerous authors it is now possible to define the perturbation expansion and bound it in a very few pages the present version is based on the renormalized tree expansion adapted to the continuous renormalization group all detailed results are proved by induction on the size of the tree the continuous rg version presented here has one big advantage over the discrete rg version discussed elsewhere in the continuous version a tree has a more restrictive structure there is a one to one correspondence between forks of the tree and lines of feynman graphs this extra structure eliminates the need to introduce feynman graphs in the first place it also reduces the number of cases to be analyzed at a given inductive step and simplifies the combinatorical estimates

the t hooft reparametrization respects borel summability in a renormalizable field theory with one coupling constant one may redefine the coupling in the sense of formal power series such that the function in the new coupling consists of the first two terms only it is shown that this change of coupling is borel summable if the original function was borel summable

construction and borel summability of planar 4 dimensional euclidean field theory we use the methods of 1 to show that the planar part of the renormalized perturbation theory for 4 4 euclidean field theory is borel summable on the asymptotically free side of the theory the borel sum can therefore be taken as a rigorous definition of then limit of a massiven n matrix model with a trg 4 interaction hence with wrong sign ofg our construction is relevant for a solution of the ultra violet problem for planar qcd we also propose a program for studying the structure of the renormalons singularities within the planar world

normal structure and the generalized james and zbăganu constants abstract we present several sufficient conditions for normal structure of a banach space in terms of the generalized james von neumann jordan zb ganu constants and the coefficient of weak orthogonality of sims our results significantly improve many known results in the literatures a negative answer is given to the question of llorens fuster e llorens fuster zbganu constant and normal structure fixed point theory 9 2008 159 172

extremal structure of absolute normalized norms on r2 and the james constant abstract we denote by an2 the set of all absolute normalized norms on r 2 the set an2 has a convex structure with respect to the usual operation in this paper we calculate the james constant of r 2 when is an extreme point of an2

existence uniqueness and stability of solutions of generalized tikhonov phillips functionals abstract the tikhonov phillips method is widely used for regularizing ill posed inverse problems mainly due to the simplicity of its formulation as an optimization problem the use of different penalizers in the functionals associated to the corresponding optimization problems has originated a variety of other methods which can be considered as variants of the traditional tikhonov phillips method of order zero such is the case for instance of the tikhonov phillips method of order one the total variation regularization method etc in this article we find sufficient conditions on the penalizers in generalized tikhonov phillips functionals which guarantee existence uniqueness and stability of the minimizers the particular cases in which the penalizers are given by the bounded variation norm by powers of seminorms and by linear combinations of powers of seminorms associated to closed operators are studied several examples are presented and a few results on image restoration are shown

on james and von neumann jordan constants and sufficient conditions for the fixed point property abstract in this paper we prove that a banach space x and its dual space x have uniform normal structure if c nj x 1 3 2 the garcia falset coefficient r x is estimated by the c nj x constant and the weak orthogonality coefficient introduced by b sims finally we present an affirmative answer to a conjecture by l maligranda concerning the relation between the james and c nj x constants for a banach space

the ptolemy and zbăganu constants of normed spaces abstract in every inner product space h the ptolemy inequality holds the product of the diagonals of a quadrilateral is less than or equal to the sum of the products of the opposite sides in other words x y z w x z y w z y x w for any points w x y z in h it is known that for each normed space x there exists a constant c such that for any w x y z x we have x y z w c x z y w z y x w the smallest such c is called the ptolemy constant of x and is denoted by c p x we study the relationships between this constant and the geometry of the space x and hence with metric fixed point theory in particular we relate the ptolemy constant c p to the zb ganu constant c z and prove that if x is a banach space with c z x 1 3 2 then x has uniform normal structure and therefore the fixed point property for nonexpansive mappings we derive general lower and upper bounds for both c p and c z and calculate the precise values of these two constants for several normed spaces we also present a number of conjectures and open problems

the fixed point property in banach spaces with the nus property abstract in this paper we show that the weak nearly uniform smooth banach spaces have the fixed point property for nonexpansive mappings

rotundity structure of local nature for generalized orlicz lorentz function spaces abstract criteria for extreme points and rotund points in generalized orlicz lorentz function spaces which were introduced in foralewski 2011 27 are given some examples show that in these spaces the notion of rotund point is essentially stronger than the notion of extreme point finally the criteria obtained in this paper are interpreted in the case of classical orlicz lorentz spaces results of this paper are related to the results from carothers et al 1992 9 kaminska 1990 4 foralewski et al 2008 26

bounds on renormalized feynman graphs we prove two bounds on the value of renormalized euclidean feynman graphs one is a relatively crude but widely applicable bound the other a finer bound applicable to 4 4 like models

local borel summability of euclidean 311 1311 1311 1a simple proof via differential flow equations it is shown how the differential flow equation or equivalently the continous renormalization group method can be employed to give an astonishingly easy proof of the local borel summability of the renormalized perturbative euclidean massive 44

bases and comparison results for linear elliptic eigenproblems abstract this paper describes some results about the construction and comparison of sequences of eigenvalues and eigenvectors of a pair a m of continuous symmetric bilinear forms on a real hilbert space v the results are used to describe the properties of some non standard self adjoint linear elliptic eigenproblems on h 1 where is a nice bounded region in r n n 2 these include eigenproblems with robin type boundary conditions steklov eigenproblems and problems where the eigenvalue appears in both the equation and the boundary conditions different variational principles for the eigenvalues and eigenvectors are introduced and convex analysis is used both minimax and maximin characterizations of higher eigenvalues are described various orthogonal decompositions are described and criteria for the eigenfunctions to be orthogonal bases of specific subspaces are found comparison results for the eigenvalues of different pairs of bilinear forms are proved finally these results are used to obtain spectral formulae for weak solutions of parametrized linear systems

von neumann jordan constant of absolute normalized norms on c2 abstract we determine and estimate the von neumann jordan constant of absolute normalized norms on c 2 by means of their corresponding continuous convex functions on 0 1 this provides many new interesting examples including those of non lp type as well as some previous ones it is also shown that all such norms are uniformly non square except l1 and l norms

error estimate for godunov approximation of locally constrained conservation laws we consider a model of traffic flow with unilateral constraint on the flux introduced by colombo and goatin j differential equations 234 2007 pp 654 675 for which the convergence of numerical approximation using monotone finite volume schemes has been performed by andreianov goatin and seguin numer math 115 2010 pp 609 645 we derive for this problem a new rm bv estimate and make use of it to provide an error estimate for the godunov approximation of the problem of order h 1 3 that is improved into the optimal order h 1 2 under a reasonable assumption numerical experiments are then provided to illustrate the optimality of the result

a lipatov bound for φ 4 4 euclidean field theory we bound the large order behavior of these pieces of the renormalized perturbation expansion for 4 4 which do not contain renormalons 1 the bound we obtain has the form of the leading asymptotic behavior computed by the lipatov method with the exact value of the lipatov constant therefore this paper is a step towards the rigorous study of the large order behavior of 4 4 and towards a proof of existence of the first renormalon singularity which should prevent the theory from being borel summable using the results of this paper and the techniques of 15 one can for instance improve 17 the estimate 18 on the finiteness of the radius of convergence of the borel transform of renormalized 4 4 and obtain that this radius is at least the exact value conjectured in 1

leading large order asymptotics for φ4 2 perturbation theory we develop a rigorous semiclassical expansion to compute the radius of convergence of the borel transform for the pressure in 4 2 field theory this result gives a partial justification for the lipatov method of finding large order perturbation theory asymptotics in quantum field theory

analytic regularization of the ψiψi d2 model at finite temperature and density simultaneously using the dimensional and analytic regularization methods we reexamine the gross neveu model at finite temperature and density chemical potential in a d dimensional space time the regularized effective potential is presented at the 1 n large n approximation it is found that in d 3 the effective potential is finite

on the convergence of planar diagram expansions renormalizable quantum field theories whose perturbation expansions are described by planar feynman diagrams only such as su gauge theory are considered in 4 dimensional euclidean space for studying asymptotic properties of the perturbation series one might wish to isolate first all those planar diagrams that do not contain any ultraviolet divergent subgraphs in this paper it is proved that this infinite set of diagrams when summed converges within a finite radius of convergence for the coupling constant

laplacian eigenproblems on product regions and tensor products of sobolev spaces abstract characterizations of eigenvalues and eigenfunctions of the laplacian on a product domain p 1 2 are obtained when zero dirichlet robin or neumann conditions are specified on each factor then the eigenfunctions on p are precisely the products of the eigenfunctions on the sets 1 2 separately there is a related result when steklov boundary conditions are specified on 2 these results enable the characterization of h 1 p and h 0 1 p as tensor products and descriptions of some orthogonal bases of the spaces a different characterization of the trace space of h 1 p is found

local existence of the borel transform in euclidean massless φ 4 4 we extend the methods of 1 to prove large order estimates on the renormalized feynman amplitudes of massless 4 4 euclidean field theory at non exceptional momenta the borel transform of the perturbative series is analytic in a disk centered at the origin of the complex plane this result is a step towards the rigorous investigation of the infra red singularities in the borel plane for theories containing massless particles like the gauge theories

dual of two dimensional lorentz sequence spaces abstract in m kato and l maligranda on james and jordan von neumann constants of lorentz sequence spaces j math anal appl 258 2001 457 465 it is an open problem to compute the james constant of the dual space of two dimensional lorentz sequence space d 2 w q in this paper we shall determine the dual norm of d 2 w q and completely compute the james constant of d 2 w q

on the calculation of the james constant of lorentz sequence spaces abstract in m kato l maligranda on james and jordan von neumann constants of lorentz sequence spaces j math anal appl 258 2001 457 465 the james constant of the 2 dimensional lorentz sequence space d 2 q is computed in the case where 2 q it is an open problem to compute it in the case where 1 q 2 in this paper we completely determine the james constant of d 2 q in the case where 1 q 2

bounds on completely convergent euclidean feynman graphs letg be a euclidean feynman graph containingl g lines we prove that ifg has massive propagators and does not contain any divergent subgraphs its value is bounded bykl g we also prove the infrared analogue of this bound

the equations for the moduli space of n points on the line a central question in invariant theory is that of determining the relations among invariants geometric invariant theory git quotients come with a natural ample line bundle and hence often a natural projective embedding this question translates to determining the equations of the moduli space under this embedding this article deals with one of the most classical quotients the space of ordered points on the projective line we show that under any weighting of the points this quotient is cut out scheme theoretically by a particularly simple set of quadric relations with the single exception of the segre cubic threefold the space of six points with equal weight we also show that the ideal of relations is generated in degree at most four and we give an explicit description of the generators if all the weights are even e g in the case of equal weight for odd n then we show that the ideal of relations is generated by quadrics

on the james constant and b convexity of cesaro and cesaro orlicz sequence spaces abstract the classical james constant and the nth james constants which are measure of b convexity for the cesaro sequence spaces ces p and the cesaro orlicz sequence spaces ces m are calculated these investigations show that ces p ces m are not uniformly non square and even they are not b convex therefore the classical cesaro sequence spaces ces p are natural examples of reflexive spaces which are not b convex moreover the james constant for the two dimensional cesaro space ces 2 2 is calculated

construction and borel summability of infrared φ 4 4 by a phase space expansion we construct the thermodynamic limit of the critical massless 4 model in 4 dimensions with an ultraviolet cutoff by means of a partly renormalized phase space expansion this expansion requires in a natural way the introduction of effective or running constants and the infrared asymptotic freedom of the model i e the decay of the running coupling constant plays a crucial role we prove also that the correlation functions of the model are the borel sums of their perturbation expansion

convexity conditions and normal structure of banach spaces we prove that f convexity the property dual to p convexity of kottman implies uniform normal structure moreover in the presence of the worth property normal structure follows from a weaker convexity condition than f convexity the latter result improves the known fact that every uniformly nonsquare space with the worth property has normal structure

geometric analysis of φ4 fields and ising models parts i and ii we provide here the details of the proof announced in 1 that ind 4 dimensions the even 4 euclidean field theory with a lattice cut off is inevitably free in the continuum limit in the single phase regime the analysis is nonperturbative and is based on a representation of the field variables or spins in ising systems as source sink creation operators in a system of random currents which may be viewed as the mediators of correlations in this dual representation the onset of long range order is attributed to percolation in an ensemble of sourceless currents and the physical interaction in the 4 field and other aspects of the critical behavior in ising models are directly related to the intersection properties of long current clusters an insight into the criticality of the dimensiond 4 is derived from an analogy foreseen by k symanzik with the intersection properties of paths of brownian motion other results include the proof that in certain respect the critical behavior in ising models is in exact agreement with the mean field approximation in high dimensionsd 4 but not in the low dimensiond 2 for which we establish the universality of hyperscaling

regularized perimeter for topology optimization the perimeter functional is known to oppose serious difficulties when it has to be handled within a topology optimization procedure in this paper a regularized perimeter functional mbox per varepsilon defined for two and three dimensional domains is introduced on one hand the convergence of mbox per varepsilon to the exact perimeter when varepsilon tends to zero is proved on the other hand the topological differentiability of mbox per varepsilon for varepsilon 0 is analyzed these features lead to the design of a topology optimization algorithm suitable for perimeter dependent objective functionals several numerical results illustrate the method

nonlinear stochastic partial differential equations with singular diffusivity and gradient stratonovich noise abstract we study existence and uniqueness of a variational solution in terms of stochastic variational inequalities svi to stochastic nonlinear diffusion equations with a highly singular diffusivity term and multiplicative stratonovich gradient type noise we derive a commutator relation for the unbounded noise coefficients in terms of a geometric killing vector condition the drift term is given by the total variation flow respectively by a singular p laplace type operator we impose nonlinear zero neumann boundary conditions and precisely investigate their connection with the coefficient fields of the noise this solves an open problem posed in barbu et al 2013 7 and barbu and rockner 2015 10

banach space properties sufficient for normal structure in this paper we establish lower bounds for the weakly convergent sequence coefficient wcs x of a banach space x in terms of some well known moduli and coefficients by mean of these bounds we identify several properties of geometrical nature which imply normal structure we show that these properties are strictly more general than other previously known sufficient conditions for normal structure

sufficient conditions for uniform normal structure of banach spaces and their duals in this paper we present some sufficient conditions for the uniform normal structure of banach spaces and their dual spaces more precisely many known conditions implying the uniform normal structure of banach spaces are shown to imply uniform normal structure of their dual spaces as well

on the stability of some groups of formal diffeomorphisms by the birkhoff decomposition abstract let g be the group of one parameter identity tangent diffeomorphisms on the line whose coefficients are formal laurent series in the parameter e with a pole of finite order at 0 it is well known that the birkhoff decomposition can be defined in such a group we investigate the stability of the birkhoff decomposition in subgroups of g and give a formula for this decomposition these results are strongly related to renormalization in quantum field theory since it was proved by a connes and d kreimer that after dimensional regularization the unrenormalized effective coupling constants are the image by a formal identity tangent diffeomorphism of the coupling constants of the theory in the massless 6 3 theory this diffeomorphism is in g and its birkhoff decomposition gives directly the bare coupling constants and the renormalized coupling constants

on convexity properties of ψ direct sums of banach spaces the direct sum of banach spaces is strictly convex respectively uniformly convex locally uniformly convex uniformly convex in every direction if each of the banach spaces are strictly convex respectively uniformly convex locally uniformly convex uniformly convex in every direction and the corresponding norm is strictly convex

some geometric measures of spheres in banach spaces in this paper we first give relations between pythagorean parameters and other well known parameters the coefficient of weak orthogonality james and von neumann jordan constants consequently some known results in j gao on the generalized pythagorean parameters and the applications in banach spaces discrete contin dyn syst ser b 8 3 2007 557 567 j gao on some geometric parameters in banach spaces j math anal appl 344 2007 114 122 a jimenez melado e llorens fuster s saejung the von neumann jordan constant weak orthogonality and normal structure in banach spaces proc am math soc 134 2006 355 364 are deduced and strengthened secondly we present several sufficient conditions for a banach space and its dual to have normal structure finally some open questions posed at the end of gao 2007 are answered in the negative

a renormalizable field theory the massive gross neveu model in two dimensions the euclidean massive gross neveu model in two dimensions is just renormalizable and asymptotically free thanks to the pauli principle bare perturbation theory with an ultra violet cut off and the correct ansatz for the bare mass is convergent in a disk whose radius corresponds by asymptotic freedom to a small finite renormalized coupling constant therefore the theory can be fully constructed in a perturbative way it satisfies the o s axioms and is the borel sum of the renormalized perturbation expansion of the model

rigorous construction of planar diagram field theories in four dimensional euclidean space asymptotically free quantum field theories with planar feynman diagrams such as su gauge theory are considered in 4 dimensional euclidean space it is shown that if all particles involved have non vanishing masses and if the coupling constant s org2 are small enough crit then an absolutely convergent procedure exists to obtain green functions that uniquely solve the dyson schwinger equations