contractive type non self mappings on metric spaces of hyperbolic type abstract let x d be a metric space of hyperbolic type and k a nonempty closed subset of x in this paper we study a class of mappings from k into x not necessarily self mappings on k which are defined by the contractive condition 2 1 below and a class of pairs of mappings from k into x which satisfy the condition 2 28 below we present fixed point and common fixed point theorems which are generalizations of the corresponding fixed point theorems of ciric l b ciric quasi contraction non self mappings on banach spaces bull acad serbe sci arts 23 1998 25 31 l b ciric j s ume m s khan h k t pathak on some non self mappings math nachr 251 2003 28 33 rhoades b e rhoades a fixed point theorem for some non self mappings math japon 23 1978 457 459 and many other authors some examples are presented to show that our results are genuine generalizations of known results from this area

grassmann gaussian integrals and generalized star products in quantum scattering on networks there is a nonlinear composition rule for on shell scattering matrices which serves as a replacement for the multiplicative rule of transfer matrices valid in other physical contexts in this paper we show how this composition rule is obtained using berezin integration theory with grassmann variables

common fixed points for maps on cone metric space the purpose of this paper is to generalize and to unify fixed point theorems of das and naik ciric jungck huang and zhang on complete cone metric space

distribution theory for discontinuous test functions and differential operators with generalized coefficients investigation of the differential operators with the generalized coefficients having singular support on a disjoint set of points requires the consideration of the distribution theory with the set of discontinuous test functions such a distribution theory for test functions having discontinuity at one point is developed a four parameter family of schrodinger operators formed by the operators with singular potential singular metrics and singular gauge field is considered it is proved that this family of singular interactions describes all possible selfadjoint extensions of the second derivative operator defined on the functions vanishing in a neighbourhood of the point approximation by operators with smooth coefficients is discussed c 1996 academic press inc

the generalized star product and the factorization of scattering matrices on graphs in this article we continue our analysis of schrodinger operators on arbitrary graphs given as certain laplace operators in the present article we give the proof of the composition rule for the scattering matrices this composition rule gives the scattering matrix of a graph as a generalized star product of the scattering matrices corresponding to its subgraphs we perform a detailed analysis of the generalized star product for arbitrary unitary matrices the relation to the theory of transfer matrices is also discussed

hermitian symplectic geometry and the factorization of the scattering matrix on graphs hermitian symplectic spaces provide a natural framework for the extension theory of symmetric operators here we show that hermitian symplectic spaces may also be used to describe the solution to the factorization problem for the scattering matrix on a graph i e we derive a formula for the scattering matrix of a graph in terms of the scattering matrices of its subgraphs the solution of this problem is shown to be given by the intersection of a lagrange plane and a coisotropic subspace which in an appropriate hermitian symplectic space forms a new lagrange plane the scattering matrix is given by a distinguished basis to the lagrange plane using our construction we are also able to give a simple proof of the unitarity of the scattering matrix as well as provide a characterization of the discrete eigenvalues embedded in the continuous spectrum

sur quelques problemes de courbure scalaire abstract in this article we prove among other things some results about two problems which are the subject of announces these last decades 1 the compactness of the set of the solutions of the yamabe equation on a compact riemannian manifold 2 a generalization of a result of the author which is necessary to solve the yamabe problem when 2 n 6

on common fixed point theorems for non self hybrid mappings in convex metric spaces abstract in this paper we introduce the concept of a contractive type non self mappings for a two pair of multi valued and single valued mappings in metric spaces and prove some results on coincidence and common fixed points in complete convex metric spaces our theorems generalize and improve the theorems of imdad and khan m imdad l khan some common fixed point theorems for a family of mappings in metrically convex spaces nonlinear anal theor 67 9 2007 2717 2726 m imdad l khan fixed point theorems for a family of hybrid pairs of mappings in metrically convex spaces fixed point theory appl 2005 3 2005 281 294 and of assad n a assad fixed point theorems for set valued transformations on compact sets boll un math ital 4 1973 1 7 and several others theorems to accomplish that we shall use slightly improved version of methods of proofs usually used in proving fixed point theorems for non self mappings an example is constructed to show that our results are genuine generalizations of the above mentioned results

four parameter point interaction in 1d quantum systems the author constructs a four parameter point interaction for a nonrelativistic particle moving on a line as the limit of a short range interaction with a range tending toward zero for particular choices of the parameters one can obtain a delta interaction or the so called delta interaction the hamiltonian corresponding to the four parameter point interaction is shown to correspond to the four parameter self adjoint hamiltonian of the free particle moving on the line with the origin excluded

a single mode quantum transport in serial structure geometric scatterers we study transport in quantum systems consisting of a finite array of n identical single channel scatterers a general expression of the s matrix in terms of the individual element data obtained recently for potential scattering is rederived in this wider context it shows in particular how the band spectrum of the infinite periodic system arises in the limit n we illustrate the result on two kinds of examples the first are serial graphs obtained by chaining loops or t junctions another example concerns geometric scatterers where the individual element consists of a surface with a pair of leads we show that apart from the resonances coming from the decoupled surface eigenvalues such scatterers exhibit the high energy behavior typical for the interaction for the physically interesting couplings

rhoades type fixed point theorems for a pair of nonself mappings abstract using suitable conditions of weak commutativity we prove theorems for a pair of nonself mappings which generalize earlier results due to rhoades and assad et al some illustrative examples and applications are also discussed

a remark on discrete wave scattering we consider the spectral problem for the adjacency matrix of a discrete star graph composed of a compact cluster and a few semi infinite periodic leads attached based on the spectral properties of the adjacency matrix we develop the lax phillips scattering theory for the corresponding discrete wave equation

a factorization of the scattering matrix for the schrodinger equation and for the wave equation in one dimension for the one dimensional schrodinger equation with a potential decaying at both ends of the real axis the scattering matrix of the potential is given explicitly in terms of the scattering matrices corresponding to the fragments of this potential a similar result also holds for the wave equation in a nonhomogeneous nondispersive medium where the wave speed has the same asymptotics at both ends of the real line

blow up phenomena for the yamabe equation it is well known that the pde 1 has at least one positive solution for any choice of m g if n 6 and m g is not locally conformally flat this follows from results of t aubin 3 the remaining cases were solved by r schoen using the positive mass theorem 16 solutions to 1 are not usually unique as an example consider the product metric on 51 l x 5n 1 l if l is sufficiently small then the yamabe pde has a unique solution on the other hand there are many non minimizing solutions if l is large d pollack 14 has used gluing techniques to construct high energy solutions on more general background manifolds given any conformai class with positive yamabe constant and any positive integer iv there exists a new conformai class which is close to the original one in the c norm and contains at least n metrics of constant scalar curvature see 14 theorem 0 1 it is an interesting question whether the set of all solutions to the yamabe pde is compact in the c2 topology say a well known conjecture states that this should be true unless m p is conformally equivalent to the round sphere see 17 18 19 this conjecture has been verified in low dimensions and in the locally conformally flat case if m g is locally conformally flat compactness follows from work of r schoen 17 18 moreover schoen proposed a strategy for proving the conjecture in the non locally conformally flat case based on the pohozaev identity

inverse eigenvalue problems on directed graphs the differential operators id and d2 p are constructed on certain finite directed weighted graphs two types of inverse spectral problems are considered first information about the graph weights and boundary conditions is extracted from the spectrum of d2 second the compactness of isospectral sets for d2 p is established by computation of the residues of the zeta function

some new fixed point theorems in menger pm spaces with application to volterra type integral equation abstract we establish some fixed point theorems by introducing two new classes of contractive mappings in menger pm spaces first we prove our results for an type contractive mapping and then for a generalized type contractive mapping some examples and an application to volterra type integral equation are given to support the obtained results

green function approach for general quantum graphs we present a recursive prescription to calculate the exact green function for general quantum graphs for the closed case the expression for the poles of g which gives the individual eigenstates has the structure of a semiclassical formula where the sum over the periodic orbit is already performed as applications we discuss eigenstate localization for a three arm closed star and filter like mechanisms for transmission throughout an open trident graph

on the spectrum of the laplace operator of metric graphs attached at a vertex spectral determinant approach we consider a metric graph made of two graphs and attached at one point we derive a formula relating the spectral determinant of the laplace operator in terms of the spectral determinants of the two subgraphs the result is generalized to describe the attachment of n graphs the formulae are also valid for the spectral determinant of the schrodinger operator

on the number of states bound by one dimensional finite periodic potentials bound states and zero energy resonances of one dimensional finite periodic potentials are investigated by means of levinson s theorem for finite range potentials supporting no bound states a lower bound for the reduced time delay at threshold is derived

common fixed point theorems for non self mappings in metric spaces of hyperbolic type in this paper the concept of a pair of non linear contraction type mappings in a metric space of hyperbolic type is introduced and the conditions guaranteeing the existence of a common fixed point for such non linear contractions are established presented results generalize and improve some of the known results an example is constructed to show that our theorems are genuine generalizations of the main theorems of assad ciric khan et al rhoades and imdad and kumar one of the possible applications of our results is also presented

jump start in the analytic perturbation procedure for the friedrichs model for the friedrichs model obtained as a one dimensional perturbation of the orthogonal sum of the momentum and a finite hermitian matrix the scattering matrix is presented as s p i i m p 1 i i m p the rational nevanlinna class krein weyl function m is associated with the operator a and has poles at the eigenvalues of a it is proven that for any eigenvalue 0 of a there exists an intermediate operator which is constructed as a one dimensional perturbation of the orthogonal sum of the momentum and an appropriate one dimensional operator a solvable model which plays the role of an intermediate operator in the scattering problem to the pair the scattering matrix s0 to the pair is an analytic function of and the total scattering matrix to the pair can be factorized as a product where s 0 is the scattering matrix to the pair it is represented by a single blaschke factor with a pole and zero approaching 0 when 0 the non analytic factor describes creation of the resonance from the eigenvalue 0 of the operator a

fixed point theorems for multi valued contractions with w distance some fixed point theorems for a few nonlinear multi valued contraction mappings in complete metric spaces with w distance are proved the results presented in this paper generalize the recent results due to ciric 2009 3 feng and liu 2006 4 klim and wardowski 2007 8 latif and abdou 2011 12 and liu et al 2010 14 seven examples are given to explain our results

common fixed points for maps on metric space with w distance abstract the purpose of this paper is to generalize and to unify fixed point theorems of das and naik ciric jungck and ume in terms of a w distance on complete metric space

common fixed points for four maps in cone metric spaces the existence of coincidence points and common fixed points for four mappings satisfying generalized contractive conditions without exploiting the notion of continuity of any map involved therein in a cone metric space is proved these results extend unify and generalize several well known comparable results in the existing literature

pair of non self mappings and common fixed points we study quasi contraction type non self mappings on takahashi convex metric spaces and common fixed point theorems for a pair of maps results generalizing and unifying fixed point theorems of imdad and kumar das and naik jungck ciric ume khan and pathak and ciric are established

solution complete de la c0 compacite de l ensemble des solutions de l equation de yamabe abstract on a compact riemannian manifold v n g n 2 a long standing question is does the set of the solutions of the yamabe equation compact in c 0 there are three cases in the yamabe problem see aubin t aubin some nonlinear problems in riemannian geometry springer verlag new york 1998 according to the sign of the inf of the yamabe functional we prove the c 0 compactness of the set of the solutions of the yamabe equation except on the sphere in the positive case the only case which makes difficulties

on the inverse scattering problem on branching graphs the inverse scattering problem on branching graphs is studied the definition of the schrodinger operator on such graphs is discussed the operator is defined with real potentials with finite first momentum and using special boundary conditions connecting values of the functions at the vertices it is shown that in general the scattering matrix does not determine the topology of the graph the potentials on the edges and the boundary conditions uniquely

equivariant yamabe problem and hebey vaugon conjecture abstract in their study of the yamabe problem in the presence of isometry groups e hebey and m vaugon announced a conjecture this conjecture generalizes t aubin s conjecture which has already been proven and is sufficient to solve the yamabe problem in this paper we generalize aubin s theorem and we prove the hebey vaugon conjecture in dimensions less or equal to 37

fixed point theorems related to ciric s contraction principle abstract in this paper we prove fixed point theorems in a complete metric space using the concept of a w distance and more general contractive mapping than quasi contractive mapping these theorems improve fixed point theorems of kannan ciric and kada suzuki and takashi

kirchhoff s rule for quantum wires we formulate and discuss one particle quantum scattering theory on an arbitrary finite graph with n open ends and where we define the hamiltonian to be minus the laplace operator with general boundary conditions at the vertices this results in a scattering theory with n channels the corresponding on shell s matrix formed by the reflection and transmission amplitudes for incoming plane waves of energy e 0 is given explicitly in terms of the boundary conditions and the lengths of the internal lines it is shown to be unitary which may be viewed as the quantum version of kirchhoff s law we exhibit covariance and symmetry properties it is symmetric if the boundary conditions are real also there is a duality transformation on the set of boundary conditions and the lengths of the internal lines such that the low energy behaviour of one theory gives the high energy behaviour of the transformed theory finally we provide a composition rule by which the on shell s matrix of a graph is factorizable in terms of the s matrices of its subgraphs all proofs use only known facts from the theory of self adjoint extensions standard linear algebra complex function theory and elementary arguments from the theory of hermitian symplectic forms

an extension of lakzian rhoades results in the structure of ordered b metric spaces via wt distance with an application abstract in this present article we establish two new kinds of nonlinear contraction mappings to obtain fixed point results in the structure of ordered b metric space via wt distance in fact our presented results are extensions of recent theorems due to lakzian rhoades 2019 appl math comput and other existing classical results of fixed point theory furthermore we provide examples to show the validity of our new investigations as an application we apply our new findings to obtain solution of a matrix equation finally we verify the accuracy of our new results numerically

demonstration de la conjecture de la masse positive abstract on a compact riemannian manifold v n g n 2 when the conformal laplacian l is invertible we show under necessary hypotheses that if the green function g l of l is of the form here r d p q g l p q 1 n 2 n 1 r n 2 h p q with h p q bounded on v then lim r 0 r 1 n b p r h p q d q 0 applications to the positive mass conjecture and to the c 0 compactness of the set of the solutions of the yamabe equation

convergence of spectra of mesoscopic systems collapsing onto a graph abstract let m be a finite graph in the plane and let me be a domain that looks like the e fattened graph m exact conditions on the domain are given it is shown that the spectrum of the neumann laplacian on me converges when e 0 to the spectrum of an ode problem on m the presence of an electromagnetic field is also allowed considerations of this kind arise naturally in mesoscopic physics and other areas of physics and chemistry the results of the paper extend the ones previously obtained by j rubinstein and m schatzman

classifying the general family of 1d point interactions a scattering approach we propose a classification scheme for the complete family of 1d point interactions to do so we first review the solutions of the wavefunctions and green functions of the problem second we derive the exact time dependent propagators in such a way that we can write the expressions for the k s in a very compact form as they should such expressions do reduce to the known results in the literature according to the potential parameter values then we analyse in general terms how the different point interactions scatter off arbitrary initially localized wave packets finally we show that the physical features associated with the scattering process can be used to establish a classification procedure moreover these physical characteristics are directly related to the potential parameters leading to the many formulae for the k s as an application we present numerical calculations for gaussian wave packets

nodal statistics on quantum graphs it has been suggested that the distribution of the suitably normalized number of zeros of laplacian eigenfunctions contains information about the geometry of the underlying domain we study this distribution more precisely the distribution of the nodal surplus for laplacian eigenfunctions of a metric graph the existence of the distribution is established along with its symmetry one consequence of the symmetry is that the graph s first betti number can be recovered as twice the average nodal surplus of its eigenfunctions furthermore for graphs with disjoint cycles it is proven that the distribution has a universal form it is binomial over the allowed range of values of the surplus to prove the latter result we introduce the notion of a local nodal surplus and study its symmetry and dependence properties establishing that the local nodal surpluses of disjoint cycles behave like independent bernoulli variables

global bounds for the lyapunov exponent and the integrated density of states of random schrodinger operators in one dimension in this paper we prove an upper bound for the lyapunov exponent e and a two sided bound for the integrated density of states n e at an arbitrary energy e 0 of random schrodinger operators in one dimension these schrodinger operators are given by potentials of identical shape centred at every lattice site but with non overlapping supports and with randomly varying coupling constants both types of bounds only involve scattering data for the single site potential they show in particular that both e and n e e 1 2 decay at infinity at least like 1 e 1 2 as an example we consider the random kronig penney model

mathematical aspects of vacuum energy on quantum graphs we use quantum graphs as a model to study various mathematical aspects of the vacuum energy such as convergence of periodic path expansions consistency among different methods trace formulae versus method of images and the possible connection with the underlying classical dynamics in our study we derive an expansion for the vacuum energy in terms of periodic paths on the graph and prove its convergence and smooth dependence on the bond lengths of the graph for an important special case of graphs with equal bond lengths we derive a simpler explicit formula with minor changes this formula also applies to graphs with rational up to a common factor bond lengths the main results are derived using the trace formula we also discuss an alternative approach using the method of images and prove that the results are consistent this may have important consequences for other systems since the method of images unlike the trace formula includes a sum over special bounce paths we succeed in showing that in our model bounce paths do not contribute to the vacuum energy finally we discuss the proposed possible link between the magnitude of the vacuum energy and the type chaotic versus integrable of the underlying classical dynamics within a random matrix model we calculate the variance of the vacuum energy over several ensembles and find evidence that the level repulsion leads to suppression of the vacuum energy