eigenvalues of elliptic boundary value problems with an indefinite weight function on etudie les problemes aux valeurs propres elliptiques autoadjoints au r x u dans un ensemble ouvert r k a est un operateur positif d ordre 2m et le poids r est une fonction qui change de signe dans et peut etre discontinue on determine le comportement asymptotique des valeurs propres

the similarity problem for j nonnegative sturm liouville operators abstract sufficient conditions for the similarity of the operator a 1 r x d 2 d x 2 q x with an indefinite weight r x sgn x r x are obtained these conditions are formulated in terms of titchmarsh weyl m coefficients sufficient conditions for the regularity of the critical points 0 and of j nonnegative sturm liouville operators are also obtained this result is exploited to prove the regularity of 0 for various classes of sturm liouville operators this implies the similarity of the considered operators to self adjoint ones in particular in the case r x sgn x and q l 1 r 1 x d x we prove that a is similar to a self adjoint operator if and only if a is j nonnegative the latter condition on q is sharp i e we construct q 1 l 1 r 1 x d x such that a is j nonnegative with the singular critical point 0 hence a is not similar to a self adjoint operator for periodic and infinite zone potentials we show that j positivity is sufficient for the similarity of a to a self adjoint operator in the case q 0 we prove the regularity of the critical point 0 for a wide class of weights r this yields new results for forward backward diffusion equations

inverse spectral problems for differential pencils on the half line with turning points the inverse spectral problem of recovering pencils of second order differential operators on the half line with turning points is studied we establish properties of the spectral characteristics give a formulation of the inverse problem prove a uniqueness theorem and provide a constructive procedure for the solution of the inverse problem

boundary and initial boundary value problems for separable backward forward parabolic problems a backward forward parabolic equation is considered in a strip which is infinite in the timelike direction with boundary conditions on the sides of the strip the unique bounded solution of the problem is given explicitly by separation of variables in addition a similar problem in a semi infinite strip is treated with initial data at the end of the strip it is shown that the solution can be represented arbitrarily closely in the maximum norm by a sum of functions obtain by separation of variables

inverse spectral problems for left definite sturm liouville equations with indefinite weight abstract inverse sturm liouville problems with indefinite weight are considered theorems analogous to those of both hochstadt and gelfand levitan are proved as a sample result under suitable symmetry conditions we show that half of one spectrum suffices to determine the potential function uniquely

elliptic eigenvalue problems with eigenparameter dependent boundary conditions abstract let a be a uniformly elliptic second order linear operator on a smooth bounded domain r n we study the eigenvalue problem au u subject to boundary conditions b0u b1u on where bj are linear boundary operators the problem is recast in the form a u u in a hilbert or krein space and results are given on the location and type of the spectrum full and half range completeness and regularity of critical points

indefinite sturm liouville problems and half range completeness where the function h changes sign on i such problems occur in certain physical models particularly in transport theory and statistical physics see 2 9 11 131 and references therein as for the standard eigenvalue problem it is true under quite general conditions and not difficult to prove that there is a set of eigenfunctions un which is complete in an appropriate hilbert space of functions this is known as full range completeness for the physical problems the question of interest is generally that of half range completeness to formulate this we set

abstract time dependent transport equations abstract we consider the abstract time dependent linear transport equation as an initial boundary value evolution problem in the banach spaces lp 1 p

elliptic problems involving an indefinite weight we consider a selfadjoint elliptic eigenvalue problem which is derived formally from a variational problem of the form lu a o x u in q b1u 0 on f j 1 m where l is a linear elliptic operator of order 2m defined in a bounded open set q c rn n 2 with boundary f the bj are linear differential operators defined on f and w is a real valued function assuming both positive and negative values for our problem we prove the completeness of the eigenvectors and associated vectors in two function spaces which arise naturally in such an indefinite problem we also establish some results concerning the eigenvalues of the problem which complement the known results and investigate the structure of the principal subspaces

half range solutions of indefinite sturm liouville problems abstract for diffusion equations of indefinite sturm liouville type we develop two equivalent methods of constructing explicit representations for the solutions the first method is based on an eigenfunction expansion whereas the second uses a wiener hopf type integral equation and factorization some illustrative examples are worked out

space like loxodromes on rotational surfaces in minkowski 3 space abstract we find all space like loxodromes on rotational surfaces which have space like meridians or time like meridians respectively by using a relevant lorentzian angle in minkowski 3 space to understand loxodromes better we draw some pictures of them via mathematica computer program

optimal unidirectional error detecting correcting codes in this correspondence a class of t error correcting and multiple unidirectional error detecting systematic codes is presented these codes are significantly more efficient than the earlier codes the efficiency of these codes approaches the efficiency of the bch codes asymptotically furthermore it is shown that these codes can be easily decoded also in this correspondence we have presented a generalization of berger codes over zq these new codes are also shown to be optimal

stability of stationary transport equations with accretive collision operators abstract in this paper we consider transport equations with accretive collision operators we characterize when the equation has a unique solution and show that in this case the solution is stable under small perturbations of the collision operator and the initial value in one case in which there is more than one solution we show how to make a special selection of a solution which is then stable again under small perturbations of both the collision operator and the initial value the results obtained here parallel those obtained earlier for the case where the collision operator is positive semidefinite

half range completeness for the fokker planck equation half range completeness theorems are proved for eigenfunctions associated to the one dimensional fokker planck equation in a semi infinite medium existence and uniqueness results for perfectly absorbing partially absorbing and purely specularly reflecting boundary conditions are deduced for the stationary and time dependent problems similar results are obtained for a slab geometry

half range completeness for the fokker planck equation with an external force this paper deals with a generalization of a classical result obtained by r beals and v protopopescu for the fokker planck equations to the case in which a constant external force is present

the similarity problem for indefinite sturm liouville operators and the help inequality abstract we study two problems the first one is the similarity problem for the indefinite sturm liouville operator a sgn x d w d x d r d x acting in l w 2 b b it is assumed that w r l loc 1 b b are even and positive a e on b b the second object is the so called help inequality 0 b 1 r f d x 2 k 2 0 b f 2 w d x 0 b 1 w 1 r f 2 w d x where the coefficients w r l loc 1 0 b are positive a e on 0 b both problems are well understood when the corresponding sturm liouville differential expression is regular the main objective of the present paper is to give criteria for both the validity of the help inequality and the similarity to a self adjoint operator in the singular case namely we establish new criteria formulated in terms of the behavior of the corresponding weyl titchmarsh m functions at 0 and at as a biproduct of this result we show that both problems are closely connected namely the operator a is similar to a self adjoint one precisely if the help inequality with w r and r w is valid next we characterize the behavior of m functions in terms of coefficients and then these results enable us to reformulate the obtained criteria in terms of coefficients finally we apply these results for the study of the two way diffusion equation also known as the time independent fokker planck equation

a krein space approach to symmetric ordinary differential operators with an indefinite weight function on considere les proprietes spectrales du probleme differentiel l f 1 n p 0 f n n 1 n 1 p 1 f n 1 n 1 p n f rf sur un intervalle fini ou infini a b avec des coefficients reels localement sommables 1 p 0 p 1 p n r sous l hypothese que p 0 0 et que la fonction poids r change de signe sur a b

full and partial range eigenfunction expansions for sturm liouville problems with indefinite weights this article is concerned with eigenvalue problems of the form au tu in a hilbert space h where ais a selfadjoint positive operator generated by a second order sturm liouville differential expression and t a selfadjoint indefinite multiplicative operator which is one to one emphasis is on the full range and partial range expansionproperties of the eigenfunctions

partial range completeness and existence of solutions to two way diffusion equations separating variables to solve a two way diffusion equation leads to a nonstandard eigenvalue problem in one variable it is shown that the eigenfunctions having negative eigenvalues are complete on the part of the domain where initial conditions are imposed while those with positive eigenvalues are complete where final conditions are imposed the corresponding exponentially growing and exponentially decaying solutions may be used to expand arbitrary solutions on semi infinite intervals in the time variable a natural iterative procedure for obtaining solutions on finite intervals is shown to converge in some cases a linearly growing solution must also be taken into account

estimates on the non real eigenvalues of regular indefinite sturm liouville problems regular sturm liouville problems with indefinite weight functions may possess finitely many non real eigenvalues in this paper we prove explicit bounds on the real and imaginary parts of these eigenvalues in terms of the coefficients of the differential expression

position vector of a time like slant helix in minkowski 3 space in this paper position vector of a time like slant helix with respect to standard frame of minkowski space e31 is studied in terms of frenet equations first a vector differential equation of third order is constructed to determine position vector of an arbitrary time like slant helix in terms of solution we determine the parametric representation of the slant helices from the intrinsic equations thereafter we apply this method to find the representation of a time like salkowski and time like anti salkowski curves as examples of a slant helices by means of intrinsic equations moreover we present some new characterizations of slant helices and illustrate some examples of our main results

lym type inequalities for tec aued codes some lym type inequalities are introduced to obtain a relationship between the parameters of t error correcting all unidirectional error detecting codes of length n as an application of these inequalities new lower bounds on the redundancies of systematic tec aued codes are derived and an extensive table is given

on constant slope spacelike surfaces in 3 dimensional minkowski space abstract a spacelike surface in the minkowski 3 space is called a constant slope surface if its position vector makes a constant angle with the normal at each point on the surface in this work we study such surfaces and classify all of them

spectral properties of singular sturm liouville operators with indefinite weight sgn x we consider a singular sturm liouville expression with the indefinite weight sgnx to this expression there is naturally a self adjoint operator in some krein space associated we characterize the local definitizability of this operator in a neighbourhood of 1 moreover in this situation the point 1 is a regular critical point we construct an operator a sgnx id 2 dx 2 q with non real spectrum accumulating to a real point the obtained results are applied to several classes of sturm liouville operators