a non oscillation theorem for the emden fowler equation ground states for semilinear elliptic equations with critical exponents abstract let be a ball centered at the origin in r n n 2 its boundary and 0 0 a given function this article is concerned with radial solutions of the boundary value problem u x u p 0 u 0 in u 0 on 1 radial solutions of 1 are functions u of the variable r x that satisfy the ordinary differential equation u n 1 r u r u p 0 2 it is shown that if p p where p is the critical sobolev exponent p n 2 n 2 then 2 is non oscillatory at the origin if there exists a 0 such that the function r r log 1 r is non decreasing near the origin the result is a corollary of a similar result for the emden fowler equation x t 2 1 g t x 1 2 0 3 where g is a given positive valued function and a positive constant the relation between the solutions of 2 and 3 is established via the transformations x t u r g t r where t n 2 r n 2 it is shown that 3 is nonoscillatory at infinity if there exists a 0 such that the function t g t log t is non increasing for all sufficiently large t the proof of this result constitutes the core of the article the result is of independent interest in the theory of the emden fowler equation and improves earlier oscillation results of nehari and chiou

the inverse eigenvalue problem for symmetric anti bidiagonal matrices abstract the inverse eigenvalue problem for real symmetric matrices of the form 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 is solved the solution is shown to be unique the problem is also shown to be equivalent to the inverse eigenvalue problem for a certain subclass of jacobi matrices

hermite biehler routh hurwitz and total positivity simple proofs of the hermite biehler and routh hurwitz theorems are presented the total nonnegativity of the hurwitz matrix of a stable real polynomial follows as an immediate corollary

operations on fuzzy ideals in this paper we give suitable definitions of the operations of l fuzzy ideals in a ring as intersection addition multiplication and residual division and we prove some fundamental properties of the operations analogous to those that hold for the operations of ordinary ideals see 3

on existence of oscillatory solutions of second order emden fowler equations abstract we study the second order emden fowler equation e y t a x y sgn y 0 0 where a x is a positive and absolutely continuous function on 0 let x a x x 3 2 1 and bounded away from zero we prove the following theorem if x l 1 0 where x min x 0 then eq e has oscillatory solutions in particular this result embodies earlier results by jasny kurzweil heidel and hinton chiou and erbe and muldowney

inverse spectral problems for structured pseudo symmetric matrices abstract inverse spectral problems for jacobi and periodic jacobi matrices with certain sign patterns are investigated necessary and sufficient conditions under which the problems are solvable are presented uniqueness results are also discussed algorithms to construct the solutions from the spectral data are provided and illustrative examples are given

on fuzzy ideals of a ring 1 abstract the aim of this paper is to study fuzzy ideals of a ring to characterise regular rings and noetherian rings by fuzzy ideals and to determine all fuzzy prime ideals of the ring z of integers

a nonoscillation theorem for superlinear emden fowler equations with near critical coefficients we are interested in the oscillatory behavior of solutions of the emden fowler equation y a x y 1y 0 1 where a x is a positive continuous function on 0 in the special case when the coefficient a x is a power of x i e a x x for some constant the value 3 2 plays a critical role the equation has both oscillatory and nonoscillatory solutions if while all solutions are nonoscillatory if 0 then all solutions are nonoscillatory in this paper this result is further extended to include a class of coefficients in which the above condition with log x can be replaced by loglog x or logloglog x and so on

fuzzy maximal radical and primary ideals of a ring we introduce the concepts of fuzzy maximal ideal the fuzzy radical of a fuzzy ideal and fuzzy primary ideal of a ring we show that a fuzzy left right ideal a of a ring r is a fuzzy maximal ideal if and only a 0 1 and a x r a x a 0 is a maximal left right ideal of r we also show that a fuzzy ideal a of a commutative ring r with unity is a fuzzy primary ideal of r if and only a 0 1 a is two valued and a is a primary ideal of r

asymptotic behavior of positive solutions of sublinear differential equations of emden fowler type this paper is concerned with asymptotic analysis of positive solutions of the second order nonlinear differential equation a x t q t f x t 0 where q a 0 is a continuous function which is regularly varying and f 0 0 is a continuous increasing function which is regularly varying of index c 0 1 an application of the theory of regular variation gives the possibility of determining precise information about the asymptotic behavior at infinity of intermediate solutions of eq a

the inverse eigenvalue problem for symmetric quasi anti bidiagonal matrices in this paper we construct the symmetric quasi anti bidiagonal matrix that its eigenvalues are given and show that the problem is also equivalent to the inverse eigenvalue problem for a certain symmetric tridiagonal matrix which has the same eigenvalues not only elements of the tridiagonal matrix come from quasi anti bidiagonal matrix but also the places of elements exchange based on some conditions

least squares solutions of quadratic inverse eigenvalue problem with partially bisymmetric matrices under prescribed submatrix constraints abstract the inverse eigenvalue problems play an important role in broad application areas such as system identification hopfield neural networks control design mass spring system and molecular spectroscopy this paper proposes an algorithm that yields a new method to efficiently and accurately compute the partially bisymmetric solutions m c k under prescribed submatrix constraints of the quadratic inverse eigenvalue problem m x 2 c x k x 0 the algorithm is developed based on the conjugate gradient normal equations residual minimizing cgnr method we discuss the convergence properties of the algorithm finally the performance of the algorithm is tested on two numerical examples and compared to the previous algorithm

fuzzy prime ideals of rings abstract the notions of fuzzy ideal and fuzzy prime ideal of a ring with truth values in a complete lattice satisfying the infinite meet distributive law are introduced which generalize the existing notions with truth values in the unit interval of real numbers a procedure to construct any fuzzy ideal from a family of ideals with certain conditions is established all fuzzy prime maximal ideals of a given ring are determined by establishing a one to one correspondence between fuzzy prime maximal ideals and the pairs p where p is a prime maximal ideal of the ring and is a prime element dual atom in the complete lattice

structured matrices continued fractions and root localization of polynomials we give a detailed account of various connections between several classes of objects hankel hurwitz toeplitz vandermonde and other structured matrices stietjes and jacobi type continued fractions cauchy indices moment problems total positivity and root localization of univariate polynomials along with a survey of many classical facts we provide a number of new results

self interlacing polynomials abstract we describe a new subclass of the class of real polynomials with real simple roots called self interlacing polynomials this subclass is isomorphic to the class of real hurwitz stable polynomials all roots in the open left half plane in the work we present basic properties of self interlacing polynomials and their relations with hurwitz and hankel matrices as well as with stiltjes type of continued fractions we also establish self interlacing analogues of the well known hurwitz and lienard chipart criterions for stable polynomials a criterion of hurwitz stability of polynomials in terms of minors of certain hankel matrices is established

some results on a galois connection between lattices of l fuzzy ideals in this paper first we present a cl semigroup structure on l fuzzy ideals and conclude that the set of all l fuzzy quasi ideals is a cl monoid with zero then we obtain a galois connection between two cl semigroups of l fuzzy ideals of homomorphic rings finally by using galois connections we give the concepts of contracted and extended l fuzzy ideals and some related results are given

fuzzy invariant subgroups and fuzzy ideals abstract the purpose of this paper is to introduce some basic concepts of fuzzy algebra as fuzzy invariant subgroups fuzzy ideals and to prove some fundamental properties in particular it will give a characteristic of a field by a fuzzy ideal

an inverse eigenvalue problem and an associated approximation problem for generalized k centrohermitian matrices a partially described inverse eigenvalue problem and an associated optimal approximation problem for generalized k centrohermitian matrices are considered it is shown under which conditions the inverse eigenproblem has a solution an expression of its general solution is given in case a solution of the inverse eigenproblem exists the optimal approximation problem can be solved the formula of its unique solution is given

on zero sector reducing operators abstract we prove a jensen disc type theorem for polynomials p r z having all their zeros in a sector of the complex plane this result is then used to prove the existence of a collection of linear operators t r z r z which map polynomials with their zeros in a closed convex sector arg z 2 to polynomials with zeros in a smaller sector arg z we therefore provide the first example of a zero sector reducing operator

a characterization of l fuzzy prime ideals abstract in this paper the concepts of a l fuzzy prime and a l fuzzy completely prime ideal are given and some fundamental lemmas are proved in particular bijections among some of the l fuzzy prime ideals of two homomorphic rings are constructed also a characterization of a l fuzzy prime ideal of a ring is given

a nonoscillation theorem for emden fowler equations abstract we study the second order emden fowler equation e y a x y 1 y 0 0 where a x is positive and absolutely continuous on 0 let x x 3 2 where is any positive number theorem let 1 if x satisfies a lim x x k 0 and b x dx then eq e is nonoscillatory

inverse spectral problem for pseudo jacobi matrices with partial spectral data in this paper we study a special kind of matrices which are pseudo jacobi matrices four inverse eigenvalue problems are discussed and the necessary and sufficient conditions are presented under which these problems are solvable the corresponding algorithms and some examples are given numerical results demonstrate that these methods are of practical utility

a nonoscillation theorem for sublinear emden fowler equations abstract consider the sublinear emden fowler equation e y a x y 1 y 0 0 1 and where a x is a positive continuous function on 0 define x x 3 2 a x we prove in this paper that if x is nonincreasing and lim x x 0 then equation e is nonoscillatory