the sharp conditions of the uniqueness for inverse nodal problems abstract in this paper we provide the sharp conditions of the uniqueness for inverse nodal sturm liouville problems defined on interval 0 1 with separated boundary conditions we prove that the potential and boundary parameters can be uniquely determined by a dense nodal subset contained on a 1 a 2 0 1 with 1 2 a 1 a 2 through two cases of a 1 0 and a 1 0 where in the latter case the nodal subset also need to be paired note that the dense nodal subset was required to be twin for both cases in the previous works

an equivalence classes model of fuzzy relational databases abstract the technique of employing sets of values for tuple components to express imprecision in relational databases was proposed by buckles and petry in their classic works on fuzzy relational databases in addition to providing an intuitively appealing scheme for representing fuzzy information the model of buckles and petry possesses several key properties of the classical relational model by employing finite scalar domains with similarity relations and special fuzzy number domains buckles and petry have demonstrated that the classical properties of uniqueness of tuple interpretations and well definedness of the relational algebra can be retained in the fuzzy relational database model the key to the preservation of these properties is the fact that scalar domains with similarity relations and the fuzzy number domains can be partitioned into equivalence classes however since equivalence classes can be constructed without assuming the existence of similarity relations or special fuzzy number domains it is desirable to generalize the fuzzy relational database model to one based only on equivalence classes in this work we show that the important properties of classical relational databases and of fuzzy relational databases are preserved in a generalized model built on equivalence relations on finite database domains further we generalize the notion of a functional dependency to the fuzzy relational model

on the equivalence of mceliece s and niederreiter s public key cryptosystems it is shown that mceliece s and niederreiter s public key cryptosystems are equivalent when set up for corresponding choices of parameters a security analysis for the two systems based on this equivalence observation is presented

stability of spiky solution of keller segel s minimal chemotaxis model abstract a huge volume of research has been done for the simplest chemotaxis model keller segel s minimal model and its variants yet some of the basic issues remain unresolved until now for example it is known that the minimal model has spiky steady states that can be used to model the important cell aggregation phenomenon but the stability of monotone spiky steady states was not shown in this paper we derive first formally and then rigorously the asymptotic expansion of these monotone steady states and then we use this fine information on the spike to prove its local asymptotic stability moreover we obtain the uniqueness of such steady states we expect that the new ideas and techniques for rigorous asymptotic expansion and spectrum analysis presented in this paper will be useful in attacking and hence stimulating research on other more sophisticated chemotaxis models

an approach to solve division like queries in fuzzy object databases the division operator is well known in the context of fuzzy relational databases fuzzy approaches to this operator can be found in the literature to solve flexible queries these approaches try to compute to which extent each element of a candidate set is connected with a given fuzzy set of elements this kind of queries is also interesting in the framework of fuzzy object databases where the management of complex objects instead of plain tuples causes additional difficulties the presence of fuzzily described objects in the database makes necessary to use suitable operators that take into account the resemblance that governs the comparison in the underlying reference universe in this paper we propose a method to solve this type of queries founded on the use of fuzzy inclusion operators we study two different alternatives for the way resemblance is considered and we also analyze the role of cardinality in the process

the uniqueness in inverse problems for dirac operators with the interior twin dense nodal subset abstract inverse nodal problems for dirac operators on a finite interval 0 are studied we prove that the specification of twin dense nodal subsets on the interior interval 1 e 0 2 1 e 1 2 0 e 0 e 1 1 uniquely determines the operator we also discuss the case e 1 0

functional dependencies with null values fuzzy values and crisp values based on the concepts of the semantic proximity we present a definition of the fuzzy functional dependency we show that the inference rules for fuzzy functional dependencies which are the same as armstrong s axioms for the crisp case are correct and complete we also show that dependent constraints with dull values constitute a lattice functional dependencies in classical relational databases and null functional dependencies can be viewed as a special case of fuzzy functional dependencies by applying the unified functional dependencies to the relational database design we can represent the data with fuzzy values null values and crisp values under relational database management systems by using fuzzy functional dependencies we can compress the range of a fuzzy value and make this fuzzy value clearer

solving low density subset sum problems the subset sum problem is to decide whether or not the 0 l integer programming problem s n i l a i x i m i x i 0 or 1 has a solution where the a i and m are given positive integers this problem is np complete and the difficulty of solving it is the basis of public key cryptosystems of knapsack type an algorithm is proposed that searches for a solution when given an instance of the subset sum problem this algorithm always halts in polynomial time but does not always find a solution when one exists it converts the problem to one of finding a particular short vector v in a lattice and then uses a lattice basis reduction algorithm due to a k lenstra h w lenstra jr and l lovasz to attempt to find v the performance of the proposed algorithm is analyzed let the density d of a subset sum problem be defined by d n log 2 max i a i then for almost all problems of density d d n it is proved that the lattice basis reduction algorithm locates v extensive computational tests of the algorithm suggest that it works for densities d d c n where d c n is a cutoff value that is substantially larger than 1 n this method gives a polynomial time attack on knapsack public key cryptosystems that can be expected to break them if they transmit information at rates below d c n as n

modeling bit flipping decoding based on nonorthogonal check sums with application to iterative decoding attack of mceliece cryptosystem in this correspondence iteration 1 of bit flipping decoding based on a set of nonorthogonal check sums is analyzed for both regular and irregular models in particular the tradeoff between the hamming weight and overlapping of the check sums and the number of redundant check sums required to start converging under iterative decoding is investigated the model is then applied to an iterative attack of mceliece public key cryptosystem since a successful attack of this system can be achieved by algebraic bounded distance decoding of a random code based on this model the attack can be decomposed into two phases a preprocessing phase which for one particular key kappa consists of finding a sufficiently large set s of check sums up to a certain hamming weight and a bit flipping decoding phase which uses the set s for each message encrypted with the key kappa

data summarization in relational databases through fuzzy dependencies in this paper we deal with the problem of treating with dependencies in relational databases which do not hold in an exact manner as classical functional dependencies but in a weaker sense i e we face with relations which satisfy dependencies such that people with similar age and height have similar weight we model this relationship through the concept of fuzzy dependency we see that these dependencies imply some kind of fuzzy redundancy and in order to avoid it we propose to use a projection operator which leads us to partition a relation r into two projections say r1 and r2 with a less amount of information then we proceed to replace the original relation by these projections in this process we must guarantee that we can recover the data we had in the original relation this will be possible by using a special join operator applied to r1 and r2 we must also guarantee that we can test the fuzzy dependency for new entries to the database in the same way either if we consider the original relation r or if we work with the projections r1 and r2 we also show that this definition of dependency maintains the good properties of completeness of the classical case 1999 elsevier science inc all rights reserved

extending the fuzzy database with fuzzy numbers abstract the fuzzy relational database model originated by the authors permits fuzzy domain values from a discrete finite universe the model is extended here by demonstrating that fuzzy numbers may be employed as domain values without loss of consistency with respect to representation or the relational algebra where equivalence is required in an ordinary relational database similarity is employed in a fuzzy relational database for discrete finite universes similarity between atomic elements is described via a fuzzy similarity relation with max min transitivity two or more fuzzy numbers are defined to be similar if their union forms a continuous level set over the real line this convention effects the partitioning of fuzzy number domains that is necessary to assure the well definedness of the fuzzy relational algebra

remarks on a new inverse nodal problem in a recent paper x f yang proved a uniqueness theorem on inverse nodal problems that links to inverse spectral theory on one hand and reduces the redundancy of the classical inverse nodal problems on the other hand in this note we improve yang s theorem by weakening its conditions and simplifying its proof we also discuss variants of yang s theorem

reconstruction and stability of inverse nodal problems for energy dependent p laplacian equations abstract we investigate inverse nodal problems for energy dependent p laplacian equations the first part of the study applies the tikhonov regularization method to reconstruct potential functions by only using zeros of one eigenfunction we show the existence of the minimizer for the tikhonov functional and derive the euler lagrange equations for the minimizer in the second part we show that the space of the p laplacian operator is homeomorphic to the partition set of the space of nodal sequences this solves the stability of the inverse nodal problem

generalizing database relational algebra for the treatment of incomplete or uncertain information and vague queries abstract this paper deals with relational databases which are extended in the sense that fuzzily known values are allowed for attributes precise as well as partial imprecise uncertain knowledge concerning the value of the attributes are represented by means of 0 1 valued possibility distributions in zadeh s sense thus we have to manipulate ordinary relations on cartesian products of sets of fuzzy subsets rather than fuzzy relations besides vague queries whose contents are also represented by possibility distributions can be taken into account the basic operations of relational algebra union intersection cartesian product projection and selection are extended in order to deal with partial information and vague queries approximate equalities and inequalities modeled by fuzzy relations can also be taken into account in the selection operation then the main features of a query language based on the extended relational algebra are presented an illustrative example is provided this approach which enables a very general treatment of relational databases with fuzzy attribute values makes an extensive use of dual possibility and necessity measures

inverse problems dense nodal subset on an interior subinterval abstract the inverse nodal problem for the sturm liouville problems defined on interval 0 1 with separated boundary conditions is considered we prove that a twin dense subset of the nodal set in interior subinterval a 1 a 2 0 1 uniquely determines the potential on 0 1 and the boundary conditions through two cases of 1 2 a 1 a 2 and 1 2 a 1 a 2 note that for the latter we need additional spectral information which is associated with the derivatives of eigenfunctions at some known nodal points

a tikhonov regularization for the inverse nodal problem for p laplacian abstract we apply the tikhonov regularization method to reconstruct potentials of a p laplacian eigenvalue problem using only zeros of one eigenfunction with explicit error bounds this is an inverse problem on a class of nonlinear equations when p 2 the study is motivated by our previous work on sturm liouville operators chen et al 2011 6

fuzzy division in fuzzy relational databases an approach an approach to calculate the relational division in fuzzy databases is presented starting with the gefred model the tuples of the division are obtained with a possibility degree that indicates the extent to which they comply with the relational division requisites the results obtained are those expected a priori furthermore in order to formalize this method of fuzzy relational division two new operators are defined which may be useful in other operations the qualified fuzzy intersection and the generalized fuzzy projection with group functions some examples are included in order to clarify the method proposed here and the defined operators a comparison with other fuzzy division approaches that appear in the literature is included too

optimal bounds for ratios of eigenvalues of one dimensional schrodinger operators with dirichlet boundary conditions and positive potentials consider the schrodinger equation u v x u u on the intervali wherev x 0 forx i and where dirichlet boundary conditions are imposed at the endpoints ofi we prove the optimal bound frac lambda n lambda 1 leqq n 2 for n 2 3 4 on the ratio of thenth eigenvalue to the first eigenvalue for this problem this leads to a complete treatment of bounds on ratios of eigenvalues for such problems extensions of these results to singular problems are also presented a modified prufer transformation and comparison techniques are the key elements of the proof

on extended fuzzy relational model with proximity relations in this paper shenoi and melton s model of fuzzy relational database is considered proximity relation being an important tool of the model is characterized theoretically an optimal distribution in 0 1 and consequently the domain partition are defined and studied with examples on fuzzy queries

fuzzy functional dependencies and independencies in extended fuzzy relational database models abstract in this paper we have considered data dependencies more specifically restricted fuzzy functional dependencies in the framework of extended fuzzy relational database model a formal system is presented for the derivation of fuzzy functional dependencies which is both sound and complete the problem of lossless join decomposition is discussed in the framework of extended fuzzy relational model then we introduce a formal statement of fuzzy functional independency which expresses the fact that the corresponding restricted fuzzy functional dependency is not a legitimate constraint of the real world a formal system is presented for the derivation of restricted fuzzy functional dependencies and independencies the various problems such as the membership problem the contradiction problem and the problem of canonical represents are discussed a cover called minimal cover of restricted fuzzy functional independencies is shown to be unique

fuzzy relations and fuzzy relational databases abstract this paper deals with the connections existing between fuzzy set theory and fuzzy relational databases our new result dealing with fuzzy relations is how to calculate the greatest lower bound glb of two similarity relations our main contributions in fuzzy relational databases are establishing from fuzzy set theory what a fuzzy relational database should be the result is both surprising and elegant and making fuzzy relational databases even more robust our work in fuzzy relations and in fuzzy databases had led us into other interesting problems two of which we mention in this paper the first is primarily mathematical and the second provides yet another connection between fuzzy set theory and artificial intelligence in understanding similarity relations in terms of other fuzzy relations and in making fuzzy databases more robust we work with closure and interior operators we present some important properties of these operators in establishing the connection between fuzzy set theory and artificial intelligence we show that an abstraction on a set is in fact a partition on the set that is an abstraction defines an equivalence relation on the underlying set

flexible queries in relational databases the example of the division operator abstract allowing for flexible queries enables database users to express preferences inside minimal requirements and if necessary priorities inside compound queries in other words clear cut properties can be refined by ordering the interpretations compatible with them according to user s preferences often the representation of these preferences can be viewed as modelling linguistic like terms in requests in this paper the theoretical issues raised by the introduction of flexible queries are studied in the case of the division operator in the framework of fuzzy sets and possibility theory the notion of division is well known in the context of regular relations and the extension of this operation to fuzzy relations induced by the flexible queries is investigated several types of extended divisions can be envisaged depending on the meaning of the grades attached to the tuples of the fuzzy relations degree of fulfillment of gradual properties level of importance of components in a query or uncertainty pervading data we focus on the first two meanings which are associated with different multiple valued logic implications and we examine their properties and their expression in the framework of an extended sql like language where no specific construct for the division is available

proximity relations in the fuzzy relational database model abstract the fuzzy relational model of buckles and petry is a rigorous scheme for incorporating non ideal or fuzzy information in a relational database in addition to providing a consistent scheme for representing fuzzy information in the relational structure the model possesses two critical properties that hold for classical relational databases these properties are that no two tuples have identical interpretations and each relational operation has a unique result the fuzzy relational model relies on similarity relations for each scalar domain in the fuzzy database these relations are reflexive symmetric and max min transitive in addition to introducing fuzziness into the relational model each similarity relation induces equivalence classes in its domain it is the existence of these equivalence classes that provides the model with the important properties possessed by classical relational databases in this paper we extend the fuzzy relational database model of buckles and petry to deal with proximity relations for scalar domains since reflexivity and symmetry are the only constraints placed on proximity relations they generalize the notion of similarity relations we show that it is possible to induce equivalence classes from proximity relations thus the nice properties of the fuzzy relational model of buckles and petry are preserved furthermore the removal of the max min transitivity restriction also provides database users with more freedom to express their value structures

gefred a generalized model of fuzzy relational databases abstract in this paper we present a fuzzy relational databases model whose main characteristics are the integration of previous models in the same framework representation capabilities for a wide series of fuzzy information and a coherent and flexible handling of it this model aims to solve each problem of representation and handling of fuzzy information taking into account its specific nature and hence it allows the user to choose the comparison operator and the fuzzy compatibility measure to be used in a query besides it permits the user to specify the precision with which the conditions involved in a query are satisfied

on the inverse nodal problems for discontinuous sturm liouville operators in this paper we discuss the inverse nodal problems for discontinuous sturm liouville operators with robin boundary conditions we show that the potential q up to its mean value on the interval 0 1 and coefficients h h ba can be uniquely determined by the twin dense nodal subset on the subinterval a0 b0 a0 12 b0 in addition we still establish several uniqueness theorems by the left twin dense nodal subset on the interval a0 12 and additional information respectively