positive unbounded and monotone solutions of the singular second painleve equation on the half line abstract in this paper we study singular boundary value problems on the half line and we prove the existence of a global monotone positive and unbounded solution the latter satisfies a neumann condition at the origin and has prescribed asymptotic behavior at infinity our approach is based on a generalization of the kneser s property continuum of the cross sections of the solutions funnel i e on the properties of the so called consequent mapping and on properties of the associated vector field on the face space two applications one on the well known second painleve type equation which is related to superconductivity theory and a second in the theory of colloids clarify our results

blow up of solutions of semilinear euler poisson darboux equations with nonlocal boundary conditions this article studies the hyperbolic initial nonlocal boundary value problem u t t k t u t u x x u 0 0 u x 0 u 0 x u t x 0 0 0 0 u a t 0 an y u y t q dy t 0 where k is a real number p and q are nonnegative constants and u 0 m and n are given functions criteria for u to blow up in finite time are given

an efficient algorithm for link prediction in temporal uncertain social networks present a link prediction algorithm in temporal uncertain social networks we transform the link prediction in uncertain network to a random walk in a deterministic one we compute the similarity scores between a node and its neighbors within a subgraph instead of computations in the whole network present an o v 3 method to compute the similarity matrix instead of enumerating the 2 e possible worlds in the network we propose a method for integrating temporal and global topological information in temporal uncertain networks due to the inaccuracy incompleteness and noise in data from real applications uncertainty is a natural feature of real world networks in such networks each edge is associated with a probability value indicating its existence in the network predicting links in uncertain networks is computationally more challenging and differs semantically from predicting connections in deterministic networks this paper presents a method for link prediction in temporal uncertain networks in our method the predicting problem is formalized by designing a random walk in temporal uncertain networks the algorithm first transforms the link prediction problem in uncertain networks to a random walk in a deterministic network then the similarity scores between a node and its neighbors are computed within a sub graph around this node to reduce the computational time the proposed method integrates temporal and global topological information in temporal uncertain networks and can obtain more accurate results experimental results on real social networks show that our method can predict future links efficiently in temporal uncertain social networks and achieves higher quality results than other similar methods

multiple solutions of singular three point boundary value problems on 0 abstract in this paper we study the existence of single and multiple solutions of three point boundary value problems for the following nonlinear singular second order differential equations x t p x t q x t h t f t x t 0 t 0 a x 0 b x 0 k x c 0 lim t x t e r t d 0 where p b 0 a k 0 q 0 0 r 0 p p 2 4 q 2 h 0 0 is continuous and may be singular at t 0 f 0 0 is continuous and may take a negative value by applying the technique of lower and upper solutions and the theory of topological degree we obtain the conditions for the existence of at least one solution and at least three solutions respectively

multiple positive solutions for first order nonlinear integro differential equations in banach spaces by using the fixed point index theory the author obtains the existence of two positive solutions for a boundary value problem of first order nonlinear integro differential equations on an infinite interval in a real banach space

singular boundary value problems on a half line singular boundary value problems of nonlinear second order differential equations on a half line are considered the main methods used are modified upper and lower solution techniques necessary and sufficient conditions for the existence of solutions to a class of sublinear singular boundary value problems are obtained

the existence of countably many positive solutions for some nonlinear three point boundary problems on the half line abstract in this paper we study the existence of countably many positive solutions for some nonlinear singular three point boundary problems on the half line u t a t f t u t 0 0 t u 0 b 0 u 0 u 0 where s r r is an increasing homeomorphism and positive homomorphism and 0 0 and 0 a 0 0 and has countably many singularities on 0 by using the fixed point index theorem and a new fixed point theorem in cones the existence of countably many solutions for singular three point boundary value problem are obtained under conditions weaker than those used by liu and zhang b f liu j h zhang the existence of positive solutions for some nonlinear boundary value problems with linear mixed boundary conditions j math anal appl 309 2005 505 516

the existence of countably many positive solutions for one dimensional p laplacian with infinitely many singularities on the half line we study the existence of countably many positive solutions of boundary value problems on the half line for differential equations of second order the fixed point index theory and a new fixed point theorem in cones are used

link prediction in multi relational networks based on relational similarity presented a belief propagation method to calculate the belief of each node in a network proposed a measurement of influence between different types of relations using belief vectors presented a nonnegative matrix factorization based algorithm for link prediction in multi relational networks theoretically proved the convergence and correctness of the proposed algorithm empirically demonstrated the proposed algorithm can achieve higher quality prediction results many real world networks contain multiple types of interactions and relations link prediction in such multi relational networks has become an important area in network analysis for link prediction in multi relational networks we should consider the similarity and influence between different types of relations in this paper we propose a link prediction algorithm in multi relational networks based on relational similarity in the algorithm a belief propagation method is presented to calculate the belief of each node and to construct the belief vector for each type of link we use the similarity between belief vectors to measure the influence between different types of relations based on the influence between different relations we present a nonnegative matrix factorization based method for link prediction in multi relational networks the convergence and correctness of the presented method are proved our experimental results show that our method can achieve higher quality prediction results than other similar algorithms

existence theory for nonlinear fredholm and volterra integral equations on half open intervals in this chapter we present existence theory for the nonlinear fredholm integral equation y t h t smallint 0 t k t s g s y s ds 4 1 1 and the nonlinear volterra integral equation y t h t smallint 0 t k t s g s y s ds 4 1 2 when both are defined on the compact interval 0 t naturally we first concern ourselves with existence principles for both equations

positive solution of singular dirichlet boundary value problems for second order differential equation system this paper investigates the existence of positive solutions of singular dirichlet boundary value problems for second order differential system a necessary and sufficient condition for the existence of c 0 1 c 0 1 positive solutions as well as c1 0 1 c1 0 1 positive solutions is given by means of the method of lower and upper solutions and the fixed point theorems our nonlinearity fi t x1 x2 may be singular at x1 0 x2 0 t 0 and or t 1 i 1 2

multiple positive solutions of the singular boundary value problems for second order differential equations on the half line abstract in this paper the existence of multiple positive solutions for singular sturm liouville boundary value problems on the half line is investigated by applying the fixed point index theorem of cone map some existence and multiplicity results of positive solutions are derived our results improve and generalize many well known results two examples are presented to demonstrate the application of our main results

more on the complexity of slice functions abstract one of the hardest problems in complexity theory seems to be to find a proof that the circuit complexity of some explicitly defined boolean function is nonlinear in the number of inputs and outputs an interesting approach for such a bound is the investigation of slice functions since for these functions circuits over a complete basis monotone circuits and the so called set circuits are nearly equivalent in this paper the theory of slice functions is extended a monotone representation of each boolean function whose monotone complexity is at most a factor n larger than its circuit complexity is presented for some slice functions and some other functions new pseudocomplements with small monotone complexity are presented these results lead to new and intuitive problems whose solution would lead to nonlinear lower bounds on circuit complexity some connections between the complexity of n output and 1 output slices and between the complexity of the k slice and the k 1 slice of the same function are discussed

twin solutions to singular dirichlet problems the existence of two nonnegative solutions to dirichlet second order boundary value problems is established in this paper our nonlinearity may be singular at y 0 t 0 and or t 1

solutions in weighted spaces of singular boundary value problems on the half line in this paper we establish the existence of an unbounded solution to a second order boundary value problem on the half line also the existence of multiple unbounded positive solutions is discussed using the theory of fixed point index

the complexity of central slice functions let f be a monotone boolean function over x x1 xn the k slice of f is the function fk f tkn vtk 1n where tkn is the kth threshold function berkowitz has shown that sufficiently large superlinear lower bounds on the monotone network complexity of kk imply lower bounds of the same order on the combinational complexity of f and that if f has large combinational complexity then some slice of f must have large monotone complexity however this latter result does not specify any particular slice and it is known that some nontrivial slice functions of np complete predicates have linear complexity in this paper we consider the 12n slice functions and show that for three basic monotone boolean np complete functions this slice is also np complete in addition the 12n slice of some boolean matrix functions f is studied and is proved to be no easier to compute than f

transformation techniques and fixed point theories to establish the positive solutions of second order impulsive differential equations abstract using a new method for dealing with the impulse term of second impulsive differential equations we are concerned with determining values of for which there exist positive solutions of the following boundary value problems in the form of x t f t x t 0 t j t t k x t k x t k c k x t k k 1 2 n a x 0 b x 0 a x 1 b x 1 0 1 h s x t d t where 0 is a positive parameter c k is a real sequence with c k 1 k 1 2 n the dependence of positive solution x t on the parameter is also studied i e lim x or lim x 0 the proof of our main result is based upon transformation techniques and fixed point theories this is probably the first time the existence of positive solutions of second order impulsive differential equations has been studied by applying this technique

existence of positive solutions for second order semipositone differential equations on the half line in this paper by means of constructing a special cone we obtain a sufficient condition for the existence of positive solution for semipositone singular sturm liouville boundary value problem on the half line the results obtained generalize and improve the corresponding results of zhang and liu in papers x g zhang l s liu positive solutions of superlinear semipositone singular dirichlet boundary value problems j math anal appl 316 2006 525 537 y s liu existence and unboundedness of positive solutions for singular boundary value problems on half line appl math comput 144 2003 543 556

on monotone simulations of nonmonotone networks we consider the following problem given some n argument monotone boolean function f xn with formal arguments xn x1 xn compute f using the 2n 1 inputs xn f0 f1 fn here fk is the k slice of f i e the n argument monotone boolean function fk xn f tnk tnk 1 where tnk is the n argument monotone boolean function which takes the value 1 iff at least k of its arguments are 1 it is easy to see that if nonmonotone operations are permitted then o n gates are sufficient by using the relation f v nk 0 fk tnk 1 the properties of slice functions imply th efficient monotone solutions would allow superlinear lower bounds on the combinational complexity of f to be obtained from large enough lower bounds on the monotone complexity of f since negation is known to be superpolynomially powerful some monotone functions must have superpolynomial complexity even if all the slice functions are given as extra inputs however it is possible that efficient simulations using slice functions exist for restricted classes of monotone functions in this paper we examine a broad class of monotone boolean functions proving that for almost all of the functions in the class no such simulation exists and that in a very weak sense negation is exponentially powerful in contrast to this an example of an efficient construction is given again for a natural class of monotone boolean functions

calculus of variations for a boundary value problem of differential system on the half line boundary value problem of second order differential equations on the half line is investigated in this paper the method mainly depends on the calculus of variations to the classical functionals sufficient conditions are obtained for the existence of the solutions

the existence of countably many positive solutions for nonlinear singular m point boundary value problems on the half line in this paper by introducing a new operator improving and generating a p laplace operator for some p 1 we study the existence of countably many positive solutions for nonlinear boundary value problems on the half line f u a t f u t 0 0r is the increasing homeomorphism and positive homomorphism and f 0 0 we show the sufficient conditions for the existence of countably many positive solutions by using the fixed point index theory and a new fixed point theorem in cones

existence of solutions of boundary value problems with integral boundary conditions for second order impulsive integro differential equations in banach spaces this paper investigates the existence of solutions for a class of second order boundary value problems with integral boundary conditions of nonlinear impulsive integro differential equations in banach spaces the arguments are based upon the fixed point theorem of strict set contraction operators meanwhile an example is worked out to demonstrate the main results

on the complexity of branching programs and decision trees for clique functions exponential lower bounds on the complexity of computing the clique functions in the boolean decision tree model are proved for one time only branching programs large polynomial lower bounds are proved for k clique functions if k is fixed and exponential lower bounds if k increases with n finally the hierarchy of the classes bp d p of all sequences of boolean functions that may be computed by d times only branching programs of polynomial size is introduced it is shown constructively that bp 1 p is a proper subset of bp 2 p

a class of three point boundary value problems for second order impulsive integro differential equations in banach spaces abstract in this paper we consider the following boundary value problems for second order three point nonlinear impulsive integro differential equation of mixed type in a real banach space e x t f t x t x t a x t b x t t j t t k x t t k i k x t k x t t k i k x t k x t k k 1 2 m x 0 x 1 x where is the zero element of e a x t 0 t g t s x s d s b x t 0 1 h t s x s d s g c d r d t s j j t s h c j j r and x t t k denotes the jump of x t at t t k x t t k denotes the jump of x t at t t k some new results are obtained for the existence and multiplicity of positive solutions of the above problems by using the fixed point index theory and fixed point theorem in the cone of strict set contraction operators meanwhile an example is worked out to demonstrate the main results

structure of a class of singular boundary value problem with superlinear effect abstract this paper investigates the structure of solutions of singular boundary value problem with superlinear effect it is proved that the closure of positive solution set possesses a maximal subcontinuum c i e a maximal closed connected subset of solutions which comes from 0 and tends to 0 finally as a corollary the existence of multiple positive solutions and the behavior of solutions according to parameter are obtained

boundary value problems for impulsive integro differential equations on unbounded domains in a banach space in this paper the fixed point theory is used to investigate the existence and uniqueness of solutions of two point boundary value problems bvps for second order non linear impulsive integro differential equations on infinite intervals in a banach space

unbounded solutions for singular boundary value problems on the semi infinite interval upper and lower solutions and multiplicity this paper presents a lower and upper solution technique for singular second order boundary value problems on the half line and discusses sufficient and necessary conditions for the existence of positive solutions also multiplicity is discussed using the fixed point index

heteroclinic connections for fully non linear non autonomous second order differential equations we investigate the solvability of the following strongly non linear non autonomous boundary value problem p a x t x t f t x t x t a e t r x x with given constants where a x is a generic continuous positive function and f is a caratheodory non linear function we show that the solvability of p is strictly connected to a sharp relation between the behaviors of f t x as x 0 and f x x as t such a relation is optimal for a wide class of problems for which we prove that p is not solvable when it does not hold

triple positive solutions for boundary value problems on infinite intervals abstract this paper deals with the existence of triple positive solutions for sturm liouville boundary value problems of second order nonlinear differential equation on a half line by using a fixed point theorem in a cone due to avery peterson we show the existence of at least three positive solutions with suitable growth conditions imposed on the nonlinear term

boolean functions whose monotone complexity is of size n2 log n we construct a sequence of monotone boolean functions hn 0 1 n 0 1 n such that the monotone complexity of hn is of order n2 log n this result includes the largest known lower bound of this kind previously there were an n3 2 bound for the boolean matrix product an n5 3 bound for boolean sums and an n2 log2n bound of the author for the same functions hn this new lower bound is proved by new methods which probably will turn out to be useful also for other problems

on the complexity of negation limited boolean networks a theorem of markov precisely determines the number r of negation gates necessary and sufficient to compute a system of boolean functions f for a system of boolean functions on n variables r leq b n lceil log 2 n 1 rceil we call a circuit using b n negation gates negation limited we continue recent investigations into negation limited circuit complexity giving both upper and lower bounds a circuit with inputs x1 xn and outputs neg x 1 ldots neg x n is called an inverter for which r lceil log 2 n 1 rceil fischer has constructed negation limited inverters of size o n2 log n and depth o log n recently tanaka and nishino have reduced the circuit size to o n log2 n at the expense of increasing the depth to log2 n we construct negation limited inverters of size o n log n with depth only o log n and we conjecture that this is optimal we also improve a technique of valiant for constructing monotone circuits for slice functions introduced by berkowitz next we introduce some lower bound techniques for negation limited circuits we provide a 5n 3 log n 1 c lower bound for the size of a negation limited inverter in addition we show that for two different restricted classes of circuit negation limited inverters require superlinear size

the conjunctive complexity of quadratic boolean functions abstract the minimal number of conjuctions in monotone circuits for quadratic boolean functions i e disjunctions of quadratic monomials x i x j is investigated single level circuits which have only one level of conjuctions are compared with arbitrary monotone circuits the computation of the single level complexity is shown to be np complete for almost all quadratic functions almost optimal circuits can be computed in polynomial time the single level conjecture is disproved i e a quadratic function is defined whose single level complexity is larger than its conjuctive complexity

a class of second order impulsive integro differential equations on unbounded domain in a banach space by establishing a comparison result the author obtains the existence of maximal and minimal solutions of the initial value problem ivp for a class of second order impulsive integro differential equations in a banach space

information filtering based on transferring similarity in this brief report we propose an index of user similarity namely the transferring similarity which involves all high order similarities between users accordingly we design a modified collaborative filtering algorithm which provides remarkably higher accurate predictions than the standard collaborative filtering more interestingly we find that the algorithmic performance will approach its optimal value when the parameter contained in the definition of transferring similarity gets close to its critical value before which the series expansion of transferring similarity is convergent and after which it is divergent our study is complementary to the one reported in e a leicht p holme and m e j newman phys rev e 73 026120 2006 and is relevant to the missing link prediction problem

positive solutions for three point boundary value problem on the half line in this paper we consider the existence of positive solutions for the following boundary value problem on the half line r t x t f t x t x t 0 email protected 0 x 0 email protected x limt x t 0 by applying fixed point theorems we obtain a variety of existence results in particular the nonlinear term is involved with the first order derivative

solutions of impulsive boundary value problems on the half line abstract this paper presents some existence results for a class of impulsive boundary value problems with nonhomogeneous boundary data on the half line by applying fixed point theorems on cones we obtain the existence of positive bounded and unbounded solutions our methods are integral equations approximate solutions a priori bounds and modified arzela techniques

solutions of two point bvps at resonance for higher order impulsive differential equations in this paper the resonance two point boundary value problems for impulsive 2n order differential equation x 2n t f t x t x t x 2n 1 t 0 t 1 x i sk ii k x sk x 2n 1 sk i 1 2n 1 k 1 p with following two point boundary value conditions x 2i 1 0 x 2i 1 1 i 0 n 1 and for n order differential equation x n t f t x t x t x n 1 t 0 t 1 x i sk ii k x sk x 2n 1 sk i 1 n 1 k 1 p with following periodic boundary value conditions x i 0 x i 1 0 i 0 n 1 are considered sufficient conditions which guarantee the existence of at least one solution for these problems are established the interest is that we allow the degree of variables of f to be greater than 1 the methods used and results obtained are new and they shows us that the solvability of these two problems are very much alike

the existence of multiple positive solutions for multi point boundary value problems on the half line in this paper we consider the existence of multiple positive solutions for some nonlinear m point boundary value problems on the half line f u a t f t u t 0 0r is an increasing homeomorphism and positive homomorphism and f 0 0 using a fixed point theorem for operator on a cone we provide sufficient conditions for the existence of multiple positive solutions to the above boundary value problem

multiple solutions of second order three point singular boundary value problems on the half line in this paper the existence of multiple solutions of second order three point singular boundary value problems on the half line is discussed by using the technique of upper and lower solutions and the theory of fixed point index in a cone moreover it generalizes and includes some known results

negation is powerless for boolean slice functions it is shown that for any slice function of n variables the monotone circuit complexity exceeds the circuit complexity over a universal basis by at most a multiplicative constant factor and an additive term of order o n log n 2

positive solutions for multi point boundary value problem on the half line this paper presents a variety of existence results for nonlinear multi point boundary value problem on the half line in particular we consider x t px t qx t f t x t 0 t 0 x 0 x 0 i 1nkix i a limt x t ert b r 0 p p2 4q2 existence results are established using fixed point theorems on cone

existence and unboundedness of positive solutions for singular boundary value problems on half line by constructing a special cone and using cone compression and expansion fixed point theorem this paper presents some existence results of positive solutions of singular boundary value problem bvp for short on half line for a class of second order differential equations at the same time the boundedness and unboundedness of positive solutions for bvp are considered also

solutions of lidstone bvps for higher order impulsive differential equations abstract in this paper the lidstone boundary value problems for 2 n order impulsive differential equation x 2 n t f t x t x t x 2 n 1 t 0 t 1 x i s k i i k x s k x 2 n 1 s k i 1 2 n 1 k 1 p with one of following boundary conditions x 2 i 0 x 2 i 1 0 i 0 n 1 and x 2 i 1 0 x 2 i 1 0 i 0 n 1 are considered sufficient conditions which guarantee the existence of at least one solution for these problems are established the results are new examples illustrate our main results

global structure of solutions for a class of two point boundary value problems involving singular and convex or concave nonlinearities abstract this paper investigates the following two point singular boundary value problems bvp x t x q x p t 0 1 x t 0 t 0 1 x 0 x 1 0 where q 0 and p 0 are fixed given numbers r 0 is a parameter the results obtained are the global structure of solutions and exact number of solutions when p 1 or p 1 and q is sufficiently small

on the complexity of slice functions abstract by a result of berkowitz 1982 the monotone circuit complexity of slice functions cannot be much larger than the circuit combinational complexity of these functions for arbitrary complete bases this result strengthens the importance of the theory of monotone circuits we show in this paper that monotone circuits for slice functions can be understood as special circuits called set circuits here disjunction and conjunction are replaced by set union and set intersection all the main methods known for proving lower bounds on the monotone complexity of boolean functions fail to work in their present form for slice functions furthermore we show that the canonical slice functions of the boolean convolution the nechiporuk boolean sums and the clique function can be computed with a linear number of gates

an n superscript 3 2 lower bound on the monotone network complexity of the boolean convolution in this paper a general lower bound on the monotone network complexity of semidisjoint bilinear forms is proved by this method an n3 2 lower bound for the boolean convolution is obtained up to now the best known lower bound for the boolean convolution was of size n4 3 blum 1981 ieee annual sympos found comput sci 22 101 108