Existence Results for Abstract Partial Neutral Integro-differential Equation with Unbounded Delay

In this paper we study the existence and regularity of mild solutions for a class of abstract partial neutral integro-differential equations with unbounded delay.

GLOBAL SOLUTIONS FOR ABSTRACT FUNCTIONAL DIFFERENTIAL EQUATIONS WITH NONLOCAL CONDITIONS

In this paper we study the existence of global solutions for a class of abstract functional differential equation with nonlocal conditions. An application is considered.

Periódicos científicos eletrônicos: definições e histórico

The scientific electronic journal have had many transformations since its begginings in the 70's till nowadays. This papes discusses the definitions of scientific eletronic journal presented in the literature and traces a brief historic of its development in the last three decades, including the modifications occurred since it appeared only in paper support till that publications developed just to the online environment. Discuss some brazilian experiences like ProBe, SciElo and Portal Periodicos Capes.

An algorithmic Friedman-Pippenger theorem on tree embeddings and applications

An (n, d)-expander is a graph G = (V, E) such that for every X subset of V with vertical bar X vertical bar <= 2n - 2 we have vertical bar Gamma(G)(X) vertical bar >= (d + 1) vertical bar X vertical bar. A tree T is small if it has at most n vertices and has maximum degree at most d. Friedman and Pippenger (1987) proved that any ( n; d)- expander contains every small tree. However, their elegant proof does not seem to yield an efficient algorithm for obtaining the tree. In this paper, we give an alternative result that does admit a polynomial time algorithm for finding the immersion of any small tree in subgraphs G of (N, D, lambda)-graphs Lambda, as long as G contains a positive fraction of the edges of Lambda and lambda/D is small enough. In several applications of the Friedman-Pippenger theorem, including the ones in the original paper of those authors, the (n, d)-expander G is a subgraph of an (N, D, lambda)-graph as above. Therefore, our result suffices to provide efficient algorithms for such previously non-constructive applications. As an example, we discuss a recent result of Alon, Krivelevich, and Sudakov (2007) concerning embedding nearly spanning bounded degree trees, the proof of which makes use of the Friedman-Pippenger theorem. We shall also show a construction inspired on Wigderson-Zuckerman expander graphs for which any sufficiently dense subgraph contains all trees of sizes and maximum degrees achieving essentially optimal parameters. Our algorithmic approach is based on a reduction of the tree embedding problem to a certain on-line matching problem for bipartite graphs, solved by Aggarwal et al. (1996).

On the resilience of long cycles in random graphs

In this paper we determine the local and global resilience of random graphs G(n,p) (p >> n(-1)) with respect to the property of containing a cycle of length at least (1 - alpha)n. Roughly speaking, given alpha > 0, we determine the smallest r(g) (G, alpha) with the property that almost surely every subgraph of G = G(n,p) having more than r(g) (G, alpha)vertical bar E(G)vertical bar edges contains a cycle of length at least (1 - alpha)n (global resilience). We also obtain, for alpha < 1/2, the smallest r(l) (G, alpha) such that any H subset of G having deg(H) (v) larger than r(l) (G, alpha) deg(G) (v) for all v is an element of V(G) contains a cycle of length at least (1 - alpha)n (local resilience). The results above are in fact proved in the more general setting of pseudorandom graphs.

Survival time of random walk in random environment among soft obstacles

We consider a Random Walk in Random Environment (RWRE) moving in an i.i.d. random field of obstacles. When the particle hits an obstacle, it disappears with a positive probability. We obtain quenched and annealed bounds on the tails of the survival time in the general d-dimensional case. We then consider a simplified one-dimensional model (where transition probabilities and obstacles are independent and the RWRE only moves to neighbour sites), and obtain finer results for the tail of the survival time. In addition, we study also the ""mixed"" probability measures (quenched with respect to the obstacles and annealed with respect to the transition probabilities and vice-versa) and give results for tails of the survival time with respect to these probability measures. Further, we apply the same methods to obtain bounds for the tails of hitting times of Branching Random Walks in Random Environment (BRWRE).

Random perturbations of stochastic processes with unbounded variable length memory

We consider binary infinite order stochastic chains perturbed by a random noise. This means that at each time step, the value assumed by the chain can be randomly and independently flipped with a small fixed probability. We show that the transition probabilities of the perturbed chain are uniformly close to the corresponding transition probabilities of the original chain. As a consequence, in the case of stochastic chains with unbounded but otherwise finite variable length memory, we show that it is possible to recover the context tree of the original chain, using a suitable version of the algorithm Context, provided that the noise is small enough.

An oracle approach for interaction neighborhood estimation in random fields

We consider the problem of interaction neighborhood estimation from the partial observation of a finite number of realizations of a random field. We introduce a model selection rule to choose estimators of conditional probabilities among natural candidates. Our main result is an oracle inequality satisfied by the resulting estimator. We use then this selection rule in a two-step procedure to evaluate the interacting neighborhoods. The selection rule selects a small prior set of possible interacting points and a cutting step remove from this prior set the irrelevant points. We also prove that the Ising models satisfy the assumptions of the main theorems, without restrictions on the temperature, on the structure of the interacting graph or on the range of the interactions. It provides therefore a large class of applications for our results. We give a computationally efficient procedure in these models. We finally show the practical efficiency of our approach in a simulation study.

The Lobel-Komlos-Sos conjecture for trees of diameter 5 and for certain caterpillars

Loebl, Komlos, and Sos conjectured that if at least half the vertices of a graph G have degree at least some k is an element of N, then every tree with at most k edges is a subgraph of G. We prove the conjecture for all trees of diameter at most 5 and for a class of caterpillars. Our result implies a bound on the Ramsey number r( T, T') of trees T, T' from the above classes.

Biochemical properties of an extracellular beta-D-fructofuranosidase II produced by Aspergillus phoenicis under Solid-Sate Fermentation using soy bran as substrate

The filamentous fungus A. phoenicis produced high levels of beta-D-fructofuranosidase (FFase) when grown for 72 hrs under Solid-State Fermentation (SSF), using soy bran moistened with tap water (1:0.5 w/v) as substrate/carbon source. Two isoforms (I and II) were obtained, and FFase II was purified 18-fold to apparent homogeneity with 14% recovery. The native molecular mass of the glycoprotein (12% of carbohydrate content) was 158.5 kDa with two subunits of 85 kDa estimated by SDS-PAGE. Optima of temperature and pH were 55 degrees C and 4.5. The enzyme was stable for more than 1 hr at 50 degrees C and was also stable in a pH range from 7.0 to 8.0. FFase II retained 80% of activity after storage at 4 degrees C by 200 hrs. Dichroism analysis showed the presence of random and beta-sheet structure. A. phoenicis FFase II was activated by Mn(2+), Mg(2+) and Co(2+), and inhibited by Cu(2+), Hg(2+) and EDTA. The enzyme hydrolyzed sucrose, inulin and raffinose. K(d) and V(max) values were 18 mM and 189 U/mg protein using sucrose as substrate.

Plant-antivenom: Database of anti-venom medicinal plants

Plant-antivenom is a computational Websystem about medicinal plants with anti-venom properties. The system consists of a database of these plants, including scientific publications on this subject and amino acid sequences of active principles from venomous animals. The system relates these data allowing their integration through different search applications. For the development of the system, the first surveys were conducted in scientific literature, allowing the creation of a publication database in a library for reading and user interaction. Then, classes of categories were created, allowing the use of tags and the organization of content. This database on medicinal plants has information such as family, species, isolated compounds, activity, inhibited animal venoms, among others. Provision is made for submission of new information by registered users, by the use of wiki tools. Content submitted is released in accordance to permission rules defined by the system. The database on biological venom protein amino acid sequences was structured from the essential information from National Center for Biotechnology Information (NCBI). Plant-antivenom`s interface is simple, contributing to a fast and functional access to the system and the integration of different data registered on it. Plant-antivenom system is available on the Internet at http://gbi.fmrp.usp.br/plantantivenom.

Skolem-type difference sets for cycle systems

Cyclic m-cycle systems of order v are constructed for all m greater than or equal to 3, and all v = 1(mod 2m). This result has been settled previously by several authors. In this paper, we provide a different solution, as a consequence of a more general result, which handles all cases using similar methods and which also allows us to prove necessary and sufficient conditions for the existence of a cyclic m-cycle system of K-v - F for all m greater than or equal to 3, and all v = 2(mod 2m).

The K-Th derivatives of the immanant and the X-symmetric power of an operator

In recent papers, formulas are obtained for directional derivatives, of all orders, of the determinant, the permanent, the m-th compound map and the m-th induced power map. This paper generalizes these results for immanants and for other symmetric powers of a matrix.

The norm of the K- Th derivative of the X-symmetric power of an operator

In this paper, the exact value for the norm of directional derivatives, of all orders, for symmetric tensor powers of operators on finite dimensional vector spaces is presented. Using this result, an upper bound for the norm of all directional derivatives of immanants is obtained.