On a Class Almost Contact Manifolds with Norden Metric

Certain curvature properties and scalar invariants of the mani- folds belonging to one of the main classes almost contact manifolds with Norden metric are considered. An example illustrating the obtained results is given and studied.

Linear Connections on Normal Almost Contact Manifolds with Norden Metric

Families of linear connections are constructed on almost con- tact manifolds with Norden metric. An analogous connection to the symmetric Yano connection is obtained on a normal almost contact manifold with Norden metric and closed structural 1-form. The curvature properties of this connec- tion are studied on two basic classes of normal almost contact manifolds with Norden metric.

Natural Connections with Totally Skew-Symmetric Torsion on Manifolds with Norden-Type Metrics

This paper is a survey of results obtained by the authors on the geometry of connections with totally skew-symmetric torsion on the following manifolds: almost complex manifolds with Norden metric, almost contact manifolds with B-metric and almost hypercomplex manifolds with Hermitian and anti-Hermitian metric.

Global, Local and Vector-Valued Tb Theorems on Non-Homogeneous Metric Spaces

Various Tb theorems play a key role in the modern harmonic analysis. They provide characterizations for the boundedness of Calderón-Zygmund type singular integral operators. The general philosophy is that to conclude the boundedness of an operator T on some function space, one needs only to test it on some suitable function b. The main object of this dissertation is to prove very general Tb theorems. The dissertation consists of four research articles and an introductory part. The framework is general with respect to the domain (a metric space), the measure (an upper doubling measure) and the range (a UMD Banach space). Moreover, the used testing conditions are weak. In the first article a (global) Tb theorem on non-homogeneous metric spaces is proved. One of the main technical components is the construction of a randomization procedure for the metric dyadic cubes. The difficulty lies in the fact that metric spaces do not, in general, have a translation group. Also, the measures considered are more general than in the existing literature. This generality is genuinely important for some applications, including the result of Volberg and Wick concerning the characterization of measures for which the analytic Besov-Sobolev space embeds continuously into the space of square integrable functions. In the second article a vector-valued extension of the main result of the first article is considered. This theorem is a new contribution to the vector-valued literature, since previously such general domains and measures were not allowed. The third article deals with local Tb theorems both in the homogeneous and non-homogeneous situations. A modified version of the general non-homogeneous proof technique of Nazarov, Treil and Volberg is extended to cover the case of upper doubling measures. This technique is also used in the homogeneous setting to prove local Tb theorems with weak testing conditions introduced by Auscher, Hofmann, Muscalu, Tao and Thiele. This gives a completely new and direct proof of such results utilizing the full force of non-homogeneous analysis. The final article has to do with sharp weighted theory for maximal truncations of Calderón-Zygmund operators. This includes a reduction to certain Sawyer-type testing conditions, which are in the spirit of Tb theorems and thus of the dissertation. The article extends the sharp bounds previously known only for untruncated operators, and also proves sharp weak type results, which are new even for untruncated operators. New techniques are introduced to overcome the difficulties introduced by the non-linearity of maximal truncations.

On the SIG-dimension of trees under the L (a)-metric

Let where be a set of points in d-dimensional space with a given metric rho. For a point let r (p) be the distance of p with respect to rho from its nearest neighbor in Let B(p,r (p) ) be the open ball with respect to rho centered at p and having the radius r (p) . We define the sphere-of-influence graph (SIG) of as the intersection graph of the family of sets Given a graph G, a set of points in d-dimensional space with the metric rho is called a d-dimensional SIG-representation of G, if G is isomorphic to the SIG of It is known that the absence of isolated vertices is a necessary and sufficient condition for a graph to have a SIG-representation under the L (a)-metric in some space of finite dimension. The SIG-dimension under the L (a)-metric of a graph G without isolated vertices is defined to be the minimum positive integer d such that G has a d-dimensional SIG-representation under the L (a)-metric. It is denoted by SIG (a)(G). We study the SIG-dimension of trees under the L (a)-metric and almost completely answer an open problem posed by Michael and Quint (Discrete Appl Math 127:447-460, 2003). Let T be a tree with at least two vertices. For each let leaf-degree(v) denote the number of neighbors of v that are leaves. We define the maximum leaf-degree as leaf-degree(x). Let leaf-degree{(v) = alpha}. If |S| = 1, we define beta(T) = alpha(T) - 1. Otherwise define beta(T) = alpha(T). We show that for a tree where beta = beta (T), provided beta is not of the form 2 (k) - 1, for some positive integer k a parts per thousand yen 1. If beta = 2 (k) - 1, then We show that both values are possible.

QoS Aware Trust Metric based Framework for Wireless Sensor Networks

Wireless Sensor Networks have gained popularity due to their real time applications and low-cost nature. These networks provide solutions to scenarios that are critical, complicated and sensitive like military fields, habitat monitoring, and disaster management. The nodes in wireless sensor networks are highly resource constrained. Routing protocols are designed to make efficient utilization of the available resources in communicating a message from source to destination. In addition to the resource management, the trustworthiness of neighboring nodes or forwarding nodes and the energy level of the nodes to keep the network alive for longer duration is to be considered. This paper proposes a QoS Aware Trust Metric based Framework for Wireless Sensor Networks. The proposed framework safeguards a wireless sensor network from intruders by considering the trustworthiness of the forwarder node at every stage of multi-hop routing. Increases network lifetime by considering the energy level of the node, prevents the adversary from tracing the route from source to destination by providing path variation. The framework is built on NS2 Simulator. Experimental results show that the framework provides energy balance through establishment of trustworthy paths from the source to the destination. (C) 2015 The Authors. Published by Elsevier B.V.

Approximate Best Proximity Points of Cyclic Self-maps in Metric Spaces and Cyclic Asymptotic Regularity

3rd International Conference on Mathematical Modeling in Physical Sciences (IC-MSQUARE) Madrid, AUG 28-31, 2014 / editado por Vagenas, EC; Vlachos, DS; Bastos, C; Hofer, T; Kominis, Y; Kosmas, O; LeLay, G; DePadova, P; Rode, B; Suraud, E; Varga, K

Inference and Labeling of Metric-Induced Network Topologies

The development and deployment of distributed network-aware applications and services over the Internet require the ability to compile and maintain a model of the underlying network resources with respect to (one or more) characteristic properties of interest. To be manageable, such models must be compact, and must enable a representation of properties along temporal, spatial, and measurement resolution dimensions. In this paper, we propose a general framework for the construction of such metric-induced models using end-to-end measurements. We instantiate our approach using one such property, packet loss rates, and present an analytical framework for the characterization of Internet loss topologies. From the perspective of a server the loss topology is a logical tree rooted at the server with clients at its leaves, in which edges represent lossy paths between a pair of internal network nodes. We show how end-to-end unicast packet probing techniques could b e used to (1) infer a loss topology and (2) identify the loss rates of links in an existing loss topology. Correct, efficient inference of loss topology information enables new techniques for aggregate congestion control, QoS admission control, connection scheduling and mirror site selection. We report on simulation, implementation, and Internet deployment results that show the effectiveness of our approach and its robustness in terms of its accuracy and convergence over a wide range of network conditions.

Genotipificación de HLA-B en pacientes colombianos afectados por el síndrome Stevens-Johnson y la Necrólisis Epidérmica Tóxica

Las reacciones alérgicas a medicamentos cutáneas severas (RAM) como el Síndrome Stevens Johnson (SJS) y la Necrólisis Epidérmica Tóxica (NET),caracterizadas por exantema, erosión de la piel y las membranas mucosas, flictenas, desprendimiento de la piel secundario a la muerte de queratinocitos y compromiso ocular. Son infrecuentes en la población pero con elevada morbi-mortalidad, se presentan luego de la administración de diferentes fármacos. En Asia se ha asociado el alelo HLA-B*15:02 como marcador genético para SJS. En Colombia no hay datos de la incidencia de estas RAM, ni de la relación con medicamentos específicos o potenciales y tampoco estudios de aproximación genómica de genes de susceptibilidad.

Evaluation of two hybrid metric-conceptual models, for simulating phosphorus transfer from agricultural land in the river enborne, a lowland UK catchment

Across Europe, elevated phosphorus (P) concentrations in lowland rivers have made them particularly susceptible to eutrophication. This is compounded in southern and central UK by increasing pressures on water resources, which may be further enhanced by the potential effects of climate change. The EU Water Framework Directive requires an integrated approach to water resources management at the catchment scale and highlights the need for modelling tools that can distinguish relative contributions from multiple nutrient sources and are consistent with the information content of the available data. Two such models are introduced and evaluated within a stochastic framework using daily flow and total phosphorus concentrations recorded in a clay catchment typical of many areas of the lowland UK. Both models disaggregate empirical annual load estimates, derived from land use data, as a function of surface/near surface runoff, generated using a simple conceptual rainfall-runoff model. Estimates of the daily load from agricultural land, together with those from baseflow and point sources, feed into an in-stream routing algorithm. The first model assumes constant concentrations in runoff via surface/near surface pathways and incorporates an additional P store in the river-bed sediments, depleted above a critical discharge, to explicitly simulate resuspension. The second model, which is simpler, simulates P concentrations as a function of surface/near surface runoff, thus emphasising the influence of non-point source loads during flow peaks and mixing of baseflow and point sources during low flows. The temporal consistency of parameter estimates and thus the suitability of each approach is assessed dynamically following a new approach based on Monte-Carlo analysis. (c) 2004 Elsevier B.V. All rights reserved.

Slicing the metric space to provide quick indexing of complex data in the main memory

Searching in a dataset for elements that are similar to a given query element is a core problem in applications that manage complex data, and has been aided by metric access methods (MAMs). A growing number of applications require indices that must be built faster and repeatedly, also providing faster response for similarity queries. The increase in the main memory capacity and its lowering costs also motivate using memory-based MAMs. In this paper. we propose the Onion-tree, a new and robust dynamic memory-based MAM that slices the metric space into disjoint subspaces to provide quick indexing of complex data. It introduces three major characteristics: (i) a partitioning method that controls the number of disjoint subspaces generated at each node; (ii) a replacement technique that can change the leaf node pivots in insertion operations; and (iii) range and k-NN extended query algorithms to support the new partitioning method, including a new visit order of the subspaces in k-NN queries. Performance tests with both real-world and synthetic datasets showed that the Onion-tree is very compact. Comparisons of the Onion-tree with the MM-tree and a memory-based version of the Slim-tree showed that the Onion-tree was always faster to build the index. The experiments also showed that the Onion-tree significantly improved range and k-NN query processing performance and was the most efficient MAM, followed by the MM-tree, which in turn outperformed the Slim-tree in almost all the tests. (C) 2010 Elsevier B.V. All rights reserved.

Efficient bulk-loading on dynamic metric access methods

This paper presents a new technique and two algorithms to bulk-load data into multi-way dynamic metric access methods, based on the covering radius of representative elements employed to organize data in hierarchical data structures. The proposed algorithms are sample-based, and they always build a valid and height-balanced tree. We compare the proposed algorithm with existing ones, showing the behavior to bulk-load data into the Slim-tree metric access method. After having identified the worst case of our first algorithm, we describe adequate counteractions in an elegant way creating the second algorithm. Experiments performed to evaluate their performance show that our bulk-loading methods build trees faster than the sequential insertion method regarding construction time, and that it also significantly improves search performance. (C) 2009 Elsevier B.V. All rights reserved.

The C(K, X) spaces for compact metric spaces K and X with a uniformly convex maximal factor

In this paper, we prove that if a Banach space X contains some uniformly convex subspace in certain geometric position, then the C(K, X) spaces of all X-valued continuous functions defined on the compact metric spaces K have exactly the same isomorphism classes that the C(K) spaces. This provides a vector-valued extension of classical results of Bessaga and Pelczynski (1960) [2] and Milutin (1966) [13] on the isomorphic classification of the separable C(K) spaces. As a consequence, we show that if 1 < p < q < infinity then for every infinite countable compact metric spaces K(1), K(2), K(3) and K(4) are equivalent: (a) C(K(1), l(p)) circle plus C(K(2), l(q)) is isomorphic to C(K(3), l(p)) circle plus (K(4), l(q)). (b) C(K(1)) is isomorphic to C(K(3)) and C(K(2)) is isomorphic to C(K(4)). (C) 2011 Elsevier Inc. All rights reserved.

The Wijsman hyperspace of a metric hereditarily Baire space is Baire

In this paper, we show that the Wijsman hyperspace of a metric hereditarily Baire space is Baire. This solves a recent question posed by Zsilinszky. (C) 2009 Elsevier B.V. All rights reserved.

A fixed point theorem for Meir-Keeler contractions in ordered metric spaces

[EN] The purpose of this paper is to present some fixed point theorems for Meir-Keeler contractions in a complete metric space endowed with a partial order. MSC: 47H10.