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The discoveries of intrinsically magnetic topological materials, including semimetals with a large anomalous Hall effect and axion insulators.sup.1-3, have directed fundamental research in solid-state materials. Topological quantum chemistry.sup.4 has enabled the understanding of and the search for paramagnetic topological materials.sup.5,6. Using magnetic topological indices obtained from magnetic topological quantum chemistry (MTQC).sup.7, here we perform a high-throughput search for magnetic topological materials based on first-principles calculations. We use as our starting point the Magnetic Materials Database on the Bilbao Crystallographic Server, which contains more than 549 magnetic compounds with magnetic structures deduced from neutron-scattering experiments, and identify 130 enforced semimetals (for which the band crossings are implied by symmetry eigenvalues), and topological insulators. For each compound, we perform complete electronic structure calculations, which include complete topological phase diagrams using different values of the Hubbard potential. Using a custom code to find the magnetic co-representations of all bands in all magnetic space groups, we generate data to be fed into the algorithm of MTQC to determine the topology of each magnetic material. Several of these materials display previously unknown topological phases, including symmetry-indicated magnetic semimetals, three-dimensional anomalous Hall insulators and higher-order magnetic semimetals. We analyse topological trends in the materials under varying interactions: 60 per cent of the 130 topological materials have topologies sensitive to interactions, and the others have stable topologies under varying interactions. We provide a materials database for future experimental studies and open-source code for diagnosing topologies of magnetic materials. High-throughput calculations are performed to predict approximately 130 magnetic topological materials, with complete electronic structure calculations and topological phase diagrams., Author(s): Yuanfeng Xu [sup.1] , Luis Elcoro [sup.2] , Zhi-Da Song [sup.3] , Benjamin J. Wieder [sup.3] [sup.4] [sup.5] , M. G. Vergniory [sup.6] [sup.7] , Nicolas Regnault [sup.3] [sup.8] [...]

Confining photons in a finite volume is highly desirable in modern photonic devices, such as waveguides, lasers and cavities. Decades ago, this motivated the study and application of photonic crystals, which have a photonic bandgap that forbids light propagation in all directions.sup.1-3. Recently, inspired by the discoveries of topological insulators.sup.4,5, the confinement of photons with topological protection has been demonstrated in two-dimensional (2D) photonic structures known as photonic topological insulators.sup.6-8, with promising applications in topological lasers.sup.9,10 and robust optical delay lines.sup.11. However, a fully three-dimensional (3D) topological photonic bandgap has not been achieved. Here we experimentally demonstrate a 3D photonic topological insulator with an extremely wide (more than 25 per cent bandwidth) 3D topological bandgap. The composite material (metallic patterns on printed circuit boards) consists of split-ring resonators (classical electromagnetic artificial atoms) with strong magneto-electric coupling and behaves like a 'weak' topological insulator (that is, with an even number of surface Dirac cones), or a stack of 2D quantum spin Hall insulators. Using direct field measurements, we map out both the gapped bulk band structure and the Dirac-like dispersion of the photonic surface states, and demonstrate robust photonic propagation along a non-planar surface. Our work extends the family of 3D topological insulators from fermions to bosons and paves the way for applications in topological photonic cavities, circuits and lasers in 3D geometries.A three-dimensional photonic topological insulator is presented, made of split-ring resonators with strong magneto-electric coupling, which has an extremely wide topological bandgap, forbidding light propagation., Author(s): Yihao Yang [sup.1] [sup.2] [sup.3] [sup.4] , Zhen Gao [sup.3] [sup.4] , Haoran Xue [sup.3] [sup.4] , Li Zhang [sup.1] [sup.2] , Mengjia He [sup.1] [sup.2] , Zhaoju Yang [...]

Real materials rarely behave like their digital counterparts. Stability of the compounds must be part of the burden of proof for predicting the complex properties of matter, urges Alex Zunger. Real materials rarely behave like their digital counterparts. Stability of the compounds must be part of the burden of proof for predicting the complex properties of matter, urges Alex Zunger., Author(s): Alex Zunger Author Affiliations: Beware of plausible predictions of fantasy materials The surface of a topological insulator, as seen under a scanning tunnelling microscope. [see PDF for image] Credit: [...]

The aim of this paper is to introduce the notions of [[lambda].sub.J]-Closed sets in generalized topological spaces and supplement their properties. We also investigate their characterizations. Keywords J-closed set, J-open set, gJA-closed set, J[lambda]g-closed set, [[lambda].sub.J]-closed set. 2000 Mathematics Subject Classification: 54A05,54A10, [section]1. Introduction and preliminaries A. Csaszar [1] has introduced and studied generalized open sets of a set X denned in terms of monotonic functions [gamma] : P(X) [right arrow] P(X). [...]

In materials called Weyl semimetals, electrons form structures that have distinct topological properties. The discovery of an ultrafast switch between two of these structures could have many practical applications.Ultrafast manipulation of a topological material., Author(s): Young-Woo SonAuthor Affiliations:Topological properties controlled by light In the late 1920s, the physicist Paul Dirac discovered an equation that governs the behaviour of relativistic (high-speed) particles, and that combines [...]

A compact and broadband 0.8-77.5-GHz passive distributed drain mixer using standard 0.13-[micro]m CMOS technology is presented in this paper. To extend the operation bandwidth, a uniform distributed topology is utilized for wideband matching. This paper also analyzes the device size and number of stages for the bandwidth of the CMOS distributed drain mixer. To optimize the conversion gain performance of the CMOS drain mixer, a gate bias optimization method is proposed and successfully implemented in the mixer design. This mixer consumes zero dc power and exhibits a measured conversion loss of 5.5 [+ or -] 1 dB from 0.8 to 77.5 GHz with a compact size of 0.67 x 0.58 [mm.sup.2]. The output 1-dB compression point is -8.5 dBm at 20 GHz. To best of our knowledge, this monolithic microwave integrated circuit has the widest operation bandwidth among CMOS wideband mixers to date with good conversion efficiency and zero dc power consumption. Index Terms--CMOS, distributed mixer, drain mixer, millimeter wave (MMW).

In an unreliable packet network setting, we study the performance gains of optimal transmission strategies in the presence and absence of coding capability at the transmitter, where performance is measured in delay and throughput. Although our results apply to a large class of coding strategies including maximum-distance separable (MDS) and Digital Fountain codes, we use random network codes in our discussions because these codes have a greater applicability for complex network topologies. To that end, after introducing a key setting in which performance analysis and comparison can be carried out, we provide closed-form as well as asymptotic expressions for the delay performance with and without network coding. We show that the network coding capability can lead to arbitrarily better delay performance as the system parameters scale when compared to traditional transmission strategies without coding. We further develop a joint scheduling and random-access scheme to extend our results to general wireless network topologies. Index Terms--Broadcast, delay analysis, erasure channel, maximum-distance separable (MDS) codes, network coding.

In this paper we present the application of a hyper radial basis function network as a topology description function. A hyper radial basis function network is used to parameterize the material distribution (density) for topology optimization. The density of each finite element in the continuum topology optimization domain is governed by a single network of hyper radial function bases. Thus, the topology optimization problem is to determine the parameters governing the hyper radial basis function network to satisfy certain design criteria. Here we present the solution to a minimum compliance topology design. A hyper radial basis function network is used to parameterize the material density during the finite element analysis stage. An efficient optimization algorithm that makes use of perturbation and sequential linear programming is developed to obtain the hyper radial basis function network parameters. Examples are presented to demonstrate the proposed approach and to compare it with the traditional solid isotropic microstructures with penalization topology optimization. Some of the advantages of the proposed approach are that it can yield checkerboard-free, manufacturable topologies using coarse-mesh finite element analysis models as opposed to the traditional approach, which requires fine meshes. This results in a reduction in the solution time for finite element analysis while couserving the ability to yield a smooth topology.

This paper investigates the stability and boundary of a swarm with a general directed and weighted topology. The stability of a swarm is generally considered as cohesiveness. We construct a symmetric eigenmatrix and define an orthogonal eigenparameter which reflects the degree of orthogonality between the left eigenvector of the coupling matrix corresponding to its zero eigenvalue and the eigenvectors of the eigenmatrix corresponding to its nonzero eigenvalues. We prove that, if the topology of the underlying swarm is strongly connected, the swarm is then stable in the sense that all agents will globally and exponentially converge to a hyperellipsoid in finite time, both in open space and profiles, whether the center of the hyperellipsoid is moving or not. The swarm boundary and convergence rate are characterized by the eigenparameters of the swarm, which reveals the quantitative relationship between the swarming behavior and characteristics of the coupling topology. Index Terms--Eigenstructure, multi-agent, stability, swarm boundary.

This paper is devoted to the presentation of a simple but powerful topological approach for the computation of basis functions involved in the expression of finite element interpolants. It deals with the so-called nodal and edge elements but similar considerations can be made for the construction of facet ones. All standard cells are treated including pyramids. Index Terms--Algebraic topology, finite element methods.

A new topology preserving non-negative matrix factorization (TPNMF) technique for face recognition is proposed. Experimental results show that the proposed approach provides better representation of face patterns and achieves greater recognition rate, as compared to the non-negative matrix factorization (NMF).

For further studying the theories and applications of rough sets (RS), this paper proposes a new theory on RS, which mainly includes topological space, topological properties, homeomorphism, and its properties on RS by some new definitions and theorems given. The relationship between partition and countable open covering is discussed, and some applications based on the topological rough space and its topological properties are introduced. Moreover, some perspectives for future research are given. Throughout this paper, the advancements of the new theory on RS and topological algebra not only represent an important theoretical value but also exhibit significant applications of RS and topology. Index Terms--Closed set, compact rough space, compact subset, homeomorphism, open set, rough sets (RS), topological space, topology.

A fractal is a space with its topological dimension definitely less than its Hausdorff dimension, with the Sierpinski triangle being a typical example. A novel approach for constructing the Sierpinski triangle and different other fractals are presented.

Many systems and strategies have been proposed for processing nonterminating data streams. Each approach has advantages and disadvantages, including the kinds of queries that can be executed. We present a framework for characterizing the kinds of queries that can be executed over streams based on a notion of compact sets from topology. We first apply our framework to queries over punctuated data streams. Previous work on punctuations focused primarily on the behavior of individual query operators. We use our framework to determine if an entire query can benefit from punctuations available from stream sources. We then consider other common strategies proposed in the literature for executing queries over streams, and we discuss how our framework can characterize the kinds of queries each strategy can answer. Index Terms--Data streams, query execution, punctuation.

Radiation effects on four common DC linear voltage regulators are investigated. Increasing total dose is shown to degrade converter regulation by degrading the loop gain and phase response. Regulator single event transient (SET) response is characterized, and a mitigation technique is proposed. Shunt regulator topologies are found to be superior to series regulator topologies in terms of radiation tolerance. Index Terms--Frequency response, linear voltage regulator, single event transient (SET), total ionizing dose.

A method for fully automated morphological and topological quantification of microvascular structures in confocal laser scanning microscopy (CLSM) volume datasets is presented. Several characteristic morphological and topological quantifies are calculated in a series of image-processing steps and can be used to compare single components as well as whole networks of microvascular structures to each other. The effect of the individual image-processing steps is illustrated and characteristic quantities of measured volume datasets are presented and discussed. Index Terms--Angiogenesis, anisotropic skeletonization, characteristic quantities, compactness, confocal laser scanning microscopy (CLSM), morphology, topology.

Black start, the restoration of a power system after a complete blackout, is a key issue to the safety of power systems. The reasonable network reconfiguration is necessary for establishing the main network and restoring loads quickly. Based on topological characteristics of scale-free networks and discrete particle swarm optimization, a skeleton-network reconfiguration strategy is proposed in this paper. Through calculating node importance degrees, priorities of sources and loads could be scaled quantitatively. Then, network reconfiguration efficiency, an index represented by network structure and subjected to restoration constrains, is used to evaluate the reconfiguration effect. Furthermore, discrete particle swarm optimization is employed in reconstructing skeleton networks that relieve reconfiguration burden considerably. Application examples verify that several optimal reconfiguration schemes achieved from the strategy can provide dispatchers an effective decision support under the uncertain system situation. Index Terms--Black start, network reconfiguration, power systems, particle swarm optimization, scale-free networks, system restoration.

This paper presents a novel current tripler rectification (CTR) topology for secondary-side rectification in high-current low-voltage isolated dc--dc converters. Compared with the conventional center-tapped and current doubler rectifiers, the CTR topology has three filter inductors to share the output current, and thus higher current capability and better thermal management can be achieved. Theoretical analysis and experimental results verify that the proposed CTR is a good candidate for rectification topology in high-current dc-dc converters. Index Terms--Current tripler rectification (CTR), dc-dc converter, high current, low voltage, rectifier, secondary-side, thermal management.

A soft-switching inverter topology (the Class [PHI]) is presented which draws dc source current through a transmission line or a lumped-network approximation of a distributed line. By aligning the inverter switching frequency just below the line's [lambda]/4-wave resonance, the Class [PHI] topology enforces odd-and even-harmonic content in its drain voltage and input current, respectively. The symmetrizing action of the transmission-line dynamics results in natural square-wave operation of the switch, reducing the inverter stresses (relative to a Class E) for a given power throughput. The inverter waveforms and normalized power-output capability are analyzed in simple terms, and supported by measurements of an inverter built around a length of distributed line, and an inverter incorporating a lumped L-C ladder network. The latter implementation is constructed with air-core magnetics and inter-layer capacitances that are integrated into the thickness of a printed-circuit board. A comparison with a Class E inverter of similar size and ratings demonstrates the small passive-component values and manufacturing advantages afforded by the Class [PHI] topology. Index Terms--Distributed system, inverter, lumped model, transmission line.

In this paper, a new digital deadbeat controller is designed, implemented, and applied to a three-phase series-parallel line-interactive uninterruptible power supply (UPS). This kind of UPS system provides input power factor correction, output voltage conditioning, and high efficiency. The objective of the controller is to achieve deadbeat dynamic response for the parallel and series converters. The proposed controller adjusts the current of the parallel converter and voltage of the series converter with two and four sampling periods, respectively. A reduced-parts topology is also introduced that has less number of power electronics components as well as switching functions. The power flow of the system in the presence of current and voltage harmonics is discussed. Simulation and experimental results are presented, which show the viability of the proposed controller for this topology. Index Terms--Digital control, reduced parts, topology, uninterruptible power supply (UPS).

Abstract--In most of the popular implementation of Parallel GAs the whole population is divided into a set of subpopulations, each subpopulation executes GA independently and some individuals are migrated at [...]

G, a type-definable subset of a definable manifold in [M.sup.n] that induces on G a group topology is shown by taking M to be big O-minimal structure and G a type-definable group in [M.sup.n]. Result withstand for the wider class of so-called invariant groups and each invariant group G in [M.sup.n] has a unique topology making it a topological group and having the same topology on a large invariant subset of the group as [M.sup.n]

A concept of approximation of a topological algebraic system A by finite algebraic systems from a given class A is discussed. A similar characterization of approximability of a locally compact system A by systems from A applying the language of nonstandard analysis is obtained and the results show that there do not exist arbitrarily accurate computer arithmetics for the reals that are associative rings.

The LSB (Lusternik-Schnirelmann-Borsuk) theorem and the KKM (Knaster-Kuratowski-Mazurkiewicz) lemma are connected with equivalent formulations in topology, by which the Brouwer fixed point theorem equivalent to the KKM lemma can be obtained as a consequence of the Borsuk-Ulam theorem equivalent to the LSB theorem. Hence, a direct proof of the KKM lemma using the LSB theorem is examined, and a proof is presented that the LSB theorem implies the KKM lemma.

The effectiveness of the dynamical systems method (DSM) as a tool for providing theoretical results is illustrated through an example. The DSM is used to prove a Hadamard-type theorem on global homeomorphisms and a sufficient condition for the surjectivity of a nonlinear map in a Hilbert space.

A formulation for the automatic synthesis of two-dimensional bistable, compliant periodic structures is presented, based on standard methods for topology optimization. The design space is parametrized using nonlinear beam elements and a ground structure approach. A performance criterion is suggested, based on characteristics of the load-deformation curve of the compliant structure. A genetic algorithm is used to find candidate solutions. A numerical implementation of this methodology is discussed and illustrated using simple examples. [DOI: 10.1115/1.2338576]

A paradigm shift is underway in which the classical materials selection approach in engineering design is being replaced by the design of material structure and processing paths on a hierarchy of length scales for multifunctional performance requirements. In this paper, the focus is on designing mesoscopic material topology--the spatial arrangement of solid phases and voids on length scales larger than microstructures but smaller than the characteristic dimensions of an overall product. A robust topology design method is presented for designing materials on mesoscopic scales by topologically and parametrically tailoring them to achieve properties that are superior to those of standard or heuristic designs, customized for large-scale applications, and less sensitive to imperfections in the material Imperfections are observed regularly in cellular material mesostructure and other classes of materials because of the stochastic influence of feasible processing paths. The robust topology design method allows us to consider these imperfections explicitly in a materials design process. As part of the method, guidelines are established for modeling dimensional and topological imperfections, such as tolerances and cracked cell walls, as deviations from intended material structure. Also, as part of the method, robust topology design problems are formulated as compromise Decision Support Problems, and local Taylor-series approximations and strategic experimentation techniques are established for evaluating the impact of dimensional and topological imperfections, respectively, on material properties. Key aspects of the approach are demonstrated by designing ordered, prismatic cellular materials with customized elastic properties that are robust to dimensional tolerances and topological imperfections. [DOI: 10.1115/1.2338575] Keywords: robust design, topology design, cellular materials, material mesostructure, materials design

We demonstrate the effect of using multiple estimations from independent single wireless motes in order to decrease network topology dependence on location estimation in a wireless sensor network. A method of determining the location of a target by using multiple compact semi-directional antennas is shown to give an independent estimate of location from each sensor mote in a network, each estimate not relying on the data from neighboring motes as in the case of traditional triangulation. We begin by demonstrating a method of using angular diversity through multiple semi-directional antennas in order to ascertain the location of a target. The estimation of both range and angle is demonstrated in the presence of a noisy and/or faded channel. An efficient and fast algorithm on a wireless sensor mote is presented through a Taylor series expansion of the simulated antenna pattern. Furthermore, using the results from the location estimation from a single node, location determination in a realistic network is explored through both theory and simulation. The results indicate that our proposed algorithm depends significantly less on the topology (spatial arrangement) of the anchor nodes. While network planning for a variety of topologies of anchor nodes is shown to be necessary when using triangulation, our proposed algorithm is insensitive to the deployments of the anchor nodes. A testbed was created in order to experimentally demonstrate that the predictions are accurate even in triangulation-adverse topologies. The experimental testbed shows that a linear arrangement of closely spaced sensors can reduce the location error to one-fourth of the location error using triangulation. Index Terms--Directional antennas, location determination, sensor networks, topology, triangulation.

A construct of the peer-to-peer (P2P) overlay topology, using a heterogeneity-aware multitier topology to balance the load at peers with varying capacities in a superior way and to check low-capability nodes from strangling the system's performance, is presented. The analytical outcome demonstrates that the multitier technology improves the messaging cost by 8-10 times, 2-3 times better load balancing and 7-8 times reduced topology construction and maintenance costs in comparison with Gnutella's random power-law topology.

The transmission of information within a data network is constrained by the network topology and link capacities. In this paper, we study the fundamental upper bound of information dissemination rates with these constraints in undirected networks, given the unique replicable and encodable properties of information flows. Based on recent advances in network coding and classical modeling techniques in flow networks, we provide a natural linear programming formulation of the maximum multicast rate problem. By applying Lagrangian relaxation on the primal and the dual linear programs (LPs), respectively, we derive a) a necessary and sufficient condition characterizing multicast rate feasibility, and b) an efficient and distributed subgradient algorithm for computing the maximum multicast rate. We also extend our discussions to multiple communication sessions, as well as to overlay and ad hoc network models. Both our theoretical and simulation results conclude that, network coding may not be instrumental to achieve better maximum multicast rates in most cases; rather, it facilitates the design of significantly more efficient algorithms to achieve such optimality. Index Terms--Duality, multicast, network coding, network flow, Steiner tree, subgradient optimization, undirected networks.

Wireless planar networks have been used to model wireless networks in a tradition that dates back to 1961 to the work of E. N. Gilbert. Indeed, the study of connected components in wireless networks was the motivation for his pioneering work that spawned the modern field of continuum percolation theory. Given that node locations in wireless networks are not known, random planar modeling can be used to provide preliminary assessments of important quantities such as range, number of neighbors, power consumption, and connectivity, and issues such as spatial reuse and capacity. In this paper, the problem of connectivity based on nearest neighbors is addressed. The exact threshold function for [theta]-coverage is found for wireless networks modeled as n points uniformly distributed in a unit square, with every node connecting to its [[PHI].sub.n] nearest neighbors. A network is called [theta]-covered if every node, except those near the boundary, can find one of its [[PHI].sub.n] nearest neighbors in any sector of angle [theta]. For all [theta] [member of] (0, 2[pi]), if [[PHI].sub.n] = (1 + [delta]) log 2[pi]/2[pi]-[theta] n, it is shown that the probability of [theta]-coverage goes to one as n goes to infinity, for any [delta] > 0; on the other hand, if [[PHI].sub.n] : (1 -[delta]) log 2[pi]/2[pi]-[theta] n, the probability of [theta]-coverage goes to zero. This sharp characterization of [theta]-coverage is used to show, via further geometric arguments, that the network will be connected with probability approaching one if [[PHI].sub.n] = (1 +[delta]) [log.sub.2] n. Connections between these results and the performance analysis of wireless networks, especially for routing and topology control algorithms, are discussed. Index Terms--Ad hoc networks, connectivity, coverage, random geometric graphs, sensor networks, topology control, transmission power control, wireless networks.

This paper attempts to incorporate the structure of the cerebellar-model-articulation-controller (CMAC) network into the Kohonen layer of the self-organizing map (SOM) to construct a self-organizing CMAC (SOCMAC) network. The proposed SOCMAC network can perform the function of an SOM and can distribute the learning error into the memory contents of all addressed hypercubes as a CMAC. The learning of the SOCMAC is in an unsupervised manner. The neighborhood region of the SOCMAC is implicit in the structure of a two-dimensional CMAC network and needs not be defined in advance. Based on gray relational analysis, a credit-assignment technique for SOCMAC learning is introduced to hasten the overall learning process. This paper also analyzes the convergence properties of the SOCMAC. It is shown that under the proposed updating rule, both the memory contents and the state outputs of the SOCMAC converge almost surely. The SOCMAC is applied to solve both data-clustering and data-classification problems, and simulation results show that the proposed network achieves better performance than other known SOMs. Index Terms--Cerebellar model articulation controller (CMAC), credit assignment, gray relational analysis, neural gas (NG), self-organizing map (SOM), topology-conserving map.

The objective of this paper is to establish general guidelines on the considerations and needs in the development of effective restoration plans for electric utilities serving large metropolitan areas. Power system performance requirements to enhance system reliability and adequacy concerns are proposed to minimize the time it takes to bring a power system into a viable post-restorative operating state. Issues such as use of system resources and network topology, equipment unavailability, electric stiffness of supply points, self-excitation assessment in areas of the system exhibiting large charging currents, and the development of a restoration plan that minimizes disruption and loss of assets in an emergency operating state are addressed. Index Terms--Electric stiffness, equipment availability, over-voltage, protection, restoration, self-excitation, source startup.

It is necessary to develop a write head having a large recording field and small stray field in adjacent tracks and adjacent bits in perpendicular magnetic recording systems. In this paper, a practical three-dimensional topology optimization technique combined with the edge-based finite-element method is proposed. A technique for obtaining a smooth topology is also shown. The optimization of single-pole-type head having a magnetic shield is performed by using the topology optimization technique so that the leakage flux in the adjacent bit can be reduced. A useful shape of the magnetic shield obtained by the proposed technique is illustrated. Index Terms--ON/OFF method, sensitivity analysis, single-pole-type-head, three-dimensional (3-D) topology optimization.

Byline: Guillermo Restrepo (1), Eugenio J. Llanos (2), Heber Mesa (3) Keywords: chemical elements; periodic table; topology; cluster analysis; chemotopology; 54A10; 05C05; 80A50 Abstract: We carried out a mathematical study of 72 chemical elements taking advantage of the chemotopological method. We selected 128 properties to define the elements (physico-chemical, geochemical and chemical properties). Then, we looked for correlated properties and we reduced the number of them to 90. In this way we defined each element as a 90-tuple. Afterwards, we applied principal component analysis and cluster analysis (4 similarity functions and 5 grouping methodologies). Then, we calculated a consensus tree for the 20 dendrograms generated by the CA. Afterwards, we extracted the similarity relationships from the consensus tree and built up a basis for a topology on the set of chemical elements. Finally, we calculated some topological properties (closures, derived sets, boundaries, interiors and exteriors) of several subsets of chemical elements. We found that alkali metals, alkaline earth metals and noble gases appear not related to the rest of the elements. Also, we found that the boundary of non-metals are the semimetals with a stair-shape on the periodic table Author Affiliation: (1) Laboratorio de Quimica Teorica, Universidad de Pamplona, Pamplona, Colombia (2) Observatorio Colombiano de Ciencia y Tecnologia, Carrera 7 No. 39-08, Bogota, Colombia (3) Departamento de Matematicas, Universidad del Valle, Edificio 320, Oficina, 3190, Cali, Colombia Article History: Registration Date: 22/11/2005 Received Date: 20/04/2005 Online Date: 30/12/2005