Common Edges Research Articles

No pyroanions: The representatives of the lanthanoid(III) fluoride oxidodimolybdates(VI) LnFMo2O7 with the Smaller Cations (Ln = Eu – Yb)

The representatives of lanthanoid(III) fluoride oxidodimolybdates(VI) with the formula LnFMo2O7 (Ln = Eu – Yb) occur during reactions of Ln2O3 and LnF3 with MoO3 in 1: 1: 6molar ratio after 6 days in evacuated silica ampoules at 850°C. The title compounds crystallize monoclinically in space group P2/c (a = 421 – 436, b = 651 – 667, c = 1133 – 1140pm and β = 90.4 – 90.6°, Z =2). The crystal structures contain crystallographically unique Ln3+ cations, which are surrounded by two F– and five O2– anions each, forming distorted pentagonal bypramids with the F− anions as apical vertices by which these bipyramids are fused together to strands according to {[LnF2/2vO5/1t]8−}∞1 running parallel to the a axis. The Mo6+ cations show a distorted square-pyramidal coordination environment of five O2− anions. These pyramids are interconnected by common edges and vertices to form chains with the formula {[MoO2/2eO1/2vO2/1t]−}∞1 which are arranged parallel to [001]. Besides the crystal structure determination single crystal Raman spectroscopy was performed and the magnetic behavior of HoFMo2O7 was determined.

Simultaneous Embedding: Edge Orderings, Relative Positions, Cutvertices

A simultaneous embedding (with fixed edges) of two graphs $$G^{\textcircled {1}}$$ and $$G^{\textcircled {2}}$$ with common graph $$G=G^{\textcircled {1}} \cap G^{\textcircled {2}}$$ is a pair of planar drawings of $$G^{\textcircled {1}}$$ and $$G^{\textcircled {2}}$$ that coincide on G. It is an open question whether there is a polynomial-time algorithm that decides whether two graphs admit a simultaneous embedding (problem Sefe). In this paper, we present two results. First, a set of three linear-time preprocessing algorithms that remove certain substructures from a given Sefe instance, producing a set of equivalent Sefe instances without such substructures. The structures we can remove are (1) cutvertices of the union graph $$G^\cup = G^{\textcircled {1}} \cup G^{\textcircled {2}}$$ , (2) most separating pairs of $$G^\cup $$ , and (3) connected components of G that are biconnected but not a cycle. Second, we give an $$O(n^3)$$ -time algorithm solving Sefe for instances with the following restriction. Let u be a pole of a P-node $$\mu $$ in the SPQR-tree of a block of $$G^{\textcircled {1}}$$ or $$G^{\textcircled {2}}$$ . Then at most three virtual edges of $$\mu $$ may contain common edges incident to u. All algorithms extend to the sunflower case, i.e., to the case of more than two graphs pairwise intersecting in the same common graph.

Structural study, 31P NMR and europium photoluminescence properties of a new synthetic fillowite-type phosphate: Na3SrMg11(PO4)9

A new phosphate compound, Na3SrMg11(PO4)9 was synthesized as single crystals by flux method and as powdered sample by Pechini technique and investigated by X-ray diffraction, 31P NMR and photoluminescence spectroscopies. This compound crystallizes in the rhombohedral space group R 3¯ and its equivalent hexagonal cell has the following parameters: a = 14.941(1) Ǻ, c = 42.478(2) Ǻ and Z = 12. The structure consisted of MgOx (x = 5,6), NaOx (x = 6,7) and (Na,Sr)Ox (x = 8,9) polyhedra which are linked either directly through common corners, edges and faces and by means of the PO4 tetrahedra via common corners and edges, giving rise to a three-dimensional framework, similar to that of the fillowite-like structure. 31P NMR spectroscopy confirmed the presence of six distinct phosphors sites in the structure. Finally, strontium was partially substitute by divalent europium in order to examine whether this material could be used in optical applications. Optical studies were performed on the Na3Sr0.98Eu2+0.02Mg11(PO4)9 compound. The photoluminescence are consistent with the crystal structural and show various properties as a function of the excitation wavelength.

CdX2 Coordination Polymers with 2‐Chloropyrazine and 2‐Methylpyrazine: Similar Ligands – Similar Structures – Different Reactivity

Several coordination compounds, based on Cd halides and 2‐methylpyrazine (Mepyz) or 2‐chloropyrazine (Clpyz) as N‐donor coligands, are synthesized and their crystal structures determined by either single‐crystal or X‐ray powder diffraction (XRPD). In [CdX2(2‐Clpyz)2]n (X = Cl: 1‐Cl‐Clpyz; X = Br: 1‐Br‐Clpyz; and X = I: 1‐I‐Clpyz) and [CdX2(2‐Mepyz)2]n (X = Cl: 1‐Cl‐Mepyz; X = Br: 1‐Br‐Mepyz; and X = I: 1‐I‐Mepyz), the Cd cations are octahedrally coordinated by two N‐donor ligands and are linked into chains by the halide anions that share common edges. In the ligand‐deficient compounds [CdX2(2‐methylpyrazine)]n (X = Cl: 2‐Cl‐Mepyz; X = Br: 2‐Br‐Mepyz; and X = I: 2‐I‐Mepyz), similar CdX2 chains, which are connected into layers by the N‐donor ligands, are observed. Thermal analysis of all 1‐Mepyz compounds shows a transformation into 2‐Mepyz, which is not observed for the 2‐chloropyrazine compounds. On further heating, compounds of composition [(CdX2)2(2‐Mepyz)]n (X = Cl: 3‐Cl‐Mepyz; X = Br: 3‐Br‐Mepyz) and [(CdI2)3(2‐Mepyz)2] (4‐I‐Mepyz) are observed. A discrete complex, with the composition CdI2(2‐Mepyz)2 monohydrate (1‐I‐Mepyz‐H2O), and a hydrate with the composition [(CdI2)(2‐Mepyz)]·1.5H2O (2‐I‐Mepyz‐H2O) with an unknown structure, were also synthesized. Both lose the water molecules upon heating. Luminescence measurements show blue to orange emissions in the range of ca. 22530–16276 cm–1, depending on the halide or pyrazine substituent, as well as the metal halide/ligand ratio.

Narrow-Band Red Emission in the Nitridolithoaluminate Sr4[LiAl11N14]:Eu2+

The new narrow-band red-emitting phosphor material Sr4[LiAl11N14]:Eu2+ was synthesized by solid-state reaction using a tungsten crucible with a cover plate in a tube furnace. When excited with blue light (460 nm), it exhibits red fluorescence with an emission maximum at 670 nm and a full width at half-maximum of 1880 cm–1 (∼85 nm). The crystal structure was solved and refined from single-crystal X-ray diffraction data. This new compound from the group of the nitridolithoaluminates crystallizes in the orthorhombic space group Pnnm (No. 58) with the following unit-cell parameters: a = 10.4291(7) A, b = 10.4309(7) A, and c = 3.2349(2) A. Sr4[LiAl11N14]:Eu2+ shows a pronounced tetragonal pseudo-symmetry. It consists of a framework of disordered (Al/Li)N4 and AlN4 tetrahedra that are connected to each other by common corners and edges. Along the [001] direction, the tetrahedral network creates empty four-membered-ring channels as well as five-membered-ring channels, in which the Sr2+ cations are located.

Synthesis and structural characterization of Li3Y(BO3)2

Abstract Li3Y(BO3)2 was prepared by high-temperature solid state synthesis at 900°C in a platinum crucible from lithium carbonate, boric acid, and yttrium(III) oxide. The compound crystallizes monoclinically in the space group P21/c (no. 14) (Z=4) isotypically to Li3Gd(BO3)2. The structure was refined from single-crystal X-ray diffraction data: a=8.616(3), b=6.416(3), c=10.014(2) Å, β=116.6(2)°, V=494.9(3) Å3, R1=0.0211, and wR2=0.0378 for all data. The crystal structure of Li3Y(BO3)2 consists of [Y2O14] dinuclear units, which are interconnected to each other by planar B(1)O3 groups and LiO4 tetrahedra via common edges and corners along the a axis.

Social Network Extraction Based on Web. A Comparison of Superficial Methods

The Web as a source of information has many potentials which allow to use the different treatments on social network extraction methods. The approaches generally we identified as superficial methods in unsupervised stream. However, the same resources of social networks, i.e. based on a community of social actors, reveal many of different approaches to produce social networks. Therefore, based on a treatment to another treatments, from the given treatments until the different social networks generated and it has been declared different methods. It requires comparison to reveal the properties of social networks and their methods in this paper. It is revealed that there is a core social network has similarity with other social networks is more than 1% as general property of the extracted social networks, whereby there is a social network for different methods has the common edges in graph.

The Shortest Path Problem for a Multiple Graph

In the article, the definition of an undirected multiple graph of any natural multiplicity k > 1 is stated. There are edges of three types: ordinary edges, multiple edges and multi-edges. Each edge of the last two types is the union of k linked edges, which connect 2 or k+1 vertices, correspondingly. The linked edges should be used simultaneously. If a vertex is incident to a multiple edge, it can be also incident to other multiple edges and it can be the common ending vertex to k linked edges of some multi-edge. If a vertex is the common end of some multi-edge, it cannot be the common end of any other multi-edge. Also, a class of the divisible multiple graphs is considered. The main peculiarity of them is a possibility to divide the graph into k parts, which are adjusted on the linked edges and which have no common edges. Each part is an ordinary graph. The following terms are generalized: the degree of a vertex, the connectedness of a graph, the path, the cycle, the weight of an edge, and the path length. There is stated the definition of the reachability set for the ordinary and multiple edges. The adjacency property is defined for a pair of reachability sets. It is shown, that we can check the connectedness of some multiple graph with the polynomial algorithm based on the search for the reachability sets and testing their adjacency. There is considered a criterion of the existence of a multiple path between two given vertices. The shortest multiple path problem is stated. Then we suggest an algorithm of finding the shortest path in a multiple graph. It uses Dijkstra’s algorithm of finding the shortest paths in subgraphs, which correspond to different reachability sets.

Comparison of FEM calculated heat transfer coefficient in a minichannel using two approaches: Trefftz base functions and ADINA software

The paper presents the methods of heat transfer coefficient determination for boiling research during FC-72 flow in a minichannel. The boundary condition in the form of distributions of temperature on the outer side of the minichannel heated wall was obtained using infrared thermography. It was assumed two-dimensional steady-state heat flow. The local values of the heat transfer coefficients on the surface between the heated foil and boiling liquid, were determined from the Robin boundary condition. Data necessary for the heat transfer coefficient evaluation were obtained from numerical computations using two approaches: calculation procedure based on the Trefftz functions and FEM simulations by ADINA software. The shape functions were linear combinations of the Trefftz functions. Combinations of the Trefftz functions exactly satisfy the differential equation. Coefficients of the linear combination of the shape function in the approximate solution were chosen to minimize residuals on domain boundary and along common edges of adjacent elements. Temperature measurement points were located in boundary nodes. During FEM simulations 4-node FCBI elements were used, fluid flow was assumed to be laminar, incompressible and material constants of the fluid and of the foil were independent on temperature. The results of the comparative analysis were presented and discussed.

Finite Element Model for Linear Elastic Thick Shells Using Gradient Recovery Method

This research purposed a new family of finite elements for spherical thick shell based on Nzengwa-Tagne’s model proposed in 1999. The model referred to hereafter as N-T model contains the classical Kirchhoff-Love (K-L) kinematic with additional terms related to the third fundamental form governing strain energy. Transverse shear stresses are computed andC0finite element is proposed for numerical implementation. However, using straight line triangular elements does not guarantee a correct computation of stress across common edges of adjacent elements because of gradient jumps. The gradient recovery method known as Polynomial Preserving Recovery (PPR) is used for local interpolation and applied on a hemisphere under diametrically opposite charges. A good agreement of convergence results is observed; numerical results are compared to other results obtained with the classical K-L thin shell theory. Moreover, simulation on increasing values of the ratio of the shell shows impact of the N-T model especially on transverse stresses because of the significant energy contribution due to the third fundamental form tensor present in the kinematics of this model. The analysis of the thickness ratio shows difference between the classical K-L theory and N-T model when the ratio is greater than 0.099.

Net2Align: An Algorithm For Pairwise Global Alignment of Biological Networks.

The amount of data on molecular interactions is growing at an enormous pace, whereas the progress of methods for analysing this data is still lacking behind. Particularly, in the area of comparative analysis of biological networks, where one wishes to explore the similarity between two biological networks, this holds a potential problem. In consideration that the functionality primarily runs at the network level, it advocates the need for robust comparison methods. In this paper, we describe Net2Align, an algorithm for pairwise global alignment that can perform node-to-node correspondences as well as edge-to-edge correspondences into consideration. The uniqueness of our algorithm is in the fact that it is also able to detect the type of interaction, which is essential in case of directed graphs. The existing algorithm is only able to identify the common nodes but not the common edges. Another striking feature of the algorithm is that it is able to remove duplicate entries in case of variable datasets being aligned. This is achieved through creation of a local database which helps exclude duplicate links. In a pervasive computational study on gene regulatory network, we establish that our algorithm surpasses its counterparts in its results. Net2Align has been implemented in Java 7 and the source code is available as supplementary files.

Acoustic simulation using a novel approach for reducing dispersion error

SummaryIt is well‐known that the traditional finite element method (FEM) fails to provide accurate results to the Helmholtz equation with the increase of wave number because of the ‘pollution error’ caused by numerical dispersion. In order to overcome this deficiency, a gradient‐weighted finite element method (GW‐FEM) that combines Shepard interpolation and linear shape functions is proposed in this work. Three‐node triangular and four‐node tetrahedral elements that can be generated automatically are first used to discretize the problem domain in 2D and 3D spaces, respectively. For each independent element, a compacted support domain is then formed based on the element itself and its adjacent elements sharing common edges (or faces). With the aid of Shepard interpolation, a weighted acoustic gradient field is then formulated, which will be further used to construct the discretized system equations through the generalized Galerkin weak form. Numerical examples demonstrate that the present algorithm can significantly reduces the dispersion error in computational acoustics. Copyright © 2016 John Wiley & Sons, Ltd.

Exploring local regularities for 3D object recognition

In order to find better simplicity measurements for 3D object recognition, a new set of local regularities is developed and tested in a stepwise 3D reconstruction method, including localized minimizing standard deviation of angles(L-MSDA), localized minimizing standard deviation of segment magnitudes(L-MSDSM), localized minimum standard deviation of areas of child faces (L-MSDAF), localized minimum sum of segment magnitudes of common edges (L-MSSM), and localized minimum sum of areas of child face (L-MSAF). Based on their effectiveness measurements in terms of form and size distortions, it is found that when two local regularities: L-MSDA and L-MSDSM are combined together, they can produce better performance. In addition, the best weightings for them to work together are identified as 10% for L-MSDSM and 90% for L-MSDA. The test results show that the combined usage of L-MSDA and L-MSDSM with identified weightings has a potential to be applied in other optimization based 3D recognition methods to improve their efficacy and robustness.

Completely independent spanning trees in some regular graphs

Let k≥2 be an integer and T1,…,Tk be spanning trees of a graph G. If for any pair of vertices {u,v} of V(G), the paths between u and v in every Ti, 1≤i≤k, do not contain common edges and common vertices, except the vertices u and v, then T1,…,Tk are completely independent spanning trees in G. For 2k-regular graphs which are 2k-connected, such as the Cartesian product of a complete graph of order 2k−1 and a cycle, and some Cartesian products of three cycles (for k=3), the maximum number of completely independent spanning trees contained in these graphs is determined and it turns out that this maximum is not always k.

Parameterizable consensus connectomes from the Human Connectome Project: the Budapest Reference Connectome Server v3.0.

Connections of the living human brain, on a macroscopic scale, can be mapped by a diffusion MR imaging based workflow. Since the same anatomic regions can be corresponded between distinct brains, one can compare the presence or the absence of the edges, connecting the very same two anatomic regions, among multiple cortices. Previously, we have constructed the consensus braingraphs on 1015 vertices first in five, then in 96 subjects in the Budapest Reference Connectome Server v1.0 and v2.0, respectively. Here we report the construction of the version 3.0 of the server, generating the common edges of the connectomes of variously parameterizable subsets of the 1015-vertex connectomes of 477 subjects of the Human Connectome Project's 500-subject release. The consensus connectomes are downloadable in CSV and GraphML formats, and they are also visualized on the server's page. The consensus connectomes of the server can be considered as the "average, healthy" human connectome since all of their connections are present in at least k subjects, where the default value of [Formula: see text], but it can also be modified freely at the web server. The webserver is available at http://connectome.pitgroup.org.

Total coloring of planar graphs without adjacent chordal 6-cycles

A total coloring of a graph G is a coloring such that no two adjacent or incident elements receive the same color. In this field there is a famous conjecture, named Total Coloring Conjecture, saying that the the total chromatic number of each graph G is at most $$\Delta +2$$Δ+2. Let G be a planar graph with maximum degree $$\Delta \ge 7$$Δź7 and without adjacent chordal 6-cycles, that is, two cycles of length 6 with chord do not share common edges. In this paper, it is proved that the total chromatic number of G is $$\Delta +1$$Δ+1, which partly confirmed Total Coloring Conjecture.

Hierarchical high‐order conforming C1 bases for quadrangular and triangular finite elements

SummaryWe present three new sets of C1 hierarchical high‐order tensor‐product bases for conforming finite elements. The first basis is a high‐order extension of the Bogner–Fox–Schmit basis. The edge and face functions are constructed using a combination of cubic Hermite and Jacobi polynomials with C1 global continuity on the common edges of elements. The second basis uses the tensor product of fifth‐order Hermite polynomials and high‐order functions and achieves global C1 continuity for meshes of quadrilaterals and C2 continuity on the element vertices. The third basis for triangles is also constructed using the tensor product of one‐dimensional functions defined in barycentric coordinates. It also has global C1 continuity on edges and C2 continuity on vertices. A patch test is applied to the three considered elements. Projection and plate problems with smooth fabricated solutions are solved, and the performance of the h‐ and p‐refinements are evaluated by comparing the approximation errors in the L2‐ and energy norms. A plate with singularity is then studied, and h‐ and p‐refinements are analysed. Finally, a transient problem with implicit time integration is considered. The results show exponential convergence rates with increasing polynomial order for the triangular and quadrilateral meshes of non‐distorted and distorted elements. Copyright © 2016 John Wiley & Sons, Ltd.

Lead flux crystal growth of Ce2Ru12P7

Abstract Well-shaped needles of the metal-rich phosphide Ce2Ru12P7 were grown in a lead flux, while a polycrystalline sample became available through a ceramic route followed by arc-melting. Ce2Ru12P7 crystallizes with the hexagonal Zr2Fe12P7 type: P6̅, a = 940.7(2), c = 389.8(1) pm, wR2 = 0.0342, 1001 F 2 values and 45 variables. Striking structural motifs in the Ce2Ru12P7 structure are tri-capped trigonal prisms that are centered by the phosphorus atoms: P1@Ru7Ce2, P2@Ru7Ce2 and P3@Ru9. Adjacent prisms are condensed via common edges to propeller-like building units.

Common Bayesian Network for Classification of EEG-Based Multiclass Motor Imagery BCI

Modeling and learning of brain activity patterns represent a huge challenge to the brain-computer interface (BCI) based on electroencephalography (EEG). Many existing methods estimate the uncorrelated instantaneous demixing of EEG signals to classify multiclass motor imagery (MI). However, the condition of uncorrelation does not hold true in practice, because the brain regions work with partial or complete collaboration. This work proposes a novel method, termed as a common Bayesian network (CBN), to discriminate multiclass MI EEG signals. First, with the constraints of a Gaussian mixture model on every channel, only related channels are selected to construct a normal Bayesian network. Second, the nodes that have both common and varying edges are selected to construct a CBN. Third, the probabilities on common edges are used to learn about the support vector machine for classification. To validate the proposed method, we conduct experiments on two well-known BCI datasets and perform a numerical analysis of the propose algorithm for EEG classification in a multiclass MI BCI. Experimental results show that the proposed CBN method not only has excellent classification performance, but also is highly efficient. Hence, it is suitable for the cases where a system is required to respond within a second.

Complementary Characteristics of Correlation Patterns in Morphometric Correlation Networks of Cortical Thickness, Surface Area, and Gray Matter Volume.

Morphometric correlation networks of cortical thickness, surface area, and gray matter volume have statistically different structural topology. However, there is no report directly describing their correlation patterns in view of interregional covariance. Here, we examined the characteristics of the correlation patterns in three morphometric networks of cortical thickness, surface area, and gray matter volume using a Venn diagram concept across 314 normal subjects. We found that over 60% of all nonoverlapping correlation patterns emerged with divergent unique patterns, while there were 10% of all common edges in ipsilateral and homotopic regions among the three morphometric correlation networks. It was also found that the network parameters of the three networks were different. Our findings showed that correlation patterns of the network itself can provide complementary information when compared with network properties. We demonstrate that morphometric correlation networks of distinct structural phenotypes have different correlation patterns and different network properties. This finding implies that the topology of each morphometric correlation network may reflect different aspects of each morphometric descriptor.