Skeleton Of Complex Research Articles

Towards replacing physical testing of granular materials with a Topology-based Model

In the study of packed granular materials, the performance of a sample (e.g., the detonation of a high-energy explosive) often correlates to measurements of a fluid flowing through it. The "effective surface area," the surface area accessible to the airflow, is typically measured using a permeametry apparatus that relates the flow conductance to the permeable surface area via the Carman-Kozeny equation. This equation allows calculating the flow rate of a fluid flowing through the granules packed in the sample for a given pressure drop. However, Carman-Kozeny makes inherent assumptions about tunnel shapes and flow paths that may not accurately hold in situations where the particles possess a wide distribution in shapes, sizes, and aspect ratios, as is true with many powdered systems of technological and commercial interest. To address this challenge, we replicate these measurements virtually on micro-CT images of the powdered material, introducing a new Pore Network Model based on the skeleton of the Morse-Smale complex. Pores are identified as basins of the complex, their incidence encodes adjacency, and the conductivity of the capillary between them is computed from the cross-section at their interface. We build and solve a resistive network to compute an approximate laminar fluid flow through the pore structure. We provide two means of estimating flow-permeable surface area: (i) by direct computation of conductivity, and (ii) by identifying dead-ends in the flow coupled with isosurface extraction and the application of the Carman-Kozeny equation, with the aim of establishing consistency over a range of particle shapes, sizes, porosity levels, and void distribution patterns.

A family of monomial ideals with the persistence property

In this paper, we introduce a family of monomial ideals with the persistence property. Given positive integers [Formula: see text] and [Formula: see text], we consider the monomial ideal [Formula: see text] generated by all monomials [Formula: see text], where [Formula: see text] is an independent set of vertices of the path graph [Formula: see text] of size [Formula: see text], which is indeed the facet ideal of the [Formula: see text]th skeleton of the independence complex of [Formula: see text]. We describe the set of associated primes of all powers of [Formula: see text] explicitly. It turns out that any such ideal [Formula: see text] has the persistence property. Moreover, the index of stability of [Formula: see text] and the stable set of associated prime ideals of [Formula: see text] are determined.

Dominating sets in intersection graphs of finite groups

Let $G$ be a group. The intersection graph $\Gamma (G)$ of $G$ is an undirected graph without loops and multiple edges, defined as follows: the vertex set is the set of all proper non-trivial subgroups of $G$, and there is an edge between two distinct vertices $H$ and $K$ if and only if $H\cap K \neq 1$, where $1$ denotes the trivial subgroup of $G$. In this paper, we study the dominating sets in intersection graphs of finite groups. We classify abelian groups by their domination number and find upper bounds for some specific classes of groups. Subgroup intersection is related to Burnside rings. We introduce the notion of an intersection graph of a $G$-set (somewhat generalizing the ordinary definition of an intersection graph of a group) and establish a general upper bound for the domination number of $\Gamma (G)$ in terms of subgroups satisfying a certain property in the Burnside ring. The intersection graph of $G$ is the $1$-skeleton of the simplicial complex. We name this simplicial complex intersection complex of $G$ and show that it shares the same homotopy type with the order complex of proper non-trivial subgroups of $G$. We also prove that, if the domination number of $\Gamma (G)$ is 1, then the intersection complex of $G$ is contractible.

A new approach to understanding structure, functions and classificasion of GABA-benzodiazepine receptor complex, a molecular target for creation of new anticonvulsants on the base of inhibitory amino acids

The GABA molecule was shown to the methods of quantum mechanic characteristics and molecular geometry has three conformational states: linear (GABA-1 conformer), cyclic (GABA-2 comformer) and bucket-like (GABA-3 conformer). The play different functions in the brain neurons: cyclic and bucket-like conformers play role of endogenous transmitters, and linear conformer participates in neuronal metabolism. The theoretical conformational analysis shows there are two types of GABA receptors in the CNS neurons: GABA-2 receptors, agonists of which are cyclic conformer of GABA, glycine and β-alanine and antagonists are bemegride, pentilentetrazol and strychnine; and GABA-3 receptors, agonists of which is bucket-like conformer of GABA and antagonists are picrotoxin and bicuculline. Anticonvulsive and other behavioral effects of derivatives of barbituric acid, benzazepine, benzodiazepine, gidantoine, succinimide and oxasolidindione are realized probably via GABA-2 receptors to switch on them the following functional centers of their structure are nessesary: α, γ and [δ-ε] for barbitirates; β, [δ-ε] and γ for carbamazepine; β and [δ-ε] for benzodiazepine derivatives, gabapentine and vigabatrine; α, β, γ and [δ-ε] for gidantoine and oxasolidindione derivatives; α, β, γ for succinimide derivatives. The power of any behavioral effect of anticonvulsants and inhibitory amino acids depends on power, location and numbers of hydrogen bounds developed between active centers of pharmacophore of anticonvulsant or inhibitory amino acids and active centers of functional skeleton of GABA-2 receptor complex, these properties determine absense of nootropic activity in anticonvulsive drugs and presense of them in inhibitory amino acids. It is concluded there are perspectives of synthesis of conpounds, pharmacophore of which should be like as cyclic conformer of GABA, glycine and β-alanine on their quantum mechanic characteristics and molecular geometry

Syzygies of the Veronese Modules

We study the minimal free resolution of the Veronese modules, Sn, d, k = ⊕i≥0Sk+id, where S = 𝕂[x1,…, xn], by giving a formula for the Betti numbers in terms of the reduced homology of some skeleton of a simplicial complex. We prove that Sn, d, k is Cohen–Macaulay if and only if k < d, and that its minimal resolution is pure and has some linearity features when k > d(n − 1) − n. We prove combinatorially that the resolution of S2, d, k is pure. We show that . As an application, we calculate the complete Betti diagrams of the Veronese rings 𝕂[x, y, z](d), for d = 4, 5, and 𝕂[x, y, z, u](3).

Application of molecular probe to investigate surface structure of metal passivator on copper

Copper sulfide (Cu 2 S) contaminant is semi-conductive. Its formation and migration to insulating paper and oil caused insulation breakdown. Addition of benzotriazole derivatives as metal passivator slows down the corrosion process, as the metal passivator produces a protective layer on the copper surface, which prevents the reaction between corrosive sulfur and copper. But the surface structure of this impermeable film is still unknown. Herein we reported our investigation on the orientation of metal-passivator complex on copper surface by means of molecular probe. Ageing experimental study with different steric and electronic groups in benzotriazole skeleton indicated that the second position of the molecule was sensitive to steric effect, suggesting end-on orientation preferable. Subsequently, SEM-EDX revealed the relative amount of copper sulfide on copper surface. Moreover, FTIR represented the characteristic wavenumber of C=O, C=N moiety and benzene skeleton of passivator-copper complex. XPS analysis delivered the organic elemental composition of the protective layer.

The subset of [formula omitted] realizing metrics on the curve complex

For each point V, a subset of R3, we define a distance on the one skeleton of curve complex for each point and prove that (1) for each point in V with all positive entries, the one skeleton of curve complex under this distance is a metric space and δ-hyperbolic for some δ∈R+; (2) for each point in V with at least one non-positive entry, the diameter of vertices of curve complex under this distance is finite.

Constructing convex planes in the pants complex

Our main theorem identifies a class of totally geodesic subgraphs of the $1$-skeleton of the pants complex, referred to as the pants graph, each isomorphic to the product of two Farey graphs. We deduce the existence of many convex planes in the pants graph of any surface of complexity at least $3$.

(6,7-Dimethyl-2,3-di-2-pyridylquinoxaline)bis(3-methylpyridine)platinum(II) bis(hexafluorophosphate) acetone solvate 0.5-hydrate

The crystal structure of the title compound, [Pt(C6H7N)2(C20H16N4)](PF6)2.C3H6O.0.5H2O, is composed of a bivalent square-planar platinum(II) complex, two PF6- counter-ions and solvent molecules. The di-2-pyridylquinoxaline ligands are known to confer an 'L shape' on square-planar platinum(II) complexes, which also display intercalating properties. The structural characterization reported here is a contribution to a wide-ranging study focused on structural and dynamical analyses of these substrates, which may provide better insight into their biological mechanisms and activities. The expected 'L-shaped' skeleton of the metallic complex combined with the antiparallel orientation of substituted pyridines (anti conformation) generates chiral objects, found in the solid state as a racemic mixture.

Studies of an Enneanuclear Manganese Single-Molecule Magnet

The reaction of [Mn(3)O(O(2)CMe)(6)(py)(3)] with the tripodal ligand H(3)thme (1,1,1-tris(hydroxymethyl)ethane) affords the enneanuclear complex [Mn(9)O(7)(O(2)CCH(3))(11)(thme)(py)(3)(H(2)O)(2)] 1.1MeCN.1Et(2)O. The metallic skeleton of complex 1 comprises a series of 10 edge-sharing triangles that describes part of an idealized icosahedron. Variable temperature direct current (dc) magnetic susceptibility data collected in the 1.8-300 K temperature range and in fields up to 5.5 T were fitted to give a spin ground state of S = (17)/(2) with an axial zero-field splitting parameter D = -0.29 cm(-)(1). Ac susceptibility studies indicate frequency-dependent out-of-phase signals below 4 K and an effective barrier for the relaxation of the magnetization of U(eff) = 27 K. Magnetic measurements of single crystals of 1 at low temperature show time- and temperature-dependent hysteresis loops which contain steps at regular intervals of field. Inelastic neutron scattering (INS) studies on complex 1 confirm the S = (17)/(2) ground state and analysis of the INS transitions within the zero-field split ground state leads to determination of the axial anisotropy, D = -0.249 cm(-)(1), and the crystal field parameter, B(4)(0) = 7(4) x 10(-)(6) cm(-)(1). Frequency domain magnetic resonance spectroscopy (FDMRS) determined the same parameters as D = -0.247 cm(-)(1) and B(4)(0) = 4.6 x 10(-)(6) cm(-)(1). DFT calculations are fully consistent with the experimental findings of two Mn(II) and four Mn(III) ions "spin up" and three Mn(IV) ions "spin down" resulting in the S = (17)/(2) spin ground state of the molecule, with D = -0.23 cm(-)(1) and U = 26.2 K.

Characterization of a Novel Binuclear Palladium(II) Complex Formed from the Reaction of 2‐Chloro‐3, 3‐diphenyl‐1‐(2, 4, 6‐tri‐tert‐butylphenyl)‐1, 3‐diphosphapropene with Tetrakis(triphenylphosphine)palladium(0) Including Hydrolysis

Abstract2‐Chloro‐3, 3‐diphenyl‐1‐(2, 4, 6‐tri‐tert‐butylphenyl)‐1, 3‐diphosphapropene was allowed to react with an equivalent amount of tetrakis(triphenylphosphine)palladium(0) and a novel binuclear palladium(II) complex which includes two P2O‐tridentate ligands [Mes*P(O)CH2PPh2]2[PdCl]2 (Mes* = 2, 4, 6‐tBu3C6H2) was isolated after workup procedure. A tricyclic skeleton of the binuclear complex was characterized by the X‐ray crystallography.

New Rearrangement and Fragmentation Processes of Group 6 Alkoxyalkynyl (Fischer) Carbene Complexes Induced by Aromatic Diamines

The rearrangement of chromium(0) carbene complexes 4 to isocyanides 5 occurs either thermally or by SiO2 catalysis through 1,2-diaminobenzene addition followed by breakage of the bicyclic carbene intermediate 11. Complexes 4 with 1,8-diaminonaphthalene lead in very smooth conditions to 2-substituted perimidines 9 with good yields through an unprecedented cleavage of the carbon skeleton of the metal complex in a formal retro-Aumann reaction.

Three-dimensional magnetic reconnection in the solar corona

In two dimensions the notions of magnetic topology and null-point bifurcations are straightforward. In addition, the nature of magnetic reconnection is fairly well understood and can be described by a new generation of fast reconnection mechanisms known as almost-uniform reconnection and nonuniform reconnection. However, in complex three-dimensional (3-D) magnetic fields, such as exist in the solar corona, these phenomena are only just beginning to be explored and are considerably more complex. The structural properties of the magnetic field created in turn by two, three and more magnetic sources at the photosphere have been recently studied. Passing through each 3-D magnetic null there is an isolated spine field line and a flux surface known as a fan. The fans form separatrix surfaces that separate the volume into topologically distinct regions, and the fan of one null can terminate at the spine of another null, while the spine terminates either at a source or at infinity. The skeleton of complex 3-D fields in the corona, therefore, comprises the magnetic-null points and a network of spine curves and separatrix fan surfaces. Magnetic reconnection can occur in these fields by a variety of mechanisms, including spine reconnection, fan reconnection, separator reconnection, and quasiseparatrix layer reconnection. These types of reconnection and the bifurcations of null points are described and found to be much richer than in the relatively simple two-dimensional fields.

Crystal and molecular structure of η-cyclopentadienyl[1,3,4-η-(1,2-dimethoxycarbonyl-5,5,5-trifluoro-3-trifluoromethylpent-1,3-dienyl)] triphenylphosphineruthenium. An unexpected reaction product from hexafluorobut-2-yne and a vinylruthenium complex

Crystals of [[graphic omitted]C(CF3)H(PPh3)(η-C5H5)] are triclinic, space group, P, with Z= 2 in a unit cell of dimensions a= 9.353(4), b= 16.346(16), c= 10.875(6)Å, α= 93.82(7), β= 113.07(4), γ= 94.26(6)°. The structure has been solved by conventional heavy-atom methods from 4 184 diffracted intensities measured on a diffractometer and refined by block-matrix least-squares to R 0.039. The skeleton of the vinylruthenium complex remains intact, but the chain is extended by σ-addition of one molecule of hexafluorobut-2-yne with subsequent π-bonding of this acetylene to the ruthenium atom to form a cyclic system, [graphic omitted]C(CF3)H. The co-ordination around the ruthenium atom is approximately octahedral, three sites being occupied by the η5-cyclopentadienyl ring and one by the triphenylphosphine ligand.

Synthesis of the basic nucleoside skeleton of the polyoxin complex

Synthesis of the basic nucleoside skeleton of the polyoxin complex