As part of the Better Life Index, Sustainable Development forms a multi-faceted key role in the way the OECD carries out its policy analysis. This latest blog from the OECD's Chief Statistician outlines how this is done.

The reaction of ligand 5,7-di­hydro-1H,3H-dithieno[3,4-b:3',4'-e]pyrazine (L) with CuI lead to the formation of a three-dimensional coordination polymer, incorporating the well known [CuxIx]n staircase motif (x = 4). These polymer [Cu4I4]n chains are linked via the N and S atoms of the ligand to form the three-dimensional coordination polymer poly[(μ4-5,7-di­hydro-1H,3H-dithieno[3,4-b:3',4'-e]pyrazine-κ4N:N':S:S')tetra-μ3-iodido-tetra­copper], [Cu4I4(C8H8N2S2)]n (I). The asymmetric unit is composed of half a ligand mol­ecule, with the pyrazine ring located about a center of symmetry, and two independent copper(I) atoms and two independent I− ions forming the staircase motif via centers of inversion symmetry. The framework is consolidated by C—H⋯I hydrogen bonds.

The reaction of ligand 3,4,8,10,11,13-hexa­hydro-1H,6H-bis­([1,4]di­thio­cino)[6,7-b:6',7'-e]pyrazine (L) with CuI led to the formation of a two-dimensional coordination polymer, incorporating a [Cu2I2] motif. These units are linked via the four S atoms of the ligand to form the title two-dimensional coordination poly­mer, poly[[μ4-3,4,8,10,11,13-hexa­hydro-1H,6H-bis­([1,4]di­thio­cino)[6,7-b:6',7'-e]pyrazine]di-μ-iodido-dicopper(I)], [Cu2I2(C12H16N2S4)]n, (I). The asymmetric unit is composed of a ligand mol­ecule, two copper(I) atoms and two I− ions. Both copper(I) atoms are fourfold S2I2 coordinate with almost regular trigonal-pyramidal environments. In the crystal, the layers, lying parallel to (102), are linked by C—H⋯I hydrogen bonds, forming a supra­molecular framework.

In the title compound, C61H15ClN2O3, the heterocyclic ring adopts an envelope conformation, folded across the N⋯N line, with the 2,5-di­meth­oxy­phenyl unit occupying a quasi-axial site. There are two N—H⋯O hydrogen bonds in the structure: one hydrogen bond links mol­ecules related by a 41 screw axis to form a C(6) chain, and the other links inversion-related pairs of mol­ecules to form an R22(8) ring. The ring motif links all of the chains into a continuous three-dimensional framework structure. Comparisons are made with the structures of some related compounds.

A one-dimensional ladder-type coordination polymer, poly[[(μ2-hydroxido)(μ2-1H-pyrazole-3,5-di­carboxyl­ato)gallium(III)] monohydrate], [Ga(C5H2N2O4)(OH)(H2O)]n or [Ga(HPDC)(OH)(H2O)]n, I, isotypic with a V3+ coordination polymer previously reported by Chen et al. [J. Coord. Chem. (2008). 61, 3556–3567] was prepared from Ga3+ and pyrazole-3,5-di­carb­oxy­lic acid monohydrate (H3PDC·H2O). Compound I was isolated using three distinct experimental methods: hydro­thermal (HT), microwave-assisted (MWAS) and one-pot (OP) and the crystallite size should be fine-tuned according to the method employed. The coordination polymeric structure is based on a dimeric Ga3+ moiety comprising two μ2-bridging hydroxide groups, which are inter­connected by HPDC2− anionic organic linkers. The close packing of individual polymers is strongly directed by the supra­molecular inter­actions, namely several O—H⋯O and N—H⋯O hydrogen-bonding inter­actions.

A zinc metal–organic framework, namely poly[bis­(N,N-di­ethyl­formamide)(μ4-naphthalene-2,6-di­carboxyl­ato)(μ2-naphthalene-2,6-di­carboxyl­ato)dizinc(II)], [Zn(C12H6O4)(C15H11NO)]n, built from windmill-type secondary building units and forming zigzag shaped two-dimensional stacked layers, has been solvothermally synthesized from naphthalene-2,6-di­carb­oxy­lic acid and zinc(II) acetate as the metal source in N,N-di­ethyl­formamide containing small amounts of formic acid.

The crystal structure of the title compound, [Ni3(C8H4O4)3(C3H7NO)4], is a two-dimensional coordination network formed by trinuclear linear Ni3(tp)3(DMF)4 units (tp = terephthalate = benzene-1,4-di­carboxyl­ate and DMF = di­methyl­formamide) displaying a characteristic coordination mode of acetate groups in polynuclear metal–organic compounds. Individual trinuclear units are connected through tp anions in a triangular network that forms layers. One of the DMF ligands points outwards and provides inter­actions with equivalent planes above and below, leaving the second ligand in a structural void much larger than the DMF mol­ecule, which shows positional disorder. Parallel planes are connected mainly through weak C—H⋯O, H⋯H and H⋯C inter­actions between DMF mol­ecules, as shown by Hirshfeld surface analysis.

The crystal structure of the polymeric title compound, catena-poly[[[di­aqua­lithium]-μ-γ-cyclo­dextrin(1−)-[aqua­lithium]-μ-γ-cyclo­dextrin(1−)] pentadecahydrate], {[Li2(C48H79O40)2(H2O)3]·15H2O}n, consists of deprotonated γ-cyclo­dextrin (CD) mol­ecules assembled by lithium ions into metal–organic ribbons that are cross-linked by multiple O—H⋯O hydrogen bonds into sheets extending parallel to (0overline11). Within a ribbon, one Li+ ion is coordinated by one deprotonated hydroxyl group of the first γ-CD torus and by one hydroxyl group of the second γ-CD torus as well as by two water mol­ecules. The other Li+ ion is coordinated by one deprotonated hydroxyl and by one hydroxyl group of the second γ-CD torus, by one hydroxyl group of the first γ-CD torus as well as by one water mol­ecule. The coordination spheres of both Li+ cations are distorted tetra­hedral. The packing of the structure constitute channels along the a axis. Parts of the hy­droxy­methyl groups in cyclo­dextrin molecules as well as water mol­ecules show two-component disorder. Electron density associated with additional disordered solvent mol­ecules inside the cavities was removed with the SQUEEZE [Spek (2015). Acta Cryst. C71, 9–18] routine in PLATON. These solvent mol­ecules are not considered in the given chemical formula and other crystal data. Five out of the sixteen hy­droxy­methyl groups and one water mol­ecule are disordered over two sets of sites.

The asymmetric units of the title compounds, namely, catena-poly[[(1,4,8,11-tetra­aza­cyclo­tetra­decane-κ4N1,N4,N8,N11)nickel(II)]-μ-1,3-bis­(3-carboxyl­ato­prop­yl)tetra­methyl­disiloxane-κ2O:O'], [Ni(C10H24O5Si2)(C12H24N4)]n (I), and catena-poly[[[(1,4,8,11-tetra­aza­cyclo­tetra­decane-κ4N1,N4,N8,N11)nickel(II)]-μ-4-({[(3-carb­oxy­prop­yl)di­methyl­sil­yl]­oxy}di­methyl­sil­yl)butano­ato-κ2O:O'] per­chlorate], {[Ni(C10H25O5Si2)(C12H24N4)]ClO4}n (II), consist of one (in I) or two crystallographically non-equivalent (in II) centrosymmetric macrocyclic cations and one centrosymmetric dianion (in I) or two centrosymmetric monoanions (in II). In each compound, the metal ion is coordinated by the four secondary N atoms of the macrocyclic ligand, which adopts the most energetically stable trans-III conformation, and the mutually trans O atoms of the carboxyl­ate in a slightly tetra­gonally distorted trans-NiN4O2 octa­hedral coordination geometry. The crystals of both types of compounds are composed of parallel polymeric chains of the macrocyclic cations linked by the anions of the acid running along the [101] and [110] directions in I and II, respectively. In I, each polymeric chain is linked to four neighbouring ones by hydrogen bonding between the NH groups of the macrocycle and the carboxyl­ate O atoms, thus forming a three-dimensional supra­molecular network. In II, each polymeric chain contacts with only two neighbours, forming hydrogen bonds between the partially protonated carb­oxy­lic groups of the bridging ligand. As a result, a lamellar structure is formed with the layers oriented parallel to the (1overline{1}1) plane.

A one-dimensional nickel(II) coordination polymer with the mixed ligands 6-fluoro­nicotinate (6-Fnic) and 4,4'-bi­pyridine (4,4'-bpy), namely, catena-poly[[di­aqua­bis­(6-fluoro­pyridine-3-carboxyl­ato-κO)nickel(II)]-μ-4,4'-bi­pyri­dine-κ2N:N'] trihydrate], {[Ni(6-Fnic)2(4,4'-bpy)(H2O)2]·3H2O}n, (1), was prepared by the reaction of nickel(II) sulfate hepta­hydrate, 6-fluoro­nicotinic acid (C6H4FNO2) and 4,4'-bi­pyridine (C10H8N2) in a mixture of water and ethanol. The nickel(II) ion in 1 is octa­hedrally coordinated by the O atoms of two water mol­ecules, two O atoms from O-monodentate 6-fluoro­nicotinate ligands and two N atoms from bridging 4,4'-bi­pyridine ligands, forming a trans isomer. The bridging 4,4'-bi­pyridine ligands connect symmetry-related nickel(II) ions into infinite one-dimensional polymeric chains running in the [1overline{1}0] direction. In the extended structure of 1, the polymeric chains and lattice water mol­ecules are connected into a three-dimensional hydrogen-bonded network via strong O—H⋯O and O—H⋯N hydrogen bonds, leading to the formation of distinct hydrogen-bond ring motifs: octa­meric R88(24) and hexa­meric R86(16) loops.

The two new pyrazine­ophanes, 5,7-di­hydro-1H,3H-dithieno[3,4-b:3',4'-e]pyrazine, C8H8N2S2, L1, and 3,4,8,10,11,13-hexa­hydro-1H,6H-bis­([1,4]di­thio­cino)[6,7-b:6',7'-e]pyrazine, C12H16N2S4, L2, both crystallize with half a mol­ecule in the asymmetric unit; the whole mol­ecules are generated by inversion symmetry. The mol­ecule of L1, which is planar (r.m.s. deviation = 0.008 Å), consists of two sulfur atoms linked by a rigid tetra-2,3,5,6-methyl­ene­pyrazine unit, forming planar five-membered rings. The mol­ecule of L2 is step-shaped and consists of two S–CH2–CH2–S chains linked by the central rigid tetra-2,3,5,6-methyl­ene­pyrazine unit, forming eight-membered rings that have twist-boat-chair con­fig­urations. In the crystals of both compounds, there are no significant inter­molecular inter­actions present. The reaction of L1 with silver nitrate leads to the formation of a two-dimensional coordination polymer, poly[(μ-5,7-di­hydro-1H,3H-dithieno[3,4-b;3',4'-e]pyrazine-κ2S:S')(μ-nitrato-κ2O:O')silver(I)], [Ag(NO3)(C8H8N2S2)]n, (I), with the nitrato anion bridging two equivalent silver atoms. The central pyrazine ring is situated about an inversion center and the silver atom lies on a twofold rotation axis that bis­ects the nitrato anion. The silver atom has a fourfold AgO2S2 coordination sphere with a distorted shape. The reaction of L2 with silver nitrate also leads to the formation of a two-dimensional coordination polymer, poly[[μ33,4,8,10,11,13-hexa­hydro-1H,6H-bis­([1,4]di­thio­cino)[6,7-b;6',7'-e]pyrazine-κ3S:S':S''](nitrato-κO)silver(I)], [Ag(NO3)(C12H16N2S4)]n, (II), with the nitrate anion coordinating in a monodentate manner to the silver atom. The silver atom has a fourfold AgOS3 coordination sphere with a distorted shape. In the crystals of both complexes, the networks are linked by C—H⋯O hydrogen bonds, forming supra­molecular frameworks. There are additional C—H⋯S contacts present in the supra­molecular framework of II.

A 6-chloro­nicotinate (6-Clnic) salt of a one-dimensional cationic nickel(II) coordination polymer with 4,4'-bi­pyridine (4,4'-bpy), namely, catena-poly[[[tetra­aqua­nickel(II)]-μ-4,4'-bi­pyridine-κ2N:N'] bis­(6-chloro­nicotinate) tetra­hydrate], {[Ni(C10H8N2)(H2O)4](C6H3ClNO2)2·4H2O}n or {[Ni(4,4'-bpy)(H2O)4](6-Clnic)2·4H2O}n, (1), was prepared by the reaction of nickel(II) sulfate hepta­hydrate, 6-chloro­nicotinic acid and 4,4'-bi­pyridine in a mixture of water and ethanol. The mol­ecular structure of 1 comprises a one-dimensional polymeric {[Ni(4,4'-bpy)(H2O)4]2+}n cation, two 6-chloro­nicotinate anions and four water mol­ecules of crystallization per repeating polymeric unit. The nickel(II) ion in the polymeric cation is octa­hedrally coordinated by four water mol­ecule O atoms and by two 4,4'-bi­pyridine N atoms in the trans position. The 4,4'-bi­pyridine ligands act as bridges and, thus, connect the symmetry-related nickel(II) ions into an infinite one-dimensional polymeric chain extending along the b-axis direction. In the extended structure of 1, the polymeric chains of {[Ni(4,4'-bpy)(H2O)4]2+}n, the 6-chloro­nicotinate anions and the water mol­ecules of crystallization are assembled into an infinite three-dimensional hydrogen-bonded network via strong O—H⋯O and O—H⋯N hydrogen bonds, leading to the formation of the representative hydrogen-bonded ring motifs: tetra­meric R24(8) and R44(10) loops, a dimeric R22(8) loop and a penta­meric R45(16) loop.

Owing to their combined open-framework structures and semiconducting properties, two-dimensional thio­stannates show great potential for catalytic and sensing applications. One such class of crystalline materials consists of porous polymeric [Sn3S72−]n sheets with molecular cations embedded in-between. The compounds are denoted R-SnS-1, where R is the cation. Dependent on the cation, some R-SnS-1 thio­stannates transition into amorphous phases upon dispersion in water. Knowledge about the fundamental chemical properties of the thio­stannates, including their water stability and the nature of the amorphous products, has not yet been established. This paper presents a time-resolved study of the transition from the crystalline to the amorphous phase of two violet-light absorbing thio­stannates, i.e. AEPz-SnS-1 [AEPz = 1-(2-amino­ethyl)­piperazine] and trenH-SnS-1 [tren = tris­(2-amino­ethyl)­amine]. X-ray total scattering data and pair distribution function analysis reveal no change in the local intralayer coordination during the amorphization. However, a rapid decrease in the crystalline domain sizes upon suspension in water is demonstrated. Although scanning electron microscopy shows no significant decrease of the micrometre-sized particles, transmission electron microscopy reveals the formation of small particles (∼200–400 nm) in addition to the larger particles. The amorphization is associated with disorder of the thio­stannate nanosheet stacking. For example, an average decrease in the interlayer distance (from 19.0 to 15.6 Å) is connected to the substantial loss of the organic components as shown by elemental analysis and X-ray photoelectron spectroscopy. Despite the structural changes, the light absorption properties of the amorphisized R-SnS-1 compounds remain intact, which is encouraging for future water-based applications of such materials.

Single crystals of the m = 8 member of the low-dimensional monophosphate tungsten bronzes (PO2)4(WO3)2m family were grown by chemical vapour transport technique and the high crystalline quality obtained allowed a reinvestigation of the physical and structural properties. Resistivity measurements revealed three anomalies at TC1 = 258 K, TC2 = 245 K and TC3 = 140 K, never observed until now. Parallel X-ray diffraction investigations showed a specific signature associated with three structural transitions, i.e. the appearance of different sets of satellite reflections below TC1, TC2 and TC3. Several harmonics of intense satellite reflections were observed, reflecting the non-sinusoidal nature of the structural modulations and a strong electron–phonon coupling in the material. These transitions could be associated with the formation of three successive unconventional charge density wave states.

The structure of sodium saccharinate 1.875-hydrate is presented in three- and (3+1)-dimensional space. The present model is more accurate than previously published superstructures, due to an excellent data set collected up to a high resolution of 0.89 Å−1. The present study confirms the unusual complexity of the structure comprising a very large primitive unit cell with Z' = 16. A much smaller degree of correlated disorder of parts of the unit cell is found than is present in the previously published models. As a result of pseudo-symmetry, the structure can be described in a higher-dimensional space. The X-ray diffraction data clearly indicate a (3+1)-dimensional periodic structure with stronger main reflections and weaker superstructure reflections. Furthermore, the structure is established as being commensurate. The structure description in superspace results in a four times smaller unit cell with an additional base centring of the lattice, resulting in an eightfold substructure (Z' = 2) of the 3D superstructure. Therefore, such a superspace approach is desirable to work out this high-Z' structure. The displacement and occupational modulation of the saccharinate anions have been studied, as well as their conformational variation along the fourth dimension.

Anaerobic ammonium-oxidizing (anammox) bacteria play a key role in the global nitrogen cycle and in nitrogenous wastewater treatment. The anammox bacteria ultrastructure is unique and distinctly different from that of other prokaryotic cells. The morphological structure of an organism is related to its function; however, research on the ultrastructure of intact anammox bacteria is lacking. In this study, in situ three-dimensional nondestructive ultrastructure imaging of a whole anammox cell was performed using synchrotron soft X-ray tomography (SXT) and the total variation-based simultaneous algebraic reconstruction technique (TV-SART). Statistical and quantitative analyses of the intact anammox bacteria were performed. High soft X-ray absorption composition inside anammoxosome was detected and verified to be relevant to iron-binding protein. On this basis, the shape adaptation of the anammox bacteria response to iron was explored.

Silicon nanowire-based sensors find many applications in micro- and nano-electromechanical systems, thanks to their unique characteristics of flexibility and strength that emerge at the nanoscale. This work is the first study of this class of micro- and nano-fabricated silicon-based structures adopting the scanning X-ray diffraction microscopy technique for mapping the in-plane crystalline strain (∊044) and tilt of a device which includes pillars with suspended nanowires on a substrate. It is shown how the micro- and nanostructures of this new type of nanowire system are influenced by critical steps of the fabrication process, such as electron-beam lithography and deep reactive ion etching. X-ray analysis performed on the 044 reflection shows a very low level of lattice strain (<0.00025 Δd/d) but a significant degree of lattice tilt (up to 0.214°). This work imparts new insights into the crystal structure of micro- and nanomaterial-based sensors, and their relationship with critical steps of the fabrication process.

New fitting analyses of two-dimensional diffraction-spot shapes are demonstrated to evaluate strain, strain distribution and domain size in a crystalline ultra-thin film. The evaluations are displayed as residual and population maps as a function of strain or domain size.

One of the essential components of molecular electronic circuits are switching elements that are stable in two different states and can ideally be switched on and off many times. Here, distinct buckminsterfullerenes within a self-assembled monolayer, forming a two-dimensional dodecagonal quasicrystal on a Pt-terminated Pt3Ti(111) surface, are identified to form well separated molecular rotational switching elements. Employing scanning tunneling microscopy, the molecular-orbital appearance of the fullerenes in the quasicrystalline monolayer is resolved. Thus, fullerenes adsorbed on the 36 vertex configuration are identified to exhibit a distinctly increased mobility. In addition, this finding is verified by differential conductance measurements. The rotation of these mobile fullerenes can be triggered frequently by applied voltage pulses, while keeping the neighboring molecules immobile. An extensive analysis reveals that crystallographic and energetic constraints at the molecule/metal interface induce an inequality of the local potentials for the 36 and 32.4.3.4 vertex sites and this accounts for the switching ability of fullerenes on the 36 vertex sites. Consequently, a local area of the 8/3 approximant in the two-dimensional fullerene quasicrystal consists of single rotational switching fullerenes embedded in a matrix of inert molecules. Furthermore, it is deduced that optimization of the intermolecular interactions between neighboring fullerenes hinders the realization of translational periodicity in the fullerene monolayer on the Pt-terminated Pt3Ti(111) surface.

This work considers the scaling properties characterizing the hyperuniformity (or anti-hyperuniformity) of long-wavelength fluctuations in a broad class of one-dimensional substitution tilings. A simple argument is presented which predicts the exponent α governing the scaling of Fourier intensities at small wavenumbers, tilings with α > 0 being hyperuniform, and numerical computations confirm that the predictions are accurate for quasiperiodic tilings, tilings with singular continuous spectra and limit-periodic tilings. Quasiperiodic or singular continuous cases can be constructed with α arbitrarily close to any given value between −1 and 3. Limit-periodic tilings can be constructed with α between −1 and 1 or with Fourier intensities that approach zero faster than any power law.

The com­pound poly[2-hy­droxy-N-methyl­ethan-1-aminium [μ3-cyanido-κ3C:C:N-di-μ-cyanido-κ4C:N-dicuprate(I)]], {(C3H10NO)[Cu2(CN)3]}n or [meoenH]Cu2(CN)3, crystallizes in the tetra­gonal space group P43. The structure consists of a three-dimensional (3D) anionic CuICN network with noncoordinated protonated N-methyl­ethano­lamine cations providing charge neutrality. Pairs of cuprophilic Cu atoms are bridged by the C atoms of μ3-cyanide ligands, which link these units into a 43 spiral along the c axis. The spirals are linked together into a 3D anionic network by the two other cyanide groups. The cationic moieties are linked into their own 43 spiral via N—H⋯O and O—H⋯O hydrogen bonds, and the cations inter­act with the 3D network via an unusual pair of N—H⋯N hydrogen bonds to one of the μ2-cyanide groups. Thermogravimetric analysis indicates an initial loss of the base cation and one cyanide as HCN at temperatures in the range 130–250 °C to form CuCN. We show how loss of a specific cyanide group from the 3D CuCN structure could form the linear CuCN structure. Further heating leaves a residue of elemental copper, isolated as the oxide.

The inversion of X-ray reflectivity to reveal the topography of a one-dimensional interface is evaluated through model calculations.

Accurate measurements of natural resources are a prerequisite for resource assessment. Demetrios Gatziolis, a scientist with the USDA Forest Service Pacific Northwest Research Station, and his colleagues with Washington State University developed and tested protocols for using structure-from-motion photogrammetry to obtain data that can be used to construct 3-dimensional (3-D) representations of trees, other vegetation, and down wood. This type of photogrammetry is a remote-sensing technique based on a sequence of digital images or video footage. Gatziolis and his colleagues focused on developing protocols for using it under the forest canopy. Their method can serve as a guide for others interested in obtaining inexpensive, precise 3-D data of trees in field plots. The researchers continue to perfect the technology so it can be reliably deployed by field crews with a minimal amount of training.

Applying the equivariant moving frames method, we construct convergent normal forms for real-analytic 5-dimensional totally nondegenerate CR submanifolds of C^4. These CR manifolds are divided into several biholomorphically inequivalent subclasses, each of which has its own complete normal form. Moreover it is shown that, biholomorphically, Beloshapka's cubic model is the unique member of this class with the maximum possible dimension seven of the corresponding algebra of infinitesimal CR automorphisms. Our results are also useful in the study of biholomorphic equivalence problem between CR manifolds, in question.

The $(q, mathbf{Q})$-current algebra associated with the general linear Lie algebra was introduced by the second author in the study of representation theory of cyclotomic $q$-Schur algebras. In this paper, we study the $(q, mathbf{Q})$-current algebra $U_q(mathfrak{sl}_n^{langle mathbf{Q} angle}[x])$ associated with the special linear Lie algebra $mathfrak{sl}_n$. In particular, we classify finite dimensional simple $U_q(mathfrak{sl}_n^{langle mathbf{Q} angle}[x])$-modules.

The goal of this article is to investigate infinite dimensional affine diffusion processes on the canonical state space. This includes a derivation of the corresponding system of Riccati differential equations and an existence proof for such processes, which has been missing in the literature so far. For the existence proof, we will regard affine processes as solutions to infinite dimensional stochastic differential equations with values in Hilbert spaces. This requires a suitable version of the Yamada-Watanabe theorem, which we will provide in this paper. Several examples of infinite dimensional affine processes accompany our results.

We introduce an infinite-dimensional $p$-adic affine group and construct its irreducible unitary representation. Our approach follows the one used by Vershik, Gelfand and Graev for the diffeomorphism group, but with modifications made necessary by the fact that the group does not act on the phase space. However it is possible to define its action on some classes of functions.

We consider the stochastic 2-dimensional Cahn-Hilliard equation which is driven by the derivative in space of a space-time white noise. We use two different approaches to study this equation. First we prove that there exists a unique solution $Y$ to the shifted equation (see (1.4) below), then $X:=Y+{Z}$ is the unique solution to stochastic Cahn-Hilliard equaiton, where ${Z}$ is the corresponding O-U process. Moreover, we use Dirichlet form approach in cite{Albeverio:1991hk} to construct the probabilistically weak solution the the original equation (1.1) below. By clarifying the precise relation between the solutions obtained by the Dirichlet forms aprroach and $X$, we can also get the restricted Markov uniquness of the generator and the uniqueness of martingale solutions to the equation (1.1).

High dimensional expanders is a vibrant emerging field of study. Nevertheless, the only known construction of bounded degree high dimensional expanders is based on Ramanujan complexes, whereas one dimensional bounded degree expanders are abundant.

In this work, we construct new families of bounded degree high dimensional expanders obeying the local spectral expansion property. This property has a number of important consequences, including geometric overlapping, fast mixing of high dimensional random walks, agreement testing and agreement expansion. Our construction also yields new families of expander graphs which are close to the Ramanujan bound, i.e., their spectral gap is close to optimal.

The construction is quite elementary and it is presented in a self contained manner; This is in contrary to the highly involved previously known construction of the Ramanujan complexes. The construction is also very symmetric (such symmetry properties are not known for Ramanujan complexes) ; The symmetry of the construction could be used, for example, in order to obtain good symmetric LDPC codes that were previously based on Ramanujan graphs.

The main tool that we use for is the theory of coset geometries. Coset geometries arose as a tool for studying finite simple groups. Here, we show that coset geometries arise in a very natural manner for groups of elementary matrices over any finitely generated algebra over a commutative unital ring. In other words, we show that such groups act simply transitively on the top dimensional face of a pure, partite, clique complex.

Among all dissipative solutions of the multi-dimensional isentropic Euler equations there exists at least one that minimizes the acceleration, which implies that the solution is as close to being a weak solution as possible. The argument is based on a suitable selection procedure.

Given an one-dimensional Lorenz-like expanding map we prove that the conditionlinebreak $P_{top}(phi,partial mathcal{P},ell)<P_{top}(phi,ell)$ (see, subsection 2.4 for definition), introduced by Buzzi and Sarig in [1] is satisfied for all continuous potentials $phi:[0,1]longrightarrow mathbb{R}$. We apply this to prove that quasi-H"older-continuous potentials (see, subsection 2.2 for definition) have at most one equilibrium measure and we construct a family of continuous but not H"older and neither weak H"older continuous potentials for which we observe phase transitions. Indeed, this class includes all H"older and weak-H"older continuous potentials and form an open and [2].

Avikainen proved the estimate $mathbb{E}[|f(X)-f(widehat{X})|^{q}] leq C(p,q) mathbb{E}[|X-widehat{X}|^{p}]^{frac{1}{p+1}} $ for $p,q in [1,infty)$, one-dimensional random variables $X$ with the bounded density function and $widehat{X}$, and a function $f$ of bounded variation in $mathbb{R}$. In this article, we will provide multi-dimensional analogues of this estimate for functions of bounded variation in $mathbb{R}^{d}$, Orlicz-Sobolev spaces, Sobolev spaces with variable exponents and fractional Sobolev spaces. The main idea of our arguments is to use Hardy-Littlewood maximal estimates and pointwise characterizations of these function spaces. We will apply main statements to numerical analysis on irregular functionals of a solution to stochastic differential equations based on the Euler-Maruyama scheme and the multilevel Monte Carlo method, and to estimates of the $L^{2}$-time regularity of decoupled forward-backward stochastic differential equations with irregular terminal conditions.

We consider generic optimal Bayesian inference, namely, models of signal reconstruction where the posterior distribution and all hyperparameters are known. Under a standard assumption on the concentration of the free energy, we show how replica symmetry in the strong sense of concentration of all multioverlaps can be established as a consequence of the Franz-de Sanctis identities; the identities themselves in the current setting are obtained via a novel perturbation of the prior distribution of the signal. Concentration of multioverlaps means that asymptotically the posterior distribution has a particularly simple structure encoded by a random probability measure (or, in the case of binary signal, a non-random probability measure). We believe that such strong control of the model should be key in the study of inference problems with underlying sparse graphical structure (error correcting codes, block models, etc) and, in particular, in the derivation of replica symmetric formulas for the free energy and mutual information in this context.

Generally, compositions and methods of producing dimensionally stable three dimensional objects using an additive build up process. Specifically, materials combinable in an additive build up process using a materials printer for the production of stable three dimensional molds useful in the production of molded or formed parts.

A method includes providing a design of a semiconductor device such as a stacked CMOS device comprising a plurality of circuit elements to be assigned into a layout of a plurality of tiers, and identifying at least one first type of circuit element within the plurality of circuit elements based on at least one predetermined criterion. Each respective one of the at least one first type of circuit element is to be assigned to a respective designated one of the plurality of tiers. The method further includes dividing the remainder of the plurality of circuit elements into at least two groups of circuit elements based on circuit density, and assigning the at least one first type of circuit element and the at least two groups of circuit elements to respectively different ones of the plurality of tiers of the semiconductor device.

Methods, systems, and apparatus, including computer programs encoded on computer storage media, for computing numeric representations of words. One of the methods includes obtaining a set of training data, wherein the set of training data comprises sequences of words; training a classifier and an embedding function on the set of training data, wherein training the embedding function comprises obtained trained values of the embedding function parameters; processing each word in the vocabulary using the embedding function in accordance with the trained values of the embedding function parameters to generate a respective numerical representation of each word in the vocabulary in the high-dimensional space; and associating each word in the vocabulary with the respective numeric representation of the word in the high-dimensional space.

Images are analyzed within a 3D environment that is generated based on spatial relationships of the images and that allows users to experience the images in the 3D environment. Image analysis may include ranking images based on user viewing information, such as the number of users who have viewed an image and how long an image was viewed. Image analysis may further include analyzing the spatial density of images within a 3D environment to determine points of user interest.

A three dimensional imaging system includes a first laser emitting light at a first wavelength, and a scanner for scanning the laser light in a pattern on the target area. A photo detector receives light reflected from the target area as a contrasted vein image, resulting from differential absorption and reflection therein of the first wavelength of light. The intensity of the first laser is incrementally increased, and the photo detector thereby receives a plurality of contrasted vein images, each being at incrementally distinct depths beneath the target skin surface. Image processing is performed on the plurality of vein images to successively layer the veins in the images according to their depth, to create a single processed vein image. A second laser emitting a second wavelength of light is used in combination with the scanner to project the processed vein image onto the target area to overlay the veins therein.

Curable, phase-change compositions and inks used for printing three-dimensional objects including a curable monomer, a photoinitiator, a wax and a gellant, where the composition of the cured formulation has a room temperature modulus of from about 0.01 to about 5 Gpa. The curable monomer includes acrylic monomer, polybutadiene adducted with maleic anhydride, aliphatic urethane acrylate, polyester acrylate, 3-acryloxypropyltrimethoxysilane, or acryloxypropyl t-structured siloxane.

The present disclosure includes methods, systems, and devices for prioritization of three dimensional dental elements. One method for prioritizing three dimensional dental elements includes receiving a virtual initial dental data set (IDDS) of teeth having spatial information regarding the positions of a number of teeth in the virtual IDDS with respect to each other for presentation of the teeth in a virtual three dimensional space to be viewed on a user interface, setting prioritization values of a number of elements of one or more of the number of teeth, and prioritizing the number of elements to be selected by a user based upon their prioritization values.

A noncontact optical three-dimensional measuring device that includes a projector, a first camera, and a second camera; a processor electrically coupled to the projector, the first camera and the second camera; and computer readable media which, when executed by the processor, causes the first digital signal to be collected at a first time and the second digital signal to be collected at a second time different than the first time and determines three-dimensional coordinates of a first point on the surface based at least in part on the first digital signal and the first distance and determines three-dimensional coordinates of a second point on the surface based at least in part on the second digital signal and the second distance.

A 3D image sensor includes a depth pixel that includes; a photo detector generating photo-charge, first and second floating diffusion regions, a first transfer transistor transferring photo-charge to the first floating diffusion region during a first transfer period in response to a first transfer gate signal, a second transfer transistor transferring photo-charge to the second floating diffusion region during a second transfer period in response to a second transfer gate signal, and an overflow transistor that discharges surplus photo-charge in response to a drive gate signal. Control logic unit controlling operation of the depth pixel includes a first logic element providing the first transfer gate signal, a second logic element providing the second transfer gate signal, and another logic element providing the drive gate signal to the overflow transistor when the first transfer period overlaps, at least in part, the second transfer period.

According to one embodiment, a three-dimensional shape measuring apparatus includes at least an aperture plate that is provided with a plurality of confocal apertures which are two-dimensionally arranged to have a predetermined arrangement period, and an aperture plate displacement portion that displaces the aperture plate at a constant speed in a predetermined direction perpendicular to the optical axis direction. Further, the aperture plate is provided with a cover member which is moved integrally with the aperture plate and which includes a transparent body allowing the light beams from the light source to pass therethrough and to be irradiated to the plurality of confocal apertures, and protects the plurality of confocal apertures from dust. Further, an imaging optical system, by which each of reflected light beams is guided to a photo-detector, is designed in consideration of optical properties of the whole optical system including the transparent body of the cover member.

The present invention relates to a composite of a porous substrate and one-dimensional nanomaterial, which is manufactured by a hydrothermal method. The method for manufacturing the composite of the present invention is simple and low-cost, and the one-dimensional nanomaterial is homogeneously distributed on the porous substrate with tight binding at the interface. The present invention also relates to a surface-modified composite and a method for preparing the same. The composite of the present invention which is hydrophobically modified at the surface can adsorb organic solvents such as toluene, dichlorobenzene, petroleum ether and the like, and greases such as gasoline, lubricating oil, motor oil, crude oil and the like, with a weight adsorption ratio of >10.

For a memo pad, many sheets 1 are bound at a back face as bound sheets using gum. The memo pad is provided with a cover paper on the top and a mounting paper on the bottom. The sheets 1 are printed from a central area of the sheet surface to over an outer peripheral area, with a decorative pattern. Outer peripheral non glued edges of the memo pad have a rugged shape modeled after the decorative pattern in a direction of the sheet surface and in a direction of the bound sheet thickness, such that even if the sheets 1 are turned up one by one or removed, a three dimensional decorative pattern reappears from the surface of the remaining sheets 1 to over the outer peripheral edge.

A method serves to produce a three-dimensional object by additive construction in direct construction sequence from solidifiable material, which is either present in the starting state in a fluid phase or can be liquefied, where multiple material components are discharged alternately in a programmable manner by means of multiple discharge units and configure different parts of the object joined to one another as a result of the discharge, where the geometric proportions obtained during discharge already correspond to the object, and because the material components form between them either edge regions merging into one another without boundaries or boundary regions of the different material components abutting one another without joining, a method and an object produced therewith can be provided, in which boundary and edge regions are formed “as if from one piece” between different material components even in the case of complex geometries.

Identification of maximum power scatters in an N-dimensional dataset generally requires two basic steps. The first step is to identify the max power scatters of the dataset and the second step removes neighboring power scatters (e.g., “hits”) of lower power. Current naïve approaches utilize an inefficient and computationally intensive brute force implementation which requires multiple comparisons of each initial “hit” power to all “hits” of lesser power. Such brute force implementations require 2×N×(M−1)! comparisons, where N is the number of dimensions and M is the number of “hits.” Embodiments of the present disclosure utilize vectorization to identify a plurality of neighboring hits for each max power scatter and removes the neighboring hits of lesser power that are within a predetermined isolation region. Advantageously, embodiments of the present invention perform M−1 comparisons.

An apparatus and article for cutting print media associated with a printing process. A media cutting logic-controlled head is incorporated into printing hardware. The cutting head is provided with a plurality of cutting devices that may be implemented in the form of cutting pins. Control logic is provided to individually control an extension or actuation of each of the cutting devices. Multiple cutting devices may be simultaneously extended and retracted or activated and deactivated, to cut the media at multiple locations. The cutting head can be integrated with any of existing printers transforming a printer into a media cutting device capable of cutting two-dimensional complex shapes at the full line speed without requiring change in speed or reversal of the media at any point.

An improved set of toy building or construction blocks, each block having a substantially square cross-section and a generally rectilinear configuration. Incorporated into the structure of the individual toy blocks are transversely oriented slots, grooves and protrusions of predetermined size and location. The slots, grooves and protrusions of pre-determined size and location are of either male or female configuration disposed medially along one or more plane of each block. When the male protrusion of one block is introduced perpendicular to the female slot of one end of another block, a frictional engagement is created resulting in a right angle. When the male protrusion of one block is introduced to the female slot in a linear fashion the result is a line segment. Joining a plurality of said toy building or construction blocks using various perpendicular connections in conjunction with linear connections results in the stable formation of construction or geometric structures without the use of fasteners or other connecting elements.

A method for providing a feedback circuit for a three dimensional projector. First and second input devices and a sensor for determining the rotational speed of the second input device are provided. A control device for controlling the rotational speed of the second input device and a phase locked loop (PLL) are provided. A phase reference signal is created based on the signal rate of the first input device. A phase signal is created based on the rotational speed of the second input device. The PLL compares the phase reference signal and the phase feedback signal to determine whether the first input device and the second input device are synchronized. A signal is sent to the control device for the second input device to change the rotational speed of the second input device in response to determining that the first input device and the second input device are not synchronized.