Shared Edge Research Articles

The Minimum Vulnerability Problem

We revisit the problem of finding $$k$$k paths with a minimum number of shared edges between two vertices of a graph. An edge is called shared if it is used in more than one of the $$k$$k paths. We provide a $${\lfloor {k/2}\rfloor }$$?k/2?-approximation algorithm for this problem, improving the best previous approximation factor of $$k-1$$k-1. We also provide the first approximation algorithm for the problem with a sublinear approximation factor of $$O(n^{3/4})$$O(n3/4), where $$n$$n is the number of vertices in the input graph. For sparse graphs, such as bounded-degree and planar graphs, we show that the approximation factor of our algorithm can be improved to $$O(\sqrt{n})$$O(n). While the problem is NP-hard, and even hard to approximate to within an $$O(\log n)$$O(logn) factor, we show that the problem is polynomially solvable when $$k$$k is a constant. This settles an open problem posed by Omran et al. regarding the complexity of the problem for small values of $$k$$k. We present most of our results in a more general form where each edge of the graph has a sharing cost and a sharing capacity, and there is a vulnerability parameter $$r$$r that determines the number of times an edge can be used among different paths before it is counted as a shared/vulnerable edge.

Synthesis, Crystal Structure, Vibrational and Optical Properties of (Hdea)4(V7O19F)∙0.42H2O, an Original (V7O19F)4− Cluster Oxyfluoride

Synthesis, crystal structure, IR and Raman spectroscopies and optical analysis are reported for a new fluorovanadate with organic cations (Hdea)4(V7O19F)∙0.42H2O (dea: diethylamine). The title compound crystallizes in orthorhombic system, space group P212121, a = 11.486 (5) A, b = 14.779 (5) A, c = 23.243 (5) A, Z = 4, V = 3,946 (2) A3, R = 0.025 with 6,936 reflections. The atomic arrangement can be described as an alternation of inorganic and organic layers. The anionic layer is built up of original clusters (V7O19F)4− which are composed of three VO5F octahedra and four VO4 tetrahedra combined via shared edges and corners. The cohesion between the fluorovanadate groups, organic cations and water molecules is provided by a network hydrogen-bonding. The IR and Raman spectra exhibit characteristic bands of all groups present in the structure. The optical band gap is determined to be 2.5 eV by UV–Vis-T90+ diffuse reflectance spectra, which revealed the nature of semiconductor.

A novel layered aluminophosphate with corner-sharing AlO6chains

The synthesis, Raman spectroscopy and crystal structure of a novel layered aluminophosphate is described. The new phase was derived by the sol-gel method starting from a modified low hydrothermal ALPO4-34 zeolite synthesis procedure[1].The structure was solved by direct methods using single-crystal X-ray diffraction. The synthesized layered material, with composition [AlPO3(OH)F(H2O)]-(H9C4ON), crystallizes in the monoclinic space group P21/a with a = 9.2282(5) Å, b = 6.9152(4) Å, c = 14.4615(9) Å, β = 101.57(1)0. Layered aluminophosphates with AlO6polyhedra have been previously described [2], although in these compounds Al octahedral share edges. The novel compound has corner sharing AlO4F(H2O) chains along [010], where fluorine is at the shared apex, four oxygen atoms are shared with PO4tetrahedra and the fifth oxygen is a H2O group. This kind of aluminophosphate chains is found in nature in tancoite [3]. Chains are linked along [100] through corner sharing with a PO4group of the adjacent chain plus hydrogen bonding of the H2O group. Layers are stacked along c* through hydrogen bonding with a double layer of morpholine (H9C4ON) molecules. The chemical stability field of the novel materialis strongly dependent from the fluorine/aluminum ratio of the starting gel. At lower fluorine concentrations only ALPO4-34 and/or AlPO4(berlinite) are stable depending on the morpholine content. Crystals growth morphology depends on the supersaturation conditions of the starting gel: at low concentrations crystals are well developed hexagonal like plate shaped and are very thin. At higher concentrations they show a more elongated morphology. A treatment with H2CO3leads to a complete morpholine removal, as shown by in situ Raman spectroscopy. Powder X-ray diffraction reveals that after morpholine extraction, the material diffract still coherently in two dimensions while a strong broadening is shown for basal planes.

Highly distorted uranyl ion coordination and one/two-dimensional structural relationship in the Ba2[UO2(TO4)2] (T = P, As) system: an experimental and computational study.

Uranium compounds α-Ba2[UO2(PO4)2] (1), β-Ba2[UO2(PO4)2] (2), and Ba2[UO2(AsO4)2] (3) were synthesized by H3BO3/B2O3 flux reactions, though boron is not incorporated into the structures. Phases 1 and 2 are topologically identical, but 1 is heavily distorted with respect to 2. An unusual UO7 pentagonal bipyramid occurs in 1, exhibiting a highly distorted equatorial configuration and significant bending of the uranyl group, due to edge-sharing with one neighboring PO4(3-) tetrahedron. Compound 2 contains more normal square bipyramids that share corners with four neighboring PO4(3-) tetrahedra, but the uranyl cation UO2(2+) is tilted relative to the equatorial plane. Experimental evidence as well as density functional theory (DFT) calculations suggest that 1 is more stable than 2. In theory, 1 and 2 can interconvert by forming/releasing the shared edge between the uranyl polyhedron and the phosphate tetrahedron. Similar fundamental building blocks in β-Ba2[UO2(PO4)2] and Ba2[UO2(AsO4)2] indicate a possible evolution of uranyl-based structures from chain to layer type and formation of an accretional series.

Инновационные конструкции полотен изделий из древесины при их бесшиповом склеивании

The paper discusses the features of design and technology of finger joints in the manufacture of frame-paneled platings of doors and furniture fronts. At the design stage we solve two problems: a) the choice of shapes and sizes of studs and grooves according to GOST R 9330, b) calculation of probabilistic values of the maximum deviations of landings with interference by GOST 6449. It was proposed to abandon the finger joints, restrict ourselves to assembly in tongue and groove, so with conjugation in counterprofiles groove is milled on the ends the horizontal bars after pre-pruning to eliminate chipping and tongue - on inner shared edge of vertical bars.

Thermal expansion inC2/cpyroxenes: a review and new high-temperature structural data for a pyroxene of composition (Na0.53Ca0.47)(Al0.53Fe0.47)Si2O6(Jd53Hd47)

AbstractSingle-crystal X-ray data collection was performedin situatT= 300 and 700°C on a sample synthesized along the jadeite–hedenbergite series. The structural data, together with those of a previous investigation of a crystal of the same composition, were compared to those of the endmembers. The evolution of the displacement parameters with temperature shows significant residuals for the O1, O2 and O3 oxygen atT= 0 K, most significantly in the O1, which were interpreted as an indication of positional disorder.Volume thermal expansion and axial deformation ellipsoids were calculated for the above sample together with those of a series ofC2/cpyroxenes. Pyroxenes with a divalent M2 cation, Ca, Fe and Mg have a greater expansion than those with a monovalent M2, like Na and Li; the Na pyroxene endmembers with Al, Cr and Fe were observed to show greater expansion than corresponding Li ones.The greater axial expansion is found along thebaxis, except in LiCrSi2O6; the changes along thebaxis are related to the volume thermal expansion. The axial orientation and anisotropy of the two axes onto the (010) plane is different in Na, Li and Ca-Mg-Fe pyroxenes, but the overall expansion onto the (010) plane, given by the sum of the scalar expansion along the two axes on (010), is very similar in pyroxenes.The deformation along thebaxis with temperature and composition is driven by the deformation along b of the octahedral M1 chain; most important is the contribution from the O1−O1 shared edge between M1 octahedra in the same octahedral chain.

A New Delay-Constrained Multicast Routing Algorithm Based on Shared Edges

In this paper, we made a detail analysis for the ESAMPH algorithm, and proposed ESAMPH_D algorithm according to the insufficient of ESAMPH algorithm. The ESAMPH_D algorithm does not consider those paths that do not satisfy the delay constraint, so we can ensure that all paths be taken into account will meet the limit of delay constraint, then we find the least costly path in order to build a minimum cost multicast tree. Simulation results show that the algorithm is better than ESAMPH algorithm in performance.

Two sodium(I) coordination polymers constructed by the V-shaped ligands 2,2′-[isopropylidenebis(1,4-phenyleneoxy)]diacetic acid and 2,2′-[sulfonylbis(1,4-phenyleneoxy)]diacetic acid

Two new inorganic-organic coordination polymers, namely poly[[μ6-2-(4-{1-[4-(carboxymethoxy)phenyl]-1-methylethyl}phenoxy)acetato][μ4-2-(4-{1-[4-(carboxymethoxy)phenyl]-1-methylethyl}phenoxy)acetato]disodium(I)], [Na2(C19H19O6)2]n, (I), and poly[hexa-μ-aqua-diaquabis{μ3-2,2'-[sulfonylbis(1,4-phenyleneoxy)]diacetato}tetrasodium(I)], [Na4(C16H14O8)2(H2O)8]n, (II), have been prepared. In (I), the asymmetric unit contains two Na(I) cations and two 2-(4-{1-[4-(carboxymethoxy)phenyl]-1-methylethyl}phenoxy)acetate (HL1(-)) ligands. Each Na(I) cation is octahedrally coordinated by two ether O atoms and four carboxylate O atoms of three different HL1(-) ligands. The NaO6 polyhedra share edges to form an inorganic ribbon along the a axis. These inorganic ribbons are further connected by the HL1(-) ligands to generate two-dimensional layers parallel to the (001) plane. The structure of (II) consists of ribbons of four crystallographically independent Na atoms (three six- and one five-coordinate), which are bridged by carboxylate O atoms of 4,4'-[sulfonylbis(1,4-phenyleneoxy)]diacetate (L2(2-)) ligands and water molecules. These ribbons are interlinked by L2(2-) ligands through two different coordination modes to afford a three-dimensional network.

(H2en)0.5[BiO(OH)2(H2O)]: The first organic templated layered bismuthate

A novel 2-D organic templated bismuth–oxygen compound (H 2 en) 0.5 [BiO(OH) 2 (H 2 O)] ( 1 ) (en = ethylenediamine) has been synthesized in the presence of ethylenediamine acting as a template under mild hydrothermal conditions. The structure was determined by single crystal X-ray diffraction and further characterized by IR spectrum, elemental analysis, scanning electron microscopy (SEM), photoluminescence and thermogravimetric analysis. In the compound, the Bi atom was coordinated by eight oxygen atoms. The BiO 8 polyhedra share edges or corners with their neighbors to result in an anionic inorganic layer with protonated ethylenediamine cations occupied between layers. At ambient temperature, 1 shows a blue emission band which may be assigned to the 1 P 1 – 1 S 0 transitions of the s 2 electron of the Bi 3 + ion. To our knowledge, 1 is the first example of layered bismuthate templated by an organic amine. A new 2-D organic templated bismuth–oxygen compound (H 2 en) 0.5 [BiO(OH) 2 (H 2 O)] is firstly reported. The BiO 8 polyhedra share edges or corners with the neighboring BiO 8 polyhedra resulting in a layer and the protonated ethylenediamine molecules occupied between layers. ► The first organic template bismuthate compound is reported. ► The Bi atom has eight-fold coordination. ► The compound displays photoluminescence property.

Single-Step Preparation of the Mixed BaII–NbV Oxides from a Heteropolynuclear Oxalate Complex

A novel oxalate-based complex of the formula {Ba(2)(H(2)O)(5)[NbO(C(2)O(4))(3)]HC(2)O(4)}·H(2)O (1) was prepared from an aqueous solution containing the [NbO(C(2)O(4))(3)](3-) and Ba(2+) entities in the molar ratio 1:2, and characterized by X-ray single-crystal diffraction, IR spectroscopy, and thermal analysis. The crystal packing of 1 reveals a complex three-dimensional (3D) network: the Nb polyhedron is connected to eight neighboring Ba polyhedra through the oxalate ligands and the oxo-oxygen group, whereas the Ba polyhedra share edges and vertices. The ability of compound 1 to act as a single-source precursor for the formation of bimetallic oxides was investigated by the thermal analysis (TGA and DSC) and X-ray powder diffraction. Thermal processing of 1 resulted in the formation of mixed-metal oxide phases, Ba(4)Nb(2)O(9) and Ba(5)Nb(4)O(15). Three stable polymorphs of Ba(4)Nb(2)O(9) were isolated: the known, hexagonal α- and orthorhombic γ-Ba(4)Nb(2)O(9), and another one, not previously reported, hexagonal δ-Ba(4)Nb(2)O(9) polymorph. The new, δ-Ba(4)Nb(2)O(9) polymorph has the 6H-perovskite structure (space group P6(3)/m), in which the Nb(2)O(9)(8-) face-sharing octahedral dimers are interconnected via corners to the regular BaO(6)(10-) octahedra. Formation of the mixed-metal oxides takes place at different temperatures: the Ba(5)Nb(4)O(15) oxide occurred at ∼700 °C, as the major crystalline oxide phase; by heating the sample up to 1135 °C, the α-Ba(4)Nb(2)O(9) form was obtained, whereas the heating at 1175 °C caused the crystallization of two polymorphs, γ-Ba(4)Nb(2)O(9) and δ-Ba(4)Nb(2)O(9). Special focus was set on the electrical properties of the prepared mixed Ba(II)-Nb(V) oxides obtained by this molecular pathway in a single-step preparation.

Synthesis, structure, and characterization of a new promising nonlinear optical crystal: Cd5(BO3)3F

A nonlinear optical crystal cadmium fluoroborate (Cd5(BO3)3F) has been synthesized through high-temperature solid-state reactions. In the crystal structure, CdOnFm (n = 4, 5, 7; m = 0, 1, 2) distorted polyhedra interconnect via shared edges and corners to form a 3D framework with tunnels along the c axis. BO3 planar triangles lie approximately parallel in the (001) plane. The combination of triangular BO3 groups with π-conjugated systems and the d10 cation Cd2+ with polar displacement produces large SHG responses. The second harmonic generation (SHG) measurement shows that Cd5(BO3)3F possesses a large SHG response about four times that of KH2PO4 (KDP) and is phase-matchable in the visible region. In addition, it exhibits a wide transparent region ranging from UV to near IR, which suggests that the material is a promising NLO material.

Performance and design of cycles in consensus networks

This work explores the role of cycles in consensus seeking networks for analysis and synthesis purposes. Cycles are critical for many reasons including improving the convergence rate of the system, resilience to link failures, and the overall performance of the system. The focus of this work examines how cycles impact the H2 performance of consensus networks. A first contribution shows that the addition of cycles always improves the performance of the system. We provide an analytic characterization of how the addition of edges improves the performance, and show that it is related to the inverse of the cycle lengths and the number of shared edges between independent cycles. These results are then used to consider the design of consensus networks. In this direction we present an ℓ1-relaxation method that leads to a convex program for adding a fixed number of edges to a consensus networks. We also demonstrate how this relaxation can be used to embed additional performance criteria, such as maximization of the algebraic connectivity of the graph.

Characterizing Fire-on-Fire Interactions in Three Large Wilderness Areas

The interaction of fires, where one fire burns into another recently burned area, is receiving increased attention from scientists and land managers wishing to describe the role of fire scars in affecting landscape pattern and future fire spread. Here, we quantify fire-on-fire interactions in terms of frequency, size, and time-since-previous fire (TSPF) in three large wilderness areas in Montana and Idaho, USA, from 1984 to present, using spatially consistent large fire perimeter data from the Monitoring Trends in Burn Severity (MTBS) dataset. The analysis is supplemented with less consistent fire perimeter data from a regional fire atlas in order to examine the potential role played by smaller fires in fire-on-fire interactions. We compare current rates of burning to existing estimates using the natural fire rotation (NFR) to determine whether recent fire activity falls within established historical ranges. We also compare actual fires to randomly located fires to establish whether the frequency and size of re-burns differ by chance. Finally, we systematically classify shared fire edges as fire-stopping or breached to quantify the effect of previous fires on subsequent fire spread. In total, more than half of the Frank Church, one-quarter of the Bob Marshall, and fifteen percent of the Selway-Bitterroot wilderness areas have burned since 1984. Area burned within each of the study areas yielded NFRs that are consistent with results derived from fire atlas and tree-ring research studies. The data show that re-burning occurs less frequently than chance in the Frank Church Wilderness Area, perhaps less frequently in the Bob Marshall Wilderness Area, and the same as chance in the Selway-Bitterroot Wilderness Area. In each of the study areas, the total amount of edge at which a fire met another fire was less than three percent of the total available perimeter. However, ∼80 % of the total edge encountered was breached, resulting in fire spreading onto previously burned landscapes and re-burning at least 40 ha. Year-to-year variability in re-burn occurrence was high, and the size of re-burns was typically small, implying a general resistance to re-burning, but the preponderance of small patches resulting from fire interactions has perhaps significant ecological implications. There was a systematic decrease in the frequency of small to medium sized re-burns (40 ha to 405 ha) as time between fires increased in all three wilderness areas. The frequency of large re-burns increased with time in the Frank Church wilderness area, but this trend was not apparent in the other two wilderness areas. Overall, fire-on-fire interactions show a high degree of complexity, making direct comparisons between the three wilderness areas difficult, but the evidence suggests that large wildfires generally inhibit the spread of subsequent fires, while small fires appear to have little impact on the spread of other fires. The limiting effect of large fires on small fires is potentially significant based on the number of cases observed (n = 101).

A LINE-BASED 3D ROOF MODEL RECONSTRUCTION ALGORITHM: TIN-MERGING AND RESHAPING (TMR)

Abstract. Three-dimensional building model is one of the major components of a cyber-city and is vital for the realization of 3D GIS applications. In the last decade, the airborne laser scanning (ALS) data is widely used for 3D building model reconstruction and object extraction. Instead, based on 3D roof structural lines, this paper presents a novel algorithm for automatic roof models reconstruction. A line-based roof model reconstruction algorithm, called TIN-Merging and Reshaping (TMR), is proposed. The roof structural line, such as edges, eaves and ridges, can be measured manually from aerial stereo-pair, derived by feature line matching or inferred from ALS data. The originality of the TMR algorithm for 3D roof modelling is to perform geometric analysis and topology reconstruction among those unstructured lines and then reshapes the roof-type using elevation information from the 3D structural lines. For topology reconstruction, a line constrained Delaunay Triangulation algorithm is adopted where the input structural lines act as constraint and their vertex act as input points. Thus, the constructed TINs will not across the structural lines. Later at the stage of Merging, the shared edge between two TINs will be check if the original structural line exists. If not, those two TINs will be merged into a polygon. Iterative checking and merging of any two neighboured TINs/Polygons will result in roof polygons on the horizontal plane. Finally, at the Reshaping stage any two structural lines with fixed height will be used to adjust a planar function for the whole roof polygon. In case ALS data exist, the Reshaping stage can be simplified by adjusting the point cloud within the roof polygon. The proposed scheme reduces the complexity of 3D roof modelling and makes the modelling process easier. Five test datasets provided by ISPRS WG III/4 located at downtown Toronto, Canada and Vaihingen, Germany are used for experiment. The test sites cover high rise buildings and residential area with diverse roof type. For performance evaluation, the adopted roof structural lines are manually measured from the provided stereo-pair. Experimental results indicate a nearly 100% success rate for topology reconstruction was achieved provided that the 3D structural lines can be enclosed as polygons. On the other hand, the success rate at the Reshaping stage is dependent on the complexity of the rooftop structure. Thus, a visual inspection and semi-automatic adjustment of roof-type is suggested and implemented to complete the roof modelling. The results demonstrate that the proposed scheme is robust and reliable with a high degree of completeness, correctness, and quality, even when a group of connected buildings with multiple layers and mixed roof types is processed.

Theoretical Insight into the Structural Stability of KZnB3O6 Polymorphs with Different BOx Polyhedral Networks

In general, the presence of shared edges of polyhedra for high-valence low-coordinated small cations is rarely seen except under extreme conditions such as high pressure. However, the ambient-pressure synthesis of KZnB(3)O(6) built of edge-sharing BO(4) tetrahedra is contrary to this. By investigating the molecular dynamics, lattice dynamics, and electronic properties via density functional theory, we studied the origin of the phase stability of the edge-sharing (es) and "corner-sharing (cs)" KZnB(3)O(6). Lattice dynamics results show that there are no phonon anomalies that could lead to the instability of es-KZnB(3)O(6), which is consistent with molecular dynamics analysis. For "cs-KZnB(3)O(6)", a soft mode at the G point in the phonon dispersion is identified that reflects the dynamic instability with respect to small distortions. Eigenvector analysis of the soft mode of "cs-KZnB(3)O(6)" indicates that the instability comes from the linkage of ZnO(5) polyhedra rather than BO(x) polyhedra. Electronic property calculation indicates that the edge-sharing BO(4) polyhedra connected by the longest B-O σ bonds provide a solid framework for es-KZnB(3)O(6). In the case of "cs-KZnB(3)O(6)", the overlong Zn-O bond possesses the smallest covalent nature and the least orbital overlap among the bonds in a ZnO(5) polyhedron, and these two features of the electronic structure reduce the stability of "cs-KZnB(3)O(6)" compared to es-KZnB(3)O(6). The electronic property calculation further confirms the results obtained from lattice dynamics analysis.

Beyond Swinging: Hinged Dissections that Twist or Fold

A geometric dissection is a cutting of a geometric figure into pieces that can be rearranged to form another figure. Some dissections can be connected with hinges so that the pieces form one figure when swung one way on the hinges, and form the other figure when swung another way. In addition to using “swing hinges”, which allow rotation in the plane, we can use “twist hinges”, which allow one piece to be flipped over relative to another piece via rotation by 180° through a third dimension. Furthermore, we can use “fold hinges”, which allow rotation along a shared edge, a motion that is akin to folding. This talk will introduce a variety of twist-hinged and fold-hinged dissections of regular polygons and stars, and other figures such as polyominoes. The emphasis will be on both appreciating and understanding these fascinating mathematical recreations. I will employ algorithmic and tessellation-based techniques, as well as symmetry and other geometric properties, to design the dissections. The goal will be to minimize the number of pieces, subject to the dissection being suitably hinged. Animations and video will be used to demonstrate the hinged dissections, in addition to actual physical models. Bio: Greg N. Frederickson is a Professor of Computer Science at Purdue University, in West Lafayette, Indiana. His primary area of research is the design and analysis of algorithms, and he has served on the editorial boards of SIAM Journal on Computing, SIAM Journal on Discrete Mathematics, Algorithmica, and IEEE Transactions on Computers. He also pursues interests in mathematical recreations, specifically geometric dissection. On this topic he has published three books and a number of articles. He has twice won the George Polya Award from the Mathematical Association of America.

Crystal structure and non-stoichiometry of cerium brannerite: Ce0.975Ti2O5.95

The crystal structure of cerium brannerite, Ce0.975Ti2O5.95, was determined from Rietveld analysis of high resolution neutron powder diffraction data (space group C2/m, a=9.8320(1)Å, b=3.75287(6)Å, c=6.8852(1)Å, β=119.230(1)°). The presence of both cerium and oxygen vacancies was confirmed from Rietveld analysis and defect energy calculations, combined with careful investigation of the phase diagram. Formation of oxygen vacancies at the O1 site, charge compensated by Ce vacancies, relieves considerable Coulombic repulsion and hence structural strain associated with short O1–O1 contacts forming the shared edge of neighbouring TiO6 polyhedra. Consideration of the bond valence sum of Ce4+ in Ce0.975Ti2O5.95 afforded a revised value of the r0=2.098±0.039Å for the reference bond length, based on analysis of 21 crystal structures mined from the ICSD.

Finding paths with minimum shared edges

Motivated by a security problem in geographic information systems, we study the following graph theoretical problem: given a graph G, two special nodes s and t in G, and a number k, find k paths from s to t in G so as to minimize the number of edges shared among the paths. This is a generalization of the well-known disjoint paths problem. While disjoint paths can be computed efficiently, we show that finding paths with minimum shared edges is NP-hard. Moreover, we show that it is even hard to approximate the minimum number of shared edges within a factor of $2^{\log^{1-\varepsilon}n}$ , for any constant ?>0. On the positive side, we show that there exists a (k?1)-approximation algorithm for the problem, using an adaption of a network flow algorithm. We design some heuristics to improve the quality of the output, and provide empirical results.

Cadmium-rare earth oxyborates Cd4ReO(BO3)3 (Re = Y, Gd, Lu): congruently melting compounds with large SHG responses

A new series of cadmium–rare earth (Re) oxyborates Cd4ReO(BO3)3 (Re = Y, Gd, Lu) have been synthesized through high-temperature solid-state reactions in platinum crucibles. In their crystal structures, ReO6 (Re = Y, Gd, Lu) and CdOn (n = 6, 8) are distorted polyhedra interconnected via shared edges and corners in a 3D framework with tunnels along the c-axis, where all B atoms are located. BO3 planar triangles lie approximately parallel to the (001) plane. The combination of triangular BO3 groups with π-conjugated systems and the d10 Cd2+ cation with polar displacement produces large SHG responses. Second harmonic generation (SHG) measurements indicate that Cd4YO(BO3)3, Cd4GdO(BO3)3, and Cd4LuO(BO3)3 feature large SHG responses that are approximately 5.2, 5.0, and 5.3 × KH2PO4 (KDP), respectively. They are all phase matchable nonlinear optical materials that have wide transparent regions ranging from UV to near IR. These title compounds melt congruently, suggesting that the Cd4ReO(BO3)3 (Re = Y, Gd, Lu) complexes are very promising NLO materials. Their electronic structures and optical properties were analyzed by using the Vienna ab initio theoretical method.

Dy2(SO3)2(SO4)(H2O)2: the first lanthanide mixed sulfate–sulfite inorganic compound

The first lanthanide mixed sulfate-sulfite inorganic coordination polymer, poly[diaqua-μ(4)-sulfato-di-μ(4)-sulfito-didysprosium(III)], [Dy(2)(SO(3))(2)(SO(4))(H(2)O)(2)](n), has been obtained, in which both sulfate and sulfite groups originate from the disproportionation of S(2)O(3)(2-) under hydrothermal and weakly acidic conditions. The crystal structure of the title compound exhibits a three-dimensional framework. The Dy(III) ion is surrounded by eight O atoms from one water molecule and two sulfate and five sulfite groups. These DyO(8) polyhedra have two shared edges and form an infinite zigzag Dy-O chain. In the bc plane, neighbouring chains are integrated through SO(3) trigonal pyramids, forming a two-dimensional sheet. Along the a-axial direction, the sulfate group, with the central S atom lying on a twofold axis, links adjacent two-dimensional sheets via two S-O-Dy connections, thus generating the three-dimensional framework.