Constraints on the fundamental topological parameters of spatial tessellations

Tessellations of that use convex polyhedral cells to fill the space can be extremely complicated, especially if they are not “facet‐to‐facet”, that is, if the facets of a cell do not necessarily coincide with the facets of that cell's neighbours. In a recent paper 15 , we have developed a theory which covers these complicated cases, at least with respect to their combinatorial topology. The theory required seven parameters, three of which suffice for facet‐to‐facet cases; the remaining four parameters are needed for the awkward adjacency concepts that arise in the general case. This current paper establishes constraints that apply to these seven parameters and so defines a permissible region within their seven‐dimensional space, a region which we discover is not bounded. Our constraints in the relatively simple facet‐to‐facet case are also new.     

Structural flexibility and role of vicinal 2-thienyl rings in 2,3-dicyano-5,6-di(2-thienyl)-1,4-pyrazine, [(CN)2Th2Pyz], its palladium(II) complex [(CN)2Th2Pyz(PdCl2)2], and the related pentametallic pyrazinoporphyrazines [(PdCl2)4Th8TPyzPzM] (M = Mg(II)(H2O), Zn(II))

The solid state and solution structure of 2,3-dicyano-5,6-di(2-thienyl)-1,4-pyrazine, [(CN)(2)Th(2)Pyz], and its Pd(II) derivative, [(CN)(2)Th(2)Pyz(PdCl(2))(2)]·H(2)O, formed by reaction of [(CN)(2)Th(2)Pyz] with [(C(6)H(5)CN)(2)PdCl(2)] were characterized by X-ray, UV-visible, (1)H and (13)C NMR, and extended X-ray absorption fine structure (EXAFS) spectral measurements. The X-ray crystal structure of [(CN)(2)Th(2)Pyz] shows the presence of one thienyl ring positioned orthogonal to the rest of the molecule, with the two vicinal thienyl rings lying orthogonal to each other in a rare arrangement. NMR studies of [(CN)(2)Th(2)Pyz] in the solid state and in solutions of dimethylformamide or dimethyl sulfoxide confirm a nonequivalence of the thienyl rings in the solid state and also in solution. EXAFS results indicate that two distinct Pd(II) coordination sites are formed at the di(2-thienyl)pyrazino moiety of [(CN)(2)Th(2)Pyz(PdCl(2))(2)]·H(2)O, with identical Pd-N(pyz) (2.03(3) ?) and Pd-Cl (2.36(3) ?) bond lengths but with different Pd-S1 (2.25(4) ?) and Pd-S2 (3.21(5) ?) bond distances in an overall asymmetric molecular framework. Density functional theory (DFT) and time-dependent DFT (TDDFT) theoretical studies also provide information about the structure and spectral behavior of the precursor and its metalated Pd(II) derivative. (1)H/(13)C NMR and UV-visible spectral measurements were also carried out on two heteropentametallic porphyrazine macrocycles which were prepared by a reaction of PdCl(2) with [Th(8)TPyzPzM] where Th(8)TPyzPz = tetrakis-2,3-[5,6-di-(2-thienyl)-pyrazino]porphyrazinato dianion and M = Mg(II)(H(2)O) or Zn(II). Spectroscopic data on the newly synthesized [(PdCl(2))(4)Th(8)TPyzPzM] compounds suggest that the binding of PdCl(2) involves coordination sites of the type S(2(th))PdCl(2) with the two thienyl rings of each di(2-thienyl)pyrazino fragment bound to Pd(II) in an equivalent manner ("th-th" coordination). This is similar to what was found for the corresponding octapyridinated analogues ("py-py" coordination).     

Structure and dynamics of the fast lithium ion conductor "Li7La3Zr2O12"

The solid lithium-ion electrolyte "Li(7)La(3)Zr(2)O(12)" (LLZO) with a garnet-type structure has been prepared in the cubic and tetragonal modification following conventional ceramic syntheses routes. Without aluminium doping tetragonal LLZO was obtained, which shows a two orders of magnitude lower room temperature conductivity than the cubic modification. Small concentrations of Al in the order of 1 wt% were sufficient to stabilize the cubic phase, which is known as a fast lithium-ion conductor. The structure and ion dynamics of Al-doped cubic LLZO were studied by impedance spectroscopy, dc conductivity measurements, (6)Li and (7)Li NMR, XRD, neutron powder diffraction, and TEM precession electron diffraction. From the results we conclude that aluminium is incorporated in the garnet lattice on the tetrahedral 24d Li site, thus stabilizing the cubic LLZO modification. Simulations based on diffraction data show that even at the low temperature of 4 K the Li ions are blurred over various crystallographic sites. This strong Li ion disorder in cubic Al-stabilized LLZO contributes to the high conductivity observed. The Li jump rates and the activation energy probed by NMR are in very good agreement with the transport parameters obtained from electrical conductivity measurements. The activation energy E(a) characterizing long-range ion transport in the Al-stabilized cubic LLZO amounts to 0.34 eV. Total electric conductivities determined by ac impedance and a four point dc technique also agree very well and range from 1 × 10(-4) Scm(-1) to 4 × 10(-4) Scm(-1) depending on the Al content of the samples. The room temperature conductivity of Al-free tetragonal LLZO is about two orders of magnitude lower (2 × 10(-6) Scm(-1), E(a) = 0.49 eV activation energy). The electronic partial conductivity of cubic LLZO was measured using the Hebb-Wagner polarization technique. The electronic transference number t(e-) is of the order of 10(-7). Thus, cubic LLZO is an almost exclusive lithium ion conductor at ambient temperature.     

Calorimetry

Methods for determining the heat content E ^*/A of hot nuclei formed in energetic nuclear reactions are discussed. The primary factors involved in converting raw data into thermal physics distributions include: 1) design of the detector array, 2) constraints imposed by the physics of the reaction mechanism, and 3) assumptions involved in converting the filtered data into E ^*/A. The two primary sources of uncertainty in the calorimetry are the elimination of nonequilibrium emissions from the event components and accounting for the contribution of neutron emission to the excitation energy sum.     

Sul postulato della completezza lineare dell'Hilbert

Sunto Si disente criticamente il detto postulato, con particolare riguardo al problema della sua compatibilità entro il sistema ipotetico — deduttivo dell'Hilbert. A Giovanni Sansone nel suo 70^mo compleanno.     

Sulle successioni di funzioni quasi continue negli spazi astratti

Sunto Si studia una definizione del tutto generale di funzione quasi continua; si enuncia e dimostra poi un teorema, concettualmente nuovo, per le successioni di funzioni che sono quasi continue nel senso generale studiato. A Mauro Picone nel suo 70^mo compleanno. Lavoro eseguito presso l'Istituto Nazionale per le Applicazioni del Calcolo.     

Two arc cracks around a circular rigid inclusion

Summary The problem of two symmetric arc cracks lying between a rigid circular inclusion embedded in an infinite matrix under biaxial loading at infinity is considered. By using the complex variable tecnique, the boundary value problem is solved and stress and displacement components are calculated along the inclusion boundary. Moreover, investigating the local stress field, a stress criterion, already proposed by authors, allowing either the crack extension at the interface or its deviation into the matrix to be taken into account, is applied to study the fracture response of the elastic system. The critical applied loads as well as the angle of the incipient crack extension are expressed in terms of the central angle subtended by the crack arcs.Finally the biaxial load effects are graphically shown and discussed.

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Sommario Si considera il problema piano di due «craks» simmetrici all'interfaccia tra una inclusione circolare rigida e la circostante matrice, in regime di carico biassiale. Facendo uso della tecnica delle variabili complesse, viene risolto il problema dei valori al contorno, ricavando altresi le espressioni delle tensioni e degli spostamenti lungo il contorno dell'inclusione. Inoltre, applicando un criterio tensionale, già proposto dagli autori, che consente di studiare sia la estensione del crack all'interfaccia che la sua deviazione nella matrice, si analizza la risposta del sistema considerato. I valori critici dei carichi applicati, nonchè l'angolo di frattura, risultano espressi in funzione dell'angolo al centro sotteso dai cracks.Infine, vengono illustrati graficamente e discussi gli effetti del carico laterale.

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Financial support of the National Research Council (C.N.R.) (research contribution N. 79.01625.07) is gratefully acknowledged.     

Enhanced convergence and robust performance of randomized dynamical decoupling

We demonstrate the advantages of randomization in coherent quantum dynamical control. For systems which are either time-varying or require decoupling cycles involving a large number of operations, we find that simple randomized protocols offer superior convergence and stability as compared to deterministic counterparts. In addition, we show how randomization may allow us to outperform purely deterministic schemes at long times, including combinatorial and concatenated methods. General criteria for optimally interpolating between deterministic and stochastic design are proposed and illustrated in explicit decoupling scenarios relevant to quantum information storage.