Search results for "periodic"
showing 10 items of 769 documents
The Corneal Dystrophies—Does the Literature Clarify or Confuse?
2018
Characteristic Sturmian words are extremal for the Critical Factorization Theorem
2012
We prove that characteristic Sturmian words are extremal for the Critical Factorization Theorem (CFT) in the following sense. If p x ( n ) denotes the local period of an infinite word x at point n , we prove that x is a characteristic Sturmian word if and only if p x ( n ) is smaller than or equal to n + 1 for all n ≥ 1 and it is equal to n + 1 for infinitely many integers n . This result is extremal with respect to the \{CFT\} since a consequence of the \{CFT\} is that, for any infinite recurrent word x, either the function p x is bounded, and in such a case x is periodic, or p x ( n ) ≥ n + 1 for infinitely many integers n . As a byproduct of the techniques used in the paper we extend a r…
Existence and multiplicity of periodic solutions for second order Hamiltonian systems depending on a parameter
2013
The existence of at least one nontrivial periodic solution for a class of second order Hamiltonian systems depending on a parameter is obtained, under an algebraic condition on the nonlinearity G and without requiring any asymptotic behavior neither at zero nor at infinity. The existence is still deduced in the particular case when G is subquadratic at zero. Finally, two multiplicity results are proved if G, in addition, is required to fulfill some different Ambrosetti-Rabinowitz type superquadratic conditions at infinity. The approach is fully variational. © Heldermann Verlag.
Crystal structure of SrMn2(Si2O7)(OH)2 H2O, a new mineral of the lawsonite type
1992
Crystal with the composition SrMn 2 [Si 2 O 7 ](OH) 2 .H 2 O were found in a sugilite, serandite-pectolite rich sample from the Wessels Mine, Kalahari, South Africa. The crystal structure of the nex compound with space group Cmcm, a = 6.255(1), b = 9.034(2), c = 13.397(2) A, Z = 4 was determined from X-ray single-crystal data (R = 0.048). The structure is of the lawsonite type where Al is completely replaced by Mn 3+ and Ca by Sr. [Mn 3+ O 6 ] octahedra forming edge-sharing chains parallel to a exhibit a Jahn-Teller distortion with four short and two long Mn 3+ -O distances. Sr is in eight-fold coordination and H 2 O is disordered on a split position. Together with orientite, macfallite, ru…
Cs[Ag4Zn2(SCN)9].
2002
Caesium tetrasilver dizinc nonathiocyanate, Cs[Ag4Zn2(SCN)9], forms a continuous structure, where the Ag atoms and the S atoms of the thiocyanate groups form chains which run along [101]. These chains are bonded together through the Cs and Zn atoms. It is not possible to distinguish between space groups P1 and P\overline 1, but, if the latter space group is correct, the structure contains a thiocyanate group disordered across a centre of inversion. The structure is described in space group P\overline 1, in which the Cs atom also lies on a centre of inversion.
Syntheses, X-ray structures, and redox behaviour of the group 14 bis-boraamidinates M[PhB(μ-N-t-Bu)2]2 (M = Ge, Sn) and Li2M[PhB(μ-N-t-Bu)2]2 (M = Sn…
2009
The solid-state structures of the complexes M[PhB(μ-N-t-Bu)2]2 (1a, M= Ge; 1b, M = Sn) were determined to be spirocyclic with two orthogonal boraamidinate (bam) ligands N,N′-chelated to the group 14 centre. Oxidation of 1b with SO2Cl2 afforded the thermally unstable, blue radical cation {Sn[PhB(μ-N-t-Bu)2]2}•+, identified by electron paramagnetic resonance (EPR) spectroscopy supported by density functional theory (DFT) calculations, whereas the germanium analogue 1a was inert towards SO2Cl2. The reaction between Li2[PhB(μ-N-t-Bu)2]2 and SnCl2 or PbI2 in 2:1 molar ratio in diethyl ether produced the novel heterotrimetallic complexes Li2Sn[PhB(μ-N-t-Bu)2]2 (2b) and (Et2O·Li)LiPb[PhB(μ-N-t-Bu…
Improved Approach to Liesegang Phenomena
1995
Crystallographic study of a family of Cs2BX4compounds
1990
Abstract Five compounds of the Cs2BX4 family with B = Zn, Co, Cu and X = Cl, Br were grown and studied. They belong to Pnma space group with 4 formula units per cell. From the full determination of the structure it appears that the ZnX4 tetrahedra are almost regular while the CuX4 tetrahedra are strongly distorted. This seems to be due to a strong Jahn-Teller effect induced by the Cu ions. This remark is extended to other compounds of the general family A2BX4.
Crystal Structure of the Microwave Dielectric Resonator Ba2Ti9O20
1983
A single-crystal X-ray study of dibarium nonatitanate, Ba2Ti9O20, yielded the triclinic space group P 1 with a=0.7471(1), b= 1.4081(2), c= 1.4344(2) nm, α=89.94(2)°, β= 79.43(2)°, γ= 84.45(2)°, V = 1.476 nm3 Z = 4, and Dx= 4.61 Mg/m3. A refinement of atomic coordinates and isotropic thermal parameters led to a residual of 0.03. The structure consists of hexagonally closest-packed layers of Ba and O atoms in the sequence (hch)3. All Ti atoms reside in octahedral interstices of this closest packing. The various Ti coordination octahedra share only edges and corners with each other. One-half of the Ba atoms is twelve-coordinated by oxygen atoms, the other half is eleven-coordinated.
ChemInform Abstract: Crystal Structure of the Microwave Dielectric Resonator Ba2Ti9O20.
1983
A single-crystal X-ray study of dibarium nonatitanate, Ba2Ti9O20, yielded the triclinic space group P 1 with a=0.7471(1), b= 1.4081(2), c= 1.4344(2) nm, α=89.94(2)°, β= 79.43(2)°, γ= 84.45(2)°, V = 1.476 nm3 Z = 4, and Dx= 4.61 Mg/m3. A refinement of atomic coordinates and isotropic thermal parameters led to a residual of 0.03. The structure consists of hexagonally closest-packed layers of Ba and O atoms in the sequence (hch)3. All Ti atoms reside in octahedral interstices of this closest packing. The various Ti coordination octahedra share only edges and corners with each other. One-half of the Ba atoms is twelve-coordinated by oxygen atoms, the other half is eleven-coordinated.