First Alexandroff Decomposition Theorem for Topological Lattice Group Valued Measures

Let (X, F) be an Alexandroff space, let A(F) be the Boolean subalgebra of 2 ^X generated by F, let G be a Hausdorff commutative topological lattice group and let rba_F(A(F), G) denote the set of all order bounded F-inner regular finitely additive set functions from A(F) into G. Using some special properties of the elements of rba_F(A(F), G), we extend to this setting the first decomposition theorem of Alexandroff.     

Strongly Regular Graphs and Designs with Three Intersection Numbers

We investigate BIBDs with three intersection numbers,x, y, and z, such that the relation on the block set given byA B iff the cardinality of the intersectionof A and B is not equal to x is an equivalence relation. Withsuch a design, we associate a family of strongly regular graphswith the same parameters. Two constructions producing infinitefamilies of such designs are given.     

Minimum Distance Bounds for s-Regular Codes

A code C F ⁿ is s-regular provided, forevery vertex x F ⁿ, if x is atdistance at most s from C then thenumber of codewords y C at distance ifrom x depends only on i and the distancefrom x to C. If denotesthe covering radius of C and C is -regular,then C is said to be completely regular. SupposeC is a code with minimum distance d,strength t as an orthogonal array, and dual degrees ^*. We prove that d 2t + 1 whenC is completely regular (with the exception of binaryrepetition codes). The same bound holds when C is(t + 1)-regular. For unrestricted codes, we show thatd s ^* + t unless C is a binary repetitioncode.     

Open subgroups of

Let be a locally compact group and let denote the -algebra generated by left translation operators on . Let and be the spaces of almost periodic and weakly almost periodic functionals on the Fourier algebra , respectively. It is shown that if contains an open abelian subgroup, then (1) if and only if is norm dense in ; (2) is a -algebra if is norm dense in , where denotes the set of elements in with compact support. In particular, for any amenable locally compact group which contains an open abelian subgroup, has the dual Bohr approximation property and is a -algebra.

     

On locally convex hypersurfaces in Hadamard manifolds

Locally convex compact hypersurfaces immersed in a hollow simply connected Riemannian space of nonpositive sectional curvature are considered. They are proved to be convex hypersurfaces homeomorphic to the sphere. A similar result for immersed hypersurfaces with nonpositive definite second quadratic form of rank no smaller than one is obtained. Translated fromMatematicheskie Zametki, Vol. 67, No. 4, pp. 498–507, April, 2000.     

The Positivity of Intersection Multiplicities and Symbolic Powers of Prime Ideals

Serre's nonnegativity conjecture for intersection multiplicities has recently been proven by O. Gabber. In this paper we investigate Serre's positivity conjecture using the methods which he developed. We show in particular that the positivity conjecture has implications for properties of symbolic powers of prime ideals in regular local rings.     

Elementary equivalence for the lattices of subalgebras and automorphism groups of free algebras

We find an elementary equivalence criterion for the lattices of subalgebras of free algebras in regular varieties. The question is addressed of elementary equivalence for the automorphism groups of algebras of this type.     

Characterizations of some classes of relatively regular operators

A bounded linear operator A on a Banach space is called relatively regular, if there is a bounded linear operator B such that ABA=A. In this case B is called a g₁-inverse of A. In this paper we characterize some classes of relatively regular operators A via the set {B₁-B₂:B₁ and B₂ are g₁-inverses of A}.     

Fixation of carbon dioxide into aliphatic polycarbonate,cobalt porphyrin catalyzed regio‐specific poly(propylene carbonate) with high molecular weight

Cobalt porphyrin complex (TPPCo^IIIX) (TPP = 5, 10, 15, 20‐Tetraphenyl‐ porphyrin; X = halide) in combination with ionic organic ammonium salt was used for the regio‐specific copolymerization of propylene oxide and carbon dioxide. A turnover frequency of 188 h^?1 was achieved after 5 h, and the byproduct propylene carbonate was successfully controlled to below 1%, where the obtained poly(propylene carbonate) (PPC) showed number average molecular weight (M_n) of 48 kg/mol, head‐to‐tail content of 93%, and carbonate linkage of over 99%. When the polymerization time was prolonged to 24 h, PPC with M_n over 115 kg/mol and head‐to‐tail linkage maintaining 90% was prepared, whose glass transition temperature reached 44.5 °C. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 5959–5967, 2008     

Thermodynamic approach of spin-state excitations in LaCoO3

Magnetic susceptibility and heat capacity due to spin-state excitations in LaCoO₃ were analyzed with an irregular solution model composed of Co³⁺ ions in the low-spin ground state and in the high-spin excited state. An energy-levels diagram proposed by Ropka and Radvanskii [1] was used for the high-spin excited state. This analysis showed that the entropy of mixing is less than that of ideal solutions and the enthalpy of mixing is negative, indicating that the high-spin Co ions are arranged as far apart as possible.