Magnetic properties of two double‐layer structures built from hydroxy­naphthoic acids and manganese

Double‐layer structures consisting of alternating polar and non‐polar layers have been prepared using Mn²⁺ ions and o‐hydroxy­naphthoic acids. The polar layers contain the Mn²⁺ ions, carboxylate groups, hydr­oxy groups and water mol­ecules. The non‐polar layers are built up from the naphthalene moieties. In catena‐poly[[diaqua­manganese(II)]bis­(μ‐3‐hy­droxy‐2‐naphthoato‐κ²O:O′)] (also called manganese 3‐hy­droxy‐2‐naphthoate dihydrate), [Mn(C₁₁H₇O₃)₂(H₂O)₂]_n, (I), the Mn²⁺ ions are connected by carboxylate groups to form two‐dimensional networks. This compound shows distinct antiferromagnetic inter­actions and long‐range ordering at low temperature. In contrast, tetra­aqua­bis(1‐hydr­oxy‐2‐naph­thoato‐κO)manganese(II), [Mn(C₁₁H₇O₃)₂(H₂O)₄], (II), which lacks a close linkage between the Mn²⁺ ions, reveals purely paramagnetic behaviour. In (II), the Mn²⁺ ion lies on an inversion centre.     

Complexity results in graph reconstruction

We investigate the relative complexity of the graph isomorphism problem (GI) and problems related to the reconstruction of a graph from its vertex-deleted or edge-deleted subgraphs (in particular, deck checking (DC) and legitimate deck (LD) problems). We show that these problems are closely related for all amounts c?1 of deletion:

(1)

, , , and .

(2)

For all k?2, and .

(3)

For all k?2, .

(4)

.

(5)

For all k?2, .

For many of these results, even the c=1 case was not previously known.Similar to the definition of reconstruction numbers vrn_∃(G) [F. Harary, M. Plantholt, The graph reconstruction number, J. Graph Theory 9 (1985) 451-454] and ern_∃(G) (see [J. Lauri, R. Scapellato Topics in Graph Automorphism and Reconstruction, London Mathematical Society, Cambridge University Press, Cambridge, 2003, p. 120]), we introduce two new graph parameters, vrn_∀(G) and ern_∀(G), and give an example of a family {G_n}_n?4 of graphs on n vertices for which vrn_∃(G_n)<vrn_∀(G_n). For every k?2 and n?1, we show that there exists a collection of k graphs on (2^k-1+1)n+k vertices with 2ⁿ 1-vertex-preimages, i.e., one has families of graph collections whose number of 1-vertex-preimages is huge relative to the size of the graphs involved.     

Squares of characters and finite groups

Let G be a finite group and χ be an irreducible complex character. We study the character χ² in the case that χ(1) is a prime power.     

Synthesis and photophysical behavior of a novel zinc phthalocyanine containing a single carboxylic acid and three phenylthio substituents

Zinc 2, (3)-tri-(phenylthio)-2, (3)-carboxy phthalocyanine (ZnPc(COOH)(SPh)₃), zinc 2, (3)-tetra-(phenylthio) phthalocyanine (ZnPc(SPh)₄) and 2, (3)-tetra-(phenylthio) phthalocyanine (H₂Pc(SPh)₄) were synthesized and their photophysical behavior were compared with those of a number of zinc phthalocyanine (ZnPc) derivatives. ZnPc(COOH)(SPh)₃ and ZnPc(SPh)₄ had similar fluorescence (Φ_F=0.14) and triplet state (Φ_T=0.65) quantum yields in dimethylsulfoxide, hence showing no effects of the replacement of one of the phenylthio groups with a carboxylic acid group. ZnPc(COOH)(SPh)₃ displayed a slightly shorter triplet lifetime (τ_T=331 μs) than ZnPc (τ_T=350 μs) in DMSO, but within the range of ZnPc derivatives. The triplet lifetime for ZnPc(COOH)(SPh)₃ is much longer than for the symmetrical derivative (ZnPc(SPh)₄) with τ_T=149 μs in DMSO.     

New algorithms for generalized network flows

This paper, of which a preliminary version appeared in ISTCS'92, is concerned with generalized network flow problems. In a generalized network, each edgee = (u, v) has a positive flow multipliera _e associated with it. The interpretation is that if a flow ofx _e enters the edge at nodeu, then a flow ofa _e x _e exits the edge atv. The uncapacitated generalized transshipment problem (UGT) is defined on a generalized network where demands and supplies (real numbers) are associated with the vertices and costs (real numbers) are associated with the edges. The goal is to find a flow such that the excess or deficit at each vertex equals the desired value of the supply or demand, and the sum over the edges of the product of the cost and the flow is minimized. Adler and Cosares [Operations Research 39 (1991) 955–960] reduced the restricted uncapacitated generalized transshipment problem, where only demand nodes are present, to a system of linear inequalities with two variables per inequality. The algorithms presented by the authors in [SIAM Journal on Computing, to appear result in a faster algorithm for restricted UGT.Generalized circulation is defined on a generalized network with demands at the nodes and capacity constraints on the edges (i.e., upper bounds on the amount of flow). The goal is to find a flow such that the excesses at the nodes are proportional to the demands and maximized. We present a new algorithm that solves the capacitated generalized flow problem by iteratively solving instances of UGT. The algorithm can be used to find an optimal flow or an approximation thereof. When used to find a constant factor approximation, the algorithm is not only more efficient than previous algorithms but also strongly polynomial. It is believed to be the first strongly polynomial approximation algorithm for generalized circulation. The existence of such an approximation algorithm is interesting since it is not known whether the exact problem has a strongly polynomial algorithm.Corresponding author. Research was done while the first author was attending Stanford University and IBM Almaden Research Center. Research partially supported by ONR-N00014-91-C-0026 and by NSF PYI Grant CCR-8858097, matching funds from AT&T and DEC.Research partially supported by ONR-N00014-91-C-0026.     

Cis/trans copolyamides of 1,4-bisaminomethylcyclohexane

Copolyamides prepared from cis- and trans-1,4-bisaminomethylcyclohexane with adipic, sebacic, and dodecanoic acids showed a decrease in melting point with increasing cis diamine content and increasing chain length of the diacid. Most unusual was the fact that the glass transition temperature of these copolymers were essentially independent of diamine isomer content. The existence of an intermediate conformation for some of the cyclohexane rings such as the “twistmer” is suggested to account for this discrepancy. The T_g, T_c, and T_m all decreased with increasing chain length of the diacid. The thermal stability as exemplified by the polysebacamides, was independent of diamine isomer content.