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51.
Hedrlín and Pultr proved that for any monoid M there exists a graph G with endomorphism monoid isomorphic to M . In this paper we give a construction G(M) for a graph with prescribed endomorphism monoid M . Using this construction we derive bounds on the minimum number of vertices and edges required to produce a graph with a given endomorphism monoid for various classes of finite monoids. For example we show that for every monoid M , | M |=m there is a graph G with End(G)? M and |E(G)|≤(1 + 0(1))m2. This is, up to a factor of 1/2, best possible since there are monoids requiring a graph with \begin{eqnarray*} && \frac{m^{2}}{2}(1 -0(1)) \end{eqnarray*} edges. We state bounds for the class of all monoids as well as for certain subclasses—groups, k‐cancellative monoids, commutative 3‐nilpotent monoids, rectangular groups and completely simple monoids. © 2009 Wiley Periodicals, Inc. J Graph Theory 62, 241–262, 2009 相似文献
52.
In this note we consider three questions which can be traced to our early collaboration with Jan “Honza” Pelant. We present them from the contemporary perspective, in some cases extending our earlier work. The questions relate to Ramsey theory, uniform spaces and tournaments. 相似文献
53.
For a given finite monoid , let be the number of graphs on n vertices with endomorphism monoid isomorphic to . For any nontrivial monoid we prove that where and are constants depending only on with .For every k there exists a monoid of size k with , on the other hand if a group of unity of has a size k>2 then . 相似文献
54.
We prove that finite partial orders with a linear extension form a Ramsey class. Our proof is based on the fact that the class of acyclic graphs has the Ramsey property and uses the partite construction. 相似文献
55.
Jaklová Dytrtová Jana Jakl Michal Nováková Kateřina Navrátil Tomáš Šádek Vojtěch 《Monatshefte für Chemie / Chemical Monthly》2015,146(5):831-837
Monatshefte für Chemie - Chemical Monthly - Cu(II) creates complexes with dipalmitoylphosphatidylcholine (lecithin), which are detectable using electrospray ionization mass spectrometry.... 相似文献
56.
57.
A series of lanthanide(III) complexes formulated as M[Ln(Hdo3ap)].xH(2)O (M = Li or H and Ln = Tb, Dy, Er, Lu, and Y) with the monophosphonate analogue of H(4)dota, 1,4,7,10-tetraazacyclododecane-1,4,7-triacetic-10-methylphosphonic acid (H(5)do3ap), was prepared in the solid state and studied using X-ray crystallography. All of the structures show that the (Hdo3ap)(4-) anion is octadentate coordinated to a lanthanide(III) ion similarly to the other H(4)dota-like ligands, i.e., forming O(4) and N(4) planes that are parallel and have mutual angle smaller than 3 degrees . The lanthanide(III) ions lie between these planes, closer to the O(4) base than to the N(4) plane. All of the structures present the lanthanide(III) complexes in their twisted-square-antiprismatic (TSA) configuration. Twist angles of the pendants vary in the range between -24 and -30 degrees, and for each complex, they lie in a very narrow region of 1 degree. The coordinated phosphonate oxygen is located slightly above (0.02-0.19 Angstroms) the O(3) plane formed with the coordinated acetates. A water molecule was found to be coordinated only in the terbium(III) and neodymium(III) complexes. The bond distance Tb-O(w) is unusually long (2.678 Angstroms). The O-Ln-O angles decrease from 140 degrees [Nd(III)] to 121 degrees [Lu(III)], thus confirming the increasing steric crowding around the water binding site. A comparison of a number of structures of Ln(III) complexes with DOTA-like ligands shows that the TSA arrangement is flexible. On the other hand, the SA arrangement is rigid, and the derived structural parameters are almost identical for different ligands and lanthanide(III) ions. 相似文献
58.
Solutions of Cd, Cu and Pb at concentrations of about 1000 mg/l were prepared by dissolving the pure metals in HNO3. Their concentration was verified by complexometric titration and by gravimetric analysis (Cu with salicylaldoxime, Cd with
quinaldinic acid and Pb with 8-hydroxyquinoline). The results of the two methods were very similar and the uncertainty values
were equal. However, the gravimetric determination can be regarded as more reliable, because titrimetric analysis is more
prone to error due to inaccurate end-point reading. The expanded uncertainty of the concentrations of Cd and Cu attained 1 mg/l,
which is half the value typically obtained for similar solutions from commercial manufacturers. To achieve such precise results,
the bias had to be reduced by the highest possible extent, particularly by calibrating both the balance and the volumetric
glassware. In addition to the uncertainty of the basic operations (volumetric and gravimetric), the uncertainty of the atomic
and molecular weights constituted an appreciable component in the combined standard uncertainty; this manifested itself in
the determination of Pb, where the expanded uncertainty was 2 mg/l.
Received: 24 September 1998 / Accepted: 25 January 1999 相似文献
59.
Let be a family of subsets of S and let G be a graph with vertex set such that: (xA, xB) is an edge iff . The family is called a set representation of the graph G.It is proved that the problem of finding minimum k such that G can be represented by a family of sets of cardinality at most k is NP-complete. Moreover, it is NP-complete to decide whether a graph can be represented by a family of distinct 3-element sets.The set representations of random graphs are also considered. 相似文献
60.
Vojtěch Kopský 《Journal of magnetism and magnetic materials》1976,3(3):201-211
The magnetic crystal point groups (Heesch groups) are classified according to their structure with respect to the three inversion operations: space, time, and total inversion. Accordingly the tensors are classified by the irreducible representations of the full inversion group. The groups and tensors are considered under the action of the elements Ai of the group of automorphisms of the full inversion group. The following correspondence theorem is proved: The matrix form of the tensor representation T of the group G coincides with the matrix form of the representation AiT of the group AiG. The theorem gives a clear explanation of the so-called “magic numbers” and provides a suitable short cut for the calculation and tabulation of material property tensors. 相似文献