Packing complete multipartite graphs with 4-cycles

In this paper we completely solve the problem of finding a maximum packing of any complete multipartite graph with edge-disjoint 4-cycles, and the minimum leaves are explicitly given.

Decomposition of complete tripartite graphs into gregarious 4-cycles

A 4-cycle in a tripartite graph with vertex partition {V-1, V-2, V-3} is said to be gregarious if it has at least one vertex in each V-i, 1 less than or equal to i less than or equal to 3. In this paper, necessary and sufficient conditions are given for the existence of an edge-disjoint decomposition of any complete tripartite graph into gregarious 4-cycles.

Linearly-increasing-stress testing of carbon steel in 4 N NaNO3 and in Bayer liquor

This paper reports the application of linearly increasing stress testing (LIST) to the study of stress corrosion cracking (SCC) of carbon steel in 4 N NaNO3 and in Bayer liquor. LIST is similar to the constant extension-rate testing (CERT) methodology with the essential difference that the LIST is load controlled whereas the CERT is displacement controlled. The main conclusion is that LIST is suitable for the study of the SCC of carbon steels in 4 N NaNO3 and in Bayer liquor. The low crack velocity in Bayer liquor and a measured maximum stress close to that of the reference specimen in air both indicate that a low applied stress rate is required to study SCC in this system. (C) 1998 Chapman & Hall.

Validity of (-)-[H-3]-CGP 12177A as a radioligand for the 'putative beta(4)-adrenoceptor' in rat atrium

1 We have recently suggested the existence in the heart of a 'putative beta(4)-adrenoceptor' based on the cardiostimulant effects of non-conventional partial agonists, compounds that cause cardiostimulant effects at greater concentrations than those required to block beta(1)- and Bz-adrenoceptors. We sought to obtain further evidence by establishing and validating a radioligand binding assay for this receptor with (-)-[H-3]-CGP 12177A ((-)-4-(3-tertiarybutylamino-2-hydroxypropoxy) benzimidazol-2-one) in rat atrium. We investigated (-)-[H-3]-CGP 12177A for this purpose for two reasons, because it is a nonconventional partial agonist and also because it is a hydrophilic radioligand. 2 Increasing concentrations of(-)-[H-3]-CGP 12177A, in the absence or presence of 20 mu M (-)-CGP 12177A to define non-specific binding, resulted in a biphasic saturation isotherm. Low concentrations bound to beta(1)- and beta(2)-adrenoceptors (pK(D) 9.4+/-0.1, B-max 26.9+/-3.1 fmol mg(-1) protein) and higher concentrations bound to the 'putative beta(4)-adrenoceptor' (pK(D) 7.5+/-0.1, B-max 47.7+/-4.9 fmol mg(-1) protein). In other experiments designed to exclude beta(1)- and beta(2)-adrenoceptors, (-)-[H-3]-CGP 12177A (1-200 nM) binding in the presence of 500 nM (-)-propranolol was also saturable (pK(D) 7.6+/-0.1, B-max 50.8+/-7.4 fmol mg(-1) protein). 3 The non-conventional partial agonists (-)-CGP 12177A (pK(i) 7.3+/-0.2), (+/-)-cyanopindolol (pK(i) 7.6+/-0.2), (-)-pindolol (pK(i) 6.6+/-0.1) and (+)-carazolol (pk(i), 7.2+/-0.2) and the antagonist (-)-bupranolol (pK(i) 6.6+/-0.2), all competed for (-)-[H-3]-CGP 12177A binding in the presence of 500 nM (-)-propranolol at the 'putative beta(4)-adrenoceptor', with affinities closely similar to potencies and affinities determined in organ bath studies. 4 The catecholamines competed with (-)-[H-3]-CGP 12177A at the 'putative beta(4)-adrenoceptor' in a stereoselective manner, (-)-noradrenaline (pK(iH) 6.3 +/- 0.3, pK(i), 3.5 +/- 0.1), (-)-adrenaline (pK(iH) 6.5 +/- 0.2, pK(iL) 2.9 +/- 0.1), (-)-isoprenaline (pK(iH) 6.2 +/- 0.5, pK(iL) 3.3 +/- 0.1), (+)-isoprenaline (pK(i) < 1.7), (-)-R0363 ((-)-(1-(3,4-dimethoxyphenethylamino)-3-(3,4-dihydroxyphenoxy)-2-propranol)oxalate, pK(i) 5.5 +/- 0.1). 5 The inclusion of guanosine 5-triphosphate (GTP 0.1 mM) had no effect on binding of (-)-CGP 12177A or (-)-isoprenaline to the 'putative beta(4)-adrenoceptor'. In competition binding studies, (-)-CGP 12177A competed with (-)-[H-3]-CGP 12177A for one receptor state in the absence (pK(i) 7.3 +/- 0.2) or presence of GTP (pK(i) 7.3 +/- 0.2). (-)-Isoprenaline competed with (-)-[H-3]-CGP 12177A for two states in the absence (pK(iH) 6.6 +/- 0.3, pK(iL) 3.5 +/- 0.1; % H 25 +/- 7) or presence of GTP (pK(iH) 6.2 +/- 0.5, pK(iL) 3.4 +/- 0.1; % H 37 +/- 6). In contrast, at beta(1)-adrenoceptors, GTP stabilized the low affinity state of the receptor for (-)-isoprenaline. 6 The specificity of binding to the 'putative beta(4)-adrenoceptor' was tested with compounds active at other receptors. High concentrations of the beta(4)-adrenoceptor agonists, BRL 37344 ((RR + SS)[4-[2-[[2-(3-chlorophenyl)-2-hydroxy -ethyl]amino]propyl]phenoxy]acetic acid, 6 mu M), SR 58611A (ethyl((7S)-7-[(2R)-2-(3-chlorophenyl)-2-hydroxyethylamino]-5,6,7,8-tetrahydronaphtyl-2-yloxy) acetate hydrochloride, 6 mu M), ZD 2079 ((+/-)-1-phenyl-2-(2-4-carboxymethylphenoxy)-ethylamino)ethan-1-ol, 60 mu M), CL 316243 (disodium (R,R)-5-[2-[2-(3-chlorophenyl)-2-hydroxyethyl-amino]propyl]- 1,3-benzodioxole-2,2-dicarboxylate, 60 mu M) and antagonist SR 59230A (3-(2-ethylphenoxy)-1-[(1S)-1,2,3,4-tetrahydronaphth-1-ylamino]-2S-2-propanol oxalate, 6 mu M) caused less than 22% inhibition of (-)-[H-3]-CGP 12177A binding in the presence of 500 nM (-)-propranolol. Histamine (1 mM), atropine (1 mu M), phentolamine (10 mu M), 5-HT(100 mu M) and the 5-HT4 receptor antagonist SE 207710 ((1-butyl-4-piperidinyl)-methyl 8-amino-7-iodo-1 ,4-benzodioxan-5-carboxylate, 10 nM) caused less than 26% inhibition of binding. 7 Non-conventional partial agonists, the antagonist (-)-bupranolol and catecholamines all competed for (-)-[H-3]-CGP 12177A binding in the absence of (-)-propranolol at beta(1)-adrenoceptors, with affinities (pK(i)) ranging from 1.6-3.6 log orders greater than at the 'putative beta(4)-adrenoceptor'. 8 We have established and validated a radioligand binding assay in rat atrium for the 'putative beta(4)-adrenoceptor' which is distinct from beta(1)-, beta(2)- and beta(3)-adrenoceptors. The stereoselective interaction with the catecholamines provides further support for the classification of the receptor as 'putative beta(4)-adrenoceptor'.

Synthesis, structure and magnetism of the oxalato-bridged chromium(III) complex [NBu4n](4)[Cr-2(ox)(5)]center dot 2CHCl(3)

The binuclear complex [NBu4n](4)[Cr-2(ox)(5)]. 2CHCl(3) has been prepared by an ion-exchange procedure employing Dowex 50WX2 cation-exchange resin in the n-butylammonium form and potassium tris(oxalato)chromate(III). The dimeric complex was characterised by a crystal structure determination: monoclinic, space group C2/c, a = 29.241(7), b = 15.192(2), c = 22.026(5) Angstrom, beta = 94.07(1)degrees, Z = 4. The magnetic susceptibility (300-4.2 K) indicated that the chromium(III) sites were antiferromagnetically coupled (J = -3.1 cm(-1)).

Correlation between carbon isotope discrimination and transpiration efficiency in lines of the C-4 species Sorghum bicolor in the glasshouse and the field

Transpiration efficiency, W, the ratio of plant carbon produced to water transpired and carbon isotope discrimination of leaf dry matter, Delta(d)' were measured together on 30 lines of the C-4 species, Sorghum bicolor in the glasshouse and on eight lines grown in the field. In the glasshouse, the mean W observed was 4.9 mmol C mol(-1) H2O and the range was 0.8 mmol C mol(-1) H2O The mean Delta(d) was 3.0 parts per thousand and the observed range was 0.4 parts per thousand. In the field, the mean W was lower at 2.8 mmol C mol H2O and the mean Delta(d) was 4.6 parts per thousand. Significant positive correlations between W and Delta(d) were observed for plants grown in the glasshouse and in the field. The observed correlations were consistent with theory, opposite to those for C-4 species, and showed that variation in Delta(d) was an integrated measure of long-term variation in the ratio of intercellular to ambient CO2 partial pressure, p(i)/p(a). Detailed gas exchange measurements of carbon isotope discrimination during CO2 uptake, Delta(A) and p(i)/p(a) were made on leaves of eight S. bicolor lines. The observed relationship between Delta(A) and p(i)/p(a) was linear with a negative slope of 3.7 parts per thousand in Delta(A) for a unit change in p(i)/p(a). The slope of this linear relationship between Delta(A) and p(i)/p(a) in C-4 species is dependent on the leakiness of the CO2 concentrating mechanism of the C pathway, We estimated the leakiness (defined as the fraction of CO2 released in the bundle sheath by C-4 acid decarboxylations, which is lost by leakage) to be 0.2. We conclude that, although variation in Delta(d) observed in the 30 lines of S. bicolor is smaller than that commonly observed in C-4 species, it also reflects variation in transpiration efficiency, W. Among the eight lines examined in detail and in the environments used, there was considerable genotype x environment interaction.

(-)-CGP 12177 causes cardiostimulation and binds to cardiac putative beta(4)-adrenoceptors in both wild-type and beta(3)-adrenoceptor knockout mice

Some blockers of beta(1)- and beta(2)-adrenoceptors cause cardiostimulant effects through an atypical beta-adrenoceptor (putative beta(4)-adrenoceptor) that resembles the beta(3)-adrenoceptor. It is likely but not proven that the putative beta(4)-adrenoceptor is genetically distinct from the beta(3)-adrenoceptor. We therefore investigated whether or not the cardiac atypical beta-adrenoceptor could mediate agonist effects in mice lacking a functional beta(3)-adrenoceptor gene (beta(3)KO). (-)-CGP 12177, a beta(1)- and beta(2)-adrenoceptor blocker that causes agonist effects through both beta(3)-adrenoceptors and cardiac putative beta(4)-adrenoceptors, caused cardiostimulant effects that were not different in atria from wild-type (WT) mice and beta(3)KO mice. The effects of (-)-CGP 12177 were resistant to blockade by (-)-propranolol (200 nM) but were blocked by (-)-bupranolol (1 mu M) with an equilibrium dissociation constant of 15 nM in WT and 17 nM in beta(3)KO. (-)-[H-3]CGP 12177 labeled a similar density of the putative beta(4)-adrenoceptor in ventricular membranes from the hearts of both WT (B-max = 52 fmol/mg protein) and beta(3)KO (B-max = 53 fmol/mg protein) mice. The affinity of (-)-[H-3]CGP 12177 for the cardiac putative beta(4)-adrenoceptor was not different between WT (K-d = 46 nM) and beta(3)KO (K-d = 40 nM). These results provide definitive evidence that the cardiac putative beta(4)-adrenoceptor is distinct from the beta(3)-adrenoceptor.

Iron(III) and iron(II) complexes of 1-thia-4,7-diazacyclononane ([9]aneN(2)S) and 1,4-dithia-7-azacyclononane ([9]aneNS(2)). X-Ray structural analyses, magnetic susceptibility, Mossbauer, EPR and electronic spectroscopy

The complexes [Fe([9]aneN(2)S)(2)][ClO4](2), [Fe([9]aneN(2)S)(2)][ClO4](3) and [Fe([9]aneNS(2))(2)][ClO4](2) ([9]aneN(2)S = 1-thia-4. 7-diazacyclononane and [9]aneNS(2) = 1,4-dithia-7-azacyclononane) have been prepared and the latter two characterised by X-ray crystallography. The Mossbauer spectra (isomer shift/mm s(-1), quadrupole splitting/mm s(-1), 4.2 K) for [Fe([9]aneN(2)S)(2)][ClO4](2) (0.52, 0.57), [Fe([9]aneN(2)S)(2)][ClO4](3) (0.25, 2.72) and [Fe([9]aneNS(2))(2)][ClO4](2) (0.43, 0.28) are typical for iron(II) and iron(III) complexes. Variable-temperature susceptibility measurements for [Fe([9]aneN(2)S)(2)][ClO4](2) (2-300 K) revealed temperature-dependent behaviour in both the solid state [2.95 mu(B) (300 K)-0.5 mu(B) (4.2 K)] and solution (Delta H degrees 20-22 kJ mol(-1), Delta S degrees 53-60 J mol(-1) K-1). For [Fe([9]aneN(2)S)(2)][ClO4](3) in the solid state [2.3 mu(B) (300 K)-1.9 mu(B) (4.2 K)] the magnetic data were fit to a simple model (H = -lambda L . S + mu L-z) to give the spin-orbit coupling constant (lambda) of -260 +/- 10 cm(-1). The solid-state X-band EPR spectrum of [Fe([9]aneN(2)S)(2)][ClO4](3) revealed axial symmetry (g(perpendicular to) = 2.607, g(parallel to) = 1.599). Resolution of g(perpendicular to) into two components at Q-band frequencies indicated a rhombic distortion. The low-temperature single-crystal absorption spectra of [Fe([9]aneN(2)S)(2)][ClO4](2) and [Fe([9]aneNS(2))(2)][ClO4](2) exhibited additional bands which resembled pseudotetragonal low-symmetry splitting of the parent octahedral (1)A(1g) --> T-1(2g) and (1)A(1g) ---> T-1(1g) transitions. However, the magnitude of these splittings was too large, requiring 10Dq for the thioether donors to be significantly larger than for the amine donors. Instead, these bands were tentatively assigned to weak, low-energy S --> Fe-II charge-transfer transitions. Above 200 K, thermal occupation of the high-spin T-5(2g) ground state resulted in observation of the T-5(2g) --> E-5(g) transition in the crystal spectrum of [Fe([9]aneN(2)S)(2)][ClO4](2). From a temperature-dependence study, the separation of the low-spin (1)A(1g) and high-spin T-5(2g) ground states was approximately 1700 cm(-1). The spectrum of the iron(III) complex [Fe([9]aneN(2)S)(2)][ClO4](3) is consistent with a low-spin d(5) configuration.

mRNA differential display of 2-amino-1-methyl-6-phenylinlidazo[4,5-b]pyridine-induced rat mammary gland tumors

The mRNA differential display technique was used to compare mRNAs between normal mammary gland and turner-derived epithelial cells from female Sprague-Dawley rat mammary gland tumors induced by the heterocyclic amine 2-amino-1-methyl-6-phenylimidazo[4,5-b]pyridine (PhIP) and promoted by a high-fat diet (23.5% corn oil). Two genes, beta-casein and transferrin, were identified as differentially expressed. The expression of these genes was examined across a bank of rat mammary gland tumors derived from animals on a low-fat diet (5% corn oil) or the high-fat diet. Carcinomas had over a 10- and 50-fold lower expression of beta-casein and transferrin, respectively than normal mammary gland. In addition, carcinomas from animals on the high-fat diet showed on average a 5-fold higher expression of beta-casein, and transferrin than carcinomas from animals on the low-fat diet. The results indicate the process of mammary gland tumorigenesis alters the expression of certain genes in the mammary gland, and that the level of dietary fat further modulates the expression of these genes.

Decomposing complete tripartite graphs into cycles of lengths 3 and 4

Necessary and sufficient conditions are given for the edge-disjoint decomposition of a complete tripartite graph K-r,K-s,K-t into exactly alpha 3-cycles and beta 4-cycles. (C) 1999 Elsevier Science B.V. All rights reserved.

Distribution of interleukin-2,-4,-10, tumour necrosis factor-alpha and transforming growth factor-beta mRNAs in oral lichen planus

In the present study. MRNA for the cytokines interleukin-2 (IL-2), IL-4, IL-10 tumour necrosis factor-alpha (TNF-alpha) and transforming growth factor beta-1 (TGF-beta-1) were investigated in oral lichen planus (OLP) lesions using in situ hybridization with S-35-labelled oligonucleotide probes on frozen tissue sections. In addition, the expression of interferon-gamma (IFN-gamma), IL-10 and IL-4 mRNAs was analysed in cultured lesional T lymphocytes from oral lichen planus by polymerase chain reaction. Cells expressing mRNA for IL-2, IL-4, IL-10, TNF-alpha and TGF-beta(1) were found in all the biopsies studied. Approximately 1-2% of the total number of infiltrating cells in the lesions were positive for each of the different cytokine mRNAs. Most biopsies contained basement membrane-oriented, mRNA-positive cells. In the cultured T-cell lines, message for IFN-gamma was detected in all the patients, IL-10 in all but one, and IL-4 in just one of the seven patients investigated. The results suggest that mRNA for both pro- and anti-inflammatory cytokines, i.e., mixed T-helper 1 (T(H)1) and T(H)2 cytokine profiles, are generated simultaneously by a limited number of cells in chronic lesions of OLP. (C) 1999 Elsevier Science Ltd. All rights reserved.

A consistent point-searching algorithm for solution interpolation in unstructured meshes consisting of 4-node bilinear quadrilateral elements

To translate and transfer solution data between two totally different meshes (i.e. mesh 1 and mesh 2), a consistent point-searching algorithm for solution interpolation in unstructured meshes consisting of 4-node bilinear quadrilateral elements is presented in this paper. The proposed algorithm has the following significant advantages: (1) The use of a point-searching strategy allows a point in one mesh to be accurately related to an element (containing this point) in another mesh. Thus, to translate/transfer the solution of any particular point from mesh 2 td mesh 1, only one element in mesh 2 needs to be inversely mapped. This certainly minimizes the number of elements, to which the inverse mapping is applied. In this regard, the present algorithm is very effective and efficient. (2) Analytical solutions to the local co ordinates of any point in a four-node quadrilateral element, which are derived in a rigorous mathematical manner in the context of this paper, make it possible to carry out an inverse mapping process very effectively and efficiently. (3) The use of consistent interpolation enables the interpolated solution to be compatible with an original solution and, therefore guarantees the interpolated solution of extremely high accuracy. After the mathematical formulations of the algorithm are presented, the algorithm is tested and validated through a challenging problem. The related results from the test problem have demonstrated the generality, accuracy, effectiveness, efficiency and robustness of the proposed consistent point-searching algorithm. Copyright (C) 1999 John Wiley & Sons, Ltd.

Nickel complexes with tris(2-aminoethyl)amine (tren): [Ni-3(tren)(4)(H2O)(2)][Cr(ox)(3)](2)center dot 6H(2)O (ox = oxalate), {[Ni-2(tren)(3)][ClO4](4)center dot H2O}(n), and [Ni-2(tren)(2)(aepd)][ClO4](4)center dot 2H(2)O (aepd = N-(2-aminoethyl)pyrrolidi

Reaction of K-3[Cr(ox)(3)] (ox = oxalate) with nickel(II) and tris(2-aminoethyl)amine (tren) in aqueous solution resulted in isolation of the bimetallic assembly [Ni-3(tren)(4)(H2O)(2)][Cr(ox)(3)](2). 6H(2)O. The polymeric complex {[Ni-2(tren)(3)][ClO4](4). H2O}(n) has been prepared by reaction of nickel(II) perchlorate and tren in aqueous solution. From the same reaction mixture the complex [Ni-2(tren)(2)(aepd)][ClO4](4). 2H(2)O (aepd = N-(2-aminoethyl)pyrrolidine-3,4-diamine), in which a bridging tren ligand contains a carbon-carbon bond between two arms forming a substituted pyrrolidine, has been isolated. The complexes have been characterized by X-ray crystallography. The magnetic susceptibility (300-4.2 K) and magnetization data (2, 4 K, H = 0-5 T) for {[Ni-2(tren)(3)][ClO4](4). H2O}(n) (300 K , 4.23 mu(B)) exhibit evidence of weak antiferromagnetic coupling and zero field splitting (2J = -1.8 cm(-1); \ D\ = 2 cm(-1)) at low temperature. For [Ni-3(tren)(4)(H2O)(2)][Cr(ox)(3)](2). 6H(2)O the susceptibility data at 300 K are indicative of uncoupled nickel(II) and chromium(III) sites with zero-field splitting and intramolecular antiferromagnetic coupling predicted at low temperature.