Singularities of optimal control problems on some 6-D lie groups

This paper considers the motion planning problem for oriented vehicles travelling at unit speed in a 3-D space. A Lie group formulation arises naturally and the vehicles are modeled as kinematic control systems with drift defined on the orthonormal frame bundles of particular Riemannian manifolds, specifically, the 3-D space forms Euclidean space E-3, the sphere S-3, and the hyperboloid H'. The corresponding frame bundles are equal to the Euclidean group of motions SE(3), the rotation group SO(4), and the Lorentz group SO (1, 3). The maximum principle of optimal control shifts the emphasis for these systems to the associated Hamiltonian formalism. For an integrable case, the extremal curves are explicitly expressed in terms of elliptic functions. In this paper, a study at the singularities of the extremal curves are given, which correspond to critical points of these elliptic functions. The extremal curves are characterized as the intersections of invariant surfaces and are illustrated graphically at the singular points. It. is then shown that the projections, of the extremals onto the base space, called elastica, at these singular points, are curves of constant curvature and torsion, which in turn implies that the oriented vehicles trace helices.

The influence of pomegranate by-product and punicalagins on selected groups of human intestinal microbiota.

We have examined the gut bacterial metabolism of pomegranate by-product (POMx) and major pomegranate polyphenols, punicalagins, using pH-controlled, stirred, batch culture fermentation systems reflective of the distal region of the human large intestine. Incubation of POMx or punicalagins with faecal bacteria resulted in formation of the dibenzopyranone-type urolithins. The time course profile confirmed the tetrahydroxylated urolithin D as the first product of microbial transformation, followed by compounds with decreasing number of phenolic hydroxy groups: the trihydroxy analogue urolithin C and dihydroxylated urolithin A. POMx exposure enhanced the growth of total bacteria, Bifidobacterium spp. and Lactobacillus spp., without influencing the Clostridium coccoides–Eubacterium rectale group and the C. histolyticum group. In addition, POMx increased concentrations of short chain fatty acids (SCFA) viz. acetate, propionate and butyrate in the fermentation medium. Punicalagins did not affect the growth of bacteria or production of SCFA. The results suggest that POMx oligomers, composed of gallic acid, ellagic acid and glucose units, may account for the enhanced growth of probiotic bacteria.

Effects of dietary fatty acid composition on basal and hormonestimulated hepatic lipogenesis and on circulating lipids in the rat

Thirty male rats were randomly assigned to one of three dietary groups in which the source of dietary fat was either a mixed oil, maize oil or fish oil. Effects of dietary fatty acid composition on in virro rates of [U-'4C]glucose incorporation into hepatic total lipids and into hepatic triacylglycerol were measured under basal, insulin (4 nM)-, gastric inhibitory polypeptide (GIP; 6 mi)- and insulin + GIP (4 nM + 6 n ~ ) - stimulated conditions. Effects of the three diets on postprandial plasma triacylglycerol, cholesterol, insulin and GIP concentrations were also measured. The fish-oil diet decreased rates of basal glucose incorporation into hepatic total lipids (P < 0.05) and hepatic triacylglycerol (P < 0.01) compared with the mixed-oil diet. The presence of insulin + GIP in the incubation medium stimulated glucose incorporation into hepatic total lipids in the maize-oil (P < 0.01) and fish-oil groups (P < OW), as well as into hepatic triacylglycerol in the maize-oil group (P < 0.005). In addition, the fish-oil diet decreased postprandial plasma triacylglycerol levels compared with both other dietary groups (P < 0-05 both cases), and the mixed-oil diet markedly increased postprandial plasma insulin levels compared with the other dietary groups (P c 0.001).

The influence of dietary fatty acid composition on N-ethyl-Nnitrosourea-induced mammary tumour incidence in the rat and on the composition of inositol- and ethanolamine-phospholipids of normal and tumour mammary tissue

This study has investigated the influence of dietary fatty acid composition on mammary tumour incidence in N-ethyl-N-nitrosourea (ENU)-treated rats and has compared the susceptibility to dietary fatty acid modification of the membrane phospholipids phosphatidyliuositol (PI) and phosphatidylethanolamine (PE) from normal and tumour tissue of rat mammary gland. The incidence of mammary tumours was significantly lower in fish oil- (29%), compared with olive oil- (75%; P < 0.04) but not maize oil- (63%; P < 0.1) fed animals. No differences in PI fatty acid composition were found in normal or tumour tissue between rats fed on maize oil, olive oil or fish oil in diets from weaning. When normal and tumour tissue PI fatty acids were compared, significantly higher amounts of stearic acid (18:O) were found in tumour than normal tissue in rats given olive oil (P < 0.05). A similar trend was found in animals fed on maize oil, although differences between normal and tumour tissue did not reach a level of statistical significance (P < 0.1). In mammary PE, maize oil-fed control animals had significantly higher levels of linoleic acid (18:2n-6) than either olive oil- or fish oil-fed animals (P < 0.05, both cases) and levels of arachidonic acid were also higher in maize oil- compared with fish oil-fed animals (P < 0.05). In tumourbearing animals no differences in PE fatty acid composition were found between the three dietary groups. When normal and tumour tissue PE fatty acids were compared, significantly lower amounts of liuoleic acid (18:2n-6; P < 0.01) and significantly greater amounts of arachidonic acid (20:4n-6; P < 0.05) were found in tumour than normal tissue of rats fed on maize oil. The present study shows that the fatty acid composition of PI from both normal and tumour tissue of the mammary gland is resistant to dietary fatty acid modification. The PE fraction is more susceptible to dietary modification and in this fraction there is evidence of increased conversion of linoleic acid to arachidonic acid in tumour compared with normal tissue. Lower tumour incidence rates in rats given fish oils may in part be due to alteration in prostanoid metabolism secondary to displacement of arachidonic acid by eicosapentaenoic acid, but PE rather than PI would appear to be the most likely locus for diet-induced alteration in prostanoid synthesis in this tissue. Effects of dietary fatty acids other than on the balance of n-6 and n-3 fatty acids, and on prostanoid metabolism, should also be considered. The significance of increased stearic acid content of PI in tumours of olive oil-fed animals and the possible influence of dietary fatty acids on the capacity for stearic acid accumulation requires further study.

Effect of dietary fatty acid composition on inositol-, choline- and ethanolamine-phospholipids of mammary tissue and erythrocytes in the rat

The present study investigated the effect of feeding maize-oil, olive-oil and fish-oil diets, from weaning to adulthood, on rat mammary tissue and erythrocyte phospholipid fatty acid compositions. Effects of diet on the relative proportions of membrane phospholipids in the two tissues were also investigated. Mammary tissue phosphatidylinositol (PI) fatty acids were unaltered by diet, but differences in phosphatidylethanolamine (PE) and, to a lesser extent, phosphatidylcholine (PC) fractions were found between animals fed on different diets from weaning. Differences observed were those expected from the dietary fatty acids fed; n-6 fatty acids were found in greatest amounts in maize-oil-fed rats, n-9 in olive-oil-fed rats, and n-3 in fish-oil-fed rats. In erythrocytes the relative susceptibilities of the individual phospholipids to dietary modification were: PE > PC > PI, but enrichment with n-9 and n-3 fatty acids was not observed in olive-oil- and fish-oil-fed animals and in PC and PE significantly greater amounts of saturated fatty acids were found when animals fed on olive oil or fish oil were compared with maize-oil-fed animals. The polyunsaturated:saturated fatty acid ratios of PE and PC fractions were significantly lower in olive-oil- and fish-oil-fed animals. No differences in the relative proportions of phospholipid classes were found between the three dietary groups. It is suggested that differences in erythrocyte fatty acid composition may reflect dietary-induced changes in membrane cholesterol content and may form part of a homoeostatic response the aim of which is to maintain normal erythrocyte membrane fluidity. The resistance of mammary tissue PI fatty acids to dietary modification suggests that alteration of PI fatty acids is unlikely to underlie effects of dietary fat on mammary tumour incidence rates.

Effects of dietary polyunsaturated fatty acid supplementation on fatty acid composition in muscle and subcutaneous adipose tissue of lambs

Lambs (n = 48) were used in a 2 × 2 factorial arrangement of treatments to evaluate effects of inclusion of oil containing PUFA in high-concentrate diets (with or without) and duration of oil supplementation (pre- vs. postweaning) on CLA concentration of muscle and adipose tissue. Lambs were fed preweaning creep diets (with or without oil) corresponding to the dietary lactation treatment diet (with or without oil) of the dam. Dams blocked by lambing date and rearing type were randomly assigned to 1 of 2 lactation dietary treatments with or without oil supplementation. Creep diets contained approximately 70% concentrate and 30% roughage and were provided to lambs for ad libitum intake. At weaning (58.7 ± 2.5 d of age), lambs (n = 48) were randomly assigned within preweaning treatment groups to 1 of 2 postweaning dietary treatments (with or without oil) and 16 pens in a randomized block design, blocked by sex and BW. Postweaning diets were formulated to contain approximately 80% concentrate and 20% roughage and were fed once daily for ad libitum intake. Soybean and linseed oil (2:1, respectively) replaced ground corn and provided 3% additional fat in pre- and postweaning diets. Lambs were slaughtered at 60.3 ± 4.2 kg of BW. A subcutaneous fat (SQ) sample was obtained within 1 h postmortem and a LM sample at the 12th rib was obtained 24 h postmortem, and both were analyzed for fatty acid profile. Feedlot performance and carcass measurements were not affected (P ≥ 0.26) by oil supplementation. Total CLA content of LM and SQ was not affected (P ≥ 0.08) by oil supplementation pre- or postweaning, but trans-10, cis-12 CLA was greater (P = 0.02) in SQ from lambs supplemented with oil postweaning. Total PUFA content in LM was greater (P = 0.02) in lambs supplemented with oil pre- or postweaning as a result of increased concentrations of 18:2cis-9, cis-12 and longer chain PUFA. Conversely, pre- and postweaning oil supplementation resulted in less (P = 0.04) MUFA content in LM. Only postweaning oil supplementation increased (P = 0.001) SQ PUFA content. Feeding oils containing PUFA to lambs pre- and postweaning did not increase CLA content of muscle, whereas postweaning oil supplementation minimally increased CLA concentration of SQ fat. Inclusion of soybean and linseed oil in pre- and postweaning diets increased total PUFA content of SQ fat and muscle tissue without adversely affecting growth performance or carcass characteristics.

Facile oxidation of phenylphosphinic acid to phenylphosphonic acid using [Cu2(μ-O2CCH3)4(H2O)2]: X-ray crystal structures of monomeric [Cu(PhPO3H)2(C5H5N)4]·2CH3OH and [Cu(PhPO3H)2(C5H5N)4]

Phenylphosphinic acid (HPhPO2H) is oxidized to phenylphosphonic acid (PhPO3H2) at room temperature using a solution of [Cu2(μ-O2CCH3)4(H2O)2] in pyridine. The phenylphosphonic acid was recovered as the monomeric copper(II) complex [Cu(PhPO3H)2(C5H5N)4]·H2O (1a), and the reaction thought to proceed via a copper(I) intermediate. Recrystallization of 1a from methanol gave [Cu(PhPO3H)2(C5H5N)4]·2CH3OH (1b). The unsolvated complex [Cu(PhPO3H)2(C5H5N)4] (1c) was prepared by refluxing polymeric [Cu(PhPO3)(H2O)] (2) in pyridine. The X-ray crystal structures of 1b and 1c show that in each of these monomeric complexes the copper(II) ion is ligated by four equatorial pyridine molecules and two axial monoanionic phenylphosphonate groups. A cyclic voltammetric study of 1a revealed a quasi-reversible Cu2+/Cu+ couple with E1/2 = +228 mV (vs Ag/AgCl).

Synthesis of the μ-PH hexaosmium clusters [Os6H2(CO)20L(μ3-PH)](L = CO or MeCN) and their reactions with base: X-ray crystal structures of [Os6H2(CO)20(MeCN)(μ3-PH)] and [Os6H3(CO)19(CO2Me)(μ3-PH)]

Mild heating of the phosphidotriosmium cluster [Os3H(CO)10(µ2-PH2)](1) with [Os3(CO)12 –n(MeCN)n](n= 1 or 2) gives high yields of the (µ3-PH) bridged hexaosmium clusters (2) and (3); reactions of (2) and (3) with bases and X-ray structure analyses of (3) and of (6), which was obtained from (3) and MeO– followed by acid treatment are described.

Anticancer activity of organotin compounds. 2. Interaction of diorganotin dihalides with nucleic acid bases and nucleosides; the synthesis of adenine, adenosine and 9-methyladenine adducts

The syntheses of the complexes formulated as SnMe2Cl2(Ad)2 (I), SnMe2Cl2(Ado)2 (II), SnMe2Cl2- (9-MeAd)2 (III) [Ad = adenine, Ado = adenosine, 9-MeAd = 9-methyladenine] as well as the more unexpected SnPhCl2(OH)(Ad)2·3H2O (IV) and SnPhCl3(Ado)2 (V) by reaction of SnMe2Cl2 or SnPh2Cl2 with the appropriate bases in methanol is described. 1H NMR studies suggest that coordination is through the N-7 position of the adenine base.

SATgene dietary model to implement diets of differing fat composition in prospectively genotyped groups (apoE) using commercially available foods

esponse to dietary fat manipulation is highly heterogeneous, yet generic population-based recommendations aimed at reducing the burden of CVD are given. The APOE epsilon genotype has been proposed to be an important determinant of this response. The present study reports on the dietary strategy employed in the SATgenɛ (SATurated fat and gene APOE) study, to assess the impact of altered fat content and composition on the blood lipid profile according to the APOE genotype. A flexible dietary exchange model was developed to implement three isoenergetic diets: a low-fat (LF) diet (target composition: 24 % of energy (%E) as fat, 8 %E SFA and 59 %E carbohydrate), a high-saturated fat (HSF) diet (38 %E fat, 18 %E SFA and 45 %E carbohydrate) and a HSF-DHA diet (HSF diet with 3 g DHA/d). Free-living participants (n 88; n 44 E3/E3 and n 44 E3/E4) followed the diets in a sequential design for 8 weeks, each using commercially available spreads, oils and snacks with specific fatty acid profiles. Dietary compositional targets were broadly met with significantly higher total fat (42·8 %E and 41·0 %E v. 25·1 %E, P ≤ 0·0011) and SFA (19·3 %E and 18·6 %E v. 8·33 %E, P ≤ 0·0011) intakes during the HSF and HSF-DHA diets compared with the LF diet, in addition to significantly higher DHA intake during the HSF-DHA diet (P ≤ 0·0011). Plasma phospholipid fatty acid analysis revealed a 2-fold increase in the proportion of DHA after consumption of the HSF-DHA diet for 8 weeks, which was independent of the APOE genotype. In summary, the dietary strategy was successfully implemented in a free-living population resulting in well-tolerated diets which broadly met the dietary targets set.

In vitro fermentation of a red wine extract by human gut microbiota: changes in microbial groups and formation of phenolic metabolites

An in vitro batch culture fermentation experiment was conducted with fecal inocula from three healthy volunteers in the presence and absence of a red wine extract. Changes in main bacterial groups were determined by FISH during a 48 h fermentation period. The catabolism of main flavonoids (i.e., flavan-3-ols and anthocyanins) and the formation of a wide a range of phenolic microbial metabolites were determined by a targeted UPLC-PAD-ESI-TQ MS method. Statistical analysis revealed that catechol/pyrocatechol, as well as 4-hydroxy-5-(phenyl)-valeric, 3- and 4-hydroxyphenylacetic, phenylacetic, phenylpropionic, and benzoic acids, showed the greatest increases in concentration during fermentation, whereas 5-(3′-hydroxyphenyl)-γ-valerolactone, its open form 4-hydroxy-5-(3′-hydroxyphenyl)-valeric acid, and 3,4-dihydroxyphenylacetic acid represented the largest interindividual variations in the catabolism of red wine polyphenols. Despite these changes, microbial catabolism did not produce significant changes in the main bacterial groups detected, although a slight inhibition of the Clostridium histolyticum group was observed.

Syntheses, characterization and X-ray crystal structures of a mono- and a penta-nuclear nickel(II) complex with oximato Schiff base ligands

A mononuclear octahedral nickel(II) complex [Ni(HL(1))(2)](SCN)(2) (1) and an unusual penta-nuclear complex [{(NiL(2))(mu-SCN)}(4)Ni(NCS)(2)]center dot 2CH(3)CN (2) where HL(1) = 3-(2-aminoethylimino)butan-2-one oxime and HL(2) = 3-(hydroxyimino)butan-2-ylidene)amino)propylimino)butan-2-one oxime have been prepared and characterized by X-ray crystallography. The mono-condensed ligand, HL(1), was prepared by the 1:1 condensation of the 1,2-diaminoethane with diacetylmonoxime in methanol under high dilution. Complex 1 is found to be a mer isomer and the amine hydrogen atoms are involved in extensive hydrogen bonding with the thiocyanate anions. The dicondensed ligand, HL(2), was prepared by the 1:2 condensation of the 1,3-diaminopropane with diacetylmonoxime in methanol. The central nickel(II) in 2 is coordinated by six nitrogen atoms of six thiocyanate groups, four of which utilize their sulphur atoms to connect four NiL2 moieties to form a penta-nuclear complex and it is unique in the sense that this is the first thiocyanato bridged penta-nuclear nickel(II) compound with Schiff base ligands.

Anion-directed template synthesis and hydrolysis of mono-condensed Schiff base of 1,3-pentanediamine ando-hydroxyacetophenone in NiII and CuII Complexes

Bis(o-hydroxyacetophenone)nickel(II) dihydrate, on reaction with 1,3-pentanediamine, yields a bis-chelate complex [NiL2]·2H2O (1) of mono-condensed tridentate Schiff baseligand HL {2-[1-(3-aminopentylimino)ethyl]phenol}. The Schiff base has been freed from the complex by precipitating the NiII as a dimethylglyoximato complex. HL reacts smoothly with Ni(SCN)2·4H2O furnishing the complex [NiL(NCS)] (2) and with CuCl2·2H2O in the presence of NaN3 or NH4SCN producing [CuL(N3)]2 (3) or [CuL(NCS)] (4). On the other hand, upon reaction with Cu(ClO4)2·6H2O and Cu(NO3)2·3H2O, the Schiff base undergoes hydrolysis to yield ternary complexes [Cu(hap)(pn)(H2O)]ClO4 (5) and [Cu(hap)(pn)(H2O)]NO3 (6), respectively (Hhap = o-hydroxyacetophenone and pn = 1,3-pentanediamine). The ligand HL undergoes hydrolysis also on reaction with Ni(ClO4)2·6H2O or Ni(NO3)2·6H2O to yield [Ni(hap)2] (7). The structures of the complexes 2, 3, 5, 6, and 7 have been confirmed by single-crystal X-ray analysis. In complex 2, NiII possesses square-planar geometry, being coordinated by the tridentate mono-negative Schiff base, L and the isothiocyanate group. The coordination environment around CuII in complex 3 is very similar to that in complex 2 but here two units are joined together by end-on, axial-equatorial azide bridges to result in a dimer in which the geometry around CuII is square pyramidal. In both 5 and 6, the CuII atoms display the square-pyramidal environment; the equatorial sites being coordinated by the two amine groups of 1,3-pentanediamine and two oxygen atoms of o-hydroxyacetophenone. The axial site is coordinated by a water molecule. Complex 7 is a square-planar complex with the Ni atom bonded to four oxygen atoms from two hap moieties. The mononuclear units of 2 and dinuclear units of 3 are linked by strong hydrogen bonds to form a one-dimensional network. The mononuclear units of 5 and 6 are joined together to form a dimer by very strong hydrogen bonds through the coordinated water molecule. These dimers are further involved in hydrogen bonding with the respective counteranions to form 2-D net-like open frameworks.

Pairwise assembly of organopalladium(II) units with cyanurato(3-) and trithiocyanurato(3-) ligands: formation of chiral Pd12, Pd10 and Pd9 cage-molecules

The o-palladated, chloro-bridged dimers [Pd{2-phenylpyridine(-H)}-μ-Cl]2 and [Pd{N,N-dimethylbenzylamine(-H)}-μ-Cl]2 react with cyanuric acid in the presence of base to afford closed, chiral cage-molecules in which twelve organo-Pd(II) centers, located in pairs at the vertices of an octahedron, are linked by four tetrahedrally-arranged cyanurato(3-) ligands. Incomplete (Pd10) cages, having structures derived from the corresponding Pd12 cages by replacing one pair of organopalladium centers with two protons, have also been isolated. Reaction of [Pd{2-phenylpyridine(-H)}-μ-Cl]2 with trithiocyanuric acid gives an entirely different and more open type of cage-complex, comprising only nine organopalladium centers and three thiocyanurato(3-) ligands: cage-closure in this latter system appears to be inhibited by steric crowding of the thiocarbonyl groups.

Impact of geographical region on urinary metabolomic and plasma fatty acid profiles in subjects with the metabolic syndrome across Europe: the LIPGENE study

The application of metabolomics in multi-centre studies is increasing. The aim of the present study was to assess the effects of geographical location on the metabolic profiles of individuals with the metabolic syndrome. Blood and urine samples were collected from 219 adults from seven European centres participating in the LIPGENE project (Diet, genomics and the metabolic syndrome: an integrated nutrition, agro-food, social and economic analysis). Nutrient intakes, BMI, waist:hip ratio, blood pressure, and plasma glucose, insulin and blood lipid levels were assessed. Plasma fatty acid levels and urine were assessed using a metabolomic technique. The separation of three European geographical groups (NW, northwest; NE, northeast; SW, southwest) was identified using partial least-squares discriminant analysis models for urine (R 2 X: 0•33, Q 2: 0•39) and plasma fatty acid (R 2 X: 0•32, Q 2: 0•60) data. The NW group was characterised by higher levels of urinary hippurate and N-methylnicotinate. The NE group was characterised by higher levels of urinary creatine and citrate and plasma EPA (20 : 5 n-3). The SW group was characterised by higher levels of urinary trimethylamine oxide and lower levels of plasma EPA. The indicators of metabolic health appeared to be consistent across the groups. The SW group had higher intakes of total fat and MUFA compared with both the NW and NE groups (P≤ 0•001). The NE group had higher intakes of fibre and n-3 and n-6 fatty acids compared with both the NW and SW groups (all P< 0•001). It is likely that differences in dietary intakes contributed to the separation of the three groups. Evaluation of geographical factors including diet should be considered in the interpretation of metabolomic data from multi-centre studies.