Casimirs and Lax operators from the structure of Lie algebras

This paper uses the structure of the Lie algebras to identify the Casimir invariant functions and Lax operators for matrix Lie groups. A novel mapping is found from the cotangent space to the dual Lie algebra which enables Lax operators to be found. The coordinate equations of motion are given in terms of the structure constants and the Hamiltonian.

Assessing the performance of a building integrated BP c-Si PV system

In this study, the performance, yield and characteristics of a 16 year old photovoltaic (PV) system installation have been investigated. The technology, BP Saturn modules which were steel-blue polycrystalline silicon cells are no longer in production. A bespoke monitoring system has been designed to monitor the characteristics of 6 refurbished strings, of 18 modules connected in series. The total output of the system is configured to 6.5 kWp (series to parallel configuration). In addition to experimental results, the performance ratio (PR) of known values was simulated using PVSyst, a simulation software package. From calculations using experimental values, the PV system showed approximately 10% inferior power outputs to what would have been expected as standard test conditions. However, efficiency values in comparison to standard test conditions and the performance ratio (w75% from PVSyst simulations) over the past decade have remained practically the same. This output though very relevant to the possible performance and stability of aging cells, requires additional parametric studies to develop a more robust argument. The result presented in this paper is part of an on-going investigation into PV system aging effects.

���Very sore nights and days���: the child���s experience of illness in early modern England, c. 1580-1720

Sick children were ubiquitous in early modern England, and yet they have received very little attention from historians. Taking the elusive perspective of the child, this article explores the physical, emotional, and spiritual experience of illness in England between approximately 1580 and 1720. What was it like being ill and suffering pain? How did the young respond emotionally to the anticipation of death? It is argued that children���s experiences were characterised by profound ambivalence: illness could be terrifying and distressing, but also a source of emotional and spiritual fulfilment and joy. This interpretation challenges the common assumption amongst medical historians that the experiences of early modern patients were utterly miserable. It also sheds light on children���s emotional feelings for their parents, a subject often overlooked in the historiography of childhood. The primary sources used in this article include diaries, autobiographies, letters, the biographies of pious children, printed possession cases, doctors��� casebooks, and theological treatises concerning the afterlife.

Expression of protein kinase C isoforms during cardiac ventricular development.

The expression of protein kinase C (PKC) isoforms (PKC-alpha, PKC-beta 1, PKC-delta, PKC-epsilon, and PKC-zeta) was studied by immunoblotting in whole ventricles of rat hearts during postnatal development (1-26 days) and in the adult. PKC-alpha, PKC-beta 1, PKC-delta, PKC-epsilon, and PKC-zeta were detected in ventricles of 1-day-old rats, although PKC-alpha and PKC-beta 1 were only barely detectable. All isoforms were rapidly downregulated during development, with abundances relative to total protein declining in the adult to < 25% of 1-day-old values. PKC-beta 1 was not detectable in adult ventricles. The specific activity of PKC was also downregulated. The rat ventricular myocyte becomes amitotic soon after birth but continues to grow, increasing its protein content 40- to 50-fold between the neonate and the 300-g adult. An important question is thus whether the amount of PKC per myocyte is downregulated. With the use of isolated cells, immunoblotting showed that the contents per myocyte of PKC-alpha and PKC-epsilon increased approximately 10-fold between the neonatal and adult stages. In rat ventricles, the rank of association with the particulate fraction was PKC-delta > PKC-epsilon > PKC-zeta. Association of these isoforms with the particulate fraction was less in the adult than in the neonate. In primary cultures of ventricular myocytes prepared from neonatal rat hearts, 1 microM 12-O-tetradecanoylphorbol-13-acetate (TPA) elicited translocation of PKC-alpha, PKC-delta, and PKC-epsilon from the soluble to the particulate fraction in < 1 min, after which time no further translocation was observed. Prolonged exposure (16 h) of myocytes to 1 microM TPA caused essentially complete downregulation of these isoforms, although downregulation of PKC-epsilon was slower than for PKC-delta. In contrast, PKC-zeta was neither translocated nor downregulated by 1 microM TPA. Immunoblotting of human ventricular samples also revealed downregulation of PKC relative to total protein during fetal/postnatal development.

Stimulation of phosphatidylinositol hydrolysis, protein kinase C translocation, and mitogen-activated protein kinase activity by bradykinin in rat ventricular myocytes: dissociation from the hypertrophic response.

In ventricular myocytes cultured from neonatal rat hearts, bradykinin (BK), kallidin or BK(1-8) [(Des-Arg9)BK] stimulated PtdinsP2 hydrolysis by 3-4-fold. EC50 values were 6 nM (BK), 2 nM (kallidin), and 14 microM [BK(1-8)]. BK or kallidin stimulated the rapid (less than 30 s) translocation of more than 80% of the novel protein kinase C (PKC) isoforms nPKC-delta and nPKC-epsilon from the soluble to the particulate fraction. EC50 values for nPKC-delta translocation by BK or kallidin were 10 and 2 nM respectively. EC50 values for nPKC-epsilon translocation by BK or kallidin were 2 and 0.6 nM respectively. EC50 values for the translocation of nPKC-delta and nPKC-epsilon by BK(1-8) were more than 5 microM. The classical PKC, cPKC-alpha, and the atypical PKC, nPKC-zeta, did not translocate. BK caused activation and phosphorylation of p42-mitogen-activated protein kinase (MAPK) (maximal at 3-5 min, 30-35% of p42-MAPK phosphorylated). p44-MAPK was similarly activated. EC50 values for p42/p44-MAPK activation by BK were less than 1 nM whereas values for BK(1-8) were more than 10 microM. The order of potency [BK approximately equal to kallidin > BK (1-8)] for the stimulation of PtdInsP2 hydrolysis, nPKC-delta and nPKC-epsilon translocation, and p42/p44-MAPK activities suggests involvement of the B2 BK receptor subtype. In addition, stimulation of all three processes by BK was inhibited by the B2BK receptor-selective antagonist HOE140 but not by the B1-selective antagonist Leu8BK(1-8). Exposure of cells to phorbol 12-myristate 13-acetate for 24 h inhibited subsequent activation of p42/p44-MAPK by BK suggesting participation of nPKC (and possibly cPKC) isoforms in the activation process. Thus, like hypertrophic agents such as endothelin-1 (ET-1) and phenylephrine (PE), BK activates PtdInsP2 hydrolysis, translocates nPKC-delta, and nPKC-epsilon, and activates p42/p44-MAPK. However, in comparison with ET-1 and PE, BK was only weakly hypertrophic as assessed by cell morphology and patterns of gene expression. This difference could not be attributed to dissimilarities between the duration of activation of p42/p44-MAPK by BK or ET-1. Thus activation of these signalling pathways alone may be insufficient to induce a powerful hypertrophic response.

The p38-MAPK inhibitor, SB203580, inhibits cardiac stress-activated protein kinases/c-Jun N-terminal kinases (SAPKs/JNKs).

SB203580 is a recognised inhibitor of p38-MAPKs. Here, we investigated the effects of SB203580 on cardiac SAPKs/JNKs. The IC50 for inhibition of p38-MAPK stimulation of MAPKAPK2 was approximately 0.07 microM, whereas that for total SAPK/JNK activity was 3-10 microM. SB203580 did not inhibit immunoprecipitated JNK1 isoforms. Three peaks of SAPK/JNK activity were separated by anion exchange chromatography, eluting in the isocratic wash (44 kDa), and at 0.08 M (46 and 52 kDa) and 0.15 M NaCl (54 kDa). SB203580 (10 microM) completely inhibited the 0.15 M NaCl activity and partially inhibited the 0.08 M NaCl activity. Since JNK1 antibodies immunoprecipitate the 46 kDa activity, this indicates that SB203580 selectively inhibits 52 and 54 kDa SAPKs/JNKs.

Activation of c-Jun N-terminal kinases and p38-mitogen-activated protein kinases in human heart failure secondary to ischaemic heart disease.

Three well-characterized mitogen-activated protein kinase (MAPK) subfamilies are expressed in rodent and rabbit hearts, and are activated by pathophysiological stimuli. We have determined and compared the expression and activation of these MAPKs in donor and failing human hearts. The amount and activation of MAPKs was assessed in samples from the left ventricles of 4 unused donor hearts and 12 explanted hearts from patients with heart failure secondary to ischaemic heart disease. Total MAPKs or dually phosphorylated (activated) MAPKs were detected by Western blotting and MAPK activities were measured by in gel kinase assays. As in rat heart, c-Jun N-terminal kinases (JNKs) were detected in human hearts as bands corresponding to 46 and 54 kDa; p38-MAPK(s) was detected as a band corresponding to approximately 40 kDa, and extracellularly regulated kinases, ERK1 and ERK2, were detected as 44- and 42-kDa bands respectively. The total amounts of 54 kDa JNK, p38-MAPK and ERK2 were similar in all samples, although 46-kDa JNK was reduced in the failing hearts. However, the mean activities of JNKs and p38-MAPK(s) were significantly higher in failing heart samples than in those from donor hearts (P<0.05). There was no significant difference in phosphorylated (activated) ERKs between the two groups. In conclusion, JNKs, p38-MAPK(s) and ERKs are expressed in the human heart and the activities of JNKs and p38-MAPK(s) were increased in heart failure secondary to ischaemic heart disease. These data indicate that JNKs and p38-MAPKs may be important in human cardiac pathology.

Up-regulation of c-jun mRNA in cardiac myocytes requires the extracellular signal-regulated kinase cascade, but c-Jun N-terminal kinases are required for efficient up-regulation of c-Jun protein.

Cardiac hypertrophy, an important adaptational response, is associated with up-regulation of the immediate early gene, c- jun, which encodes the c-Jun transcription factor. c-Jun may feed back to up-regulate its own transcription and, since the c-Jun N-terminal kinase (JNK) family of mitogen-activated protein kinases (MAPKs) phosphorylate c-Jun(Ser-63/73) to increase its transactivating activity, JNKs are thought to be the principal factors involved in c- jun up-regulation. Hypertrophy in primary cultures of cardiac myocytes is induced by endothelin-1, phenylephrine or PMA, probably through activation of one or more of the MAPK family. These three agonists increased c- jun mRNA with the rank order of potency of PMA approximately endothelin-1>phenylephrine. Up-regulation of c- jun mRNA by endothelin-1 was attenuated by inhibitors of protein kinase C (GF109203X) and the extracellular signal-regulated kinase (ERK) cascade (PD98059 or U0126), but not by inhibitors of the JNK (SP600125) or p38-MAPK (SB203580) cascades. Hyperosmotic shock (0.5 M sorbitol) powerfully activates JNKs, but did not increase c- jun mRNA. These data suggest that ERKs, rather than JNKs, are required for c- jun up-regulation. However, endothelin-1 and phenylephrine induced greater up-regulation of c-Jun protein than PMA and phosphorylation of c-Jun(Ser-63/73) correlated with the level of c-Jun protein. Up-regulation of c-Jun protein by endothelin-1 was attenuated by inhibitors of protein kinase C and the ERK cascade, probably correlating with a primary input of ERKs into transcription. In addition, SP600125 inhibited the phosphorylation of c-Jun(Ser-63/73), attenuated the increase in c-Jun protein induced by endothelin-1 and increased the rate of c-Jun degradation. Thus whereas ERKs are the principal MAPKs required for c- jun transcription, JNKs are necessary to stabilize c-Jun for efficient up-regulation of the protein.

Bayesian coalescent analysis reveals a high rate of molecular evolution in GB virus C

GB virus C/hepatitis G (GBV-C) is an RNA virus of the family Flaviviridae. Despite replicating with an RNA-dependent RNA polymerase, some previous estimates of rates of evolutionary change in GBV-C suggest that it fixes mutations at the anomalously low rate of similar to 100(-7) nucleotide substitution per site, per year. However, these estimates were largely based on the assumption that GBV-C and its close relative GBV-A (New World monkey GB viruses) codiverged with their primate hosts over millions of years. Herein, we estimated the substitution rate of GBV-C using the largest set of dated GBV-C isolates compiled to date and a Bayesian coalescent approach that utilizes the year of sampling and so is independent of the assumption of codivergence. This revealed a rate of evolutionary change approximately four orders of magnitude higher than that estimated previously, in the range of 10(-2) to 10(-3) sub/site/year, and hence in line with those previously determined for RNA viruses in general and the Flaviviridae in particular. In addition, we tested the assumption of host-virus codivergence in GBV-A by performing a reconciliation analysis of host and virus phylogenies. Strikingly, we found no statistical evidence for host-virus codivergence in GBV-A, indicating that substitution rates in the GB viruses should not be estimated from host divergence times.

Study of the mechanism of action of anoplin, a helical antimicrobial decapeptide with ion channel-like activity, and the role of the amidated C-terminus

Anoplin, an antimicrobial, helical decapeptide from wasp venom, looses its biological activities by mere deamidation of its C-terminus. Secondary structure determination, by circular dichroism spectroscopy in amphipathic environments, and lytic activity in zwitterionic and anionic vesicles showed quite similar results for the amidated and the carboxylated forms of the peptide. The deamidation of the C-terminus introduced a negative charge at an all-positive charged peptide, causing a loss of amphipathicity, as indicated by molecular dynamics simulations in TFE/water mixtures and this subtle modification in a peptide`s primary structure disturbed the interaction with bilayers and biological membranes. Although being poorly lytic, the amidated form, but not the carboxylated, presented ion channel-like activity on anionic bilayers with a well-defined conductance step; at approximately the same concentration it showed antimicrobial activity. The pores remain open at trans-negative potentials, preferentially conducting cations, and this situation is equivalent to the interaction of the peptide with bacterial membranes that also maintain a high negative potential inside. Copyright (C) 2007 European Peptide Society and John Wiley & Sons, Ltd.

Indecomposable and noncrossed product division algebras over function fields of smooth p-adic curves

We construct indecomposable and noncrossed product division algebras over function fields of connected smooth curves X over Z(p). This is done by defining an index preserving morphism s: Br(<(K(X))over cap>)` --> Br(K(X))` which splits res : Br(K (X)) --> Br(<(K(X))over cap>), where <(K(X))over cap> is the completion of K (X) at the special fiber, and using it to lift indecomposable and noncrossed product division algebras over <(K(X))over cap>. (C) 2010 Elsevier Inc. All rights reserved.

Hyperbolic unit groups and quaternion algebras

We classify the quadratic extensions K = Q[root d] and the finite groups G for which the group ring o(K)[G] of G over the ring o(K) of integers of K has the property that the group U(1)(o(K)[G]) of units of augmentation 1 is hyperbolic. We also construct units in the Z-order H(o(K)) of the quaternion algebra H(K) = (-1, -1/K), when it is a division algebra.

COMMUTATIVE FINITE-DIMENSIONAL ALGEBRAS SATISFYING x(x(xy))=0 ARE NILPOTENT

We investigate the structure of commutative non-associative algebras satisfying the identity x(x(xy)) = 0. Recently, Correa and Hentzel proved that every commutative algebra satisfying above identity over a field of characteristic not equal 2 is solvable. We prove that every commutative finite-dimensional algebra u over a field F of characteristic not equal 2, 3 which satisfies the identity x(x(xy)) = 0 is nilpotent. Furthermore, we obtain new identities and properties for this class of algebras.

Examples of Self-Iterating Lie Algebras, 2

We study properties of self-iterating Lie algebras in positive characteristic. Let R = K[t(i)vertical bar i is an element of N]/(t(i)(p)vertical bar i is an element of N) be the truncated polynomial ring. Let partial derivative(i) = partial derivative/partial derivative t(i), i is an element of N, denote the respective derivations. Consider the operators v(1) = partial derivative(1) + t(0)(partial derivative(2) + t(1)(partial derivative(3) + t(2)(partial derivative(4) + t(3)(partial derivative(5) + t(4)(partial derivative(6) + ...))))); v(2) = partial derivative(2) + t(1)(partial derivative(3) + t(2)(partial derivative(4) + t(3)(partial derivative(5) + t(4)(partial derivative(6) + ...)))). Let L = Lie(p)(v(1), v(2)) subset of Der R be the restricted Lie algebra generated by these derivations. We establish the following properties of this algebra in case p = 2, 3. a) L has a polynomial growth with Gelfand-Kirillov dimension lnp/ln((1+root 5)/2). b) the associative envelope A = Alg(v(1), v(2)) of L has Gelfand-Kirillov dimension 2 lnp/ln((1+root 5)/2). c) L has a nil-p-mapping. d) L, A and the augmentation ideal of the restricted enveloping algebra u = u(0)(L) are direct sums of two locally nilpotent subalgebras. The question whether u is a nil-algebra remains open. e) the restricted enveloping algebra u(L) is of intermediate growth. These properties resemble those of Grigorchuk and Gupta-Sidki groups.

Crossed products by twisted partial actions and graded algebras

For a twisted partial action e of a group G on an (associative non-necessarily unital) algebra A over a commutative unital ring k, the crossed product A x(Theta) G is proved to be associative. Given a G-graded k-algebra B = circle plus(g is an element of G) B-g with the mild restriction of homogeneous non-degeneracy, a criteria is established for B to be isomorphic to the crossed product B-1 x(Theta) G for some twisted partial action of G on B-1. The equality BgBg-1 B-g = B-g (for all g is an element of G) is one of the ingredients of the criteria, and if it holds and, moreover, B has enough local units, then it is shown that B is stably isomorphic to a crossed product by a twisted partial action of G. (c) 2008 Elsevier Inc. All rights reserved.