On the structure of maximal solvable extensions and of Levi extensions of nilpotent algebras

We establish an improved upper estimate on dimension of any solvable algebra s with its nilradical isomorphic to a given nilpotent Lie algebra n. Next we consider Levi decomposable algebras with a given nilradical n and investigate restrictions on possible Levi factors originating from the structure of characteristic ideals of n. We present a new perspective on Turkowski's classification of Levi decomposable algebras up to dimension 9.Comment: 21 pages; major revision - one section added, another erased; author's version of the published pape

All solvable extensions of a class of nilpotent Lie algebras of dimension n and degree of nilpotency n-1

We construct all solvable Lie algebras with a specific n-dimensional nilradical n_(n,2) (of degree of nilpotency (n-1) and with an (n-2)-dimensional maximal Abelian ideal). We find that for given n such a solvable algebra is unique up to isomorphisms. Using the method of moving frames we construct a basis for the Casimir invariants of the nilradical n_(n,2). We also construct a basis for the generalized Casimir invariants of its solvable extension s_(n+1) consisting entirely of rational functions of the chosen invariants of the nilradical.Comment: 19 pages; added references, changes mainly in introduction and conclusions, typos corrected; submitted to J. Phys. A, version to be publishe

Developmental regulation of CB1-mediated spike-time dependent depression at immature mossy fiber-CA3 synapses

Early in postnatal life, mossy fibres (MF), the axons of granule cells in the dentate gyrus, release GABA which is depolarizing and excitatory. Synaptic currents undergo spike-time dependent long-term depression (STD-LTD) regardless of the temporal order of stimulation (pre versus post and viceversa). Here we show that at P3 but not at P21, STD-LTD, induced by negative pairing, is mediated by endocannabinoids mobilized from the postsynaptic cell during spiking-induced membrane depolarization. By diffusing backward, endocannabinoids activate cannabinoid type-1 (CB1) receptors probably expressed on MF. Thus, STD-LTD was prevented by CB1 receptor antagonists and was absent in CB1-KO mice. Consistent with these data, in situ hybridization experiments revealed detectable level of CB1 mRNA in the granule cell layer at P3 but not at P21. These results indicate that CB1 receptors are transiently expressed on immature MF terminals where they counteract the enhanced neuronal excitability induced by the excitatory action of GABA

Immunogold electron microscopic evidence of in situ formation of homo- and heteromeric purinergic adenosine A1 and P2Y2 receptors in rat brain

<p>Abstract</p> <p>Background</p> <p>Purines such as adenosine and ATP are now generally recognized as the regulators of many physiological functions, such as neurotransmission, pain, cardiac function, and immune responses. Purines exert their functions via purinergic receptors, which are divided into adenosine and P2 receptors. Recently, we demonstrated that the G_i/o-coupled adenosine A₁receptor (A₁R) and G_q/11-coupled P2Y₂receptor (P2Y₂R) form a heteromeric complex with unique pharmacology in co-transfected human embryonic kidney cells (HEK293T). However, the heteromeric interaction of A₁R and P2Y₂R <it>in situ </it>in brain is still largely unknown.</p> <p>Findings</p> <p>In the present study, we visualized the surface expression and co-localization of A₁R and P2Y₂R in both transfected HEK293T cells and in rat brain by confocal microscopy and more precisely by immunogold electron microscopy. Immunogold electron microscopy showed the evidence for the existence of homo- and hetero-dimers among A₁R and P2Y₂R at the neurons in cortex, cerebellum, and particularly cerebellar Purkinje cells, also supported by co-immunoprecipitation study.</p> <p>Conclusion</p> <p>The results suggest that evidence for the existence of homo- and hetero-dimers of A₁R and P2Y₂R, not only in co-transfected cultured cells, but also <it>in situ </it>on the surface of neurons in various brain regions. While the homo-dimerization ratios displayed similar patterns in all three regions, the rates of hetero-dimerization were prominent in hippocampal pyramidal cells among the three regions.</p

Exploring and developing a shared understanding of the issues surrounding engineering mathematics

Abstract: - Although Mathematics is a pillar which many of the subjects of any Engineering degree are based on, and in spite of being used as a tool in almost all of such subjects, it is sometimes difficult for students to assimilate the mathematical concepts. Since this relationship between Engineering and Mathematics is unavoidable, a consortium of universities from different countries is working on a project, EngiMath, to, on the one hand, make it easier for teachers to teach Mathematics in the first years of Engineering degrees; and, on the other hand, to promote study from a “student-centric” point of view. As a previous step to the development of educational material that fulfills these purposes, a study of the students' feelings about Mathematics and their experience in studying them has been carried out.info:eu-repo/semantics/publishedVersio

Investigation of Mitochondrial Dysfunction by Sequential Microplate-Based Respiration Measurements from Intact and Permeabilized Neurons

Mitochondrial dysfunction is a component of many neurodegenerative conditions. Measurement of oxygen consumption from intact neurons enables evaluation of mitochondrial bioenergetics under conditions that are more physiologically realistic compared to isolated mitochondria. However, mechanistic analysis of mitochondrial function in cells is complicated by changing energy demands and lack of substrate control. Here we describe a technique for sequentially measuring respiration from intact and saponin-permeabilized cortical neurons on single microplates. This technique allows control of substrates to individual electron transport chain complexes following permeabilization, as well as side-by-side comparisons to intact cells. To illustrate the utility of the technique, we demonstrate that inhibition of respiration by the drug KB-R7943 in intact neurons is relieved by delivery of the complex II substrate succinate, but not by complex I substrates, via acute saponin permeabilization. In contrast, methyl succinate, a putative cell permeable complex II substrate, failed to rescue respiration in intact neurons and was a poor complex II substrate in permeabilized cells. Sequential measurements of intact and permeabilized cell respiration should be particularly useful for evaluating indirect mitochondrial toxicity due to drugs or cellular signaling events which cannot be readily studied using isolated mitochondria

Bafilomycin A1 activates respiration of neuronal cells via uncoupling associated with flickering depolarization of mitochondria

Bafilomycin A1 (Baf) induces an elevation of cytosolic Ca2+ and acidification in neuronal cells via inhibition of the V-ATPase. Also, Baf uncouples mitochondria in differentiated PC12 (dPC12), dSH-SY5Y cells and cerebellar granule neurons, and markedly elevates their respiration. This respiratory response in dPC12 is accompanied by morphological changes in the mitochondria and decreases the mitochondrial pH, Ca2+ and ΔΨm. The response to Baf is regulated by cytosolic Ca2+ fluxes from the endoplasmic reticulum. Inhibition of permeability transition pore opening increases the depolarizing effect of Baf on the ΔΨm. Baf induces stochastic flickering of the ΔΨm with a period of 20 ± 10 s. Under conditions of suppressed ATP production by glycolysis, oxidative phosphorylation impaired by Baf does not provide cells with sufficient ATP levels. Cells treated with Baf become more susceptible to excitation with KCl. Such mitochondrial uncoupling may play a role in a number of (patho)physiological conditions induced by Baf

Role of P2 purinergic receptors in synaptic transmission under normoxic and ischaemic conditions in the CA1 region of rat hippocampal slices

The role of ATP and its stable analogue ATPγS [adenosine-5′-o-(3-thio)triphosphate] was studied in rat hippocampal neurotransmission under normoxic conditions and during oxygen and glucose deprivation (OGD). Field excitatory postsynaptic potentials (fEPSPs) from the dendritic layer or population spikes (PSs) from the soma were extracellularly recorded in the CA1 area of the rat hippocampus. Exogenous application of ATP or ATPγS reduced fEPSP and PS amplitudes. In both cases the inhibitory effect was blocked by the selective A1 adenosine receptor antagonist DPCPX (8-cyclopentyl-1,3-dipropylxanthine) and was potentiated by different ecto-ATPase inhibitors: ARL 67156 (6-N,N-diethyl-D-β,γ-dibromomethylene), BGO 136 (1-hydroxynaphthalene-3,6-disulfonate) and PV4 [hexapotassium dihydrogen monotitanoundecatungstocobaltate(II) tridecahydrate, K6H2[TiW11CoO40]·13H2O]. ATPγS-mediated inhibition was reduced by the P2 antagonist suramin [8-(3-benzamido-4-methylbenzamido)naphthalene-1,3,5-trisulfonate] at the somatic level and by other P2 blockers, PPADS (pyridoxalphosphate-6-azophenyl-2′,4′-disulfonate) and MRS 2179 (2′-deoxy-N6-methyladenosine 3′,5′-bisphosphate), at the dendritic level. After removal of both P2 agonists, a persistent increase in evoked synaptic responses was recorded both at the dendritic and somatic levels. This effect was prevented in the presence of different P2 antagonists. A 7-min OGD induced tissue anoxic depolarization and was invariably followed by irreversible loss of fEPSP. PPADS, suramin, MRS2179 or BBG (brilliant blue G) significantly prevented the irreversible failure of neurotransmission induced by 7-min OGD. Furthermore, in the presence of these P2 antagonists, the development of anoxic depolarization was blocked or significantly delayed. Our results indicate that P2 receptors modulate CA1 synaptic transmission under normoxic conditions by eliciting both inhibitory and excitatory effects. In the same brain region, P2 receptor stimulation plays a deleterious role during a severe OGD insult

Extraction of Palladium from Spent Nuclear Fuel Reprocessing Solutions

New solvent systems for selective separation of palladium from nuclear wastes represent a prospective way to reduce the total waste volume and induce this metal’s extraction. For this purpose, the potential of modern green solvent room-temperature ionic liquid was assessed with diamide-type extractants based on N-heterocycles and S-donating thiodiglicolic acid. The N-donating heterocyclic extractants demonstrate structure-dependent high selectivity toward palladium in the presence of various impurity metals (such as Zr, Cs, Sr, Mo, Ce, Fe, and Cr) from spent nuclear fuel. Palladium is extracted into the organic phase quite selectively with a separation factor greater than a thousand for all extractants. Ionic liquid media are capable of selective palladium separation from platinum group metals and synergetically increase the selectivity of the extractants