The Decomposition of Lie Powers

Let G be a group, F a field of prime characteristic p and V a finite-dimensional FG-module. Let L(V) denote the free Lie algebra on V regarded as an FG-submodule of the free associative algebra (or tensor algebra) T(V). For each positive integer r, let L^r(V) and T^r(V) be the rth homogeneous components of L(V) and T(V), respectively. Here L^r(V) is called the rth Lie power of V. Our main result is that there are submodules B_1, B_2, ... of L(V) such that, for all r, B_r is a direct summand of T^r(V) and, whenever m \geq 0 and k is not divisible by p, $$L^{p^mk}(V) = L^{p^m}(B_k) \oplus L^{p^{m-1}}(B_{pk}) \oplus ... \oplus L^p(B_{p^{m-1}k}) \oplus L^1(B_{p^mk}).$$ Thus every Lie power is a direct sum of Lie powers of p-power degree. The approach builds on an analysis of T^r(V) as a bimodule for G and the Solomon descent algebra.Comment: 32 page

Biosilica-nanogold composite: Easy-to-prepare catalyst for soman degradation

A very fast single-step biosynthesis of gold nanoparticles (AuNPs) using algal cells of Mallomonas kalinae (MK) is introduced. The average particle size of crystalline AuNPs was approximately 10 nm. Subsequently, the catalytic activity of two systems - MK-biosilica scales and MK-biosilica scales with AuNPs - was compared with a control hydrolysis of soman (GD) performed in demineralized water. The kinetics of GD degradation was studied using a gas chromatography with mass detector (GC-MS) and solid-phase microextraction. The residual content of GD was 3.8% and 3.5% for both initial concentrations of GD (68 mu g mL(-1) and 340 mu g L-1, respectively) after 48 h of testing when nanogold was used as a catalyst. Experimental results confirmed the catalytic activity of biosynthesized AuNPs, as well as the role of biosilica itself in the degradation of GD.Web of Science12227126

PENGEMBANGAN INVENTORI KESIAPAN KERJA PADA SISWA SMK JURUSAN ADMINISTRASI PERKANTORAN DI SMK N 1 PURBALINGGA

PENGEMBANGAN INVENTORI KESIAPAN KERJA PADA SISWA SMK JURUSAN ADMINISTRASI PERKANTORAN DI SMK N 1 PURBALINGGA Oleh: Desiana Puji Lestari 07104244059 ABSTRAK Penelitian ini bertujuan unt uk m engem ban gkan inventori kesi apan k erj a si swa S MK J urusan Administrasi Perkant ora n ya n g memenuhi persyaratan validitas dan rel i abi l i t as ya n g dapat di gun akan un t uk m engun gk ap kesi ap a n kerj a si swa S MK J urusan Adm i ni st rasi P erkan t oran. P enel i t i an i ni m erupakan penel i t i an pe ngem b an gan, prosedu r pengem ban gan m en ga c u pada l an gk ah -l an gk ah dasa r pe ranc an gan dan pen yusun an skal a psi kol ogi s dari S ai ffudi n Az w ar yan g t erdi ri da ri 10 l angk ah ya i t u: (1) i dent i fi kasi t uj uan ukur. (2) opeasi onal i sasi konsep. (3) penskal aan & pem i l i han form at st i m ulus. (4) penul i san i t em . (5) uj i coba. (6) anal i si s it em . (7) kom pi l asi 1 sel eksi i t e m . (8) p en guj i an r el i a bi l i t as. (9) val i di t as da n (10) kom pi l asi II form at fi nal . S ub yek yan g di gun aka n adal ah ahl i yan g berko m pet en (expert judgedment) dan si swa kel as X II J urus an Adm i ni st rasi P erkant or a n S MK N 1 P urbal i ngga, den ga n t ekni k random sampling. Inst rum en yan g di gunakan dal am pengum pul an dat a adal ah peni l ai an i nven t ori kesi apan kerj a si sw a S MK J urusan Adm i n i st rasi P erkant oran yan g t el ah di susun dan angket peni l ai an unt uk si swa. Tekni k an al i si s dat a unt uk dat a ku al i t at i f berupa sa ran, k ri t i k, dan t anggapan di deskri psi ka n sesuai dat a yan g ada. Dan unt uk m en ghi t un g v al i di t as i t em di gunakan t ekni k korel asi i t em -t ot al product moment pearson, dan unt uk m enghi t un g ko efi si en r e l i abi l i t as m enggunak an t ekni k anal i si s Alfa Cronbach. Dari hasi l uj i rel i abi l i t as di perol eh koefi si en al pha sebesar 0,944. Hasi l review i t em ol eh ahl i t erdapat beber apa m a sukan sehi ngga i nve nt ori kesi apan ke rj a si swa S MK J urusan Adm i nist rasi P erkant oran di n ya t akan m em enuhi val i di t as i si . Uj i coba kel om pok k ec i l pada 30 si swa d an u j i coba kel om pok besar di l akukan pada 81 si swa. Form at fi nal Invent ori Kesi ap an kerj a si swa S MK J urusan Adm i ni st ra si P erkant oran t erdi ri dari 61 i t em pern yat aan dengan koefi si en rel i abi l i t as 0,944. Dengan d e m i ki an i nvent ori kesi apan kerj a si swa S MK J urusan Adm i ni st rasi P erkant oran di n yat ak an val i d dan rel i abel sehi ngga l a ya k di gunak a n seba gai i nst rum en. Kata kunci : inventori, kesiapan kerja, siswa SMK Jurusan Administrasi Perkantora

Improved Approximation Algorithm for Steiner k-Forest with Nearly Uniform Weights

In the Steiner k-Forest problem we are given an edge weighted graph, a collection D of node pairs, and an integer k leq |D|. The goal is to find a minimum cost subgraph that connects at least k pairs. The best known ratio for this problem is min{O(sqrt{n}),O(sqrt{k})} [Gupta et al., 2008]. In [Gupta et al., 2008] it is also shown that ratio rho for Steiner k-Forest implies ratio O(rho log^2 n) for the Dial-a-Ride problem: given an edge weighted graph and a set of items with a source and a destination each, find a minimum length tour to move each object from its source to destination, but carrying at most k objects at a time. The only other algorithm known for Dial-a-Ride, besides the one resulting from [Gupta et al., 2008], has ratio O(sqrt{n}) [Charikar and Raghavachari, 1998]. We obtain ratio n^{0.448} for Steiner k-Forest and Dial-a-Ride with unit weights, breaking the O(sqrt{n}) ratio barrier for this natural special case. We also show that if the maximum weight of an edge is O(n^{epsilon}), then one can achieve ratio O(n^{(1+epsilon) 0.448}), which is less than sqrt{n} if epsilon is small enough. To prove our main result we consider the following generalization of the Minimum k-Edge Subgraph (Mk-ES) problem, which we call Min-Cost l-Edge-Profit Subgraph (MCl-EPS): Given a graph G=(V,E) with edge-profits p={p_e: e in E} and node-costs c={c_v: v in V}, and a lower profit bound l, find a minimum node-cost subgraph of G of edge profit at least l. The Mk-ES problem is a special case of MCl-EPS with unit node costs and unit edge profits. The currently best known ratio for Mk-ES is n^{3-2*sqrt{2} + epsilon} (note that 3-2*sqrt{2} < 0.1716). We extend this ratio to MCl-EPS for arbitrary node weights and edge profits that are polynomial in n, which may be of independent interest

Ambiguity of context-free languages as a function of the word length

Englische Fassung der Diplomarbeit "Grad der Mehrdeutigkeit kontextfreier Grammatiken und Sprachen". In dieser Arbeit definieren wir ein Maß für den Grad der Mehrdeutigkeit (degree of ambiguity da) kontextfreier Grammatiken und Sprachen als die Anzahl der Ableitungsbäume in Abhängigkeit von der Länge n eines Wortes. Wir zeigen, dass es weder Sprachen noch zyklenfreie Grammatiken gibt, deren Mehrdeutigkeitsgrad stärker als 2£(n) wächst (wie z B. £(nn)). Aus [10] ist es außerdem bekannt, dass es keine Grammatiken (und somit keine Sprachen) gibt, deren Mehrdeutigkeit stärker als polynomiell, aber schwächer als exponentiell wächst (wie z. B. £(2pn). Deshalb untersuchen wir in dieser Arbeit hauptsächlich konstant mehrdeutige, polynomiell mehrdeutige und exponentiell mehrdeutige Grammatiken und Sprachen. Für jede feste, ganze Zahl k 2 N hat Maurer [8] die Existenz einer k-deutigen kontextfreien Sprache nachgewiesen. Durch Verwendung einer einfacheren Sprache, nämlich der Sprache Lk := fambm1 1 bm2 2 : : : bmk k jm;m1;m2; : : : ;mk ¸ 1; 9 i mit m = mig, und mit Hilfe von Ogden's Lemma1 erhalten wir einen wesentlich kürzeren Beweis. Ferner zeigen wir die Existenz exponentiell mehrdeutiger Sprachen. Wir zeigen, dass die Sprache L¤ { wobei L = faibicj ji; j ¸ 1g [ faibjciji; j ¸ 1g-exponentiell mehrdeutig ist, indem wir beweisen, dass das Wort (ah+h!bh+h!ch+h!)k mindestens 2k Ableitungen in jeder Grammatik G für L¤ hat, wobei k aus N ist und h die Konstante aus Ogden's Lemma für G ist. Für beliebig kleines c aus R+ entwerfen wir eine Grammatik Gc für L¤, so dass daGc · 2cn gilt. Somit gilt, dass die Sprache L¤ zwar exponentiell mehrdeutig ist, aber es gibt kein festes c aus R+ , so dass L¤ 2cn-deutig ist. Wir geben polynomiell mehrdeutige Grammatiken an und zeigen die Existenz von polynomiell mehrdeutigen Sprachen, indem wir mit Hilfe von Ogden's Lemma beweisen, dass die Anzahl der Ableitungsbäume eines Wortes der Länge n in jeder Grammatik für die Sprache Lk in der Größenordnung von ­(nk) liegt, wobei k eine Konstante aus N ist, und L := fambm1cbm2c : : : bmpcjp 2 N; m;m1;m2; : : : ;mp 2 N; 9i 2 f1; 2; : : : ; pg mit m = mig gilt. Durch Angabe einer O(nk){deutigen Grammatik zeigen wir schließlich, dass Lk polynomiell vom Grad k mehrdeutig ist. Außerdem entwerfen wir für jedes feste d aus R+ eine Grammatik Gd für L, so dass daGd · dn dn für genügend großes n ist.In this paper we discus the concept of ambiguity of context{free languages and grammars. We prove the existence of constant ambigu- ous, exponential ambiguous and polynomial ambiguous languages and we give examples for these classes of ambiguity

Diamagnetic response of cylindrical normal metal - superconductor proximity structures with low concentration of scattering centers

We have investigated the diamagnetic response of composite NS proximity wires, consisting of a clean silver or copper coating, in good electrical contact to a superconducting niobium or tantalum core. The samples show strong induced diamagnetism in the normal layer, resulting in a nearly complete Meissner screening at low temperatures. The temperature dependence of the linear diamagnetic susceptibility data is successfully described by the quasiclassical Eilenberger theory including elastic scattering characterised by a mean free path l. Using the mean free path as the only fit parameter we found values of l in the range 0.1-1 of the normal metal layer thickness d_N, which are in rough agreement with the ones obtained from residual resistivity measurements. The fits are satisfactory over the whole temperature range between 5 mK and 7 K for values of d_N varying between 1.6 my m and 30 my m. Although a finite mean free path is necessary to correctly describe the temperature dependence of the linear response diamagnetic susceptibility, the measured breakdown fields in the nonlinear regime follow the temperature and thickness dependence given by the clean limit theory. However, there is a discrepancy in the absolute values. We argue that in order to reach quantitative agreement one needs to take into account the mean free path from the fits of the linear response. [PACS numbers: 74.50.+r, 74.80.-g]Comment: 10 pages, 9 figure

Unraveling monoamine receptors involved in the action of typical and atypical antipsychotics on glutamatergic and serotonergic transmission in prefrontal cortex

El pdf del artículo es la versión post-print.The systemic administration of noncompetitive N-methyl-D-aspartate (NMDA) receptor antagonists has been considered as a pharmacological model of schizophrenia. In the present work, we used in vivo microdialysis to examine: first, the effects of MK-801, on the efflux of glutamate and serotonin (5-HT) in the medial prefrontal cortex (mPFC) of the rat; second, whether the MK-801-induced changes in the cortical efflux of both transmitters could be blocked by atypical (clozapine and olanzapine) and classical (haloperidol and chlorpromazine) antipsychotic drugs given intra-mPFC; and third, the role of local blockade of dopamine D2/D3/D4, serotonin 5-HT2A and α1-adrenergic receptors as well as agonism at dopamine D1/D5 and 5-HT1A receptors in the mPFC on the increased efflux of glutamate and 5-HT elicited by MK-801. The four antipsychotic drugs blocked the MK-801-induced increase in glutamate, whereas only clozapine and olanzapine were able to block the increased efflux of 5-HT. Furthermore, M100907 (5-HT2A antagonist), BAY x 3702 (5-HT1A agonist) and prazosin (α1-adrenergic antagonist) blocked the MK-801-induced increase of 5-HT and glutamate in the mPFC. In contrast, raclopride (D2/D3 antagonist) and L-745,870 (D4 antagonist) were able to prevent the increased efflux of glutamate (but not that of 5-HT) elicited by MK-801. SKF-38393 (dopamine D1/D5 agonist) also prevented the MK-801-induced increase of glutamate in the mPFC, but the same effect on cortical 5-HT was reached only at the highest concentration tested. We suggest that the blockade of an exacerbated 5-HT release in the mPFC induced by NMDA antagonists can be a characteristic of atypical antipsychotic drugs. Moreover, we propose that D 2/D3/D4 receptor antagonists would act predominantly on a subpopulation of GABAergic interneurons of the mPFC, thus enhancing cortical inhibition, which would prevent an excessive glutamatergic transmission. Dopamine D1/D5 agonists would further stimulate GABA release from other subpopulation of interneurons controlling cortical output to the dorsal raphe nucleus. Atypical antipsychotic drugs might further act upon 5-HT2A, 5-HT1A and α1- adrenoceptors present in pyramidal cells (including those projecting to the dorsal raphe nucleus), which would directly inhibit an excessive excitability of these cells. © 2010 Bentham Science Publishers Ltd.This work was supported by the Spanish Ministry of Health (FIS Grant PI070111 to A. A.), the Spanish Ministry of Education and Science (Grant SAF 2007-62378 to F.A.), and the Generalitat de Catalunya (SGR2005/00758). X.L.- G. is the recipient of a predoctoral fellowship from the Consejo Superior de Investigaciones Cientificas (CSIC).Peer Reviewe