The Maslov Gerbe

Let Lag(E) be the grassmannian of lagrangian subspaces of a complex symplectic vector space E. We construct a Maslov class which generates the second integral cohomology of Lag(E), and we show that its mod 2 reduction is the characteristic class of a flat gerbe with structure group Z_2. We explain the relation of this gerbe to the well-known flat Maslov line bundle with structure group Z_4 over the real lagrangian grassmannian, whose characteristic class is the mod 4 reduction of the real Maslov class.Comment: 8 page

Lens space surgeries on A'Campo's divide knots

It is proved that every knot in the major subfamilies of J. Berge's lens space surgery (i.e., knots yielding a lens space by Dehn surgery) is presented by an L-shaped (real) plane curve as a "divide knot" defined by N. A'Campo in the context of singularity theory of complex curves. For each knot given by Berge's parameters, the corresponding plane curve is constructed. The surgery coefficients are also considered. Such presentations support us to study each knot itself, and the relationship among the knots in the set of lens space surgeries.Comment: 26 pages, 19 figures. The proofs of Theorem 1.3 and Lemma 3.5 are written down by braid calculus. Section 4 (on the operation Adding squares) is revised and improved the most. Section 5 is adde

Weak KAM for commuting Hamiltonians

For two commuting Tonelli Hamiltonians, we recover the commutation of the Lax-Oleinik semi-groups, a result of Barles and Tourin ([BT01]), using a direct geometrical method (Stoke's theorem). We also obtain a "generalization" of a theorem of Maderna ([Mad02]). More precisely, we prove that if the phase space is the cotangent of a compact manifold then the weak KAM solutions (or viscosity solutions of the critical stationary Hamilton-Jacobi equation) for G and for H are the same. As a corrolary we obtain the equality of the Aubry sets, of the Peierls barrier and of flat parts of Mather's $\alpha$ functions. This is also related to works of Sorrentino ([Sor09]) and Bernard ([Ber07b]).Comment: 23 pages, accepted for publication in NonLinearity (january 29th 2010). Minor corrections, fifth part added on Mather's $\alpha$ function (or effective Hamiltonian

On the flow map for 2D Euler equations with unbounded vorticity

In Part I, we construct a class of examples of initial velocities for which the unique solution to the Euler equations in the plane has an associated flow map that lies in no Holder space of positive exponent for any positive time. In Part II, we explore inverse problems that arise in attempting to construct an example of an initial velocity producing an arbitrarily poor modulus of continuity of the flow map.Comment: http://iopscience.iop.org/0951-7715/24/9/013/ for published versio

Critical Decay at Higher-Order Glass-Transition Singularities

Within the mode-coupling theory for the evolution of structural relaxation in glass-forming systems, it is shown that the correlation functions for density fluctuations for states at A_3- and A_4-glass-transition singularities can be presented as an asymptotic series in increasing inverse powers of the logarithm of the time t: $\phi(t)-f\propto \sum_i g_i(x)$, where $g_n(x)=p_n(\ln x)/x^n$ with p_n denoting some polynomial and x=ln (t/t_0). The results are demonstrated for schematic models describing the system by solely one or two correlators and also for a colloid model with a square-well-interaction potential.Comment: 26 pages, 7 figures, Proceedings of "Structural Arrest Transitions in Colloidal Systems with Short-Range Attractions", Messina, Italy, December 2003 (submitted

Struktur Komunitas Moluska Di Vegetasi Mangrove Desa Kulu, Kecamatan Wori, Kabupaten Minahasa Utara

Di daerah mangrove terdapat biota akuatik yang hidup berasosiasi dengan mangrove antara lain moluska, krustasea dan ikan. Moluska sangat banyak ditemukan pada daerah mangrove di Indonesia. Jenis-jenis moluska ini ada yang menempati akar dan ada juga yang mendiami batang mangrove antara lain famili Littorinidae dan yang menempati daerah lumpur di dasar akar antara lain famili Ellobiidae dan Pottamidae. Tujuan dari pernelitian ini yaitu untuk mengidenifikasi moluska yang berasosiasi dengan vegetasi mangrove; mendeskripsikan struktur komunitas melalui analisa nilai indeks keanekaragaman, kekayaan jenis, kepadatan, frekuensi, dominasi dan indeks nilai penting. Metode yang digunakan yakni, metode kuadran, dengan cara meletakan lima buah kuadran 1 x 1 meter pada masing-masing stasiun. Terdapat 11 spesies dari 8 famili yaitu, Littoraria scabra, Nerita planospira, Chicoreus capucinus, Nerita undata, Chrithidea cingulata, Terebralia sulcata, Telecopiun telescopium, Polymesoda expansa, Isognomon ephippium, Saccostrea cucculata, Anomalocardia squamosa. Nilai indeks keanekaragaman yaitu 2,060, nilai indeks kekayaan yakni 2,387, kepadatan 0,660 ind/m², frekuensi kemunculan bervariasi antara 0,067-0,667, nilai indeks dominasi yakni 0,152 dan indeks nilai penting tertinggi yakni Littoraria scabra 75,67 dan terendah terdapat 3 spesies yakni Polymesoda expansa, Saccostrea cucculata dan Anomalocardia squamosa dengan nilai indeks 3,54

A Nonperturbative Eliasson's Reducibility Theorem

This paper is concerned with discrete, one-dimensional Schr\"odinger operators with real analytic potentials and one Diophantine frequency. Using localization and duality we show that almost every point in the spectrum admits a quasi-periodic Bloch wave if the potential is smaller than a certain constant which does not depend on the precise Diophantine conditions. The associated first-order system, a quasi-periodic skew-product, is shown to be reducible for almost all values of the energy. This is a partial nonperturbative generalization of a reducibility theorem by Eliasson. We also extend nonperturbatively the genericity of Cantor spectrum for these Schr\"odinger operators. Finally we prove that in our setting, Cantor spectrum implies the existence of a $G_\delta$-set of energies whose Schr\"odinger cocycle is not reducible to constant coefficients

Entropy of a Turbulent Bose-Einstein Condensate

Quantum turbulence deals with the phenomenon of turbulence in quantum fluids, such as superfluid helium and trapped Bose-Einstein condensates (BECs). Although much progress has been made in understanding quantum turbulence, several fundamental questions remain to be answered. In this work, we investigated the entropy of a trapped BEC in several regimes, including equilibrium, small excitations, the onset of turbulence, and a turbulent state. We considered the time evolution when the system is perturbed and let to evolve after the external excitation is turned off. We derived an expression for the entropy consistent with the accessible experimental data, that is, using the assumption that the momentum distribution is well-known. We related the excitation amplitude to different stages of the perturbed system, and we found distinct features of the entropy in each of them. In particular, we observed a sudden increase in the entropy following the establishment of a particle cascade. We argue that entropy and related quantities can be used to investigate and characterize quantum turbulence.Comment: 14 pages, 5 figure

High-mobility group box-1 protein, lipopolysaccharide-binding protein, interleukin-6 and C-reactive protein in children with community acquired infections and bacteraemia: a prospective study

<p>Abstract</p> <p>Introduction</p> <p>Even though sepsis is one of the common causes of children morbidity and mortality, specific inflammatory markers for identifying sepsis are less studied in children. The main aim of this study was to compare the levels of high-mobility group box-1 protein (HMGB1), Lipopolysaccharide-binding protein (LBP), Interleukin-6 (IL-6) and C-reactive protein (CRP) between infected children without systemic inflammatory response syndrome (SIRS) and children with severe and less severe sepsis. The second aim was to examine HMGB1, LBP, IL6 and CRP as markers for of bacteraemia.</p> <p>Methods</p> <p>Totally, 140 children with suspected or proven infections admitted to the Children's Clinical University Hospital of Latvia during 2008 and 2009 were included. Clinical and demographical information as well as infection focus were assessed in all patients. HMGB1, LBP, IL-6 and CRP blood samples were determined. Children with suspected or diagnosed infections were categorized into three groups of severity of infection: (i) infected without SIRS (n = 36), (ii) sepsis (n = 91) and, (iii) severe sepsis (n = 13). They were furthermore classified according bacteraemia into (i) bacteremia (n = 30) and (ii) no bacteraemia (n = 74).</p> <p>Results</p> <p>There was no statistically significant difference in HMGB1 levels between children with different levels of sepsis or with and without bacteraemia. The levels of LBP, IL-6 and CRP were statistically significantly higher among patients with sepsis compared to those infected but without SIRS (<it>p </it>< 0.001). Furthermore, LBP, IL-6 and CRP were significantly higher in children with severe sepsis compared to those ones with less severe sepsis (<it>p </it>< 0.001). Median values of LBP, IL6 and CRP were significantly higher in children with bacteraemia compared to those without bacteraemia. The area under the receiver operating curve (ROC) for detecting bacteraemia was 0.87 for both IL6 and CRP and 0.82 for LBP, respectively.</p> <p>Conclusion</p> <p>Elevated levels of LBP, IL-6 and CRP were associated with a more severe level of infection in children. Whereas LBP, IL-6 and CRP seem to be good markers to detect patients with bacteraemia, HMGB1 seem to be of minor importance. LBP, IL-6 and CRP levels may serve as good biomarkers for identifying children with severe sepsis and bacteraemia and, thus, may be routinely used in clinical practice.</p