Motion of single long DNA molecules through arrays of magnetic columns

We present a videomicroscopy study of T4 DNA (169 kbp) in microfluidic arrays of posts formed by the self-assembly of magnetic beads. We observe DNA moving through an area of 10 000 microm(2), typically containing 100-600 posts. We determine the distribution of the contact times with the posts and the distribution of passage times across the field of view for hundreds of DNA per experiment. The contact time is well approximated by a Poisson process, scaling like the inverse of the field strength, independent of the density of the array. The distribution of passage times allows us to estimate the mean velocity and dispersivity of the DNA during its motion over distances long compared to our field of view. We compare these values with those computed from a lattice Monte Carlo model and geometration theory. We find reasonable quantitative agreement between the lattice Monte Carlo model and experiment, with the error increasing with increasing post density. The deviation between theory and experiment is attributed to the high mobility of DNA after disengaging from the posts, which leads to a difference between the contact time and the total time lost by colliding. Classical geometration theory furnishes surprisingly good agreement for the dispersivity, while geometration theory with a mean free path significantly overestimates the dispersivity.     

Characterization and reactivity of Pt/Al2O3/SS thin films

Summary A catalytic system was obtained by impregnation with platinum of thin alumina films electrochemically deposited on stainless steel. The composition, morphology and structure of the Pt/Al2O3/SS and Pt/CeO2/Al2O3/SS samples were characterized by XPS, SEM and BET. Catalytic tests of the samples were performed in a stoichiometric gas mixture.     

Direct Bioelectrocatalysis of PQQ‐Dependent Glucose Dehydrogenase

The direct bioelectrocatalysis was demonstrated for pyrroloquinoline quinone‐dependent glucose dehydrogenase (PQQ‐dependent GDH) covalently attached to single‐walled carbon nanotubes (SWNTs). The homogeneous ink‐like SWNT suspension was used for both creating the SWNT network on the microelectrode carbon surface and for enzyme immobilization. Functionalization of the SWNT surface by forming active ester groups was found to considerably enhance SWNT solubility in water with a range from 0.1 to 1.0 mg/mL. The PQQ‐dependent GDH immobilized on the surface of the SWNTs exhibited fast heterogeneous electron transfer with a rate constant of 3.6 s^?1. Moreover, the immobilized PQQ‐dependent GDH retained its enzymatic activity for glucose oxidation. A fusion of PQQ‐dependent GDH with SWNTs has a great potential for the development of low‐cost and reagentless glucose sensors and biofuel cells.     

The generic quantum superintegrable system on the sphere and Racah operators

We consider the generic quantum superintegrable system on the d-sphere with potential \(V(y)=\sum _{k=1}^{d+1}\frac{b_k}{y_k^2}\), where \(b_k\) are parameters. Appropriately normalized, the symmetry operators for the Hamiltonian define a representation of the Kohno–Drinfeld Lie algebra on the space of polynomials orthogonal with respect to the Dirichlet distribution. The Gaudin subalgebras generated by Jucys–Murphy elements are diagonalized by families of Jacobi polynomials in d variables on the simplex. We define a set of generators for the symmetry algebra, and we prove that their action on the Jacobi polynomials is represented by the multivariable Racah operators introduced in Geronimo and Iliev (Constr Approx 31(3):417–457, 2010). The constructions also yield a new Lie-theoretic interpretation of the bispectral property for Tratnik’s multivariable Racah polynomials.     

Smoothness of solutions of a nonlinear ode

Smoothness of aC -functionf is measured by (Carleman) sequence {M _k} ₀ ; we sayfC _M [0, 1] if|f ^(k) (t)|CR ^k M _k,k=0, 1, ... withC, R>0. A typical statement proven in this paper isTHEOREM: Let u, b be two C -functions on [0, 1]such that (a) u=u ²+b, (b) |b ^(k) (t)|CR ^k (k!) , >1,k_–.Then |u^(k)(t)|C₁R^k((k–1)!),k_–.The first author acknowledges the hospitality of Mathematical Research Institute of the Ohio State University during his one month visit there in the spring of 1999     

Asymptotics of instability zones of Hill operators with a two term potential

We give a sharp asymptotics of the instability zones of the Hill operator $Ly=?y^{″}+(acos2x+bcos4x)y$ for arbitrary real $a\text{,}b\ne 0$. To cite this article: P. Djakov, B. Mityagin, C. R. Acad. Sci. Paris, Ser. I 339 (2004).     

Instability Zones of a Periodic 1D Dirac Operator and Smoothness of its Potential

Let L be the differential operatorwhere P(x),Q(x) are 1-periodic functions such that The operator L, considered on [0,1] with periodic (y(0)=y(1)), or antiperiodic (y(0)=−y(1)) boundary conditions, is self-adjoint, and moreover, for large |n| it has, close to nπ, a pair of periodic (if n is even), or antiperiodic (if n is odd) eigenvalues λ⁺_n , λ^-_n. We study the relationship between the decay rate of the instability zone sequence γ_n = λ_n⁺ - λ_n^-, n → ± ∞, and the smoothness of the potential function P(x).The first author acknowledges the hospitality of The Mathematics Department of The Ohio State University during academic year 2003/2004. His research is partially supported by Grant MM–1401/04 of the Bulgarian Ministry of Education and Science.     

Spectral and Scattering Theory for teh Linear Boltzmann Equation in Exterior Domain

It is well-known that functions u ? W^m,p (Ω) can be extended by a bounded linear operator E to functions Eu ≦ W^m,p( R ⁿ), if Ω is C^M-regular and m ≦ M. Here we prove a corresponding result for grid-functions with extension operators E_h converging to E and mention some applications.     

GK dimension of the relatively free algebra for sl_2

Let \(sl_2(K)\) be the Lie algebra of the \(2\times 2\) traceless matrices over an infinite field \(K\) of characteristic different from 2, denote by \(R_m= R_m(sl_2(K))\) the relatively free (also called universal) algebra of rank \(m\) in the variety of Lie algebras generated by \(sl_2(K).\) In this paper we compute the Gelfand–Kirillov dimension of the Lie algebra \(R_m(sl_2(K)).\) It turns out that whenever \(m\ge 2\) one has \(\mathrm{GK}\dim R_m = 3(m-1).\) In order to compute it we use the explicit form of the Hilbert series of \(R_m\) described by Drensky. This result is new for \(m>2\) ; the case \(m=2\) was dealt with by Bahturin in 1979.