bluuebunny/crossref_metadata_2025 huggingface dataset:
Zero dissipation limit to rarefaction waves for the one‐dimensional navier‐stokes equations of compressible isentropic gases
Authors: Xin Zhouping
Published: April 2007

We study the zero dissipation limit problem for the one‐dimensional Navier‐Stokes equations of compressible, isentropic gases in the case that the corresponding Euler equations have rarefaction wave solutions. We prove that the solutions of the Navier‐Stokes equations with centered rarefaction wave data exist for all time, and converge to the centered rarefaction waves as the viscosity vanishes, uniformly away from the initial discontinuities. In the case that either the effects of initial layers are ignored or the rarefaction waves are smooth, we then obtain a rate of convergence which is valid uniformly for all time. Our method of proof consists of a scaling argument and elementary energy analysis, based on the underlying wave structure. © 1993 John Wiley & Sons, Inc.
On the stability of KdV multi‐solitons
Authors: Maddocks John H. , Sachs Robert L.
Published: April 2007

We consider the stability of multi‐ or n‐soliton solutions to the Korteweg‐de Vries equation (KdV) posed on the real line. It is shown that in the standard variational characterization of KdV multi‐solitons as critical points, the n‐solitons actually realize non‐isolated constrained minimizers. (The case n = 1 was already known to Benjamin; see [6].) From this fact a precise dynamic stability result for multi‐solitons follows, namely, that initial data close to a given n‐soliton evolves in time so as to remain close (in the Hn(𝔑) Sobolev norm) to the n‐dimensional manifold of all n‐solitons with appropriate wave speeds, i.e., to the set of constrained minimizers. Our techniques are also applicable to other Hamiltonian systems with several conserved quantities. In particular the inverse scattering formalism of KdV is not explicitly exploited. © 1993 John Wiley & Sons, Inc.
The periodicity in stable equivariant surgery
Authors: Yan Min
Published: April 2007

The classical surgery theory (see [5] and [23]) computes the structure set Sm (M, rel ∂) of manifolds homotopy equivalent to M relative to the boundary. Siebenmann showed that in topological category, the structure set is 4‐periodic: Sm(M, rel ∂) ≅ Sm+4(M × D4, rel ∂) up to a copy of ℤ; see [12]. Cappell and Weinberger gave a geometric interpretation of this periodicity in [8]. By using Weinberger's stratified surgery theory (see [24]), we extend this to an equivariant periodicity result for topological manifolds with homotopically stratified actions by compact Lie groups, with D4 replaced by the unit ball of certain group representations. In particular, if G is an odd order group acting on a topological manifold M, then the equivariant stable structure sets satisfy S (M, rel ∂) ≅ S(M × D(ℝ4 ⊗ ℝG), rel ∂) up to copies of ℤ. © 1993 John Wiley & Sons, Inc.
On the regularity of spherically symmetric wave maps
Authors: Christodoulou Demetrios , Tahvildar‐Zadeh A. Shadi
Published: April 2007

Wave maps are critical points U: M → N of the Lagrangian ℒ︁[U] = ∞M ‖dU‖2, where M is an Einsteinian manifold and N a Riemannian one. For the case M = ℝ2,1 and U a spherically symmetric map, it is shown that the solution to the Cauchy problem for U with smooth initial data of arbitrary size is smooth for all time, provided the target manifold N satisfies the two conditions that: (1) it is either compact or there exists an orthonormal frame of smooth vectorfields on N whose structure functions are bounded; and (2) there are two constants c and C such that the smallest eigenvalue λ and the largest eigenvalue λ of the second fundamental form kAB of any geodesic sphere Σ(p, s) of radius s centered at p ϵ N satisfy sλ ≧ c and s A ≦ C(1 + s).

This is proved by first analyzing the energy‐momentum tensor and using the second condition to show that near the first possible singularity, the energy of the solution cannot concentrate, and hence is small. One then proves that for targets satisfying the first condition, initial data of small energy imply global regularity of the solution. © 1993 John Wiley & Sons, Inc.
Growth rates for the linearized motion of fluid interfaces away from equilibrium
Authors: Beale J. Thomas , Hou Thomas Y. , Lowengrub John S.
Published: April 2007

We consider the motion of a two‐dimensional interface separating an inviscid, incompressible, irrotational fluid, influenced by gravity, from a region of zero density. We show that under certain conditions the equations of motion, linearized about a presumed time‐dependent solution, are wellposed; that is, linear disturbances have a bounded rate of growth. If surface tension is neglected, the linear equations are well‐posed provided the underlying exact motion satisfies a condition on the acceleration of the interface relative to gravity, similar to the criterion formulated by G. I. Taylor. If surface tension is included, the linear equations are well‐posed without qualifications, whether the fluid is above or below the interface. An interesting qualitative structure is found for the linear equations. A Lagrangian approach is used, like that of numerical work such as [3], except that the interface is assumed horizontal at infinity. Certain integral equations which occur, involving double layer potentials, are shown to be solvable in the present case. © 1993 John Wiley & Sons, Inc.
On singular diffusion equations with applications to self‐organized criticality
Authors: Chayes J. T. , Osher S. J. , Ralston J. V.
Published: April 2007

We consider solutions of the singular diffusion equation t, = (um−1 ux)x, m ≦ 0, associated with the flux boundary condition limx→−∞ (um−1ux)x = λ > 0. The evolutions defined by this problem depend on both m and λ. We prove existence and stability of traveling wave solutions, parameterized by λ. Each traveling wave is stable in its appropriate evolution. These traveling waves are in L1 for −1 < m ≦ 0, but have non‐integrable tails for m ≦ −1. We also show that these traveling waves are the same as those for the scalar conservation law ut = −[f(u)]x + uxx for a particular nonlinear convection term f(u) = f(u;m, λ). © 1993 John Wiley & Sons, Inc.
Localized instabilities of vortex rings with swirl
Authors: Lifschitz Alexander , Hameiri Eliezer
Published: April 2007

Axisymmetric vortex rings with swirl in an inviscid incompressible fluid are considered and it is demonstrated how the geometrical optics method can be used for investigating their stability. The evolution of rapidly oscillating initial data is studied and it is shown that the corresponding rings are unstable if the transport equations associated with the wave which is advected by the flow have unbounded solutions. It is shown that unbounded solutions grow either exponentially or algebraically. By means of the analysis of the corresponding transport equations effective stability conditions for general vortex rings with swirl are obtained. © 1993 John Wiley & Sons, Inc.
Uniqueness via the adjoint problems for systems of conservation laws
Authors: Le Floch Philippe , Xin Zhouping
Published: April 2007

We prove a result of uniqueness of the entropy weak solution to the Cauchy problem for a class of nonlinear hyperbolic systems of conservation laws that includes in particular the p‐system of isentropic gas dynamics. Our result concerns weak solutions satisfying the, as we call it, Wave Entropy Condition, or WEC for short, introduced in this paper. The main feature of this condition is that it concerns both shock waves and rarefaction waves present in a solution. For the proof of uniqueness, we derive an existence result (respectively a uniqueness result) for the backward (respectively forward) adjoint problem associated with the nonlinear system. Our method also applies to obtain results of existence or uniqueness for some linear hyperbolic systems with discontinuous coefficients. © 1993 John Wiley & Sons, Inc.
Compatible poisson structures and the virasoro algebra
Authors: Adler Mark , Van Moerbeke Pierre
Published: April 2007

This paper is dedicated to Henry McKean, whose master craftsmanship enriched such diverse areas of mathematics and provided his disciples with a lofty measure by which to gauge their efforts, and so redouble them.
A class of laplace transforms arising in a diffusion problem
Authors: Berman S. M.
Published: April 2007

It is shown that the function [α + (1 + 2s)1/2]−1, s ≥ 0, with fixed α ≥ −1, is the Laplace transform of an explicitly given non‐negative function g(x;α), × ≥ 0. This class of functions has easily computable convolutions. This property is used to identify the distribution of a sojourn time integral for the diffusion defined as Brownian motion on the real line with constant drift to the origin. © 1994 John Wiley & Sons, Inc.
Qualitative analysis of radiating breathers
Authors: Birnir Björn
Published: April 2007

Perturbed sine‐Gordon equations are investigated numerically to see if they have breather solutions. It is shown that breathers radiate, blow up, and split into kink‐antikink pairs under most perturbations. The two perturbations proven by Birnir, McKean, and Weinstein not to produce radiation, of the first order in the perturbation parameter, a sin(u) + b ucos(u) and 1+3cos(u) ‐ 4cos(u/2) + 4cos(u)log(cos(u/4)), stop radiating first‐order radiation after adjusting the initial breather by the emission of such radiation. The first perturbation is a scaling of the breather, the second is shown to give a quasi‐periodic orbit, which is a two‐breather, on a torus. © 1994 John Wiley & Sons, Inc.
Speed of parallel processing for random task graphs
Authors: Isopi Marco , Newman Charles M.
Published: April 2007

The random graph model of parallel computation introduced by Gelenbe et al. depends on three parameters: n, the number of tasks (vertices); F, the common distribution of T1,…︁, Tn, the task processing times, and p = pn, the probability for a given i < j that task i must be completed before task j is started. The total processing time is Rn, the maximum sum of Ti's along directed paths of the graph. We study the large n behavior of Rn when npn grows sublinearly but superlogarithmically, the regime where the longest directed path contains about enpn tasks. For an exponential (mean one) F, we prove that Rn is about 4npn. The “discrepancy” between 4 and e is a large deviation effect. Related results are obtained when npn grows exactly logarithmically and when F is not exponential, but has a tail which decays (at least) exponentially fast. © 1994 John Wiley L Sons, Inc.
Asymptotics of heavy atoms in high magnetic fields: I. Lowest landau band regions
Authors: Lieb Elliott H. , Solovej Jan Philip , Yngvason Jakob
Published: April 2007

The ground state energy of an atom of nuclear charge Ze in a magnetic field B is evaluated exactly to leading order as Z → ∞. In this and a companion work (see [28]) we show that there are five regions as Z → ∞: B < Z4/3, B ∼ Z4/3, Z4/3 < B < Z3, B ∼ Z3, B > Z3. Regions 1, 2, 3, and 4 (and conceivably 5) are relevant for neutron stars. Different regions have different physics and different asymptotic theories. Regions 1, 2, and 3 are described by a simple density functional theory of the semiclassical Thomas‐Fermi form. Here we concentrate mainly on regions 4 and 5 which cannot be so described, although 3, 4, and 5 have the common feature (as shown here) that essentially all electrons are in the lowest Landau band. Region 5 does have, however, a simple non‐classical density functional theory (which can be solved exactly). Region 4 does not, but, surprisingly, it can be described by a novel density matrix functional theory. © 1994 John Wiley & Sons, Inc.
Smooth approximation of mather sets of monotone twist mappings
Authors: Moser JÜRgen
Published: April 2007

In the theory of monotone twist mappings of a cylinder one constructs for every rotation number α invariant minimal sets Mα. In this paper an approximation of these Mather sets by smooth invariant curves Mvα is devised, which for v → 0 converge to Mα almost everywhere. The main point of the construction is that the approximating curves Mvα form for v > 0 a smooth foliation. The approximation is achieved with the help of a regularized version of the Percival variational problem. © 1994 John Wiley & Sons, Inc.
Pointwise fourier inversion and related eigenfunction expansions
Authors: Pinsky Mark A.
Published: April 2007

Necessary and sufficient conditions are found for the convergence at a pre‐assigned point of the spherical partial sums (resp. integrals) of the Fourier series (resp. integral) in the class of piecewise smooth functions on Euclidean space. These results carry over unchanged to spherical harmonic expansions, Fourier transforms on hyperbolic space, and Dirichlet eigenfunction expansions with respect to the Laplace operator on a class of Riemannian manifolds. © 1994 John Wiley & Sons, Inc.
Finite dimensional lie‐poisson approximations to vlasov‐poisson equations
Authors: Scovel Clint , Weinstein Alan
Published: April 2007

Many of the basic equations of conservative continuum mechanics (Euler, Vlasov‐Poisson, Vlasov‐Maxwell, MHD, etc.) are Hamiltonian systems with respect to Lie‐Poisson brackets on dual spaces of infinite dimensional Lie algebras. The development of Lie‐Poisson integrators for finite dimensional Lie‐Poisson systems has shown that they are superior in the numerical simulations of these systems, especially with regard to long term phenomena.

This paper shows how to truncate one of these systems, the Vlasov‐Poisson equation of plasma physics, to a finite dimensional Lie‐Poisson system. This requires replacing the functions on single‐particle phase space, with their Poisson bracket Lie algebra structure, by a finite dimensional Lie algebra. Replacing the densities by their moments of order up to k about a fixed reference point corresponds to replacing the functions by their Taylor expansions up to order k. Unfortunately, these truncated Taylor expansions do not form a Lie algebra, since the functions which vanish through order k do not form an ideal under Poisson bracket. Geometrically, this corresponds to the fact that canonical transformations which fix the reference point do not form a normal subgroup.

Introducing the location of a reference point in phase space as an extra variable and truncating with respect to this moving point turns out to decouple the “location” from “shape” coordinates of a lump of density in phase space, as far as the Poisson bracket is concerned. One can then replace the shape coordinates by a finite number of moments.

The central result of the paper is a construction of the decoupling map described above in the general context of the decomposition of a Lie group as a product of subgroups. The main theorem is first proved by the general theory of Poisson reduction, then by explicit calculation, and lastly by showing that the Poisson isomorphism follows from the lift of a natural groupoid isomorphism. The groupoid aspect of the theory also provides natural Poisson maps, useful in the application of Ruth‐type integration techniques, which do not seem easily derivable from the general theory of Poisson reduction. © 1994 John Wiley & Sons, Inc.
Stochastic levi sums
Authors: Watanabe Shinzo
Published: April 2007

An analogy of Levi sums is considered for a class of stochastic partial differential equations to construct their stochastic fundamental solutions. These notions are shown to coincide with Donsker's delta functions, typical generalized Wiener functionals, which have been studied in the frame of the Malliavin calculus. © 1994 John Wiley & Sons, Inc.
On the nonlinear stability of plane waves for the ginzburg‐landau equation
Authors: Kapitula Todd
Published: April 2007

I consider the nonlinear stability of plane wave solutions to a Ginzburg‐Landau equation with additional fifth‐order terms and cubic terms containing spatial derivatives. I show that, under the constraint that the diffusion coefficient be real, these waves are stable. Furthermore, it is shown that the radial component of the perturbation decays at a faster rate than the phase component of the perturbation as t → ∞. The result is also applicable to the classical Ginzburg‐Landau equation. © 1994 John Wiley & Sons, Inc.
The rate function of hypoelliptic diffusions
Authors: Arous Gérard Ben , Deuschel Jean‐Dominique
Published: April 2007

Let be a hypoelliptic diffusion operator on a compact manifold M. Given an a priori smooth reference measure λ on M, we can then rewrite L as the sum of a λ‐symmetric part L0 and a first‐order drift part Y. The paper investigates the effect of the drift Y on the Donsker‐Varadhan rate function corresponding to the large deviations of the empirical measure of the diffusion. When Y is in the linear span of the first and second‐order Lie brackets of the Xi's, we derive an affine bound relating the rate functions associated with L and L0. As soon as one point exists where Y is not in the linear span of the first and second‐order Lie brackets of the Xi's, we show that such an affine bound is impossible. © 1994 John Wiley & Sons, Inc.
The spectral theory for a pencil of skewsymmetrical differential operators of the third order
Authors: Gelfand Israel M. , Zakharevich Ilya
Published: April 2007

We consider the linear algebra of a pair of skewsymmetrical forms in the space of periodic functions defined by differential operators. By linear transform in the space of functions we reduce this pair to the simplest possible form. In this process, we prove the theorem of reduction in rather general context. © 1994 John Wiley & Sons, Inc.
L1 asymptotic behavior of compressible, isentropic, viscous 1‐D flow
Authors: Zeng Yanni
Published: April 2007

We study the large time behavior in L1 of the compressible, isentropic, viscous 1‐D flow. Under the assumption that the initial data are smooth and small, we show that the solutions are approximated by the solutions of a parabolic system, and in turn by diffusion waves, which are solutions of Burgers equations. Decay rates in L1 are obtained. Our method is based on the study of pointwise properties in the physical space of the fundamental solution to the linearized system. © 1994 John Wiley & Sons, Inc.
Convergence of euler‐stokes splitting of the navier‐stokes equations
Authors: Beale J. Thomas , Greengard Claude
Published: April 2007

We consider approximation by partial time steps of a smooth solution of the Navier‐Stokes equations in a smooth domain in two or three space dimensions with no‐slip boundary condition. For small k > 0, we alternate the solution for time k of the inviscid Euler equations, with tangential boundary condition, and the solution of the linear Stokes equations for time k, with the no‐slip condition imposed. We show that this approximation remains bounded in H2,p and is accurate to order k in Lp for p > ∞. The principal difficulty is that the initial state for each Stokes step has tangential velocity at the boundary generated during the Euler step, and thus does not satisfy the boundary condition for the Stokes step. The validity of such a fractional step method or splitting is an underlying principle for some computational methods. © 1994 John Wiley & Sons, Inc.
On the numerical solution of two‐point boundary value problems II
Authors: Starr Page , Rokhlin Vladimir
Published: April 2007

In a recent paper (L. Greengard and V. Rokhlin, On the Numerical Solution of Two‐Point Boundary Value Problems. in Communications on Pure and Applied Mathematics, Volume XLIV, 1991, pages 419‐452). L. Greengard and V. Rokhlin introduce a numerical technique for the rapid solution of integral equations resulting from linear two‐point boundary value problems for second‐order ordinary differential equations. In this paper, we extend the method to systems of ordinary differential equations. After reducing the system of differential equations to a system of second kind integral equations, we discretize the latter via a high‐order Nyström scheme. A somewhat involved analytical apparatus is then constructed which allows for the solution of the discrete system using O(N.p2.n3) operations with N the number of nodes on the interval, p the desired order of convergence, and n the number of equations in the system. Thus, the advantages of the integral equation formulation (small condition number, insensitivity to boundary layers, insensitivity to endpoint singularities, etc.) are retained, while achieving a computational efficiency previously available only to finite difference or finite element methods.

We in addition present a Newton method for solving boundary value problems for nonlinear first‐order systems in which each Newton iterate is the solution of a second kind integral equation; the analytical and numerical advantages of integral equations are thus obtained for nonlinear boundary value problems. © 1994 John Wiley & Sons. Inc.
Hydrodynamical limit for a nongradient system: The generalized symmetric exclusion process
Authors: Kipnis C. , Landim C. , Olla S.
Published: April 2007

We consider a symmetric simple exclusion process where at most two particles per site are permitted. This model turns out to be nongradient. We prove that the particles' densities, under a diffusive rescaling of space and time, converge to the solution of a diffusion equation. We give a variational characterization of the diffusion coefficent. We also prove, for the generator of the process in finite volume, a lower bound on the spectral gap uniform in the volume. © 1994 John Wiley & Sons, Inc.
Morse‐type information on palais‐smale sequences obtained by min‐max principles
Authors: Fang G. , Ghoussoub N.
Published: April 2007

In the context of the min‐max approach to critical point theory, but without the usual compactness assumptions à la Palais‐Smale and the nondegeneracy conditions à la Fredholm, we construct almost critical points with two‐sided estimates on their approximate Morse indices which are arbitrarily close to certain—a priori given—dual sets. This additional topological and analytical information about almost critical sequences can sometimes be crucial in the proof of their convergence and therefore in solving the corresponding variational problem. © 1994 John Wiley & Sons, Inc.
Adaptive finite element methods for conservation laws based on a posteriori error estimates
Authors: Johnson Claes , Szepessy Anders
Published: April 2007

We prove a posteriori error estimates for a finite element method for systems of strictly hyperbolic conservation laws in one space dimension, and design corresponding adaptive methods. The proof of the a posteriori error estimates is based on a strong stability estimate for an associated dual problem, together with the Galerkin orthogonality of the finite‐element method. The strong stability estimate uses the entropy condition for the system in an essential way. ©1995 John Wiley & Sons, Inc.
Nonparabolic dissipative systems modeling the flow of liquid crystals
Authors: Lin Fang‐Hua , Liu Chun
Published: April 2007

We study a simplified system which retains most of the interesting mathematical properties of the original Ericksen‐Leslie equations for the flow of liquid crystals. This is a coupled nonparabolic dissipative dynamic system. We derive several energy laws which enable us to prove the global existence of the weak solutions and the classical solutions. We also discuss uniqueness and some stability properties of the system. ©1995 John Wiley & Sons, Inc.
Stability theory for dissipatively perturbed hamiltonian systems
Authors: Maddocks John H. , Overton Michael L. , Maddocks John H. , Overton Michael L.
Published: April 2007

It is shown that for an appropriate class of dissipatively perturbed Hamiltonian systems, the number of unstable modes of the dynamics linearized at a nondegenerate equilibrium is determined solely by the index of the equilibrium regarded as a critical point of the Hamiltonian. In addition, the movement of the associated eigenvalues in the limit of vanishing dissipation is analyzed. ©1995 John Wiley & Sons,
Inc.
Forced lattice vibrations: Part II
Authors: Deift Percy , Kriecherbauer Thomas , Venakides Stephanos
Published: April 2007

This is the second part of a two‐part series on forced lattice vibrations in which a semi‐infinite lattice of one‐dimensional particles {xn}n≧1,magnified image is driven from one end by a particle x0. This particle undergoes a given, periodically perturbed, uniform motion x0(t) = 2at + h(yt) where a and γ are constants and h(·) has period 2π. Results and notation from Part I are used freely and without further comment. Here the authors prove that sufficiently ample families of traveling‐wave solutions of the doubly infinite system magnified image exist in the cases γ > γ1 and γ1 > γ > γ2 for general restoring forces F. In the case with Toda forces, F(x) = ex, the authors prove that sufficiently ample families of traveling‐wave solutions exist for all k, γk > γ > γk+1. By a general result proved in Part I, this implies that there exist time‐periodic solutions of the driven system (i) with k‐phase wave asymptotics in n of the type magnified image with k = 0 or 1 for general F and k arbitrary for F(x) = ex (when k = 0, take γ0 = ∞ and X0 ≡ 0).
Addendum to “Floer Cohomology of Lagrangian Intersections and Pseudo‐Holomorphic Discs, I”
Authors: Oh Yong‐Geun
Published: April 2007

This is an addendum to the author's earlier paper “Floer Cohomology of Lagrangian Intersection and Pseudo‐Holomorphic Discs, I,” Comm. Pure Appl. Math. 46, 1993, pp. 949–993. The main result of this addendum extends the definition of the Floer cohomology of Lagrangian intersection to the case where the minimal Maslov number is equal to 2. ©1996 John Wiley & Sons, Inc.
Simultaneous Tuning of Chemical Composition and Topography of Copolymer Surfaces: Micelles as Building Blocks
Authors: Zhao Ning , Zhang Xiaoyan , Zhang Xiaoli , Xu Jian
Published: April 2007

A simple method is described for controlling the surface chemical composition and topography of the diblock copolymer poly(styrene)‐b‐poly(dimethylsiloxane)(PS‐b‐PDMS) by casting the copolymer solutions from solvents with different selectivities. The surface morphology and chemical composition were characterized by scanning electron microscopy (SEM) and X‐ray photoelectron spectroscopy (XPS), respectively, and the wetting behavior was studied by water contact angle (CA) and sliding angle (SA) and by CA hysteresis. Chemical composition and morphology of the surface depend on solvent properties, humidity of the air, solution concentration, and block lengths. If the copolymer is cast from a common solvent, the resultant surface is hydrophobic, with a flat morphology, and dominated by PDMS on the air side. From a PDMS‐selective solvent, the surface topography depends on the morphology of the micelles. Starlike micelles give rise to a featureless surface nearly completely covered by PDMS, while crew‐cut‐like micelles lead to a rough surface with a hierarchical structure that consists partly of PDMS. From a PS‐selective solvent, however, surface segregation of PDMS was restricted, and the surface morphology can be controlled by vapor‐induced phase separation. On the basis of the tunable surface roughness and PDMS concentration on the air side, water repellency of the copolymer surface could be tailored from hydrophobic to superhydrophobic. In addition, reversible switching behavior between hydrophobic and superhydrophobic can be achieved by exposing the surface to solvents with different selectivities.
Molecular Dynamics Simulations of CN− Dynamics and Spectroscopy in Myoglobin
Authors: Danielsson Jonas , Meuwly Markus
Published: April 2007

The vibrational dynamics of the cyanide anion and the heme group in MbCN (CN complexed to Myoglobin) are investigated using molecular dynamics simulations. A previously calculated quantum‐chemical heme–ligand potential‐energy surface together with a three‐center charge model for the iron–ligand center that captures both polarization and ligand‐to‐metal charge transfer allows for a detailed description of the interactions around the active site. It is found that the CN binding orientation (FeCN or FeNC) to the heme affects the stretching frequency of the ligand, with a 25 cm−1 difference in the fundamental wavenumber between the two orientations as well as a change in bond length. The charge model also captures such crucial interactions as the possible hydrogen bond between the ligand and the His64 residue. This interaction is weakened when the ligand binds in the FeNC conformation but is also sensitive to the protonation state of His64. The structural changes around the active site, the observation of water penetration for the FeNC conformation, the computed IR spectrum, and the energetics suggest that the FeCN conformation with Hisε64 is the most likely one. The water accessibility of the active site is also found to be related to the protonation state of His64. The presence of water in the active site could also affect the IR band of the CN stretch mode. Thus, IR spectroscopy of the CN stretch is a potentially useful reporter of ligand isomers and active‐site structure.
Repetitive Reversible Labeling of Proteins at Polyhistidine Sequences for Single‐Molecule Imaging in Live Cells
Authors: Guignet Emmanuel G. , Segura Jean‐Manuel , Hovius Ruud , Vogel Horst
Published: April 2007

Sensitive live‐cell fluorescence microscopy and single‐molecule imaging are severely limited by rapid photobleaching of fluorescent probes. Herein, we show how to circumvent this problem using a novel, generic labeling strategy. Small nickel–nitrilotriacetate fluorescent probes are reversibly bound to oligohistidine sequences of exposed proteins on cell surfaces, permitting selective observation of the proteins by fluorescence microscopy. Photobleached probes are removed by washing and replaced by new fluorophores, thus enabling repetitive acquisition of single‐molecule trajectories on the same cell and allowing variation of experimental conditions between acquisitions. This method offers free choice of fluorophores while being minimally perturbing. The strength of the method is demonstrated by labeling engineered polyhistidine sequences of the serotonin‐gated 5‐HT3 receptor on the surface of live mammalian cells. Single‐molecule microscopy reveals pronounced heterogeneous mobility patterns of the 5‐HT3 receptor. After activating the receptor with serotonin, the number of immobile receptors increases substantially, which might be important for receptor regulation at synapses.
LMAN lesions prevent song degradation after deafening without reducing HVC neuron addition
Authors: Scott Luisa L. , Nordeen Ernest J. , Nordeen Kathy W.
Published: April 2007

In some songbirds perturbing auditory feedback can promote changes in song structure well beyond the end of song learning. One factor that may drive vocal change in such deafened birds is the ongoing addition of new vocal‐motor neurons into the song system. Without auditory feedback to guide their incorporation, the addition of these new neurons could disrupt the established song pattern. To assess this hypothesis, the authors determined if neuronal recruitment into the vocal motor nucleus HVC is affected by neural signals that influence vocal change in adult deafened birds. Such signals appear to be conveyed via LMAN, a nucleus in the anterior forebrain that is necessary for vocal change after deafening. Here the authors tested whether LMAN lesions might restrict song degradation after deafening by reducing the addition or survival of new HVC neurons that would otherwise corrupt the ongoing song pattern. Using [3H]thymidine autoradiography to identify neurons generated in adult zebra finches, it was shown here that LMAN lesions do not reduce the number or percent of new HVC neurons surviving for either several weeks or months after [3H]thymidine labeling. However, the authors confirmed previous reports that LMAN lesions restrict vocal change after deafening. These data suggest that neurons incorporated into the adult HVC may form behaviorally adaptive connections without requiring auditory feedback, and that any role such neurons may play in promoting vocal change after adult deafening requires anterior forebrain pathway output. © 2007 Wiley Periodicals, Inc. Develop Neurobiol, 2007.
Lanthanide Complexes with a Calix[8]arene Bearing Phosphinoyl Pendant Arms
Authors: Puntus Lada N. , Chauvin Anne‐Sophie , Varbanov Sabi , Bünzli Jean‐Claude G.
Published: April 2007

The phosphinoyl‐substituted macrocyclic receptor B8bL8, derived from p‐tert‐butylcalix[8]arene, was synthesized and its structure was studied in solution. According to temperature‐dependent 1H and 31P NMR spectroscopic data, the calix[8]arene adopts a so‐called in–out cone conformation. To investigate the influence of the narrow rim substitution, interaction with trivalent lanthanide ions, LnIII (Ln = La, Eu, Tb, Lu), was probed by MS, UV/Vis and NMR spectroscopic titrations. Although both 1:1 (in the presence of triflate) and 2:1 (in the presence of nitrate) Ln:B8bL8 complexes could be isolated in the solid state, the major species present in methanol is the 1:1 complex, irrespective of the anion. NMR spectroscopic data point to a common conformation for the 1:1 complexes in solution, the lanthanide ions being coordinated by four of the eight phosphinoyl arms, with a coordination sphere completed by methanol molecules or by nitrate ions, as ascertained by IR and MS spectra. The ligand displays a weak absorption at 360 nm that can be assigned to an intraligand charge‐transfer (ILCT) state, which is very sensitive to coordination. Photophysical data of the EuIII 2:1 complex point to both metal ion sites providing a very similar chemical environment for the lanthanide ions, with no coordinated water, which is contrary to what is observed for the 1:1 complex. The use of optical electronegativity to predict the energy of the charge‐transfer states in the lanthanide systems with inequivalent ligands is discussed and extensive analysis of the vibronic satellites of the Eu(5D0→7FJ) transitions ascertains conclusions drawn on the EuIII coordination. (© Wiley‐VCH Verlag GmbH & Co. KGaA, 69451 Weinheim, Germany, 2007)
Synthesis of Chiral Imidazolinium Carbene from a Carbohydrate and Its Rhodium(I) Complex
Authors: Shi Ji‐cheng , Lei Ni , Tong Qingsong , Peng Yiru , Wei Junfa , Jia Li
Published: April 2007

A chiral imidazolinium salt with two bulky carbohydrate subunits, N,N′‐1,3‐bis(methyl 4,6‐O‐benzylidene‐3‐deoxy‐α‐D‐altropyrano‐3‐yl)imidazolinium chloride (4), was synthesized in high yield. Deprotonation of 4 with sodium tert‐butoxide in the presence of [RhCl(COD)]2 produced NHC‐coordinated rhodium complex 5 along with water adduct 6 to a lesser extent depending on the moisture content of the reaction mixture. These compounds were fully characterized by IR, MS, and 1H and 13C{1H} NMR spectroscopy.(© Wiley‐VCH Verlag GmbH & Co. KGaA, 69451 Weinheim, Germany, 2007)
A 1,10‐Phenanthroline‐Containing Ring Connected to a Porphyrin by a Rigid Aromatic Spacer and Its Copper‐Complexed Pseudorotaxane
Authors: Frey Julien , Dobbs William , Heitz Valérie , Sauvage Jean‐Pierre
Published: April 2007

A condensation reaction involving a free base tetraarylporphyrin‐2,3‐dione, a macrocyclic compound containing a 1,10‐phenanthroline‐5,6‐dione and a 1,2,4,5‐tetraminobenzene as a linker affords the corresponding conjugate in good yield. The porphyrin ring and the phenanthroline fragment of the other ring are connected in such a way that mutual rotation between these two groups is prohibited. Metallation of the porphyrinic site affords the corresponding zinc complex. By reacting this zinc porphyrin with copper(I), followed by the addition of the bidentate chelate 2,9‐bis(p‐anisyl)‐1,10‐phenanthroline, the threading reaction leading to the corresponding pseudorotaxane takes place quantitatively. (© Wiley‐VCH Verlag GmbH & Co. KGaA, 69451 Weinheim, Germany, 2007)
Acetylide Addition to Bridging Vinyliminium Ligands in Dinuclear Complexes (Eur. J. Inorg. Chem. 13/2007)
Authors: Busetto Luigi , Marchetti Fabio , Zacchini Stefano , Zanotti Valerio
Published: April 2007

The cover picture shows the crystal structures of three diiron complexes with bridging hydrocarbyl ligands of increasing size and complexity: from the bridging aminocarbyne (at the back) through to the bridging vinyliminium (in the middle) to the allylidene complex (in the front). The complexes are the result of subsequent additions of alkynes and acetylides that take place at the bridging unit. For each step, the bridging coordination provides activation and also regio‐ and stereocontrol of the addition reactions. Thus, the nature and conformation of the growing bridging organic frame can be largely predicted and properly designed. Details are discussed in the article by V. Zanotti et al. on p. 1799 ff.
Women with Saethre‐Chotzen syndrome are at increased risk of breast cancer
Authors: Sahlin Pelle , Windh Per , Lauritzen Claes , Emanuelsson Monica , Grönberg Henrik , Stenman Göran
Published: April 2007

The Saethre‐Chotzen syndrome is an autosomal, dominantly inherited craniosynostosis caused by mutations in the basic helix‐loop‐helix transcription factor gene TWIST1. This syndrome has hitherto not been associated with an increased risk of cancer. However, recent studies, using a murine breast tumor model, have shown that Twist may act as a key regulator of metastasis and that the gene is overexpressed in subsets of sporadic human breast cancers. Here, we report a novel association between the Saethre‐Chotzen syndrome and breast cancer. In 15 Swedish Saethre‐Chotzen families, 15 of 29 (52%) women carriers over the age of 25 had developed breast cancer. At least four patients developed breast cancer before 40 years of age, and five between 40 and 50 years of age. The observed cases with breast cancer (n = 15) are significantly higher than expected (n = 0.89), which gives a standardized incidence ratio (SIR) of 16.80 (95% CI 1.54–32.06). Our finding of a high frequency of breast cancer in women with the Saethre‐Chotzen syndrome identifies breast cancer as an important and previously unrecognized symptom characteristic of this syndrome. The results strongly suggest that women carriers of this syndrome would benefit from genetic counseling and enrolment in surveillance programs including yearly mammography. Our results also indicate that the TWIST1 gene may be a novel breast cancer susceptibility gene. Additional studies are, however, necessary to reveal the mechanism by which TWIST1 may predispose to early onset breast cancer in Saethre‐Chotzen patients. © 2007 Wiley‐Liss, Inc.
One hit, two hits, three hits, more? Genomic changes in the development of retinoblastoma
Authors: Corson Timothy W. , Gallie Brenda L.
Published: April 2007

The childhood eye cancer retinoblastoma is initiated by the loss of both alleles of the prototypic tumor suppressor gene, RB1. However, a large number of cytogenetic and comparative genomic hybridization (CGH) studies have shown that these M1 and M2 mutational events—although necessary for initiation—are not the only genomic changes in retinoblastoma. Some of these subsequent changes, which we have termed M3 to Mn, are likely crucial for tumor progression not only in retinoblastoma but also in other cancers. Moreover, genes showing genomic change in cancer are more stable markers and, therefore, possible therapeutic targets than genes simply differentially expressed. In this review, we provide the first comprehensive summary of the genomic evidence implicating gain of 1q, 2p, 6p, and 13q, and loss of 16q in retinoblastoma oncogenesis, including karyotype, CGH, and microarray CGH data. We discuss the search for candidate oncogenes and tumor suppressor genes within these regions, including the candidates (KIF14, MDM4, MYCN, E2F3, DEK, CDH11, and others), plus associations between genomic changes and clinical parameters. We also review studies of other regions of the retinoblastoma genome, the epigenetic changes of aberrant methylation of MGMT, RASSF1A, CASP8, and MLH1, and the roles microRNAs might play in this cancer. Although many candidate genes have yet to be functionally validated in retinoblastoma, work in this field lays out a molecular cytogenetic pathway of retinoblastoma development. Candidate cancer genes carry diagnostic, prognostic, and therapeutic implications beyond retinoblastoma. © 2007 Wiley‐Liss, Inc.
Structural brain magnetic resonance imaging of pediatric twins
Authors: Giedd Jay N. , Schmitt James Eric , Neale Michael C.
Published: April 2007

To explore the relative impact of genetic and nongenetics factors on human brain anatomy during childhood and adolescence development, a collaborative team from the Child Psychiatry Branch of the National Institute of Mental Health and Virginia Commonwealth University is applying structural equation modeling to brain morphometric data acquired via magnetic resonance imaging from a large sample of monozygotic and dizygotic pediatric subjects. In this report, we discuss methodologic issues related to pediatric neuroimaging twin studies and synthesize results to date from the project. Current sample size from the ongoing longitudinal study is approximately 150 twin pairs. Consistent themes are: (1) heritability is high and shared environmental effects low for most brain morphometric measures; (2) the cerebellum has a distinct heritability profile; (3) genetic and environmental factors contribute to the development of the cortex in a regional and age specific manner; and (4) shared genetic effects account for more of the variance than structure specific effects. Understanding of influences on trajectories of brain development may shed light on the emergence of psychopathology during childhood and adolescence and ultimately may guide therapeutic interventions. Hum Brain Mapp 2007. © 2007 Wiley‐Liss, Inc.
Mouse behavioral mutants have neuroimaging abnormalities
Authors: Nieman Brian J. , Lerch Jason P. , Bock Nicholas A. , Chen X. Josette , Sled John G. , Henkelman R. Mark
Published: April 2007

Impaired cognitive, memory, or motor performance is a distinguishing characteristic of neurological diseases. Although these symptoms are frequently the most evident in human patients, additional markers of disease are critical for proper diagnosis and staging. Noninvasive neuroimaging methods have become essential in this capacity and provide means of evaluating disease and tracking progression. These imaging methods are also becoming available to scientists in the research laboratory for assessment of animal models of neurological disease. Imaging in mouse models of neurological disease is of particular interest, owing to the availability of inbred strains and genetic manipulation tools that permit detailed investigation of the roles of various genes and gene products in disease pathogenesis. However, the relative prevalence of neuroimaging abnormalities in mice exhibiting neurological symptoms has not been reported. This prevalence has both theoretical and practical value because it is influenced by both the sensitivity of macroscopic anatomical measures to underlying genetic and disease processes and by the efficiency of neuroimaging in detecting and characterizing these effects. In this paper, we describe a meta‐analysis of studies involving behavioral mouse mutants at our laboratory. In summary, we have evaluated 15 different mutant genotypes, of which 13 showed abnormal neuroimaging findings. This indicates a surprisingly high prevalence of neuroimaging abnormalities (87%) and suggests that disease processes affecting behavior generally alter neuroanatomy as well. As a consequence, neuroimaging provides a highly sensitive marker of neurological disease in mice exhibiting abnormal behavior. Hum Brain Mapp 2007. © 2007 Wiley‐Liss, Inc.
Targeted delivery of doxorubicin to the rat brain at therapeutic levels using MRI‐guided focused ultrasound
Authors: Treat Lisa H. , McDannold Nathan , Vykhodtseva Natalia , Zhang Yongzhi , Tam Karen , Hynynen Kullervo
Published: April 2007

The clinical application of chemotherapy to brain tumors has been severely limited because antitumor agents are typically unable to penetrate an intact blood‐brain barrier (BBB). Although doxorubicin (DOX) has been named as a strong candidate for chemotherapy of the central nervous system (CNS), the BBB often prevents cytotoxic levels from being achieved. In this study, we demonstrate a noninvasive method for the targeted delivery of DOX through the BBB, such that drug levels shown to be therapeutic in human tumors are achieved in the normal rat brain. Using MRI‐guided focused ultrasound with preformed microbubbles (Optison) to locally disrupt the BBB and systemic administration of DOX, we achieved DOX concentrations of 886 ± 327 ng/g tissue in the brain with minimal tissue effects. Tissue DOX concentrations of up to 5,366 ± 659 ng/g tissue were achieved with higher Optison doses, but with more significant tissue damage. In contrast, DOX accumulation in nontargeted contralateral brain tissue remained significantly lower for all paired samples (p < 0.001). These results suggest that targeted delivery by focused ultrasound may render DOX chemotherapy a viable treatment option against CNS tumors, despite previous accessibility limitations. In addition, MRI signal enhancement in the sonicated region correlated strongly with tissue DOX concentration (r = 0.87), suggesting that contrast‐enhanced MRI could perhaps indicate drug penetration during image‐guided interventions. Our technique using MRI‐guided focused ultrasound to achieve therapeutic levels of DOX in the brain offers a large step forward in the use of chemotherapy to treat patients with CNS malignancies. © 2007 Wiley‐Liss, Inc.
Inhibition of breast tumor growth and angiogenesis by a medicinal herb: Ocimum gratissimum
Authors: Nangia‐Makker Pratima , Tait Larry , Shekhar Malathy P.V. , Palomino Eduardo , Hogan Victor , Piechocki Marie P. , Funasaka Tatsuyoshi , Raz Avraham
Published: April 2007

Ocimum sp. is a traditionally used medicinal herb, which shows anti‐oxidant, anti‐carcinogenic, radio‐protective and free radical scavenging properties. So far no detailed studies have been reported on its effects on human cancers. Thus, we analyzed its effects on human breast cancer utilizing in vitro and in vivo methodologies. Aqueous extracts were prepared from the mature leaves of Ocimum gratissimum (OG) cultivated devoid of pesticides. Tumor progression and angiogenesis related processes like chemotaxis, proliferation, apoptosis, 3D growth and morphogenesis, angiogenesis and tumor growth were studied in the presence or absence of the extract, and in some experiments a comparison was made with purified commercially available eugenol, apigenin and ursolic acid. Aqueous OG leaf extract inhibits proliferation, migration, anchorage independent growth, 3D growth and morphogenesis and induction of COX‐2 protein in breast cancer cells. A comparative analysis with eugenol, apigenin and ursolic acid showed that the inhibitory effects on chemotaxis and 3D morphogenesis of breast cancer cells were specific to OG extract. In addition, OG extracts reduced tumor size and neoangiogenesis in a MCF10 DCIS.com xenograft model of human DCIS. This is the first detailed report showing that OG leaf extract may be of value as a breast cancer preventive and therapeutic agent and might be considered as additional additive in the arsenal of components aimed at combating breast cancer progression and metastasis. © 2007 Wiley‐Liss, Inc.