bluuebunny/crossref_metadata_2025_split huggingface dataset:
Evidence‐based guidelines for following stage 1 seminoma
Authors: Martin Jarad M. , Panzarella Tony , Zwahlen Daniel R. , Chung Peter , Warde Padraig 
Published: April 2007

AbstractBACKGROUND.The authors developed evidence‐based guidelines for a follow‐up schedule after orchiectomy for stage 1 seminoma. Required investigations, frequency of assessment, overall duration of follow‐up, and management strategies were identified.METHODS.A systematic review of the literature was performed of prospective studies in stage 1 seminoma. Studies published after 1980 were considered eligible for inclusion. Data extracted included relapse‐free rates, number of patients at risk, and relapse locations. Five strategies were identified: Surveillance, Extended‐Field Radiotherapy, Para‐aortic Radiotherapy, and either 1 or 2 cycles of Carboplatin Chemotherapy. For each strategy, Kaplan‐Meier relapse‐free estimates were used to calculate weighted‐mean cumulative hazards of relapse over time. These were used to calculate semiannual weighted‐mean relapse hazards.RESULTS.Seventeen prospective studies with a total of 5561 patients were identified. Actuarial data on relapse was available in 5013 (90.1%) patients, and 92.9% of all relapses had location data reported. Annual hazard rates for relapse were determined.CONCLUSIONS.Evidence‐based recommendations for follow‐up frequency based on risk of relapse were formulated. The authors suggested 3 times per year when the risk is >5%, 2 times per year when the risk is 1% to 5%, and annually until the risk is <0.3%. Investigations should reflect location(s) at risk of relapse and include computed tomography of the abdomen and pelvis for surveillance and adjuvant carboplatin, whereas for para‐aortic radiotherapy, pelvic computed tomography alone is required. These recommendations offer the possibility of maximal patient convenience and optimal healthcare resource allocation without compromising disease control. Cancer 2007. © 2007 American Cancer Society.
Some familiar examples for which the large deviation principle does not hold
Authors: Baxter J. R. , Jain N. C. , Varadhan S. R. S. 
Published: April 2007

AbstractFor a class of Markov processes (in continuous or discrete time) we show that if the full large deviation holds for normalized occupation time measures Lt(w, ˙) with some rate function J, then the lower semicontinuous regularization of J must agree with the rate function I introduced by M. D. Donsker and S. R. S. Varadhan. As a consequence we show that for processes such as Brownian motion the full large deviation principle for Lt(w, ˙) cannot hold with any rate function.
Asymptotic behavior of high‐order differences of the partition function
Authors: Knessl Charles , Keller Joseph B. 
Published: April 2007

AbstractThe partition function p(n) is the number of partitions of an integer n into positive integers, and p(n, k) = Δkp(n) is its k‐th difference. We obtain a recursion equation for p(n, k) which we solve asymptotically for n and k both large by using the WKB method and the method of matched asymptotic expansions. The result shows that p(n, k) is positive for n greater than a critical value n0(k). while for n < n0(k), p(n, k) alternates in sign as n increases. This confirms the recent result of A. M. Odlyzko. It also yields a refinement of his approximation for n0(k). The improved approximation agrees well with exact numerical values.
Large deviation problem for some parabolic itǒ equations
Authors: Chow Pao‐Liu 
Published: April 2007

AbstractThe large deviation problem of Wentzell‐Freidlin type is considered for a class of semilinear parabolic equations perturbed by a small multiplicative noise. In a Hilbert space setting, it is proved that, under suitable conditions, the associated family of solution measures, depending on a small parameter, obeys the large deviation principle with respect to a certain rate function.
Translation representation for automorphic solutions of the wave equation in non‐euclidean spaces, IV
Authors: Lax Peter D. , Phillips Ralph S. 
Published: April 2007

AbstractIn Part I of this series of papers we have defined the incoming and outgoing translation representations for automorphic solutions of the hyperbolic wave equations; in Part II we have proved the completeness of these representations when the fundamental polyhedron F has a finite number of sides with a finite or infinite volume, but is not compact. In Part IV we present a proof of completeness which is simpler than our original proof contained in Section 7 of Part II for the case when F has cusps of less than maximal rank; and we supply a proof for the case, not covered in Section 7, when the parabolic subgroup associated with such cusps contains twists.
On uniqueness and continuation properties after blow‐up time of self‐similar solutions of nonlinear schrödinger equation with critical exponent and critical mass
Authors: Merle Frank 
Published: April 2007

AbstractWe consider the nonlinear Schrödinger equation with critical power

where u: (0, T) × ℝN → C and ø ϕ H1 ∪ {ø;|x|ø ϵ L2}. With this nonlinear term, the equation (1)‐(1′) has a conformal invariance. Thus one yields explicit “self‐similar” solutions which have the following property: they have minimum L2 norm among blow‐up solutions.In this paper, we first focus on uniqueness properties of these self‐similar solutions in a certain class. We then look at the possible continuations of these solutions after the blow‐up time.
Homogenization of linear and nonlinear transport equations
Authors: Weinan E. 
Published: April 2007

AbstractWe study the homogenization of the linear and nonlinear transport equations with oscillatory velocity fields. Two types of homogenized equations are derived. For general n‐dimensional linear and nonlinear problems, we derive homogenized equations by introducing additional independent variables to represent the small scales. For the two‐dimensional linear transport equations, we derive effective equations for the averaged quantities. Such equations take the form of either a degenerate non‐local diffusion equation with memory or a higher order hyperbolic equation. To study the nonlinear transport equations we introduce the concept of two‐scale Young measure and extend DiPerna's method to prove that it reduces to a family of Dirac measures.
Justification of the two‐dimensional equations of a linearly elastic shallow shell
Authors: Ciarlet P. G. , Miara B. 
Published: April 2007

AbstractWe consider a problem in three‐dimensional linearized elasticity, posed over a shell with a specific geometry, subjected to general loadings, and clamped on a portion of its lateral surface. We show that, as the thickness of the shell goes to zero, the solution of the three‐dimensional problem converges to the solution of two‐dimensional shallow shell equations. This approach, which provides in particular a mathematical definition of “shallowness”, clearly delineates conditions under which a three‐dimensional problem may be deemed asymptotically equivalent to a two‐dimensional shallow shell problem.
Biorthogonal bases of compactly supported wavelets
Authors: Cohen A. , Daubechies Ingrid , Feauveau J.‐C. 
Published: April 2007

AbstractOrthonormal bases of compactly supported wavelet bases correspond to subband coding schemes with exact reconstruction in which the analysis and synthesis filters coincide. We show here that under fairly general conditions, exact reconstruction schemes with synthesis filters different from the analysis filters give rise to two dual Riesz bases of compactly supported wavelets. We give necessary and sufficient conditions for biorthogonality of the corresponding scaling functions, and we present a sufficient conditions for the decay of their Fourier transforms. We study the regularity of these biorthogonal bases. We provide several families of examples, all symmetric (corresponding to “linear phase” filters). In particular we can construct symmetric biorthogonal wavelet bases with arbitraily high preassigned regularity; we also show how to construct symmetric biorthogonal wavelet bases “close” to a (nonsymmetric) orthonormal basis.
Regularity of harmonic maps from the Minkowski space into rotationally symmetric manifolds
Authors: Shath J. , Tahvildar‐Zadeh A. 
Published: April 2007

AbstractWe prove global regularity for the solution to the Cauchy problem with regular data for an equivariant harmonic map from the 2 + 1‐dimensional Minkowski space into a two‐dimensional, rotationally symmetric, and geodesically convex Riemannian manifold.
Large time behavior and homogenization of solutions of two‐dimensional conservation laws
Authors: Engquist Bjorn , Weinan E 
Published: April 2007

AbstractWe study the large time behavior of solutions of scalar conservation laws in one and two space dimensions with periodic initial data. Under a very weak nonlinearity condition, we prove that the solutions converge to constants as time goes to infinity. Even in one space dimension our results improve the earlier ones since we only require the fluxes to be nonlinear in a neighborhood of the mean value of the initial data. We then use these results to study the homogenization problem for scalar conservation laws with oscillatory initial data.
Statistical mechanics of classical particles with logarithmic interactions
Authors: Kiessling Michael K.‐H. 
Published: April 2007

AbstractThe inhomogeneous mean‐field thermodynamic limit is constructed and evaluated for both the canonical thermodynamic functions and the states of systems of classical point particles with logarithmic interactions in two space dimensions. The results apply to various physical models of translation invariant plasmas, gravitating systems, as well as to planar fluid vortex motion. For attractive interactions a critical behavior occurs which can be classified as an extreme case of a second‐order phase transition. To include in particular attractive interactions a new inequality for configurational integrals is derived from the arithmetic‐geometric mean inequality. The method developed in this paper is easily seen to apply as well to systems with fairly general interactions in all space dimensions. In addition, it also provides us with a new proof of the Trudinger‐Moser inequality known from differential geometry – in its sharp form.
Solution of the inverse spectral problem for an impedance with integrable derivative part I
Authors: Coleman Carol Flynn , McLaughlin Joyce R. 
Published: April 2007

AbstractThe inverse eigenvalue problem for a Sturm‐Liouville equation in impedance form with Dirichlet boundary conditions on a unit interval is considered. The solution of this nonlinear problem requires the investigation of a combined mapping from the logarithmic derivative of the impedance, assumed to be square integrable, to two sequences of spectral data. The first is the sequence of Dirichlet eigenvalues, shown to be locally bounded with square roots differing from the sequence of integral multiples of π by a square summable sequence. The second sequence has as first term the mean of the logarithmic derivative of the impedance. Each term in the remainder of the sequence is the logarithm of the product of the impedance and the derivative of an eigenfunction evaluated at an endpoint. It is shown that this is a locally bounded square summable sequence. The combined map is real analytic. The asymptotics and analyticity results follow from a modified Prüfer substitution. © 1993 John Wiley & Sons, Inc.
Perturbation theorems for linear hyperbolic mixed problems and applications to the compressible euler equations
Authors: Da Veiga H. Beirão 
Published: April 2007

AbstractThe main result of this paper (which is completely new, apart from our previous and less general result proved in reference [9]) states that the nonlinear system of equations (1.11) (or, equivalently, (1.10)) that describes the motion of an inviscid, compressible (barotropic) fluid in a bounded domain Ω, gives rise to a strongly well‐posed problem (in the Hadamard classical sense) in spaces Hk(Ω), k ≧ 3; see Theorem 1.4 below. Roughly speaking, if (an, ϕn) → (a, ϕ) in Hk × Hk and if fn → f in ℒ︁2(0, T;Hk), then (vn, gn) → (v, g) in 𝒞 (0, T; Hk × Hk). The method followed here (see also [8]) also applies to the non‐barotropic case p = p(ρ, s) (see [10]) and to other nonlinear problems. These results are based upon an improvement of the structural‐stability theorem for linear hyperbolic equations. See Theorem 1.2 below. Added in proof: The reader is referred to [29], Part I, for a concise explanation of some fundamental points in the method followed here. © 1993 John Wiley & Sons, Inc.
Korteweg–de vries zero dispersion limit: Through first breaking for cubic‐like analytic initial data
Authors: Wright Otis C. 
Published: April 2007

AbstractThe characteristic solution of the initial value problem for the Riemann invariant form of the Korteweg‐de Vries modulation equations is obtained locally through first breaking in the case of initial data which is analytic near a cubic inflection point. Tsarev's (see [11]) system is used to define the solution implicitly in terms of the speeds of the generalized KdV modulation equations. These “higher flow” speeds satisfy the same derivative identities obtained by Levermore for the KdV flow (see [6]).Moreover, by explicitly constructing the Lax‐Levermore (see [5]) minimizer the Tsarev solution is shown to be the unique solution of Whitham's equations corresponding to the KdV zero dispersion limit. Also the Tsarev system possesses at most one three‐sheeted solution in a uniform neighborhood of the inflection point. Finally the explicit minimizer provides phase information for the Venakides' small dispersion KdV waveform through first breaking; see [12]. © 1993 John Wiley & Sons, Inc.
Multi‐valued solutions and branch point singularities for nonlinear hyperbolic or elliptic systems
Authors: Caflisch Russel E. , Ercolani Nicholas , Hou Thomas Y. , Landis Yelena 
Published: April 2007

AbstractMulti‐valued solutions are constructed for 2 × 2 first‐order systems using a generalization of the hodograph transformation. The solution is found as a complex analytic function on a complex Riemann surface for which the branch points move as part of the solution. The branch point singularities are envelopes for the characteristics and thus move at the characteristic speeds. We perform an analysis of stability of these singularities with respect to perturbations of the initial data. The generic singularity types are folds, cusps, and nondegenerate umbilic points with non‐zero 3‐jet. An isolated singularity is generically a square root branch point corresponding to a fold. Two types of collisions between singularities are generic: At a “tangential” collision between two singularities moving at the same characteristic speed, a cube root branch point is formed, corresponding to a cusp. A “non‐tangential” collision, between two square root branch points moving at different characteristic speeds, remains a square root branch point at the collision and corresponds to a nondegenerate umbilic point. These results are also valid for a diagonalizable n‐th order system for which there are exactly two speeds. © 1993 John Wiley & Sons, Inc.
Zero dissipation limit to rarefaction waves for the one‐dimensional navier‐stokes equations of compressible isentropic gases
Authors: Xin Zhouping 
Published: April 2007

AbstractWe 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

AbstractWe 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

AbstractThe 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

AbstractWave 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

AbstractWe 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

AbstractWe 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

AbstractAxisymmetric 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

AbstractWe 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.
A class of laplace transforms arising in a diffusion problem
Authors: Berman S. M. 
Published: April 2007

AbstractIt 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.