pinecone/core-2020-05-10-deduplication huggingface dataset:
Limiting Models for Josephson Junctions and Superconducting Weak Links

AbstractOne of the broadest applications of superconductivity is the technology based on Josephson junction devices. These junction devices are formed by placing a thin layer of normal (nonsuperconducting) material between layers of superconducting material. We consider various limiting cases for models of the junction device based on the Ginzburg–Landau equations. Examples include a model for large values of the Ginzburg–Landau parameter, κ, in the high-field regime and a model for a thin normal layer. Convergence analysis for the simplified models is established and numerical simulations are presented
Mathematical Modeling of Near-Field Optics

AbstractConsider a time-harmonic electromagnetic plane wave incident on a periodic (grating) structure. An inhomogeneous (subwavelength) object is placed inside the periodic structure. The scattering problem is to study the electromagnetic field distributions. The problem arises in the study of near-field optics and has many physical and biological applications. This work is devoted to modeling and analysis of a near-field optics problem. An integral representation approach is presented to solve the problem. It is shown particularly that the perturbation due to the object decays exponentially along the periodic direction of the structure, provided that no surface waves occur. Based on the approach, a general solution method is discussed and the well-posedness of the model problems are established
Paley–Wiener-Type Theorems for a Class of Integral Transforms

AbstractA characterization of weighted L2(I) spaces in terms of their images under various integral transformations is derived, where I is an interval (finite or infinite). This characterization is then used to derive Paley–Wiener-type theorems for these spaces. Unlike the classical Paley–Wiener theorem, our theorems use real variable techniques and do not require analytic continuation to the complex plane. The class of integral transformations considered is related to singular Sturm–Liouville boundary-value problems on a half line and on the whole line
Global Qualitative Analysis for a Ratio-Dependent Predator–Prey Model with Delay

AbstractA ratio-dependent predator–prey model with time lag for predator is proposed and analyzed. Mathematical analyses of the model equations with regard to boundedness of solutions, nature of equilibria, permanence, and stability are analyzed. We note that for a ratio-dependent system local asymptotic stability of the positive steady state does not even guarantee the so-called persistence of the system and, therefore, does not imply global asymptotic stability. It is found that an orbitally asymptotically stable periodic orbit exists in that model. Some sufficient conditions which guarantee the global stability of positive equilibrium are given
Cauchy Functions for Dynamic Equations on a Measure Chain

AbstractWe consider the nth-order linear dynamic equation Px(t)=∑i=0npi(t)x(σi(t))=0, where pi(t),0≤i≤n, are real-valued functions defined on T. We define the Cauchy function K(t,s) for this dynamic equation, and then we prove a variation of constants formula. One of our main concerns is to see how the Cauchy function for an equation is related to the Cauchy functions for the factored parts of the operator P. Finally we consider the equation Px(t)=∑i=0npix(σi(t))=0, where each of the pi's is a constant, and obtain a formula for the Cauchy function. For our main results we only consider the time scale T such that every point in T is isolated
Linear Recursive Schemes and Asymptotic Expansion Associated with the Kirchoff–Carrier Operator

AbstractIn this paper we consider a nonlinear wave equation with the Kirchoff–Carrier operator, (1) utt=(b0+B(‖∇u‖2))Δu=f(x,t,u,ux,ut), x ∈ Ω = (0, 1), 0 < t < T, (2) u(0,t)=u(1,t)=0, (3) u(x,0)=ũ0(x), ut(x,0)=ũ1(x), where b0>0 is a given constant and B,f are the given functions. The above B(‖∇u‖2) depends on the integral ‖∇u‖2=∫Ω|∇u(x,t)|2dx. In this paper we associate with the above problem a linear recursive scheme for which the existence of a local and unique solution is proved by using the standard compactness argument. If B∈C2(R+),B1∈C1(R+),f∈C2([formula]Ω×[0,∞)×R3), and f1∈C1([formula]Ω×[0,∞)×R3) then an asymptotic expansion of order 2 in ε is obtained with a right-hand side of the form f(x,t,u,ux,ut)+εf1(x,t,u,ux,ut), and B stands for B+εB1, for ε sufficiently small
Multiple Solutions and Eigenvalues for Third-Order Right Focal Boundary Value Problems

AbstractWe are concerned with the right focal boundary value problemx‴(t)=f(t,x(t)),t1≤t≤t3,x(t1)=x′(t2)=x″(t3)=0,and the associated eigenvalue problemx‴(t)=λa(t)f(x(t))with the same boundary conditions. Under various assumptions on f, a, and λ we establish intervals of the parameter λ which yield the existence of a positive solution of the eigenvalue problem. By placing certain restrictions on the nonlinearity, we prove the existence of at least one, at least two, at least three, and infinitely many positive solutions of the boundary value problem by applying some known fixed-point theorems as well as some recent generalizations of these fixed-point theorems
Approximation of Martensitic Microstructure with General Homogeneous Boundary Data

AbstractWe consider the approximation of martensitic microstructure for a class of martensitic transformations. We model such microstructures by multi-well energy minimization problems with general homogeneous boundary data. Under our assumptions on such boundary data, the underlying microstructure can be nonunique. We first show that any energy-minimizing sequence converges strongly to a unique macroscopic deformation that is precisely the homogeneous deformation in the boundary condition. We then prove a series of estimates for the approximation of admissible deformations to the unique macroscopic deformation of the microstructure and for the closeness of the gradients of admissible deformations to the energy wells
Asymptotic Expansions and a New Numerical Algorithm of the Algebraic Riccati Equation for Multiparameter Singularly Perturbed Systems

AbstractIn this paper we study a continuous-time multiparameter algebraic Riccati equation (MARE) with an indefinite sign quadratic term. The existence of a unique and bounded solution of the MARE is newly established. We show that the Kleinman algorithm can be used to solve the sign indefinite MARE. The proof of the convergence and the existence of the unique solution of the Kleinman algorithm is done by using the Newton–Kantorovich theorem. Furthermore, we present new algorithms for solving the generalized multiparameter algebraic Lyapunov equation (GMALE) by means of the fixed-point algorithm
Monotonicity Method Applied to the Complex Ginzburg–Landau and Related Equations

AbstractGlobal existence of unique strong solutions is established for the complex Ginzburg–Landau equation ∂tu−(λ+iα)Δu+(κ+iβ)|u|p−1u−γu=0, where λ>0,κ>0,α,β,γ∈R,p≥1, and κ−1|β|≤2p/(p−1). The key is a new inequality in monotonicity methods. It is based on the sectorial estimates of −Δ in Lp+1 and the nonlinear operator u↦|u|p−1u appearing in the equation. The key inequality also yields the global existence of unique strong solutions of the nonlinear Schrödinger type equation with monotone nonlinearity ∂tu−iΔu+|u|p−1u=0 for all p≥1
Singularly Perturbed Markov Chains with Two Small Parameters: A Matched Asymptotic Expansion

AbstractThis work is concerned with asymptotic properties of solutions to forward equations for singularly perturbed Markov chains with two small parameters. It is motivated by the model of a cost-minimizing firm involving production planning and capacity expansion and a two-level hierarchical decomposition. Our effort focuses on obtaining asymptotic expansions of the solutions to the forward equation. Different from previous work on singularly perturbed Markov chains, the inner expansion terms are constructed by solving certain partial differential equations. The methods of undetermined coefficients are used. The error bound is obtained
Kolmogorov Vector Fields with Robustly Permanent Subsystems

AbstractThe following results are proven. All subsystems of a dissipative Kolmogorov vector field ẋi=xifi(x) are robustly permanent if and only if the external Lyapunov exponents are positive for every ergodic probability measure μ with support in the boundary of the nonnegative orthant. If the vector field is also totally competitive, its carrying simplex is C1. Applying these results to dissipative Lotka–Volterra systems, robust permanence of all subsystems is equivalent to every equilibrium x* satisfying fi(x*>0 whenever xi*=0. If in addition the Lotka–Volterra system is totally competitive, then its carrying simplex is C1
Compositions of Polynomials with Coefficients in a Given Field

AbstractLet F⊂K be fields of characteristic 0, and let K[x] denote the ring of polynomials with coefficients in K. Let p(x)=∑k=0nakxk∈K[x],an≠0. For p∈K[x]\F[x], define DF(p), the F deficit of p, to equal n−max{0≤k≤n:ak∉F}. For p∈F[x], define DF(p)=n. Let p(x)=∑k=0nakxk and let q(x)=∑j=0mbjxj, with an≠0, bm≠0, an,bm∈F, bj∉F for some j≥1. Suppose that p∈K[x],q∈K[x]\F[x],p, not constant. Our main result is that p∘q∉F[x] and DF(p∘q)=DF(q). With only the assumption that anbm∈F, we prove the inequality DF(p∘q)≥DF(q). This inequality also holds if F and K are only rings. Similar results are proven for fields of finite characteristic with the additional assumption that the characteristic of the field does not divide the degree of p. Finally we extend our results to polynomials in two variables and compositions of the form p(q(x,y)), where p is a polynomial in one variable
Global Bifurcation on Time Scales

AbstractWe consider the structure of the solution set of a nonlinear Sturm–Liouville boundary value problem defined on a general time scale. Using global bifurcation theory we show that unbounded continua of nontrivial solutions bifurcate from the trivial solution at the eigenvalues of the linearization, and we show that certain nodal properties of the solutions are preserved along these continua. These results extend the well-known results of Rabinowitz for the case of Sturm–Liouville ordinary differential equations
Metrics and T-Equalities

AbstractThe relationship between metrics and T-equalities is investigated; the latter are a special case of T-equivalences, a natural generalization of the classical concept of an equivalence relation. It is shown that in the construction of metrics from T-equalities triangular norms with an additive generator play a key role. Conversely, in the construction of T-equalities from metrics this role is played by triangular norms with a continuous additive generator or, equivalently, by continuous Archimedean triangular norms. These results are then applied to the biresidual operator ET of a triangular norm T. It is shown that ET is a T-equality on [0, 1] if and only if T is left-continuous. Furthermore, it is shown that to any left-continuous triangular norm T there correspond two particular T-equalities on F(X), the class of fuzzy sets in a given universe X; one of these T-equalities is obtained from the biresidual operator ETT by means of a natural extension procedure. These T-equalities then give rise to interesting metrics on F(X)
Asymptotic Behavior of a Nonhomogeneous Linear Recurrence System

AbstractConsider the nonhomogeneous linear recurrence systemxn+1=(A+Bn)xn+gn,where A and Bn (n=0,1,…) are square matrices and gn (n=0,1,…) are column vectors. In this paper, we describe, in terms of the initial condition, the asymptotic behavior of the solutions of this equation in the case when A has a simple dominant eigenvalue λ0,∑n=0∞⫫Bn⫫<∞ and ∑n=0∞|λ0|−n⫫gn⫫<∞. The proof is based on the duality between the solutions of the above equation and the solutions of the associated adjoint equation. As a consequence, we obtain a similar result for higher order scalar equations
Constructing an Elementary Measure on a Space of Projections

AbstractBypassing much theory from integral geometry, we construct an elementary measure on a space whose elements can represent rank k orthogonal projections in RN. By replacing the Grassmannian GN,k with a simple product space ×j=1kSN−1 we are able to reproduce certain important features of the nontrivial measure on GN,k invariant under the action of the orthogonal group (a property also enjoyed by our construction). As a motivating example we show that our construction enables the proof of a recent embedding theorem due to Foias and Olson to be completed using only standard methods of analysis
Maximal Singular Integral Operators Along Surfaces

AbstractLet b(y) be a bounded radial function and Γ(y)=(γ1(y),γ2(y),…,γm(y)), where each γj(y) (j=1,…,m) is a real-valued radial function. For x,y∈Rn and x*∈Rm, we define the maximal singular integral along the surface (y,Γ(|y|)) byT*f(x,x*)=supε>0∫|y|>εf(x−y,x*−Γ(|y|))b(y)|y|−nΩ(y′)dy.Suppose that Ω is an H1 function on the sphere Sn−1 satisfying ∫Sn−1Ω(x′)dσ(x′)=0. We prove that T* is bounded on Lp(Rn+m),1<p<∞, provided the lower dimensional maximal functionMΓg(x1,x*)=supk∈Z2−k∫2k+12k|g(x1−t,x*−Γ(t))|dtis bounded on Lp(Rm+1) for all p>1. The result is an extension and improvement of the main theorem in [S. Lu, Y. Pan, and D. Yang, Rough singular integrals associated to surfaces of revolution, Proc. Amer. Math. Soc.129 (2001), 2931–2940]
Dynamics of a Rod Made of Generalized Kelvin–Voigt Visco-elastic Material

AbstractIn this paper we develop a new mathematical model for the lateral vibration of an axially compressed visco-elastic rod. As the basis for this model we use a fractional derivative type of stress–strain relation. We show that the dynamics of the lateral vibration is governed by two coupled linear differential equations with fractional derivatives. For a special case of the generalized Kelvin–Voigt body, this system is reduced to a single fractional derivative differential equation (Eq. (19)). For a class of problems to which (19) belongs the questions of the existence of a solution and its regularity are analyzed. Both continuous and impulsive loading are treated
On the Equality Between the Maslov Index and the Spectral Index for the Semi-Riemannian Jacobi Operator

AbstractWe consider a Morse–Sturm system in Rn whose coefficient matrix is symmetric with respect to a (not necessarily positive definite) nondegenerate symmetric bilinear form on Rn. The main motivation for studying such systems comes from semi-Riemannian geometry, where the Morse–Sturm system is obtained from the Jacobi equation along a geodesic by writing the equation in terms of a parallelly transported basis of the tangent bundle along the geodesic. Two integer numbers are naturally associated to such systems: the Maslov index, which gives a sort of algebraic count of the conjugate instants, and the spectral index, which gives an algebraic count of the negative eigenvalues of the corresponding second-order differential operator. In this paper we prove that these two integer numbers are equal; in the case of Riemannian geometry, this equality is precisely the Morse Index Theorem. Such equality is already known to hold under a suitable nondegeneracy assumption on the eigenvalues of the Jacobi operator; we give a proof of the equality in the degenerate case using a perturbation argument
Stability Results for the First Eigenvalue of the Laplacian on Domains in Space Forms

AbstractWe studied the two known works on stability for isoperimetric inequalities of the first eigenvalue of the Laplacian. The earliest work is due to A. Melas who proved the stability of the Faber–Krahn inequality: for a convex domain Ω contained in Rn with λ close to λ̄, the first eigenvalue of the ball B of the same volume, the domain must be close to the ball B with respect to the Hausdorff distance. Later, Y. Xu studied the stability of the Szegö–Weinberger inequality for convex domains in Rn and Hn where Hn denotes hyperbolic space. Our work consists of extending A. Melas' result to the spaces of constant curvature S2 and H2 and Y. Xu's result to domains contained in the polar cap Bπ/4 in Sn
X-ray structure of antistasin at 1.9 Å resolution and its modelled complex with blood coagulation factor Xa

The three-dimensional structure of antistasin, a potent inhibitor of blood coagulation factor Xa, from the Mexican leech Haementeria officinalis was determined at 1.9 Å resolution by X-ray crystallography. The structure reveals a novel protein fold composed of two homologous domains, each resembling the structure of hirustasin, a related 55-residue protease inhibitor. However, hirustasin has a different overall shape than the individual antistasin domains, it contains four rather than two β-strands, and does not inhibit factor Xa. The two antistasin domains can be subdivided into two similarly sized subdomains with different relative orientations. Consequently, the domain shapes are different, the N-terminal domain being wedge-shaped and the C-terminal domain flat. Docking studies suggest that differences in domain shape enable the N-terminal, but not C-terminal, domain of antistasin to bind and inhibit factor Xa, even though both have a very similar reactive site. Furthermore, a putative exosite binding region could be defined in the N-terminal domain of antistasin, comprising residues 15–17, which is likely to interact with a cluster of positively charged residues on the factor Xa surface (Arg222/Lys223/Lys224). This exosite binding region explains the specificity and inhibitory potency of antistasin towards factor Xa. In the C-terminal domain of antistasin, these exosite interactions are prevented due to the different overall shape of this domain.
Contributions of supercoiling to Tn3 resolvase and phage Mu Gin site-specific recombination

Members of the resolvase/invertase family of site-specific recombinases require supercoiled substrates containing two recombination sites. To dissect the roles of supercoiling in recombination by the Tn3 and γδ resolvases and the phage Mu Gin invertase, we used substrates that provided some but not all of the topological features of the standard substrate. We divided the Tn3 resolvase reaction into two stages, synapsis and postsynapsis. We found the contributions of supercoiling to each stage were distinct, since substrate catenation in the absence of supercoiling or low levels of substrate supercoiling were sufficient for synapsis but not postsynapsis. Using structural and functional topological analyses, we verified that the resolvase synaptic complexes with nicked catenanes were recombination intermediates. The requirement for supercoiling was even less stringent for the γδ resolvase, which recombined nicked catenanes about half as well as it did supercoiled substrates. Gin recombination of catenanes occurred even if the recombinational enhancer was on a nicked ring, as long as both crossover sites were on a supercoiled ring. Therefore, supercoiling is required at the Gin crossover sites but not at the enhancer. We conclude that solely conformational effects of supercoiling are required for resolvase synapsis and the function of the Gin enhancer, but that a torsional effect, probably double helix unwinding, is needed for Tn3 resolvase postsynapsis and at the Gin recombination sites
Formation of knots in partially replicated DNA molecules

7 páginas, 4 figuras, -- PAGS nros.637-643Bacterial plasmids with two origins of replication in convergent orientation are frequently knotted in vivo. The knots formed are localised within the newly replicated DNA regions. Here, we analyse DNA knots tied within replication bubbles of such plasmids, and observe that the knots formed show predominantly positive signs of crossings. We propose that helical winding of replication bubbles in vivo leads to topoisomerase-mediated formation of knots on partially replicated DNA molecules. (C) 1999 Academic Press.This work was supported by the Swiss National Science Foundation grants 31-52246.97 (to J.M.S) and 31-42158.94\ud
(to Jacques Dubochet and A.S.), and by grant 96/0470 from the Spanish Fondo de Investigacion Sanitaria, grant\ud
PM95/0016 from the Spanish Direccion General de Enseñanza Superior, and grant 08.6/0016/1997 from the Comunidad de Madrid, Spain.Peer reviewe
Chronic aspirin treatment affects collagen deposition in non-infarcted myocardium during remodeling after coronary artery ligation in the rat

Low-dose aspirin (acetylsalicylic acid; ASA), inhibiting platelet thromboxane production in favor of endothelium formation of prostaglandins, is successfully used as primary or secondary prophylaxis against myocardial infarction. Although prognosis may be improved, effects of long-term ASA treatment on wound healing and cardiac remodeling are not well understood. The aim of the present study was to mimic the clinical situation by inducing myocardial infarction in low-dose ASA (25 mg/kg/day, i.p.) pretreated rats, and to determine effects on plasma eicosanoid levels, cardiac hypertrophy and collagen deposition, and left ventricular function during continued ASA treatment. The effects of this dose were verified to selectively inhibit platelet thromboxane production, and lower plasma levels of thromboxane, but did not affect plasma levels of prostacyclin and prostaglandin E2during the acute inflammatory stage following myocardial infarction. As measured by heart dry weight/body weight, cardiac hypertrophy was not affected by ASA treatment. However, interstitial fibrosis in the spared myocardium as well as perivascular fibrosis, associated with infarction-induced cardiac remodeling, were affected by ASA treatment. Replacement fibrosis in the infarct itself, considered as representing wound healing, was not significantly influenced by ASA treatment. Wall thinning following infarction was not aggravated, nor did treatment influence left ventricular cavity diameter in a relaxed state. Results fromin vitroleft ventricular function measurements showed no effects on left ventricular peak velocity of contraction or relaxation after ASA treatment. In conclusion, although low-dose ASA may not be expected to have anti-inflammatory action, it did influence post-infarct cardiac remodeling by affecting interstitial and perivascular fibrosis. ASA treatment did not have effects onin vitroleft ventricular dysfunction