The Interpretation-Construction Distinction in Patent Law

The ambiguity of claim language is generally considered to be the most important problem in patent law today. Linguistic ambiguity is believed to cause tremendous uncertainty about patent rights. Scholars and judges have accordingly devoted enormous attention to developing better linguistic tools to help courts understand patent claims. In this article, we explain why this diagnosis is fundamentally wrong. Claims are not often ambiguous, and linguistic ambiguity is not a major cause of the uncertainty in patent law today. We shall explain what really causes the uncertainty in patent rights, how the erroneous diagnosis of linguistic ambiguity has led the literature off-track, and what will get us back on track to solving the uncertainty problem

Recombination of Shower Partons at High pTp_T in Heavy-Ion Collisions

A formalism for hadron production at high \pt in heavy-ion collisions has been developed such that all partons hadronize by recombination. The fragmentation of a hard parton is accounted for by the recombination of shower partons that it creates. Such shower partons can also recombine with the thermal partons to form particles that dominate over all other possible modes of hadronization in the $3<p_T<8$ GeV range. The results for the high \pt spectra of pion, kaon, and proton agree well with experiments. Energy loss of partons in the dense medium is taken into account on the average by an effective parameter by fitting data, and is found to be universal independent of the type of particles produced, as it should. Due to the recombination of thermal and shower partons, the structure of jets produced in nuclear collisions is different from that in $pp$ collisions. The consequence on same-side correlations is discussed.Comment: This revised version contains minor changes and a new figure

Interaction effects and phase relaxation in disordered systems

This paper is intended to demonstrate that there is no need to revise the existing theory of the transport properties of disordered conductors in the so-called weak localization regime. In particular, we demonstrate explicitly that recent attempts to justify theoretically that the dephasing rate (extracted from the magnetoresistance) remains finite at zero temperature are based on the profoundly incorrect calculation. This demonstration is based on a straightforward evaluation of the effect of the electron-electron interaction on the weak localization correction to the conductivity of disordered metals. Using well-controlled perturbation theory with the inverse conductance $g$ as the small parameter, we show that this effect consists of two contributions. First contribution comes from the processes with energy transfer smaller than the temperature. This contribution is responsible for setting the energy scale for the magnetoresistance. The second contribution originates from the virtual processes with energy transfer larger than the temperature. It is shown that the latter processes have nothing to do with the dephasing, but rather manifest the second order (in $1/g$) correction to the conductance. This correction is calculated for the first time. The paper also contains a brief review of the existing experiments on the dephasing of electrons in disordered conductors and an extended qualitative discussion of the quantum corrections to the conductivity and to the density of electronic states in the weak localization regime.Comment: 34 pages, 13 .eps figure

Effective gauge field theory of the t-J model in the charge-spin separated state and its transport properties

We study the slave-boson t-J model of cuprates with high superconducting transition temperatures, and derive its low-energy effective field theory for the charge-spin separated state in a self-consistent manner. The phase degrees of freedom of the mean field for hoppings of holons and spinons can be regarded as a U(1) gauge field, $A_i$. The charge-spin separation occurs below certain temperature, $T_{\rm CSS}$, as a deconfinement phenomenon of the dynamics of $A_i$. Below certain temperature $T_{\rm SG} (< T_{\rm CSS})$, the spin-gap phase develops as the Higgs phase of the gauge-field dynamics, and $A_i$ acquires a mass $m_A$. The effective field theory near $T_{\rm SG}$ takes the form of Ginzburg-Landau theory of a complex scalar field $\lambda$ coupled with $A_i$, where $\lambda$ represents d-wave pairings of spinons. Three dimensionality of the system is crucial to realize a phase transition at $T_{\rm SG}$. By using this field theory, we calculate the dc resistivity $\rho$. At $T > T_{\rm SG}$, $\rho$ is proportional to $T$. At $T < T_{\rm SG}$, it deviates downward from the $T$-linear behavior as $\rho \propto T \{1 -c(T_{\rm SG}-T)^d \}$. When the system is near (but not) two dimensional, due to the compactness of the phase of the field $\lambda$, the exponent $d$ deviates from its mean-field value 1/2 and becomes a nonuniversal quantity which depends on temperature and doping. This significantly improves the comparison with the experimental data

Shearlets and Optimally Sparse Approximations

Multivariate functions are typically governed by anisotropic features such as edges in images or shock fronts in solutions of transport-dominated equations. One major goal both for the purpose of compression as well as for an efficient analysis is the provision of optimally sparse approximations of such functions. Recently, cartoon-like images were introduced in 2D and 3D as a suitable model class, and approximation properties were measured by considering the decay rate of the $L^2$ error of the best $N$-term approximation. Shearlet systems are to date the only representation system, which provide optimally sparse approximations of this model class in 2D as well as 3D. Even more, in contrast to all other directional representation systems, a theory for compactly supported shearlet frames was derived which moreover also satisfy this optimality benchmark. This chapter shall serve as an introduction to and a survey about sparse approximations of cartoon-like images by band-limited and also compactly supported shearlet frames as well as a reference for the state-of-the-art of this research field.Comment: in "Shearlets: Multiscale Analysis for Multivariate Data", Birkh\"auser-Springe

Bethe-Salpeter study of radially excited vector quarkonia

We solve the Bethe-Salpeter equation (BSE) for a system of a heavy quark-antiquark pair interacting with a Poincare invariant generalization of screened linear confining potential. In order to get reliable description the Lorentz scalar confining interaction is complemented by the effective one gluon exchange. Within presented model we reasonably reproduce all known radial excitations of the vector charmonia. We have found that $J/\Psi$ is the only charmonium left bellow naive quark-antiquark threshold $2m_c$, while the all excited states are situated above this threshold. We develop a method which is enable to provide solution of full four dimensional BSE for the all excited states. We discuss the consequences of the use of the free propagators for calculation of excited states above the threshold. The Bethe-Salpeter string breaking scale $\mu\simeq 350MeV$ appears to be relatively larger then the one defined in various potential models $\mu\simeq 150MeV$.Comment: typos and grammar correcte