28,645 research outputs found
Note on the practical significance of the Drazin inverse
The solution of the differential system Bx = Ax + f where A and B are n x n matrices, and A - Lambda B is not a singular pencil, may be expressed in terms of the Drazin inverse. It is shown that there is a simple reduced form for the pencil A - Lambda B which is adequate for the determination of the general solution and that although the Drazin inverse could be determined efficiently from this reduced form it is inadvisable to do so
Amplification of High Harmonics Using Weak Perturbative High Frequency Radiation
The mechanism underlying the substantial amplification of the high-order
harmonics q \pm 2K (K integer) upon the addition of a weak seed XUV field of
harmonic frequency q\omega to a strong IR field of frequency \omega is analyzed
in the framework of the quantum-mechanical Floquet formalism and the
semiclassical re-collision model. According to the Floquet analysis, the
high-frequency field induces transitions between several Floquet states and
leads to the appearance of new dipole cross terms. The semiclassical
re-collision model suggests that the origin of the enhancement lies in the
time-dependent modulation of the ground electronic state induced by the XUV
field.Comment: 8 pages, 2 figure
In Defense of American Criminal Justice
The American criminal justice system is on trial. A chorus of commentators-often but not exclusively in the legal academy-has leveled a sharp indictment of criminal process in our country. The indictment charges that large flaws infect nearly every stage of the adjudicatory process. And the prescriptions are equally far-reaching, with calls for abolition of many current practices and an overhaul of the entire system. What is more, the critics issue their condemnations essentially as givens, often claiming that all reasonable people could not help but agree that fair treatment of the accused has been fatally compromised. For these critics, We live in a time of sharply decreasing faith in the criminal justice system. \u27
As a judge with faith in that system, I am dismayed by the relentless insistence that we have it all wrong. Of course the system, like all human institutions, has its share of flaws. But the attacks have overshadowed what is good about the system and crowded out more measured calls for reform. The critics claim that major aspects of American criminal justice work to the detriment of defendants, when actually the reverse is often true. It is time for a more balanced view of our criminal process, which in fact gets a lot of things right.
A brief word as to the scope of this Essay. I have focused mainly on the adjudicatory process and on the criminal trial. I have not sought to explore police investigatory procedure on the one hand, or issues of detention and incarceration on the other, except insofar as they bear on the adjudicatory process in some way. They are vast topics in themselves, and the terrain I have covered is large enough. My own reaction to the critics is one of gratitude for their contributions but dismay that they have allowed the pursuit of perfection in criminal justice to become the enemy of the good. Much about American criminal justice is indeed good. The system provides considerable protections for the accused and sets proper limits on the brutality and deceit that human beings can inflict upon each other. Simply put, in calling for an overhaul of our criminal law and procedure, the critics have failed to appreciate the careful balance our criminal justice system strikes between competing rights and values. They have failed to respect the benefits of the system\u27s front-end features-namely, early process and early resolution. Moreover, they have sold short the democratic virtues of our system. The sensible tradeoffs reflected in American criminal justice are worthy of respect, and the system\u27s democratic tilt is deserving of praise. The critics have extended neither. Ultimately, the often harsh tone of their indictment has done an injustice to the system of criminal justice itself
Tridiagonal realization of the anti-symmetric Gaussian -ensemble
The Householder reduction of a member of the anti-symmetric Gaussian unitary
ensemble gives an anti-symmetric tridiagonal matrix with all independent
elements. The random variables permit the introduction of a positive parameter
, and the eigenvalue probability density function of the corresponding
random matrices can be computed explicitly, as can the distribution of
, the first components of the eigenvectors. Three proofs are given.
One involves an inductive construction based on bordering of a family of random
matrices which are shown to have the same distributions as the anti-symmetric
tridiagonal matrices. This proof uses the Dixon-Anderson integral from Selberg
integral theory. A second proof involves the explicit computation of the
Jacobian for the change of variables between real anti-symmetric tridiagonal
matrices, its eigenvalues and . The third proof maps matrices from the
anti-symmetric Gaussian -ensemble to those realizing particular examples
of the Laguerre -ensemble. In addition to these proofs, we note some
simple properties of the shooting eigenvector and associated Pr\"ufer phases of
the random matrices.Comment: 22 pages; replaced with a new version containing orthogonal
transformation proof for both cases (Method III
A quantum Peierls-Nabarro barrier
Kink dynamics in spatially discrete nonlinear Klein-Gordon systems is
considered. For special choices of the substrate potential, such systems
support continuous translation orbits of static kinks with no (classical)
Peierls-Nabarro barrier. It is shown that these kinks experience, nevertheless,
a lattice-periodic confining potential, due to purely quantum effects anaolgous
to the Casimir effect of quantum field theory. The resulting ``quantum
Peierls-Nabarro potential'' may be calculated in the weak coupling
approximation by a simple and computationally cheap numerical algorithm, which
is applied, for purposes of illustration, to a certain two-parameter family of
substrates.Comment: 13 pages LaTeX, 7 figure
Crystallization and preliminary crystallographic analysis of the DNA gyrase B protein from B-stearothermophilus
DNA gyrase B (GyrB) from B. stearothermophilus has been crystallized in the presence of the non-hydrolyzable ATP analogue, 5'-adenylpl-beta-gamma-imidodiphosphate (ADPNP), by the dialysis method. A complete native data set to 3.7 Angstrom has been collected from crystals which belonged to the cubic space group I23 with unit-cell dimension a = 250.6 Angstrom. Self-rotation function analysis indicates the position of a molecular twofold axis. Low-resolution data sets of a thimerosal and a selenomethionine derivative have also been analysed. The heavy-atom positions are consistent with one dimer in the asymmetric unit
- …