Abstract:
In this paper we study the existence result of classical solutions for the quasilinear equation utt ￠ ’ ”u ￠ ’M( ￠ | ￠ u|2dx) ”utt=f, with initial data u(0)=u0, u(1)=u1 and homogeneous boundary conditions.

Abstract:
A metric vector space is asymptotically metrically normable (AMN) if there exists a norm asymptotically isometric to the distance. We prove that AMN vector spaces are rigid in the class of metric vector spaces under asymptotically isometric perturbations. This result follows from a general metric normability criterium. If the distance is translation invariant and satisfies an approximate multiplicative condition then there exists a lipschitz equivalent norm. Furthermore, we give necessary and sufficient conditions for the distance to be asymptotically isometric to the norm.

Abstract:
In this article, we consider a nonlinear transmission problem for the wave equation with time dependent coefficients and linear internal damping. We prove the existence of a global solution and its exponential decay. The result is achieved by using the multiplier technique and suitable unique continuation theorem for the wave equation.

Abstract:
We review the optimal protocols for aligning spatial frames using quantum systems. The communication problem addressed here concerns a type of information that cannot be digitalized. Asher Peres referred to it as "unspeakable information". We comment on his contribution to this subject and give a brief account of his scientific interaction with the authors.

Abstract:
In this work we propose a car cellular automaton model that reproduces the experimental behavior of traffic flows in Bogot\'a. Our model includes three elements: hysteresis between the acceleration and brake gaps, a delay time in the acceleration, and an instantaneous brake. The parameters of our model were obtained from direct measurements inside a car on motorways in Bogot\'a. Next, we simulated with this model the flux-density fundamental diagram for a single-lane traffic road and compared it with experimental data. Our simulations are in very good agreement with the experimental measurements, not just in the shape of the fundamental diagram, but also in the numerical values for both the road capacity and the density of maximal flux. Our model reproduces, too, the qualitative behavior of shock waves. In addition, our work identifies the periodic boundary conditions as the source of false peaks in the fundamental diagram, when short roads are simulated, that have been also found in previous works. The phase transition between free and congested traffic is also investigated by computing both the relaxation time and the order parameter. Our work shows how different the traffic behavior from one city to another can be, and how important is to determine the model parameters for each city.

Abstract:
We classify complex projective varieties of dimension $2r \geq 8$ swept out by a family of codimension two grassmannians of lines $\mathbb{G}(1,r)$. They are either fibrations onto normal surfaces such that the general fibers are isomorphic to $\G(1,r)$ or the grassmannian $\mathbb{G}(1,r+1)$. The cases $r=2$ and $r=3$ are also considered in the more general context of varieties swept out by codimension two linear spaces or quadrics.

Abstract:
For a balanced cardcounting system we study the random variable of the true count after a number of cards are removed from the remaining deck and we prove a close formula for its standard deviation. As expected, the formula shows that the standard deviation increases with the number of cards removed. This creates a "standard deviation effect" with a two fold consequence: longer long run and presumably larger fluctuations of the bankroll, but a small gain in playing accuracy for the player sitting third base. The opposite happens for the player sitting first base. Thus the optimal position in casino blackjack in terms of shorter long run is first base.

Abstract:
In this paper Hopf bifurcation control is
implemented in order to change the bifurcation from supercritical to
subcritical in a differential equations system of Lorenz type. To achieve this
purpose: first, a region of parameters is identified where the system has a
supercritical Hopf bifurcation; second, a class of non-linear feedback control
laws is proposed; finally, it is shown that
there are control laws which the disturbed system undergoes subcritical Hopf
bifurcation.

Abstract:
The neutralino-nucleon cross section in the context of the MSSM with universal soft supersymmetry-breaking terms is compared with the limits from dark matter detectors. Our analysis is focussed on the stability of the corresponding cross sections with respect to variations of the initial scale for the running of the soft terms, finding that the smaller the scale is, the larger the cross sections become. For example, by taking $10^{10-12}$ GeV rather than $M_{GUT}$, which is a more sensible choice, in particular in the context of some superstring models, we find extensive regions in the parameter space with cross sections in the range of $10^{-6}$--$10^{-5}$ pb, i.e. where current dark matter experiments are sensitive. For instance, this can be obtained for $\tan\beta\gsim 3$.

Abstract:
We use simple comparisons of the optical and radio properties of the wide separation (3'' to 10'') quasar pairs to demonstrate that they are binary quasars rather than gravitational lenses. The most likely model is that all the pairs are binary quasars, with a one-sided 2--sigma (1--sigma) upper limit of 22% (8%) on the lens fraction. Simple models for the expected enhancement of quasar activity during galaxy mergers that are consistent with the enhancement observed at low redshift can explain the incidence, separations, redshifts, velocity differences, and radio properties of the binary quasar population. Only a modest fraction (< 5%) of all quasar activity need be associated with galaxy mergers to explain the binary quasars.