Noncommutativity Approach to Supersymmetry on the Lattice: SUSY Quantum Mechanics and an Inconsistency

It is argued that the noncommutativity approach to fully supersymmetric field theories on the lattice suffers from an inconsistency. Supersymmetric quantum mechanics is worked out in this formalism and the inconsistency is shown both in general and explicitly for that system, as well as for the Abelian super BF model.Comment: 8 pages, typo's corrected, conclusions unchange

On Multivariate Records from Random Vectors with Independent Components

Let $\boldsymbol{X}_1,\boldsymbol{X}_2,\dots$ be independent copies of a random vector $\boldsymbol{X}$ with values in $\mathbb{R}^d$ and with a continuous distribution function. The random vector $\boldsymbol{X}_n$ is a complete record, if each of its components is a record. As we require $\boldsymbol{X}$ to have independent components, crucial results for univariate records clearly carry over. But there are substantial differences as well: While there are infinitely many records in case $d=1$, there occur only finitely many in the series if $d\geq 2$. Consequently, there is a terminal complete record with probability one. We compute the distribution of the random total number of complete records and investigate the distribution of the terminal record. For complete records, the sequence of waiting times forms a Markov chain, but differently from the univariate case, now the state infinity is an absorbing element of the state space

Some Results on Joint Record Events

Let $X_1,X_2,\dots$ be independent and identically distributed random variables on the real line with a joint continuous distribution function $F$. The stochastic behavior of the sequence of subsequent records is well known. Alternatively to that, we investigate the stochastic behavior of arbitrary $X_j,X_k,j<k$, under the condition that they are records, without knowing their orders in the sequence of records. The results are completely different. In particular it turns out that the distribution of $X_k$, being a record, is not affected by the additional knowledge that $X_j$ is a record as well. On the contrary, the distribution of $X_j$, being a record, is affected by the additional knowledge that $X_k$ is a record as well. If $F$ has a density, then the gain of this additional information, measured by the corresponding Kullback-Leibler distance, is $j/k$, independent of $F$. We derive the limiting joint distribution of two records, which is not a bivariate extreme value distribution. We extend this result to the case of three records. In a special case we also derive the limiting joint distribution of increments among records

Semantic browsing of digital collections

Visiting museums is an increasingly popular pastime. Studies have shown that visitors can draw on their museum experience, long after their visit, to learn new things in practical situations. Rather than viewing a visit as a single learning event, we are interested in ways of extending the experience to allow visitors to access online resources tailored to their interests. Museums typically have extensive archives that can be made available online, the challenge is to match these resources to the visitor’s interests and present them in a manner that facilitates exploration and engages the visitor. We propose the use of knowledge level resource descriptions to identify relevant resources and create structured presentations. A system that embodies this approach, which is in use in a UK museum, is presented and the applicability of the approach to the broader semantic web is discussed

Observation of a Broad L=1 cqˉc\bar{q} State in B−→D∗+π−π−B^{-}\to D^{*+}\pi^{-}\pi^{-} at CLEO

Using 4.7 fb^-1 of data taken at CESR at energies at and near the Upsilon(4S) we have studied the decay B- -> D{*+}pi-pi- (and its conjugate). We observe a new, broad charmed meson state, which we interpret as D_J(j=1/2), in its decay to D{*+}pi-. Our preliminary results indicate the mass and width of this L=1 state to be m = (2461 +41/-3} +/-10 +/-32) MeV and Gamma = (290 +101/-79 +/-26 +/-36) MeV, with the third uncertainty associated with the parameterization of the relative strong phases. In addition we have measured several new branching fractions of charged B mesons. All quoted results are preliminary.Comment: 7 pages postscript, also available through http://w4.lns.cornell.edu/public/CLN

Mixed finite element methods for linear elasticity with weakly imposed symmetry

In this paper, we construct new finite element methods for the approximation of the equations of linear elasticity in three space dimensions that produce direct approximations to both stresses and displacements. The methods are based on a modified form of the Hellinger--Reissner variational principle that only weakly imposes the symmetry condition on the stresses. Although this approach has been previously used by a number of authors, a key new ingredient here is a constructive derivation of the elasticity complex starting from the de Rham complex. By mimicking this construction in the discrete case, we derive new mixed finite elements for elasticity in a systematic manner from known discretizations of the de Rham complex. These elements appear to be simpler than the ones previously derived. For example, we construct stable discretizations which use only piecewise linear elements to approximate the stress field and piecewise constant functions to approximate the displacement field.Comment: to appear in Mathematics of Computatio