Essay: Supersymmetry, the Cosmological Constant, and a Theory of Quantum Gravity in Our Universe

There are many theories of quantum gravity, depending on asymptotic boundary conditions, and the amount of supersymmetry. The cosmological constant is one of the fundamental parameters that characterizes different theories. If it is positive, supersymmetry must be broken. A heuristic calculation shows that a cosmological constant of the observed size predicts superpartners in the TeV range. This mechanism for SUSY breaking also puts important constraints on low energy particle physics models.     

Morphological instability induced by the interaction of a particle with a solid-liquid interface

Motivated by recent experimental findings, we investigate the possible occurrence and characteristics of quasicrystalline order in two-dimensional mixtures of point dipoles with two sorts of dipole moments. Despite the fact that the dipolar interaction potential does not exhibit an intrinsic length scale and cannot be tuned a priori to support the formation of quasicrystalline order, we find that configurations with long-range quasicrystallinity yield minima in the potential energy surface of the many particle system. These configurations emanate from an ideal or perturbed ideal decoration of a binary tiling by steepest descent relaxation. Ground state energy calculations of alternative ordered states and parallel tempering Monte-Carlo simulations reveal that the quasicrystalline configurations do not correspond to a thermodynamically stable state. On the other hand, steepest descent relaxations and conventional Monte-Carlo simulations suggest that they are rather robust against fluctuations. Local quasicrystalline order in the disordered equilibrium states can be strong.Received: 15 September 2004, Published online: 26 November 2004PACS: 61.44.Br Quasicrystals - 75.50.Kj Amorphous and quasicrystalline magnetic materials - 82.70.Dd Colloids     

Enclosure results for quasilinear systems of variational inequalities

In this paper we consider systems of quasilinear elliptic variational inequalities, and prove the existence of minimal and maximal (in the set theoretical sense) solutions within some ordered interval of an appropriately defined pair of sub- and supersolutions. We show that the notion of sub- and supersolutions of variational inequalities introduced here is consistent with the usual notion of sub-supersolutions for (variational) equations. For weakly coupled quasimonotone systems of variational inequalities the existence of smallest and greatest solutions is proved.     

A priori estimates and existence of positive solutions for strongly nonlinear problems

In this paper we study the existence of positive solutions for a nonlinear Dirichlet problem involving the m-Laplacian. The nonlinearity considered depends on the first derivatives; in such case, variational methods cannot be applied. So, we make use of topological methods to prove the existence of solutions. We combine a blow-up argument and a Liouville-type theorem to obtain a priori estimates. Some Harnack-type inequalities which are needed in our reasonings are also proved.     

On a Result of R. Turner

We study the similarity of perturbed compact operators to operators of block-diagonal structure with respect to some family of orthogonal projection operators, which allows us to refine and essentially strengthen results due to R. Turner. We obtain information about the operator realizing the similarity transformation, present estimates for the eigenvalues and eigenvectors of the perturbed operator, and also study the inverse problem of spectral analysis.     

Unforeseen formation of 2-bromo-3-hydroxybenzaldehyde by bromination of 3-hydroxybenzaldehyde

Contrary to literature reports, bromination of 3-hydroxybenzaldehyde can afford both 2-bromo-5-hydroxybenzaldehyde and 2-bromo-3-hydroxybenzaldehyde, but 4-bromo-3-hydroxybenzaldehyde was not detected. 2-Bromo-3-hydroxybenzaldehyde was converted into 2-(benzyloxy)-1-bromo-5-methoxy-7-methylnaphthalene. X-ray crystallographic analysis supports the identity of 2-bromo-3-hydroxybenzaldehyde.     

Book rewiev

Howard Anton and Robert C. Busby, John Wiley & Sons, Inc., 2002.     

Sensitivity analysis of an optimized bar-spring model with hill-top branching

Summary Characteristics of optimal solutions under nonlinear buckling constraints are investigated by using a bar-spring model. It is demonstrated that optimization under buckling constraints of a symmetric system often leads to a structure with hill-top branching, where a limit point and bifurcation points coincide. A general formulation is derived for imperfection sensitivity of the critical load factor corresponding to a hill-top branching point. It is shown that the critical load is not imperfection-sensitive even for the case where an asymmetric bifurcation point exists at the limit point.     

Estimate for the Best Approximation of Summable Functions of Several Variables with a Certain Symmetry of Fourier Coefficients

An upper bound for the best approximation of summable functions of several variables by trigonometric polynomials in the metric of L is determined in terms of Fourier coefficients. We consider functions representable by trigonometric series with certain symmetry of coefficients satisfying a multiple analog of the Sidon–Telyakovskii conditions.