Arbitrage valuation and bounds for sinking-fund bonds with multiple sinking-fund dates

The paper tackles the problem of pricing, under interest-rate risk, a default-free sinking-fund bond which allows its issuer to recurrently retire part of the issue by (a) a lottery call at par, or (b) an open market repurchase. By directly modelling zero-coupon bonds as diffusions driven by a single-dimensional Brownian motion, a pricing formula is supplied for the sinking-fund bond based on a backward induction procedure which exploits, at each step, the martingale approach to the valuation of contingent-claims. With more than one sinking-fund date, however, the pricing formula is not in closed form, not even for simple parametrizations of the process for zerocoupon bonds, so that a numerical approach is needed. Since the computational complexity increases exponentially with the number of sinking-fund dates, arbitrage-based lower and upper bounds are provided for the sinking-fund bond price. The computation of these bounds is almost effortless when zero-coupon bonds are as described by Cox, Ingersoll and Ross. Numerical comparisons between the price of the sinking-fund bond obtained via Monte Carlo simulation and these lower and upper bounds are illustrated for different choices of parameters.     

A Homological Approach to Two Problems on Finite Sets

We propose a homological approach to two conjectures descended from the Erdös-Ko-Rado Theorem, one due to Chvátal and the other to Frankl and Füredi. We apply the method to reprove, and in one case improve, results of these authors related to their conjectures.     

Codimension one symplectic foliations and regular Poisson structures

In this short note we give a complete characterization of a certain class of compact corank one Poisson manifolds, those equipped with a closed one-form defining the symplectic foliation and a closed two-form extending the symplectic form on each leaf. If such a manifold has a compact leaf, then all the leaves are compact, and furthermore the manifold is a mapping torus of a compact leaf. These manifolds and their regular Poisson structures admit an extension as the critical hypersurface of a b-Poisson manifold as we will see in [9].     

Algebraic approach for the exploration of the onset of chaos in discrete nonlinear dynamical systems

An algebraic approach based on the rank of a sequence is proposed for the exploration of the onset of chaos in discrete nonlinear dynamical systems. The rank of the partial solution is identified and a special technique based on Hankel matrices is used to decompose the solution into algebraic primitives comprising roots of the modified characteristic equation. The distribution of roots describes the dynamical complexity of a solution and is used to explore properties of the nonlinear system and the onset of chaos.     

Molecular structure and benzene ring deformation of three ethynylbenzenes from gas-phase electron diffraction and quantum chemical calculations

The molecular structures of ethynylbenzene and s-triethynylbenzene have been accurately determined by gas-phase electron diffraction and ab initio/DFT MO calculations and are compared to that of p-diethynylbenzene from a previous study [Domenicano, A.; Arcadi, A.; Ramondo, F.; Campanelli, A. R.; Portalone, G.; Schultz, G.; Hargittai, I. J. Phys. Chem. 1996, 100, 14625]. Although the equilibrium structures of the three molecules have C2v, D3h, and D2h symmetry, respectively, the corresponding average structures in the gaseous phase are best described by nonplanar models of Cs, C3v, and C2v symmetry, respectively. The lowering of symmetry is due to the large-amplitude motions of the substituents out of the plane of the benzene ring. The use of nonplanar models in the electron diffraction analysis yields ring angles consistent with those from MO calculations. The molecular structure of ethynylbenzene reported from microwave spectroscopy studies is shown to be inaccurate in the ipso region of the benzene ring. The variations of the ring C-C bonds and C-C-C angles in p-diethynylbenzene and s-triethynylbenzene are well interpreted as arising from the superposition of independent effects from each substituent. In particular, experiments and calculations consistently show that the mean length of the ring C-C bonds increases by about 0.002 A per ethynyl group. MO calculations at different levels of theory indicate that though the length of the C[triple bond]C bond of the ethynyl group is unaffected by the pattern of substitution, the C(ipso)-C(ethynyl) bonds in p-diethynylbenzene are 0.001-0.002 A shorter than the corresponding bonds in ethynylbenzene and s-triethynylbenzene. This small effect is attributed to conjugation of the two substituents through the benzene ring. Comparison of experimental and MO results shows that the differences between the lengths of the C(ipso)-C(ethynyl) and C(ipso)-C(ortho) bonds in the three molecules, 0.023-0.027 A, are correctly computed at the MP2 and B3LYP levels of theory but are overestimated by a factor of 2 when calculated at the HF level.     

On large deviations for some sequences of weighted means of Gaussian processes

In this paper we study some sequences of weighted means of continuous real valued Gaussian processes. More precisely we consider suitable generalizations of both arithmetic and logarithmic means of a Gaussian process with covariance function which satisfies either an exponential decay condition or a power decay condition. Our aim is to provide limits of variances of functionals of such weighted means which allow the application of some large deviation results in the literature.     

Eigenvalue bounds for elliptic operators

Lower bounds for the real parts of the points in the spectrum of elliptic equations are derived. These bounds, depending only on the diameter L of the domain G and on the maximum norm M of the coefficients a, b, are optimal. They are always positive and thus the spectrum is bounded away from the imaginary axis. This result is then used to prove an “anti-dynamo theorem” for magnetic fields with plane symmetry in the case of a compressible steady flow surrounded by a perfect conductor.     

Molecular dynamics simulations on the local order of liquid and amorphous ZnTe

Molecular dynamics studies of structural and dynamical correlations of molten and vitreous states under several conditions of density and temperature were performed. We use an effective recently proposed interatomic potential, consisting of two- and three-body covalent interactions which has successfully described the structural, dynamical, and structural phase transformation induced by pressure in ZnTe [D. S. Borges and J. P. Rino, Phys. Rev. B 72, 014107 (2005)]. The two-body term of the interaction potential consists of Coulomb interaction resulting from charge transfer, steric repulsion due to atomic sizes, charge-dipole interaction to include the effect of electronic polarizability of anions, and dipole-dipole (van der Waals) interactions. The three-body covalent term is a modification of the Stillinger-Weber potential. Molecular dynamics simulations in isobaric-isenthalpic ensemble have been performed for systems amounting to 4096 and 64 000 particles. Starting from a crystalline zinc-blende (ZB) structure, the system is initially heated until a very homogeneous liquid is obtained. The vitreous zinc telluride phase is attained by cooling the liquid at sufficiently fast cooling rates, while slower cooling rates lead to a disordered ZB crystalline structure. Two- and three-body correlations for the liquid and vitreous phases are analyzed through pair distribution functions, static structure factors, and bond angle distributions. In particular, the neutron static structure factor for the liquid phase is in very good agreement with both the reported experimental data and first-principles simulations.