Parametric linear programming techniques for the indefnite quadratic programming problem

In this paper, we discuss a multiparametric technique for findinga global minimum for an indefinite quadratic programming problembased on the spectral decomposition of the matrix of the quadraticform. Special attention is given to the case where this matrixhas only rank 1, where the multiparametric linear program turnsout to be a single-parameter linear program. An extension ofthe traditional linear parametric procedure is introduced whichin general solves this problem efficiently. However, an exampleis presented showing that this technique may take an exponentialnumber of steps.     

Determination of Densities of Liquids and Solids Using a Gas

An experiment for the determination of densities of solids and liquids is described. It uses Archimedes Principle with air as the fluid. It can be used in general and introductory physical chemistry courses as a regular laboratory experiment or as a demonstration. A typical calibration curve and the values of some densities measured using this method are given as examples.     

Vapour—liquid equilibrium of the square-well fluid of variable range via a hybrid simulation approach

The equilibrium between vapour and liquid in a square-well system has been determined by a hybrid simulation approach combining chemical potentials calculated via the Gibbs ensemble Monte Carlo technique with pressures calculated by the standard NVT Monte Carlo method. The phase equilibrium was determined from the thermodynamic conditions of equality of pressure and chemical potential between the two phases. The results of this hybrid approach were tested by independent NPT and μPT calculations and are shown to be of much higher accuracy than those of conventional GEMC simulations. The coexistence curves, vapour pressures and critical points were determined for SW systems of interaction ranges λ = 1.25, 1.5, 1.75 and 2. The new results show a systematic dependence on the range λ, in agreement with results from perturbation theory where previous work had shown more erratic behaviour.     

The vertical spectrum of H2CO revisited: (SC)2-CI and CC calculations

The vertical electronic spectrum of formaldehyde has been studied by means of (SC)²-MR-SDCI and CCLR methods. Two basis sets of atomic natural orbitals (ANOs) complemented with a one-centre series of Rydberg orbitals were used. The first was taken from the CASPT2 study by Merchán, M., and Roos, B. O., 1995, Theoret. Chim. Acta, 92, 221, and may be described as C,O[4s3pld]/H[2slp] with a lslpld Rydberg series centred in the charge centroid of the ²B₂ state of the cation. The second was a larger basis set that may be described as C,O[6s5p3d2f]/H[4s3p2d] + 3s3p3d in the same centre. The (SC)² dressing may be applied efficiently to an MR-SDCI method and comparison with the dressed CAS-SDCI is satisfactory, in spite of the remarkable reduction in the CI space dimension. The consistency of the (SC)²-MR-SDCI results was tested also against the CCLR and CASPT2 results using the same basis sets and against the CCLR results using Dunning's aug- and daug-cc-pVQZ basis sets. The ³A₁(π → π *) state is correctly placed as the second excited triplet while the highly multi-configurational nature of the ¹A₁(π → π *) state is confirmed as well as its greatly mixed valence-Rydberg nature. This state is predicted as lying under the 10 eV level, on top of the (n_y → 3d) Rydberg states that are predicted in the 8.9–9.5eV region. The 5 ¹B₂(n^y → 4s) Rydberg state and the ¹B₂(σ_y → π*) also are predicted in this region. The triplet states also were calculated with the (SC)²-MR-SDCI method. The vertical ordering of the 2 ¹A₁(n_y → 3p_y) and 2 ¹B₂(n_y → 3p_z) states is discussed, as well as that of the ¹B₁(σ → π*) and the Rydberg ¹B₁(n_y → 3d_xy) states. This work shows the highly reliable values that may be reached applying the dressing method along with a large basis set. Such a procedure is made possible using an MR-SDCI selection of spaces instead of the CAS-SDCI that was used up to now in most (SC)² dressing applications.     

On the low temperature anomalies in the properties of the electrochemical interface. A non-local free-energy density functional approach

The restricted primitive model has proved to be a useful system to describe the behaviour of electrical double layers. In this model, ions are represented by charged hard spheres of equal diameter and the solvent is represented by a uniform dielectric constant. Classical Gouy-Chapman's theory, and its modification by Stern, always predicts a monotonically decreasing capacitance for this system when the fluid's temperature is increased. Similar results are given by the mean spherical approximation. These predictions are in qualitative agreement with experiment for dissolved electrolytes, but disagree with molten salt experiments where capacitance increases with temperature. Additionally, recent Monte Carlo (MC) simulations for this model show that at very low temperatures, the capacitance of the interface, near its point of zero charge, increases with increasing temperature for both diluted and highly concentrated salts. In this work we apply a particular model of a non-local free-energy density functional theory to study the capacitance of the electrical interface. In our calculations we considered symmetrical 1:1 systems for both diluted electrolytes and highly concentrated salts at very low electrode surface charge. Density functional theory agrees very well with MC results for capacitance at high temperature, but fails to predict a positive slope for this property at low temperatures. Comparison of theoretical density profiles with MC results allows the exploration of possible causes of failure.     

The pseudo-Jahn—Teller effect: a CASSCF diagnostic

A simple test for the pseudo-Jahn-Teller effect is proposed, based on the behaviour of a CASSCF frequency calculation when symmetry is restricted. The test suggests that the pseudo-Jahn-Teller effect operates at the D_2h transition structure of S₀ pentalene and the D_8h transition structure of S₀ cyclooctatetraene. The D_4h transition structure of S₀ cyclooctatetraene is not subject to a pseudo-Jahn-Teller distortion according to this test. Our interpretation of the pseudo-Jahn-Teller effect differs from the conventional one based on a single-transition (CIS-like) approximation.     

Quasi diabatic CASSCF state functions

A new method to determine quasi diabatic (QD) CASSCF states is presented. The adiabatic states are subjected to a unitary transformation resulting from diagonalization of a state-selection operator. The latter is constructed from the overlap of the adiabatic states with a suitable set of reference states. The multi-state (MS) CASPT2 method is used to account for the dynamical correlation effects in an approach where the QD-CASSCF wave functions are used as reference states. The procedure is applied to avoided crossings in excited states of BeH, LiO and ozone. The advantages of the proposed formulation are discussed.     

Gabor Analysis on Finite Product of Cyclic Groups

We present a complete characterization of Gabor frame operators on finite dimensional Hilbert space $L^2(\Gamma)$, where $\Gamma = \mathbb{Z}_{m_1} \times \mathbb{Z}_{m_2} \times \dots \times \mathbb{Z}_{m_p}$ and $m_1,m_2,\dots,m_p$ are positive integers. The notion of generalized $B$-modulation and generalized $B$-translation is introduced and some significant properties of the generalized pseudo $B$-Gabor like frames are discussed.     

Therapy burden, drug resistance, and optimal treatment regimen for cancer chemotherapy

Email: boldrini{at}ime.unicamp.brAuthor to whom correspondence should be addressed. Email: michel{at}Incc.br Three nonlinear models of tumour cell growth under continuousdelivery of cycle nonspecific anticancer agents are studied.A dynamical optimization problem with the objective of minimizingthe final level of tumour cells is posed for these mathematicalsetups. The simplest setup does not possess toxicity constraints,whereas the other setups contain a dynamical equation describingthe therapy burden as a toxicity criterion. In addition, thethird setting contains the dynamics of drug resistant cells.A discussion conceming the optimal strategies of the respectivemodels is performed.