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.     

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.     

Linear Relationships for Constrained Multiple-item Inventory Systems

Inventory control is a problem common to many businesses andmanufacturing systems. Management spends a fair amount of timetrying to determine appropriate inventory policies. The firstinventory model, which is still used widely today, is the economicorder quantity (EOQ) model of Harris. This model, however, doesnot consider constraints on the problem such as storage capacityor budget Limitations. It is the purpose of this paper to examinethe multiple-item deterministic inventory system with one linearconstraint, and establish linear relationships between the Lagrangemultiplier of the constrgint and artain system characteristics.It is then discussed how the insights from these relationshipscan be used to provide tight hunds to the optimal multiplier.Computational results for these bounds are also included.     

An Ergodic Control Problem for Reflected Diffusion with Jump

The control of the drift of a stochastic differential equationwith jump term is considered for the long-run average cost.The convergence of the discounted problem is studied, as wellas the corresponding dynamic programming condition. This research was supported in part by U.S. Army Research Officeunder contract DAAG29-83-K-0014 and completed during a visitto INRIA.     

Metropolitan Optical Networks: When to Change to DWDM

In this article we propose a new methodology to estimate the change in the bandwidth demand in time, mainly in residential areas. The bandwidth demand forecast is a basic aspect to decide the evolution of metropolitan optical networks. The word evolution refers to the necessity of making changes in networks, either by upgrading or replacing different elements that are part of the network. This analysis, along with a technological alternatives analysis, provides the operator the needed information to achieve the appropriate network planning and to make investment decisions.     

Bis(salicylaldiminate) copper(II) and palladium(II) complexes: towards columnar mesophases

Copper and palladium complexes of new salicylaldimines derived from 3,4,5-tridecyloxyaniline, 2,3,4-tridecyloxyaniline and 4-decyloxyaniline have been synthesized and characterized. All the ligands bear four or more aliphatic chains with the aim of inducing columnar mesophases at low temperatures. In particular, metal complexes derived from 4-(3,4,5-tridecyloxybenzoyloxy)-salicyliden-3,4,5-tridecyloxyaninile display rectangular columnar mesophases at (or near) room temperature. These mesophase assignments have been confirmed by X-ray diffraction. A significant decrease of the melting points of the compounds is observed in the tridecyloxyaniline derivatives compared with those of similar complexes derived from mono- or di-decyloxyaniline.