Optimal control of advertising and production of a seasonal product with nondifferentiable demand

We consider an application of optimal control theory to a marketing problem, in which a firm seeks the maximum profit by producing and selling a seasonal product. We assume that the firm can advertise its product in order to improve the firm goodwill and affect the product demand positively. In particular the demand is zero when the goodwill is less than a fixed threshold. The original optimal control problem is shown to be equivalent to a nonlinear programming problem, which has an optimal solution, possibly not unique. Editor: G. Leitmann     

Preparation and physico-chemical characterisation of microporous polysaccharidic hydrogels

A new technique to obtain microporous hydrogels was realised. It permits us to obtain a microporous structure directly on the already cross-linked hydrogel. It consists in stratifying the already cross-linked hydrogel on to a filter with known porosity and forcing the CO2 bubbles, derived from the addition of HCl to a porogen salt (NaHCO3), to cross through the filter first and then the matrix. By changing the porosity of the filter, it was possible to modulate the porous morphology of the hydrogels. The polysaccharides selected were hyaluronane, alginate, and carboxymethylcellulose. The influence of the porous morphology on the physico-chemical properties of the gel has been evaluated by FT-IR, FRAP, calorimetric, water uptake, and rheological analysis.     

DVR3D: a program suite for the calculation of rotation-vibration spectra of triatomic molecules

The DVR3D program suite calculates energy levels, wavefunctions, and where appropriate dipole transition moments, for rotating and vibrating triatomic molecules. Potential energy and, where necessary, dipole surfaces must be provided. Expectation values of geometrically defined functions can be calculated, a feature which is particularly useful for fitting potential energy surfaces. The programs use an exact (within the Born-Oppenheimer approximation) Hamiltonian and offer a choice of Jacobi or Radau internal coordinates and several body-fixed axes. Rotationally excited states are treated using an efficient two-step algorithm. The programs uses a Discrete Variable Representation (DVR) based on Gauss-Jacobi and Gauss-Laguerre quadrature for all 3 internal coordinates and thus yields a fully point-wise representation of the wavefunctions. The vibrational step uses successive diagonalisation and truncation which is implemented for a number of possible coordinate orderings. The rotational, expectation value and transition dipole programs exploit the savings offered by performing integrals on a DVR grid. The new version has been rewritten in FORTRAN 90 to exploit the dynamic array allocations and the algorithm for dipole and spectra calculations have been substantially improved. New modules allow the z-axis to be embedded perpendicular to the plane of the molecule and for the calculation of expectation values.

Program summary

Title of the program: DVR3D suiteCatalogue number: ADTIProgram summary URL:http://cpc.cs.qub.ac.uk/summaries/ADTIProgram obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandProgramming language: Fortran 90No. of lines in distributed program, including test data, etc.: 61 574No. of bytes in distributed program, including test data, etc.: 972 404Distribution format: tar.gz

New version summary

Title of program: DVR3DRJZCatalogue number: ADTBProgram summary URL:http://cpc.cs.qub.ac.uk/summaries/ADTBProgram obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandReference in CPC to previous version: 86 (1995) 175Catalogue identifier of previous version: ADAKAuthors of previous version: J. Tennyson, J.R. Henderson and N.G. FultonDoes the new version supersede the original program?: DVR3DRJZ supersedes DVR3DRJComputer: PC running LinuxInstallation: desktopOther machines on which program tested: Compaq running True64 Unix; SGI Origin 2000, Sunfire V750 and V880 systems running SunOS, IBM p690 Regatta running AIXProgramming language used in the new version: Fortran 90Memory required to execute: case dependentNo. of lines in distributed program, including test data, etc.: 4203No. of bytes in distributed program, including test data, etc.: 30 087Has code been vectorised or parallelised?: The code has been extensively vectorised. A parallel version of the code, PDVR3D has been developed [1], contact the first author for detailsAdditional keywords: perpendicular embeddingDistribution format: gzNature of physical problem: DVR3DRJZ calculates the bound vibrational or Coriolis decoupled rotational-vibrational states of a triatomic system in body-fixed Jacobi (scattering) or Radau coordinates [2]Method of solution: All coordinates are treated in a discrete variable representation (DVR). The angular coordinate uses a DVR based on (associated) Legendre polynomials and the radial coordinates utilise a DVR based on either Morse oscillator-like or spherical oscillator functions. Intermediate diagonalisation and truncation is performed on the hierarchical expression of the Hamiltonian operator to yield the final secular problem. DVR3DRJ provides the vibrational wavefunctions necessary for ROTLEV3, ROLEV3B or ROTLEV3Z to calculate rotationally excited states, DIPOLE3 to calculate rotational-vibrational transition strengths and XPECT3 to compute expectation valuesRestrictions on the complexity of the problem: (1) The size of the final Hamiltonian matrix that can practically be diagonalised. (2) The order of integration in the radial coordinates that can be dealt with within the machine exponent range. Some adjustment in the code may be necessary when large order Gauss-Laguerre quadrature is usedTypical running time: Case dependent but usually dominated by the final (3D) matrix diagonalisation. The test runs take minutes on a fast PCUnusual features of the program: A user supplied subroutine containing the potential energy as an analytic function is a program requirementReferences:

[1]

H.Y. Mussa, J. Tennyson, Comput. Phys. Commun. 128 (2000) 434.

[2]

J. Tennyson, B.T. Sutcliffe, Internat. J. Quantum Chem. 42 (1992) 941.

New version summary

Title of program: ROTLEV3Catalogue number: ADTCProgram summary URL:http://cpc.cs.qub.ac.uk/summaries/ADTCProgram obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandReference in CPC to previous version: 86 (1995) 175Catalogue identifier of previous version: ADALAuthors of previous version: J. Tennyson, J.R. Henderson and N.G. FultonDoes the new version supersede the original program?: YesComputer: PC running LinuxInstallation: desktopOther machines on which program tested: Compaq running True64 Unix; SGI Origin 2000, Sunfire V750 and V880 systems running SunOSProgramming language used: Fortran 90High speed storage required: case dependentNo. of lines in distributed program, including test data, etc.: 1514No. of bytes in distributed program, including test data, etc.: 12 652Has code been vectorised or parallelised?: The code has been extensively vectorised. A parallel version of the code, PROTLEV3 has been developed [1], contact the first author for detailsDistribution format: gzNature of physical problem: ROTLEV3 performs the second step in a two-step variational calculation for the bound rotational-vibrational levels of a triatomic system represented in either Jacobi or unsymmetrised Radau coordinatesMethod of solution: A basis is constructed from the solutions of the Coriolis decoupled problem provided by DVR3DRJZ. The angular coordinate is transformed back to a basis set representation. The sparse Hamiltonian matrix can be diagonalised iteratively or in coreRestrictions on the complexity of the problem: The size of matrix that can practically be diagonalisedTypical running time: Case dependent. The sample data takes less than a minute on a fast PCUnusual features of the program: Most data is read directly from DVR3DRJZ. ROTLEV3 can provide data to drive DIPOLE3 and/or XPECT3References: [1] H.Y. Mussa, J. Tennyson, Comput. Phys. Commun. 128 (2000) 434.

New version summary

Title of program: ROTLEV3BCatalogue number: ADTDProgram summary URL:http://cpc.cs.qub.ac.uk/summaries/ADTDProgram obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandReference in CPC to previous version: 86 (1995) 175Catalogue identifier of previous version: ADAMAuthors of previous version: J. Tennyson, J.R. Henderson and N.G. FultonDoes the new version supersede the original program?: YesComputer: PC running LinuxInstallation: desktopOther machines on which program tested: Compaq running True64 Unix, Sunfire V750 and V880 systems running SunOSProgramming language used: Fortran 90High speed storage required: case dependentNo. of lines in distributed program, including test data, etc.: 2215No. of bytes in distributed program, including test data, etc.: 16 595Has code been vectorised or parallelised?: The code has been extensively vectorised. A parallel version of the code, PROTLEV3B has been developed [1], contact the first author for detailsDistribution format: gzNature of physical problem: ROTLEV3B performs the second step in a two-step variational calculation for the bound rotational-vibrational levels of a triatomic system represented by symmetrised Radau coordinates using a bisector embedding [2]Method of solution: A basis is constructed from the solutions of the Coriolis decoupled problem provided by DVR3DRJZ. The problem is constructed entirely within the DVR. The Hamiltonian matrix can be diagonalised iteratively or in coreRestrictions on the complexity of the problem: The size of matrix that can practically be diagonalisedTypical running time: Case dependent. The sample data takes a few minutes on a fast PCUnusual features of the program: Most data is read directly from DVR3DRJZ. ROTLEV3B can provide data to drive DIPOLE3 and/or XPECT3References:

[1]

H.Y. Mussa, J. Tennyson, Comput. Phys. Commun. 128 (2000) 434.

[2]

J. Tennyson, B.T. Sutcliffe, Internat. J. Quantum Chem. 42 (1992) 941.

Program summary

Title of program: ROTLEV3ZCatalogue number: ADTEProgram summary URL:http://cpc.cs.qub.ac.uk/summaries/ADTEProgram obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandComputer: PC running LinuxInstallation: desktopOther machines on which program tested: Compaq running True64 Unix, Sunfire V750 and V880 systems running SunOSProgramming language used: Fortran 90High speed storage required: case dependentNo. of lines in distributed program, including test data, etc.: 2919No. of bytes in distributed program, including test data, etc.: 17 241Keywords: rotationally excited state, Coriolis coupling, secondary variational method, sparse matrix, vectorised, perpendicular embedding, Radau coordinatesHas code been vectorised or parallelised?: The code has been extensively vectorisedDistribution format: gzNature of physical problem: ROTLEV3Z performs the second step in a two-step variational calculation for the bound rotational-vibrational levels of a triatomic system represented by symmetrised Radau coordinates using a perpendicular embedding [1]Method of solution: A basis is constructed from the solutions of the Coriolis decoupled problem provided by DVR3DRJZ. The problem is constructed entirely within the DVR. The Hamiltonian matrix is diagonalised in coreRestrictions on the complexity of the problem: The size of matrix that can practically be diagonalisedTypical running time: Case dependent. The sample data takes a few minutes on a fast PCUnusual features of the program: Most data is read directly from DVR3DRJZReferences: [1] M.A. Kostin, O.L. Polyansky, J.Tennyson, J. Chem. Phys. 116 (2002) 7564.

New version summary

Title of program: DIPOLE3Catalogue number: ADTFProgram summary URL:http://cpc.cs.qub.ac.uk/summaries/ADTFProgram obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandReference in CPC to previous version: 86 (1995) 175Catalogue identifier of previous version: ADANAuthors of previous version: J. Tennyson, J.R. Henderson and N.G. FultonDoes the new version supersede the original program?: YesComputer: PC running LinuxInstallation: desktopOther machines on which program tested: Compaq running True64 Unix; SGI Origin 2000; sunfire V750 and V880 systemsProgramming language used: Fortran 90High speed storage required: case dependentNo. of lines in distributed program, including test data, etc.: 1921No. of bytes in distributed program, including test data, etc.: 15 685Has code been vectorised or parallelised?: The code has been extensively vectorised. Commands to parallelise the code using OpenMP are included in the sourceDistribution format: gzNature of physical problem: DIPOLE3 calculates dipole transition intensities between previously calculated wavefunction for both rotational and rotational-vibrational transitionsMethod of solution: Integrals over dipole surfaces are constructed using a DVR in all three coordinates, this requires a transformation of the angular wavefunctions. Wavefunctions generated by DVR3DRJZ and ROTLEV3 or ROTLEV3B are then used to give transition intensities for individual pairs of statesRestrictions on the complexity of the problem: The complexity of the problem that can be solved by DVR3DRJZ, ROTLEV3 or ROTLEV3BTypical running time: Case dependent. The test data takes a few seconds on a fast PCUnusual features of the program: Most data is read directly from DVR3DRJZ and ROTLEV3 or ROTLEV3B. DIPOLE provides data to drive SPECTRA

New version summary

Title of program: SPECTRACatalogue number: ADTGProgram summary URL:http://cpc.cs.qub.ac.uk/summaries/ADTGProgram obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandComputer: PC running LinuxInstallation: desktopOther machines on which program tested: Compaq running True64 UnixReference in CPC to previous version: 75 (1993) 339Catalogue identifier of previous version: ACNBAuthors of previous version: J. Tennyson, S. Miller and C.R. Le SueurDoes the new version supersede the original program?: YesProgramming language used: Fortran 90High speed storage required: case dependentNo. of lines in distributed program, including test data, etc.: 1037No. of bytes in distributed program, including test data, etc.: 9159Has code been vectorised or parallelised?: As execution times are very short this is usually not importantDistribution format: gzNature of physical problem: SPECTRA generates synthetic, frequency ordered spectra as a function of temperature. Absolute intensities can be calculated if the necessary data to calculate the partition function is suppliedMethod of solution: Transitions are sorted by frequency and weighted using Boltzmann statisticsRestrictions on the complexity of the problem: The complexity of problem that can be solved by other programs in the suiteTypical running time: Case dependent, but very small for sample dataUnusual features of the program: Most data is read directly from DIPOLE3. Some data from DVR3DRJZ and ROTLEV3 or ROTLEV3B may also be required

Program summary

Title of program: XPECT3Catalogue number: ADTHProgram summary URL:http://cpc.cs.qub.ac.uk/summaries/ADTHProgram obtainable from: CPC Program Library, Queen's University of Belfast, N. IrelandComputer: PC running LinuxInstallation: desktopOther machines on which program tested: Compaq running True64 UnixProgramming language used: Fortran 90High speed storage required: case dependentNo. of lines in distributed program, including test data, etc.: 1214No. of bytes in distributed program, including test data, etc.: 9361Distribution format: gzKeywords: Expectation values, Hellmann-Feynman theorem, potential fittingHas code been vectorised or parallelised?: The code has been extensively vectorisedNature of physical problem: XPECT3 calculates expectation of geometrically defined operators using previously calculated wavefunctionsMethod of solution: Integrals over the user defined surfaces are constructed using a DVR in all three coordinates. Wavefunctions generated by DVR3DRJZ and ROTLEV3 or ROTLEV3B are then used to give expectation values for each stateRestrictions on the complexity of the problem: The complexity of problem that can be solved by DVR3DRJZ, ROTLEV3 or ROTLEV3BTypical running time: Case dependent. The test data takes a few seconds on a fast PCUnusual features of the program: Most data is read directly from DVR3DRJZ and ROTLEV3 or ROTLEV3B.     

JIDE: a new software for computer-aided design of hip prosthesis

This work is aimed at developing an innovative simulation environment supporting and improving the design of standard joint implants (JPD integrated design environment (JIDE)). The conceptual workflow starts from the design of a new implant, by using conventional CAD programmes and completes with the generation of a report that summarises the goodness for a new implant against a database of human bone anatomies. For each dataset in the database, the JPD application calculates a set of quantitative indicators that will support the designer in the evaluation of its design on a statistical basis. The resulting system is thus directed to prostheses manufacturers and addresses a market segment that appears to have a steady growth in the future.     

A goal-driven and agent-based requirements engineering framework*

The paper presents a requirements engineering framework (REF), where advanced requirements engineering techniques are combined with software quality modelling approaches to provide an environment within which the stakeholders and the analysts can easily cooperate to discover, organise, reconcile and validate the requirements for a new system. By adopting a basic and essential graphical notation, and a clear top-down methodology, REF allows for an effective involvement of the stakeholders, assisting and driving them to an early definition of the desired system's functionalities and quality attributes, while supporting the redesign of the encompassing organisational context to better exploit the new system's capabilities. As a case study, REF is applied to support the requirements engineering process for a complex software-intensive simulation system. Results demonstrate the feasibility of REF and the benefits it offers to the requirements engineering process, but also to the subsequent system development phases. As illustrated through the case study REF can, in fact, be usefully applied as a forerunner for unified modelling language (UML)-based approaches.*Part of this work was completed while the author was Senior Research Fellow with the Computing Information Systems Engineering Group, at the Royal Military College of Science, Cranfield University (UK)     

Algorithm for the retrieval of columnar water vapor from hyperspectral remotely sensed data

A new algorithm for the retrieval of columnar water vapor content is presented. The proposed procedure computes the area of the H2O absorption centered about 940 nm to allow its integrated columnar abundance as well as its density at ground level to be assessed. The procedure utilizes the HITRAN 2000 database as the source of H2O cross-section spectra. Experimental results were derived from radiometrically calibrated hyperspectral images collected by the Airborne Visible-Infrared Imaging Spectrometer (AVIRIS) sensor over the Cuprite mining district in Nevada. Numerical simulations based on the MODTRAN 4 radiative transfer code were also employed for investigating the algorithm's performance. An additional empirical H2O retrieval procedure was tested by use of data gathered by the VIRS-200 imaging spectrometer.     

Imaginary refractive-index effects on desert-aerosol extinction versus backscatter relationships at 351 nm: numerical computations and comparison with Raman lidar measurements

A numerical model is used to investigate the dependence at 351 nm of desert-aerosol extinction and backscatter coefficients on particle imaginary refractive index (mi). Three ranges (-0.005 < or = mi < or = -0.001, -0.01 < or = mi < or = -0.001, and -0.02 < or = mi < or = -0.001) are considered, showing that backscatter coefficients are reduced as /mi/ increases, whereas extinction coefficients are weakly dependent on mi. Numerical results are compared with extinction and backscatter coefficients retrieved by elastic Raman lidar measurements performed during Saharan dust storms over the Mediterranean Sea. The comparison indicates that a range of -0.01 to -0.001 can be representative of Saharan dust aerosols and that the nonsphericity of mineral particles must be considered.     

Selective refinement queries for volume visualization of unstructured tetrahedral meshes

We address the problem of the efficient visualization of large irregular volume data sets by exploiting a multiresolution model based on tetrahedral meshes. Multiresolution models, also called Level-Of-Detail (LOD) models, allow encoding the whole data set at a virtually continuous range of different resolutions. We have identified a set of queries for extracting meshes at variable resolution from a multiresolution model, based on field values, domain location, or opacity of the transfer function. Such queries allow trading off between resolution and speed in visualization. We define a new compact data structure for encoding a multiresolution tetrahedral mesh built through edge collapses to support selective refinement efficiently and show that such a structure has a storage cost from 3 to 5.5 times lower than standard data structures used for tetrahedral meshes. The data structures and variable resolution queries have been implemented together with state-of-the art visualization techniques in a system for the interactive visualization of three-dimensional scalar fields defined on tetrahedral meshes. Experimental results show that selective refinement queries can support interactive visualization of large data sets.