A method of stochastic subgradients with complete feedback stepsize rule for convex stochastic approximation problems

A stochastic subgradient algorithm for solving convex stochastic approximation problems is considered. In the algorithm, the stepsize coefficients are controlled on-line on the basis of information gathered in the course of computations according to a new, complete feedback rule derived from the concept of regularized improvement function. Convergence with probability 1 of the method is established.This work was supported by Project No. CPBP/02.15.     

PROMETHEE-MD-2T method for project selection

Project selection is a real problem of multicriteria group decision making (MCGDM) where each decision maker expresses his/her preferences depending on the nature of the alternatives and on his/her own knowledge over them. Thus, information, as much quantitative as qualitative, coexists. The traditional methods of MCGDM developed for project selection usually discriminates in favour of quantitative information at the expense of qualitative information, and this is due to the capability to integrate this first type of information inside their procedure. In this article, two new multicriteria 2-tuple group decision methods called “Preference Ranking Organisation Method for Enrichment Evaluation Multi Decision maker 2-Tuple-I and II” (PROMETHEE-MD-2T-I and II) are presented. They are able to integrate inside their procedure both quantitative and qualitative information in an uncertain context. This has been performed by integrating a 2-tuple linguistic representation model dealing with non-homogeneous and imprecise information data made up by valued intervals, numerical and linguistic values into the aggregation operators of Promethee methods. Although they have been developed for project selection problems, these proposed methods can be applied to all kinds of decision-making problems with heterogeneous and multigranular information.     

Corrections of rotation of the galaxy to measuredP of pulsars

TheP of pulsars provides important information for studying their physical processes. In an all-round way the effect of the Galactic rotation on the measuredP of pulsars is studied. It is shown that among 706 pulsars discovered so far there are 16 pulsars whose measured values ofP have been affected by the Galactic rotation. So, it is necessary to make the corresponding corrections for those pulsars Project supported by the National Natural Science Foundation of China (Grant No. 19733001).     

Second-order and related extremality conditions in nonlinear programming

This paper is concerned with the problem of characterizing a local minimum of a mathematical programming problem with equality and inequality constraints. The main object is to derive second-order conditions, involving the Hessians of the functions, or related results where some other curvature information is used. The necessary conditions are of the Fritz John type and do not require a constraint qualification. Both the necessary conditions and the sufficient conditions are given in equivalent pairs of primal and dual formulations.This research was partly supported by Project No. NR-947-021, ONR Contract No. N00014-75-0569, with the Center for Cybernetic Studies, and by the National Science Foundation, Grant No. NSF-ENG-76-10260.     

Estimates of regularized solutions of convolution-type equations in the spaces of functions with derivatives of fractional orders

The paper deals with convolution type integral equations of the first kind. For exact solutions it is typical that the solutions are discontinuous or unbounded. The aim of the paper is to construct approximate solutions which may also be discontinuous or unbounded. A priori information about the solution and estimates for the approximate solutions, as well as for the differences between the approximate solution and the exact one, are given in terms of Nikol'skii-Besov spaces with differentiation of fractional orders. Bibliography: 8 titles. Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 18, pp. 170–194, 1995. This work was supported by the Russian Fundamental Research Foundation (Project No 93-01-00255).     

A fuzzy multi-criteria decision analysis model for advanced technology assessment at Kennedy Space Center

The rapid development of computer and information technology has made project evaluation and selection a difficult task at the Kennedy Space Center (KSC) Shuttle Project Engineering Office. Decision Makers (DMs) are required to consider a vast amount of intuitive and analytical information in the decision process. Fuzzy Euclid is a Multi-criteria Decision Analysis (MCDA) model that captures the DMs’ beliefs through a series of intuitive and analytical methods such as the analytic hierarchy process (AHP) and subjective probability estimation. A defuzzification method is used to obtain crisp values from the subjective judgments provided by multiple DMs. These crisp values are synthesized with Entropy and the theory of displaced ideal to assist the DMs in their selection process by plotting the alternative projects in a four-zone graph based on their Euclidean distance from the ‘ideal choice’.     

Genetic algorithm-based multi-criteria project portfolio selection

Project portfolio selection is one of the most important decision-making problems for most organizations in project management and engineering management. Usually project portfolio decisions are very complicated when project interactions in terms of multiple selection criteria and preference information of decision makers (DMs) in terms of the criteria importance are taken into consideration simultaneously. In order to solve this complex decision-making problem, a multi-criteria project portfolio selection problem considering project interactions in terms of multiple selection criteria and DMs?? preferences is first formulated. Then a genetic algorithm (GA)-based nonlinear integer programming (NIP) approach is used to solve the multi-criteria project portfolio selection problem. Finally, two illustrative examples are presented for demonstration and verification purposes. Experimental results obtained indicate that the GA-based NIP approach can be used as a feasible and effective solution to multi-criteria project portfolio selection problems.     

The tent transformation can improve the convergence rate of quasi-Monte Carlo algorithms using digital nets

In this paper we investigate multivariate integration in reproducing kernel Sobolev spaces for which the second partial derivatives are square integrable. As quadrature points for our quasi-Monte Carlo algorithm we use digital (t,m,s)-nets over which are randomly digitally shifted and then folded using the tent transformation. For this QMC algorithm we show that the root mean square worst-case error converges with order for any ɛ > 0, where 2 ^m is the number of points. A similar result for lattice rules has previously been shown by Hickernell. Ligia L. Cristea is supported by the Austrian Research Fund (FWF), Project P 17022-N 12 and Project S 9609. Josef Dick is supported by the Australian Research Council under its Center of Excellence Program. Gunther Leobacher is supported by the Austrian Research Fund (FWF), Project S 8305. Friedrich Pillichshammer is supported by the Austrian Research Fund (FWF), Project P 17022-N 12, Project S 8305 and Project S 9609.     

Instability analysis for Faraday waves under arbitrarily periodic vibration

In the framework of linear theory of instability the pattern instability is studied for a layer of a viscous fluid in a large aspect ratio container subject to vertically arbitrarily periodic excitation. As some applications, first the instabilities for Faraday water-wave system under excitations of the triangle and square waves are analyzed. Then, the relations between relative amplitudes and phase of the excitation, and the response modes of the patterns are investigated in the double-frequency Faraday experiment. The results are satisfactory. Project supported by the National Basic Research Project of Nonlinear Science and the Natural Science Foundation of Zhejiang Province.     

<Emphasis Type="Italic">L</Emphasis><Superscript>2</Superscript>-Betti numbers of one-relator groups

We determine the L ²-Betti numbers of all one-relator groups and all surface-plus-one-relation groups. We also obtain some information about the L ²-cohomology of left-orderable groups, and deduce the non-L ² result that, in any left-orderable group of homological dimension one, all two-generator subgroups are free. Warren Dicks was Funded by the DGI (Spain) through Project BFM2003-06613.     

Modeling of individual coherent structures in wall region of a turbulent boundary layer

Models for individual coherent structures in the wall region of a turbulent boundary layer are proposed. Method of numerical simulations is used to follow the evolution of the structures. It is found that the proposed model does bear many features of coherent structures found in experiments. Project supported by the National Natural Science Foundation of China (Grant No. 19732005) and National Climbing Project.     

Incorporating operations research techniques to evaluate information systems impact on healthcare

Over the past 4 years, the Hospice Palliative Care Network Project, co-led by the Temmy Latner Centre for Palliative Care, Mount Sinai Hospital, and the Toronto Community Care Access Centre, has been working toward developing an innovative model of home palliative care coordination and service delivery. After a successful completion of stage one involving data collection of approximately 400 variables to a common Linux database repository, the current stage of the Project is to compare various modes of care delivery and disseminate the results to internal and external evaluation stakeholders. The Temmy Latner Centre's customized Panacea Information Management System (PIMS) had been linked to the Linux repository in order to customize reports to determine the optimal model of coordination and service delivery that could serve as a template for home palliative care delivery in Ontario. The objective of this paper is to outline the development and functionality of the PIMS and to evaluate its contribution in terms of improved data quality and health outcomes; in other words, to justify the information systems investment by demonstrating the relationship between this investment and improved health system delivery and effectiveness.     

Tools for resource-constrained project scheduling and control: forward and backward slack analysis

Project managers generally consider slack as a measure of the scheduling flexibility associated with the activities in the project network. Nevertheless, when resource constraints appear, this information must be calculated and analysed carefully. In this context, to handle project feasible schedules is very hard work for project managers. In order to develop useful tools for decision making, the authors extend the concepts of activity slack and define a new activity criticality index based on them that permits us to classify the activities in the resource-constrained project scheduling and control context. Additionally, these new concepts have been integrated into standard project management software as new commands. Hence the capabilities of project management software are improved. Finally, an example that illustrates the use and application of the new activity classification is also included.     

Studies on some perfectly matched layers for one-dimensional time-dependent systems

We will analyze some perfectly matched layers (PMLs) for the one-dimensional time-dependent Maxwell system, acoustic equations and hyperbolic systems in unbounded domains. The exponential decays and convergence of the PML solutions are studied. Some finite difference schemes are proposed for the PML equations and their stability and convergence are established. The work of Y. Lin was fully supported by the NSERC of Canada, of K. Zhang partially supported by a Direct Grant of CUHK (2060276) and NNSF (No. 10701039 of China), whereas the work of J. Zou was fully supported by Hong Kong RGC grants (Project 404606 and Project 404407).     

Design and observations of satellite laser ranging system for daylight tracking at Shanghai Observatory

The first satellite laser ranging system for daylight tracking in China was set up at Shanghai Observatory, Chinese Academy of Sciences. Both false alarm probability due to strong background noises and detection probability of the laser returns with single photon level from satellite in daylight for our system are analysed. The system design and performance characteristics of subsystems, adopted techniques and satellite ranging observations are given. Project supported by the astronomical council of Chinese Academy of Sciences and the National Basic Research Project “Modern Crustal Movement and Geodynamics Research”.     

Nonstandard decision methods for the solvability of real polynomial equations

For a multivariate polynomial equation with coefficients in a computable ordered field, two criteria of this equation having real solutions are given. Based on the criteria, decision methods for the existence of real zeros and the semidefiniteness of binaly polynomials are provided. With the aid of computers, these methods are used to solve several examples. The technique is to extend the original field involved in the question to a computable non-Archimedean ordered field containing infinitesimal elements. Project supported by the National Natural Science Foundation of China (Grant No. 19661002) and the Climbing Project.     

Collaborative Curriculum Investigation as a Vehicle for Teacher Enhancement and Mathematics Curriculum Reform

The Missouri Middle Mathematics (M³) Project is an NSF-funded 3-year professional development project involving teacher/administrator teams from districts statewide. Project activities focus on collaborative investigation of emerging reform-based middle school mathematics curricula to support individual and systemic reform. Collaborative review and field-testing of material facilitates awareness and exploration of alternative instructional and assessment strategies and informed decision making. Early indicators of the model's success are reflected in participants’ enthusiasm and professional growth. Project activities stimulate discussions of critical topics including questioning appropriateness of various teaching practices, research about teaching and learning, tracking policies, appropriate assessment models for gauging student learning and the importance of calculators and manipulatives as teaching and learning tools. These discussions transcend curriculum materials being reviewed and serve as a powerful vehicle for professional growth and development for individual teachers and districts.     

Some Difficulties Experienced by First Year Undergraduates— an Attempt to Remedy their Lack of Sixth Form Mathematics

Students come to universities with only O‐level Mathematics to read subjects such as Biology and Economics. These subjects now need a greater knowledge of mathematics. A Research Project at Lancaster is trying to meet their difficulties. A course is being run for 120 such students.

An account is given of experience with a variety of audio and visual aids designed for use with classes where no teacher is available and for individual learning.

The syllabus for the course is given in broad outline with reasons for choices.

Particular difficulties experienced by the students are outlined; also the clashes of interest which occur.

In an Appendix a mathematical model is suggested to relate the average rate of progress of a class to the rate of feeding in of information.     

On-line user languages

The principal differences between on-line and off-line user languages are discussed in some detail. The characteristic features of the OPL programming language are mentioned together with experiences of Project MAC, pointing at increased efficiency in the use of computers.Work reported herein was supported by Project MAC, and M. I. T. research program sponsored by the Advanced Research Projects Agency, Department of Defense, under Office of Naval Research contract NONR-4102(01). Reproduction in whole or in part is permitted for any purpose of the United States Government.     

A Stochastic Model for Combined Activity/Destination/Route Choice Problems

In travel behavior modeling, an important topic is to investigate what drives people to travel. A systematic analysis should examine why, where and when various activities are engaged in, and how activity engagement is related to the spatial and institutional organization of an urban area. In view of this, this paper presents a stochastic model for solving the combined activity/destination/route choice problem. It is a time-dependent model for long-term transport planning such as travel demand forecasting. The activity/destination choices are based on multinomial logit formulae and, the route choice is governed by stochastic user equilibrium principle. The solution algorithm is proposed together with a numerical example for demonstration. It is shown that the proposed modeling approach provides a powerful tool for fully understanding and predicting the complex travel behavior at strategic level. The work described in this paper was substantially supported by the grants from the National Natural Science Foundation of China (Project No. 79825101), the Chinese Academy of Sciences (MADIS Research Project) and the Research Grants Council of the Hong Kong Special Administrative Region (Project No. PolyU5077/97E).