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1.
《Applied Mathematical Modelling》2002,26(2):203-221
The performance of an iron-bath reactor has been studied using a comprehensive numerical model that combines a computational fluid dynamics approach for the gas phase and a heat and mass balance model for the bath. The model calculates:
- •coal, ore, flux and oxygen consumption;
- •post-combustion ratio (PCR);
- •heat-transfer efficiency (HTE);
- •off-gas temperature and composition;
- •heat transfer and chemical reactions between gas and iron and slag droplets; and
- •heat transfer between gas and bath, refractories and lance.
2.
《Historia Mathematica》2002,29(2):193-198
Analysis of the errors in two Old Babylonian “algebraic” problems shows
- •that the computations were performed on a device where additive contributions were no longer identifiable once they had entered the computation;
- •that this device must have been some kind of counting board or abacus where numbers were represented as collections of calculi;
- •that units and tens were represented in distinct ways, perhaps by means of different calculi.
- •Additive Beiträge waren nach ihrer Eintragung in die Rechnung nicht länger identifizierbar.
- •Das Gerät war eine Art Rechenbrett, auf welchem Zahlen als Haufen von Rechensteinen erschienen.
- •Einer und Zehner wurden in verschiedener Weise, evtl. mittels verschiedener Rechensteine repräsentiert.
3.
In my talk, I will present some works done in the nineties on Laplacians on graphs: from eigenvalue problems to inverse problem for resistor networks. I will focus on the motivations and the main results as well as on the main ideas:
- •A differential topology point of view on the minor relation: a nice stratification associated to a finite graph Γ whose strata are associated to the minors of Γ
- •“Discrete” (graphs) versus “continuous” (Riemannian manifolds)
- •Stability of spectra with respect to singular limits: a finite dimensional theory of operators with domains (Von Neumann theory).
4.
《European Journal of Operational Research》2006,174(2):1260-1280
In this paper, we set up a House of Profit Model, an approach of maximizing profit of a food retailing chain by targeting and promoting valuable customers. Our model combines
- •segmentation analysis of households using Loyalty Card and Scanner Data,
- •price and promotion elasticity analysis,
- •simulation of effects of pricing and promotion,
- •price and promotion optimization to maximize profit.
5.
《European Journal of Operational Research》2001,135(3):461-476
The first and major part of this presentation shows how OR education may be improved through the use of spreadsheets, with several examples:
- •in decision theory, where the drawing capabilities of Excel are used to represent decision trees and where window switching and macros allow the educator to animate his presentation;
- •in linear programming, where the solver is used (remarks are made relating to the adequacy of the solver's solutions), and where the spreadsheet's graphing capabilities are used both to represent the feasible set and the objective function, and to interactively animate the objective function or constraint movements;
- •in dynamic programming, deterministic or stochastic, where it is shown that several standard spreadsheet functions facilitate the development of specialized models;
- •in simulation, where it will be seen how stochastic simulation may be facilitated through the use of an add-in, and how a decision support system may thus be built from scratch in less than 10 minutes.
6.
《Mathematical and Computer Modelling》2000,31(10-12):157-163
An auto-sleep system is defined by the following two properties:
- 1.(i) a call for the system occurs randomly and intermittently
- 2.(ii) the system automatically goes to sleep if there occurs no call during a prespecified time T.
- 1.(a) sleep
- 2.(b) warm-up
- 3.(c) nonusage
- 4.(d) usage.
7.
Bidirected graphs generalize directed and undirected graphs in that edges are oriented locally at every node. The natural notion of the degree of a node that takes into account (local) orientations is that of net-degree. In this paper, we extend the following four topics from (un)directed graphs to bidirected graphs:
- –Erdős–Gallai-type results: characterization of net-degree sequences,
- –Havel–Hakimi-type results: complete sets of degree-preserving operations,
- –Extremal degree sequences: characterization of uniquely realizable sequences, and
- –Enumerative aspects: counting formulas for net-degree sequences.
8.
《Annals of Pure and Applied Logic》2005,131(1-3):1-63
We prove a full completeness theorem for multiplicative–additive linear logic (i.e. MALL) using a double gluing construction applied to Ehrhard’s *-autonomous category of hypercoherences. This is the first non-game-theoretic full completeness theorem for this fragment. Our main result is that every dinatural transformation between definable functors arises from the denotation of a cut-free MALL proof.Our proof consists of three steps. We show:
- •Dinatural transformations on this category satisfy Joyal’s softness property for products and coproducts.
- •Softness, together with multiplicative full completeness, guarantees that every dinatural transformation corresponds to a Girard MALL proof-structure.
- •The proof-structure associated with any dinatural transformation is a MALL proof-net, hence a denotation of a proof. This last step involves a detailed study of cycles in additive proof-structures.
9.
Given a tree, T, consider one of its longest paths, PT, not necessarily unique. We define T to be m–distant if no vertices of T are a distance greater than m away from PT. We will show that all 3–distant graphs are graceful, providing they satisfy the following properties.
- 1.They have perfect matchings.
- 2.They can be constructed by attaching paths of length 2 to the vertices of a 1–distant tree (caterpillar), by the identification of their end vertices.
10.
《Applied and Computational Harmonic Analysis》1999,6(2):197-218
It is known that superpositions of ridge functions (single hidden-layer feedforward neural networks) may give good approximations to certain kinds of multivariate functions. It remains unclear, however, how to effectively obtain such approximations. In this paper, we use ideas from harmonic analysis to attack this question. We introduce a special admissibility condition for neural activation functions. The new condition is not satisfied by the sigmoid activation in current use by the neural networks community; instead, our condition requires that the neural activation function be oscillatory. Using an admissible neuron we construct linear transforms which represent quite general functionsfas a superposition of ridge functions. We develop
- • • a continuous transform which satisfies a Parseval-like relation;
- • • a discrete transform which satisfies frame bounds.
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14.
《Applied Mathematics Letters》2003,16(5):657-662
The paper studies equation (1.1) in two cases:
- •(i)p ≡ 0,
- •(ii)p ≠ 0.
15.
《Mathematical and Computer Modelling》1998,27(9-11):335-348
The Edinburgh traveler information system, currently being designed for the Edinburgh City Council (ECC), is notable both for its multifaceted approach to the challenges of traffic management in an urban setting and its ability to integrate past, present, and future elements. Integration plays a part in the system design in the following ways:
- •• integration of new and existing systems;
- •• linking together of several disparate systems and procedures;
- •• tight integration of response capabilities with the National Driver Information and Control System (NADICS) operated by the Scottish Office, covering interurban motorways;
- •• incorporation of modularity and flexibility to accommodate future integration.
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17.
《Journal of the Egyptian Mathematical Society》2014,22(3):484-488
In 2000 [1], Zahran introduced the concept of regular open sets in fuzzifying topology. In 2004 [2], Sayed and Zahran, gave an example to illustrate that the statements:
- (1) (Lemma 2.2 [1]); and
- (2) (Theorem 2.4 [1]),
18.
《European Journal of Operational Research》2002,139(2):206-219
In some applications a minimum cost transportation model arises where supplies are fixed while demands may simultaneously vary. In this paper we analyse the structure of such a model and propose several techniques to describe its behaviour. Our approach is founded on the concept of optimal region, i.e., the subset of demand vectors where a given basic tree is optimal. The proposed algorithm consists in different pivoting strategies designed to:
- 1.build up a minimal list of basic trees such that the associated optimal regions cover the set of feasible demand vectors;
- 2.analyse the effects of either opening a new supplier or closing an existing one;
- 3.suitably treat the dual degenerate case by building up a minimal representation of every maximal region where the optimal value is linear in the demand vector.
19.
《Journal de Mathématiques Pures et Appliquées》1999,78(2):121-157
This paper is devoted to the characterization of external electrostatic potentials for which the Vlasov-Poisson-Fokker-Planck system satisfies one of the following properties:
- (i) the system admits stationary solutions,
- (ii) any solution to the evolution problem converges to a stationary solution, or, equivalently, no mass vanishes for large times,
- (iii) the free energy is bounded from below, We give conditions under which these different notions of confinement are equivalent.
20.
《Comptes Rendus de l'Academie des Sciences Series IIA Earth and Planetary Science》1997,324(6):659-663
We prove the following theorems:
- 1)Any surgery of index one on u tight contact manifold (of dimension three) gives rise to a manifold which carries a natural tight contact structure.
- 2)In a tight contact manifold, any two isotopic spheres which carry the same characteristic foliation are isotopic through a contact isolopy.
- 3)In a tight contact manifold, any two isotopic spheres have isomorphic complements.