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1.
《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.
2.
《Journal of Complexity》1995,11(3):358-376
This paper deals with issues of structural complexity in a linear version of the Blum-Shub-Smale model of computation over the real numbers. Real versions of PSPACE and of the polynomial time hierarchy are defined, and their properties are investigated. Mainly two types of results are presented:
- •Equivalence between quantification over the real numbers and over {0, 1};
- •Characterizations of recognizable subsets of {0, 1}* in terms of familiar discrete complexity classes.
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.
《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.
5.
《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.
6.
《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.
7.
8.
《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.
9.
《Mathematical and Computer Modelling》2004,39(11-12):1213-1220
This work deals with the modelling of a three-link manipulator mounted on a plane with a time-dependent inclination. Two cases are considered.
- (i)The plane is part of a rigid body.
- (ii)The plane is in a moored ship.
10.
《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.
11.
《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.
12.
《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.
13.
《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.
14.
15.
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.
16.
《Mathematical and Computer Modelling》1995,21(9):151-156
The Australian monsoonal cross-equatorial airflow is simulated in an attempt to bridge a highly simplified, while theoretically interesting model to the realities of the actual tropical meteorology. Two factors are found to be essential in the successful simulation of the monsoonal cross-equatorial flow with that model:
- 1.1) the existence of a properly-positioned quasi-elliptic monsoon depression;
- 2.2) sufficient friction to force the decay of anticyclonic inertial oscillations and hence to allow a more ‘balanced’ type of cyclonic flow around that depression.
17.
《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.
18.
《Mathematical and Computer Modelling》1996,23(1-2):1-8
Utilizing Janus (A), we analyzed the decision made by LTG Richard Ewell at Gettysburg, PA on the evening of 1 July, 1863. At this time, LTG Ewell decided not to attack Culp's Hill. Instead, he waited until the next morning to attack, to permit the mustering of both artillery support and his third division, under command of MG Johnson. Many historians contend that this was a poor tactical decision and was a direct cause of the confederate loss at Gettysburg and possibly the war. We have investigated this issue using a combat simulation model called Janus (Army).Prerequisite to the simulation, systems and weapons of the time had to be modeled in the Janus database. To keep this relatively manageable, we decided to model only the most significant system types on each side. These included the Confederate and Yankee soldier armed with a bayonet and a non-repeating rifle; the cannoneer and cannon (12 Ib ball and cannister-shot) on each side. In total, the simulation represented nearly 200,000 systems engaged at Gettysburg.Our study employed a two level, two factor experimental design. The two factors were the presence of the corp's artillery and Johnson's division. Both factors were relevant to the decision to delay the confederate attack. The levels corresponded with whether or not each factor was used in the simulation. In all, we conducted three replications of the following four design points (tactical alternatives) from which to base our conclusions:
- 1.Design Point 1 (B): Situation on 1 Jul 1863 (no change). Ewell's Corps attacks.
- 2.Design Point 2 (B+A): Corps Artillery supports the attack.
- 3.Design Point 3 (B+J): MG Johnson's Division participates in attack.
- 4.Design Point 4 (B+A+J): Corps Artillery supports and MG Johnson's Division participates in attack.We conclude that LTG Ewell made the correct tactical decision. Without either his corps artillery or Johnson's Division, the corps would have faced annihilation should he have attacked on 1 July. Had he had his corps artillery (6 guns), he probably should have pushed aggressively up the hill. If he had only Johnson's division, he probably could have taken the hill but could not have held it as a tenable position for very long.
19.
《Applied Mathematics Letters》2002,15(2):153-157
The authors use their recently proved integral inequality to obtain bounds for the covariance of two random variables
- 1.in a general setup and
- 2.for a class of special joint distributions.
20.
《Mathematical and Computer Modelling》1997,25(7):79-87
Research in graph theory has focused on studying the structure of graphs with the assumption that they are static. However, in many applications, the graphs that arise change with time, i.e., they are dynamic in nature. This is especially true of applications involving graph models in computer science. We present an expository study of dynamic graphs with the main driving force being practical applications. We first develop a formal classification of dynamic graphs. This taxonomy in the form of generalizations and extensions will in turn suggest new areas of application. Next, we discuss areas where dynamic graphs arise in computer science such as compilers, databases, fault-tolerance, artificial intelligence, and computer networks. Finally, we propose approaches that can be used for studying dynamic graphs. The main objective in any study of dynamic graphs should be to
- 1.(i) extend results developed for static graph theory to dynamic graphs,
- 2.(ii) study the properties that describe how a dynamic graph changes,
- 3.(iii) investigate problems and issues in dynamic graph theory that are raised by practical applications of dynamic graphs in computer science.