Free energy and solutions of the Vlasov-Poisson-Fokker-Planck system: external potential and confinement (Large time behavior and steady states)

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.

     

Analysis of performance of an iron-bath reactor using computational fluid dynamics

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.

The model was validated with data reported by the Nippon Steel Corporation for a 100 t pilot plant, and the calculated and measured data are in good agreement. Modelling results showed that the dominant mechanisms of heat transfer from the gas to the bath are radiation to the slag surface and convection heat transfer to droplets.     

An optimal time to sleep for an auto-sleep system considering multi-usage states

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.

It considers four states:

• 1.(a) sleep
• 2.(b) warm-up
• 3.(c) nonusage
• 4.(d) usage.

For such a system, the time to sleep has been discussed based on suitable criteria. This study extends the model for an auto-sleep system so that the model can deal with multi-usage states. With a view to determining an optimal time to sleep under the extended model, the expected energy consumed per unit time is formulated as a criterion to be minimized. The existence of an optimal time to sleep is examined under a general call distribution. Numerical examples are also provided for a Weibull as well as a log-normal call distribution.     

A decomposition of the Brownian path

The Brownian path {ω(s); 0 ⩽ s ⩽ t} is dissected and then reassembled in such a way that

• (i) the last visit γ_t at the origin, as well as the fragment {ω(s); γ_t ⩽ s ⩽ t}, are left invariant;
• (ii) on [0, γ_t], local time becomes maximum-to-date and occupation time of|R₊ becomes location of maximum; and
• (iii) the resulting process is again Brownian.

Characterizations of conditional processes are employed to establish the result. Several consequences of the latter are discussed.     

On degree sequences of undirected,directed, and bidirected graphs

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.

To underline the similarities and differences to their (un)directed counterparts, we briefly survey the undirected setting and we give a thorough account for digraphs with an emphasis on the discrete geometry of degree sequences. In particular, we determine the tight and uniquely realizable degree sequences for directed graphs.     

Chirurgies d'indice un et isotopies de sphères dans les variétés de contact tendues

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.

     

Maximizing profit of a food retailing chain by targeting and promoting valuable customers using Loyalty Card and Scanner Data

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.

These components are well-known in the literature and each of them has received considerable independent study. However, in this study we combine each of these components into one consistent, application-orientated model. We then demonstrate using panel data that the combination has a synergic effect on the efficiency of estimation and the maximization of profit (e.g., price and promotion elasticity estimation is improved by conducting it within market segments rather than across an entire hetereogeneous population). These estimates are further improved by incorporating “pass through”—a functional relationship between a retailer’s unit prices and unit costs.     

Ultrafilters,independent collections,and applications to topology

The following are consequences of the main results in this paper:

• 1.(1) The number of countably compact, completely regular spaces of density κ is 2^22κ.
• 2.(2) There are 2^2κ points in U(κ) (= space of uniform ultrafilters on κ), each of which has tightness 2^κ in U(κ) and is a limit point of a countable subset of U(κ).
• 3.(3) There are 2^2κ points in U(κ), each of which has tightness 2^κ and is a weak P-point of κ¹.
• 4.(4) For each λ ⩽ κ there are at least 2^2λ · κ points in βκ, each of which has tightness 2^λ in β κ and is a weak P-point of κ¹. Moreover, under GCH there are at least 2^2λ · κ^λ such points.

     

A Note on Old Babylonian Computational Techniques

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.

© 2002 Elsevier Science (USA).Eine Analyse der Rechenfehler in zwei altbabylonischen “algebraischen” Aufgaben läßt mehrere Rückschlüsse auf ein Hilfsmittel zu, das zur Durchführung von Rechnungen benutzt worden sein kann:

• •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.

© 2002 Elsevier Science (USA).MSC subject classification: 01A17.     

Stability and boundedness of a kind of third-order delay differential system

The paper studies equation (1.1) in two cases:

• •(i)p ≡ 0,
• •(ii)p ≠ 0.

In Case (i), the asymptotic stability of the solution x = 0 is studied; in Case (ii), the uniform boundedness and uniform ultimate boundedness of all solutions of (1.1) are proved.     

A new proof of a theorem of Dembowski

It was shown by P.Dembowski [1;Satz 3] that any finite semiaffine plane(=FSAP) is of the types:

1. A finite affine plane,
2. A finite projective plane with one line and all its points except one deleted,
3. A finite projective plane with one point deleted,
4. A finite projective plane.

This was established by using the results obtained for natural parallelisms of incidence structures. The purpose of this note is to give a new proof based on purely combinatorial arguments.     

Common knowledge revisited

We consider the common-knowledge paradox raised by Halpern and Moses: common knowledge is necessary for agreement and coordination, but common knowledge is unattainable in the real world because of temporal imprecision. We discuss two solutions to this paradox:

• 1.(1) modeling the world with a coarser granularity, and
• 2.(2) relaxing the requirements for coordination.

     

Probabilistic inequalities and remarks

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.

The same inequality is also used to estimate the difference of the expectations of two random variables. Finally, the authors study the attainability of a related inequality.     

Symplectic geometry,minors and graph Laplacians

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).

The link with topology will appear in some results about my graph parameter μ, in particular the planarity and the linkless embedding properties.     

Formal aspects of egress complexity

Egress complexity is concerned with the summative uncertainty experienced by a naive occupant of a building when faced with a challenge to evacuate without the assistance of signage. This paper takes the present model of egress complexity and recasts its basic initiative in terms of elementary order theory. Arguments are presented to demonstrate

• •the existence of distinct maximum and minimum exit complexities for a given number of compartments,
• •the monotonic nature of complexity and
• •the relationship of a given floorplan complexity to the corresponding measures of its homomorphic images

The uniqueness of the theory on which the model is developed stems from a scenario-independent nonmetric approach to egress measurement.     

Softness of hypercoherences and MALL full completeness

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.

The second step is a completely general result, while the third step relies on the concrete structure of a double gluing construction over hypercoherences.     

A dynamic network loading model for mesosimulation in transportation systems

Flow propagation models can be divided into static and dynamic network loading models. Different approaches to dynamic network loading problem formulated in the literature point out models that can be classified as disaggregate or aggregate.Applying aggregate models, it is possible to trace implicitly or explicitly vehicles movements. The second case concerns mesoscopic models. These models consider the traffic as a sequence of “packets” of vehicles. Two approaches can be followed:

• (a)continuous packets, where vehicles are distributed inside each packet, defined by the head and the tail points;
• (b)discrete packets, where all users belonging to a packet are grouped and represented by a single point, for instance the head.

In this paper, a mesoscopic model based on discrete packets has been developed, taking into account the vehicles acceleration. The proposed model, assuming discrete packets and uniformly accelerated movement, appears lifelike in the representation of outflow dynamics and quite easy to calculate.