We consider the two well knownminimax and minisum single facility location problems in the plane which has been divided into two regions, and by a straight line. The two regions are measured by various norms . We focus on three special cases in which the regions and are measured by and norms, and block norms, two distinct block norms. Based on the properties of block norms then we use linear ...

In this abstract we consider dialogues that have a normative aspect. A dialogue is regulated by norms, but can also establish new norms. Certain utterances ‘count as’ a particular dialogue move in some dialogue game, which creates obligations and permissions for the participants. But norms do not operate in isolation; we study their relation to mental attitudes of participants, in particular be...

in this paper, we introduce the notion of an action $y_x$as a generalization of the notion of a module,and the notion of a norm $vt: y_xto f$, where $f$ is a field and $vartriangle(xy)vartriangle(y') =$ $ vartriangle(y)vartriangle(xy')$ as well as the notion of fuzzy norm, where $vt: y_xto [0, 1]subseteq {bf r}$, with $bf r$  the set of all real numbers. a great many standard mappings on algebr...

Cognitive linguistics and experimental psychology have produced tantalizing hints that a substantial portion of language is encoded in the mind in the form of spatial representations that are grounded in perception and action. Researchers represent these spatial aspects using "image schemas" that depict verbs of motion or spatial prepositions via a 2-D layout of generic icons. In two experiment...

We prove an abstract Birkhoff normal form theorem for Hamiltonian Partial Differential Equations. The theorem applies to semilinear equations with nonlinearity satisfying a property that we call of Tame Modulus. Such a property is related to the classical tame inequality by Moser. In the nonresonant case we deduce that any small amplitude solution remains very close to a torus for very long tim...

We review and extend Lindsay’s work on abstract gradient and divergence operators in Fock space over a general complex Hilbert space. Precise expressions for the domains are given, the L2-equivalence of norms is proved and an abstract version of the Itô-Skorohod isometry is established. We then outline a new proof of Itô’s chaos expansion of complex Lévy-Itô space in terms of multiple Wiener-Lé...

Optimal sample path properties of stochastic processes often involve generalized Hölderor variation norms. Following a classical result of Taylor, the exact variation of Brownian motion is measured in terms of ψ (x) ≡ x/ log log (1/x) near 0+. Such ψ-variation results extend to classes of processes with values in abstract metric spaces. (No Gaussian or Markovian properties are assumed.) To esta...