Forecasting Traffic on STOL<Superscript>*</Superscript>

A subsidiary of Air Canada will be operating an experimental STOL (Short Take-Off and Landing) service between Montreal and Ottawa from downtown airports. A model was developed to forecast traffic and evaluate marketing strategies for the proposed service. Traditional forecasting methods relying on historical data are of little use as STOL will offer a level of service outside the range of existing experience. The model therefore uses attitudinal data on such things as comfort in conjunction with data on more concrete variables such as price. The data came from a market research survey.     

Time almost-periodic Stokes problem in an infinite spatially periodic pipe<Superscript>*</Superscript>

We prove the existence of a unique Poiseuille-type solution to the time almost-periodic (in Stepanov sense) Stokes problem in an infinite spatially periodic pipe.     

A Scheduling Problem<Superscript>*</Superscript>

This note treats the optimization problem of minimizing the completion time of jobs in a job-shop with no wait in process. Techniques are presented for restricted cases of the problem.     

Quotients of internally quasicontinuous functions<Superscript>*</Superscript>

In this paper, we characterize the family of quotients of internally quasicontinuous functions. Moreover, we study cardinal invariants related to quotients in the case of internally quasicontinuous functions and the complement of this family.     

State spaces of <Emphasis Type="Italic">JB</Emphasis><Superscript><Emphasis Type="Italic">*</Emphasis></Superscript>-triples<Superscript>*</Superscript>

An atomic decomposition is proved for Banach spaces which satisfy some affine geometric axioms compatible with notions from the quantum mechanical measuring process. This is then applied to yield, under appropriate assumptions, geometric characterizations, up to isometry, of the unit ball of the dual space of a JB^*-triple, and up to complete isometry, of one-sided ideals in C^*-algebras.Mathematics Subject Classification (2000):17C65, 46L07Both authors are supported by NSF grant DMS-0101153     

The Reduced Minimum Modulus in <Emphasis>C</Emphasis><Superscript>*</Superscript>-Algebras

We define the reduced minimum modulus of a nonzero element a in a unital C ^*-algebra by . We prove that . Applying this result to and its closed two side ideal , we get that dist , and for any if RR = 0, where and is the quotient homomorphism and . These results generalize corresponding results in Hilbert spaces.     

Decomposition theorem for the cd-index of Gorenstein<Superscript>*</Superscript> posets

We prove a decomposition theorem for the cd-index of a Gorenstein^* poset analogous to the decomposition theorem for the intersection cohomology of a toric variety. From this we settle a conjecture of Stanley that the cd-index of Gorenstein* lattices is minimized on Boolean algebras.     

Sample paths of generalized random linear mappings<Superscript>*</Superscript>

In this paper, generalized random linear mappings are viewed as random field indexed by random parameters. This point of view leads to questions about sample paths properties. We obtain various necessary and sufficient conditions ensuring the existence of nice sample paths of a generalized random linear mapping. We also give illustrative examples and applications.     

On the singular series for primes in arithmetic progressions<Superscript>*</Superscript>

Using \( \mathfrak{G} \)(d, k) to denote the singular series for primes in arithmetic progressions and using the word “tail” to denote the difference of \( \mathfrak{G} \)(d, k) and its partial sums, we establish some asymptotic formulas for weighted sums of the square of the tail and so give more information on the singular series \( \mathfrak{G} \)(d, k).     

Symmetries in equations of incompressible viscoelastic Maxwell medium<Superscript>*</Superscript>

We consider unsteady flows of incompressible viscoelastic Maxwell medium with upper, low, and Jaumann convective derivatives in the rheological constitutive law. We give characteristics of a system of equations that describe a three-dimensional motion of such a medium for all three types of convective derivative. In the general case, due to the incompressibility condition, the equations of motion have both real and complex characteristics. We study group properties of this system in the two-dimensional case. On this basis, we choose submodels of the Maxwell model that can be reduced to hyperbolic ones. The properties of the hyperbolic submodels obtained depend on the choice of the invariant derivative in the rheological relation. We also present concrete examples of invariant solutions.     

A Contribution to a Discussion on the Methodology of Operational Research<Superscript>*</Superscript>

The application of O.R. to policy-making at high levels implies a recognition that such decisions generally involve multiple criteria. The need to be able readily to change the weighting of these criteria in a model calls for a decision-making dialogue between the decision-maker and the model. This is discussed, and related to the development of on-going systems where the model is fitted into an organization to serve decision needs on a continuing basis.     

Approximate Isomorphisms in <Emphasis Type="Italic">C</Emphasis><Superscript>*</Superscript>-Algebras

This paper is a survey on the Hyers–Ulam–Rassias stability of the following Cauchy–Jensen functional equation in C ^*-algebras:

<Emphasis Type="Italic">tt</Emphasis><Superscript>*</Superscript>-Geometry and Pluriharmonic Maps

In this paper we use the real differential geometric definition of a metric (a unimodular oriented metric) tt^*-bundle of Cortés and the author (Topological-anti-topological fusion equations, pluriharmonic maps and special Kähler manifolds) to define a map Φ from the space of metric (unimodular oriented metric) tt^*-bundles of rank r over a complex manifold M to the space of pluriharmonic maps from M to {GL}(r)/O(p,q) (respectively {SL}(r)/SO(p,q)), where (p,q) is the signature of the metric. In the sequel the image of the map Φ is characterized. It follows, that in signature (r,0) the image of Φ is the whole space of pluriharmonic maps. This generalizes a result of Dubrovin (Comm. Math. Phys. 152 (1992; S539–S564).     

The Fredholm Index for Elements of Toeplitz-Composition C<Superscript>*</Superscript>-Algebras

We analyze the essential sectrum and index theory of elements of Toeplitz-composition C^*-algebras (algebras generated by the Toeplitz algebra and a single linear-fractional composition operator, acting on the Hardy space of the unit disk). For automorphic composition operators we show that the quotient of the Toeplitz-composition algebra by the compacts is isomorphic to the crossed product C^*-algebra for the action of the symbol on the boundary circle. Using this result we obtain sufficient conditions for polynomial elements of the algebra to be Fredholm, by analyzing the spectrum of elements of the crossed product. We also obtain an integral formula for the Fredholm index in terms of a generalized Chern character. Finally we prove an index formula for the case of the non-parabolic, non-automorphic linear fractional maps studied by Kriete, MacCluer and Moorhouse.     

The modular group and words in its two generators<Superscript>*</Superscript>

Consider the full modular group PSL₂(?) with presentation 〈U,?S|U ³,?S ²〉. Motivated by our investigations on quasi-modular forms and the Minkowski question mark function (so that this paper may be considered as a necessary appendix), we are led to the following natural question. Some words in the alphabet {U, S} are equal to the unity; for example, USU ³ SU ² is such a word of length 8, and USU ³ SUSU ³ S ³ U is such a word of length 15. We consider the following integer sequence. For each n ∈ ?₀, let t(n) be the number of words in the alphabet {U, S} that equal the identity in the group. This is the new entry A265434 into the Online Encyclopedia of Integer Sequences. We investigate the generating function of this sequence and prove that it is an algebraic function over ?(x) of degree 3. As an interesting generalization, we formulate the problem of describing all algebraic functions with a Fermat property.     

Real <Emphasis Type="Italic">AW</Emphasis><Superscript>*</Superscript>-Algebras of type I

Let R be a real AW ^*-algebra, and suppose that its complexification M = R + iR is also a (complex) AW ^*-algebra. We prove that R is of type I if and only if so is M.Translated from Funktsionalnyi Analiz i Ego Prilozheniya, Vol. 38, No. 4, pp. 79–81, 2004Original Russian Text Copyright © by Sh. A. Ayupov     

Winding behaviour of finite-time singularities of the harmonic map heat flow<Superscript>*</Superscript>

We settle a number of questions about the possible behaviour of the harmonic map heat flow at finite-time singularities. In particular, we show that a type of nonuniqueness of bubbles can occur at finite time, we show that the weak limit of the flow at the singular time can be discontinuous, we determine exactly the (polynomial) rate of blow-up in one particular example, and we show that winding behaviour of the flow can lead to an unexpected failure of convergence when the flow is (locally) lifted to the universal cover of the target manifold.Partly supported by an EPSRC Advanced Research Fellowship.