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    Conformal Field Theory at central charge c=0 and Two-Dimensional Critical Systems with Quenched Disorder

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    We examine two-dimensional conformal field theories (CFTs) at central charge c=0. These arise typically in the description of critical systems with quenched disorder, but also in other contexts including dilute self-avoiding polymers and percolation. We show that such CFTs must in general possess, in addition to their stress energy tensor T(z), an extra field whose holomorphic part, t(z), has conformal weight two. The singular part of the Operator Product Expansion (OPE) between T(z) and t(z) is uniquely fixed up to a single number b, defining a new `anomaly' which is a characteristic of any c=0 CFT, and which may be used to distinguish between different such CFTs. The extra field t(z) is not primary (unless b=0), and is a so-called `logarithmic operator' except in special cases which include affine (Kac-Moody) Lie-super current algebras. The number b controls the question of whether Virasoro null-vectors arising at certain conformal weights contained in the c=0 Kac table may be set to zero or not, in these nonunitary theories. This has, in the familiar manner, implications on the existence of differential equations satisfied by conformal blocks involving primary operators with Kac-table dimensions. It is shown that c=0 theories where t(z) is logarithmic, contain, besides T and t, additional fields with conformal weight two. If the latter are a fermionic pair, the OPEs between the holomorphic parts of all these conformal weight-two operators are automatically covariant under a global U(1|1) supersymmetry. A full extension of the Virasoro algebra by the Laurent modes of these extra conformal weight-two fields, including t(z), remains an interesting question for future work.Comment: To be published in I. Kogan Memorial Volum

    Digital computer analysis and design of a subreflector of complex shape

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    Digital computer technique for computing scattered pattern of complex hyperboloid subreflector in Cassegrain antenna feed system

    The Uniqueness Problem of Sequence Product on Operator Effect Algebra ε(H)\varepsilon (H)

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    A quantum effect is an operator on a complex Hilbert space HH that satisfies 0≤A≤I0\leq A\leq I. We denote the set of all quantum effects by E(H){\cal E}(H). In this paper we prove, Theorem 4.3, on the theory of sequential product on E(H){\cal E}(H) which shows, in fact, that there are sequential products on E(H){\cal E}(H) which are not of the generalized L\"{u}ders form. This result answers a Gudder's open problem negatively
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