The partition algebra CAk(n) is the centralizer algebra of Sn acting on the k-fold tensor product V ⊗k of its n-dimensional permutation representation V.The partition algebra CA 1 (n) k+ 2 is the centralizer algebra of the restriction of V ⊗k to Sn−1 ⊆ Sn. Weapply the theory of the basic construction (generalized matrix algebras) to the tower of partition algebras CA0(n) ⊆ CA 1 (n) CA1(n) ⊆ CA 1 (n) ⊆···.Ourmainresults are: 2 1 2 (a) a presentation on generators and relations for CAk(n); (b) aderivation of “Specht modules ” from the basic construction; (c) a proof that CAk(n) is semisimple if and only if k ≤ (n + 1)/2 (except for a few special cases); (d) Murphy elements for CAk(n);and (e) an exposition on the theory of the basic construction and semisimple algebras.

This paper describes a construction of the real numbers in the HOL theorem-prover by strictly definitional means using a version of Dedekind's method. It also outlines the theory of mathematical analysis that has been built on top of it and discusses current and potential applications in verification and computer algebra. Keywords: Mathematical Logic; Deduction and Theorem Proving 1 The real numbers For some mathematical tasks, the natural numbers N = f0; 1; 2; : : :g are sufficient. However for many purposes it is convenient to use a more extensive system, such as the integers (Z) or the rational (Q ), real (R) or complex (C ) numbers. In particular the real numbers are normally used for the measurement of physical quantities which (at least in abstract models) are continuously variable, and are therefore ubiquitous in scientific applications. 1.1 Properties of the real numbers We can characterize the reals as the unique `complete ordered field'. More precisely, the reals are a set ...

Abstract. We construct a semiorthogonal decomposition of the derived category of coherent sheaves on a quadric fibration consisting of several copies of the derived category of the base of the fibration and the derived category of coherent sheaves of modules over the sheaf of even parts of the Clifford algebras on the base corresponding to this quadric fibration generalizing the Kapranov’s description of the derived category of a single quadric. As an application we verify that the noncommutative algebraic variety (P(S 2 W ∗), B0), where B0 is the universal sheaf of even parts of Clifford algebras, is Homologically Projectively Dual to the projective space P(W) in the double Veronese embedding P(W) → P(S 2 W). Using the properties of the Homological Projective Duality we obtain a description of the derived category of coherent sheaves on a complete intersection of any number of quadrics. 1.

In spite of the fact that some of the outstanding physiologists and neurophysiologists (e.g. Hermann von Helmholtz and Horace Barlow) insisted on the central role of inductive learning processes in vision as well as in other sensory processes, there are absolutely no (computational) theories of vision that are guided by these processes. It appears that this is mainly due to the lack of understanding of what inductive learning processes are. We strongly believe in the central role of inductive learning processes, around which, we think, all other (intelligent) biological processes have evolved. In this paper we outline a (computational) theory of vision completely built around the inductive learning processes for all levels in vision. The development of such a theory became possible with the advent of the formal model of inductive learning---evolving transformation system (ETS). The proposed theory is based on the concept of structured measurement device, which is motivated by the formal model of inductive learning and is a far-reaching generalization of the concept of classical measurement device

Introduction Convergence and continuity properties of homomorphisms play an important role in the theory of topological projective planes. Grundhofer [8] showed that the set \Sigma of all automorphisms of a compact projective plane is a locally compact transformation group with respect to the topology of uniform convergence; for the special case of compact connected projective planes see also Salzmann [21]. With regards to classification, compact connected projective planes have been successfully investigated by studying their automorphism group, see Salzmann, Betten, Grundhofer, Hahl, Lowen, and Stroppel [22] for a detailed exposition. Salzmann [20] proved that if \Pi is a 2-dimensional compact projective plane, then on \Sigma the topology of pointwise convergence coincides with the topology of uniform convergence. He also showed ([19]) that any homomorphism between 2-dimensional compact projective planes is in fact a homeomorphism. Grundhofer [9] characterized the continuity of non-

We show that if a (locally compact) group G acts properly on a locally compact σ-compact space X then there is a family of G-invariant proper continuous finite-valued pseudometrics which induces the topology of X. If X is furthermore metrizable then G acts properly on X if and only if there exists a G-invariant proper compatible metric on X.

theoretic properties of convolutional codes over rings