We defined the Grothendieck groups KX and K0X. They are vector bundles, respectively coherent sheaves, modulo the relation [E] = [E ] + [E ]. We have a pullback on K: f : KX → KY. KX is a ring: [E] · [F] = [E ⊗ F]. We have a pushforward on K0: f∗[F ] = ∑ i≥0(−1) [Rf∗F ]. We obviously have a homomorphism KX → K0X. K0X is aK X-module: KX⊗K0X → X is given by [E] · [F ] = [E⊗ F ]. Unproved fact: If...

We define a p-adic character to be a continuous homomorphism from 1 + tFq [[t]] to Zp. For p > 2, we use the ring of big Witt vectors over Fq to exhibit a bijection between p-adic characters and sequences (ci)(i,p)=1 of elements in Zq , indexed by natural numbers relatively prime to p, and for which limi→∞ ci = 0. To such a p-adic character we associate an L-function, and we prove that this L-f...

In this study, we developed a compact wireless Laplacian electrode module for electromyograms (EMGs). One of the advantages of the Laplacian electrode configuration is that EMGs obtained with it are expected to be sensitive to the firing of the muscle directly beneath the measurement site. The performance of the developed electrode module was investigated in two human interface applications: ch...

Introduction 145 1. Quantum affine algebra 150 2. Quiver variety 155 3. Stratification of M0 163 4. Fixed point subvariety 167 5. Hecke correspondence and induction of quiver varieties 169 6. Equivariant K-theory 174 7. Freeness 178 8. Convolution 185 9. A homomorphism Uq(Lg)→ KGw×C ∗ (Z(w))⊗Z[q,q−1] Q(q) 192 10. Relations (I) 194 11. Relations (II) 202 12. Integral structure 214 13. Standard m...

We prove the following theorem: Let F be an algebraic closure of a finite field of characteristic p. If ρ is a continuous homomorphism from the absolute Galois group of Q to GLn(F) which is isomorphic to a direct sum of one-dimensional representations, and if p > n+1 and the conductors of the one-dimensional representations are pairwise relatively prime, and if a certain parity condition holds,...

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Let Gn,k denote the Kneser graph whose vertices are the n-element subsets of a (2n + k)-element set and whose edges are the disjoint pairs. In this paper we prove that for any non-negative integer s there is no graph homomorphism from G4,2 to G4s+1,2s+1. This confirms a conjecture of Stahl in a special case.

The Hilbert polynomial can be defined axiomatically as a group homomorphism on the Grothendieck group K(X) of a projective variety X, satisfying certain properties. The Chern polynomial can be similarly defined. We therefore define these rather abstract notions to try and find a nice description of this relationship. Introduction Let X = P be a complex projective variety over an algebraically c...

Every simple module having character height at most one for a restricted Cartantype Lie algebra g can be realized as a quotient of a module obtained by starting with a simple module S for the homogeneous component of degree zero in the natural grading of g, extending the action trivially to positive components and inducing up to g. It is shown that if S is not restricted, or if it is restricted...

An automated labeling (AL) module is developed to produce bibliographic records such as English title, vernacular title, author, affiliation, and English abstract from biomedical articles published in foreign language journals. Optical character recognition (OCR) output from scanned biomedical journals is used in this labeling process. Since frequently occurring words in a zone are important fe...