We prove a local index formula for cusp-pseudodifferential operators on a manifold with boundary. This is known to be equivalent to an index formula for manifolds with cylindrical ends, and hence we obtain a new proof of the classical Atiyah-Patodi-Singer index theorem for Dirac operators on manifolds with boundary, as well as an extension of Melrose’s b-index theorem. Our approach is based on ...

We have investigated the Mott transition in a quasi-two-dimensional Mott insulator EtMe{3}P[Pd(dmit){2}]{2} with a spin-frustrated triangular-lattice in hydrostatic pressure and magnetic-field [Et and Me denote C2H5 and CH3, respectively, and Pd(dmit){2} (dmit=1,3-dithiole-2-thione-4,5-dithiolate,dithiolate) is an electron-acceptor molecule]. In the pressure-temperature (P-T) phase diagram, a v...

We show, without using the Four Color Theorem, that for each planar triangulation, the number of its proper vertex colorings by 4 colors is a determinant and thus can be calculated in a polynomial time. In particular, we can efficiently decide if the number is non-zero.

We consider a closed set S ⊆ Rn and a linear operator Φ: R[X1, . . . , Xn]→ R[X1, . . . , Xn] that preserves nonnegative polynomials, in the following sense: if f ≥ 0 on S, then Φ(f) ≥ 0 on S as well. We show that each such operator is given by integration with respect to a measure taking nonnegative functions as its values. This can be seen as a generalization of Haviland’s Theorem, which conc...

The research into SME’s is often presented as quite distinct from strategy or general management research. This paper examines the literature on Strategic Decision Making (SDM) process, drawing in some findings from the SME sector which show some key similarities. The paper makes proposals for research into SDM processes in SME’s, which would clarify both the general management theory and theor...

Using an effective field theory framework we reconsider the problem of radiative corrections from compact dimensions to the 4D gauge couplings. We evaluate the general structure of one-loop contribution from Kaluza-Klein states to the 4D gauge couplings, in models with one-and two-dimensional orbifold compactifications. The calculation includes the additional effect of a non-vanishing constant ...

This paper investigates experimentally the generalizations made in AnderBois (2010, 2011, 2014) that a sluice may never take an appositive clause as its antecedent. We find that experimental participants rated sentences with sluiceantecedents in appositives as acceptable. We highlight two factors which influence the acceptability of appositive antecedents for sluices:whether the indefinite NP a...

Coloring planar Feynman diagrams in spinor quantum electrodynamics, is a non trivial model soluble without computer. Four colors are necessary and sufficient.

This paper presents a short and simple proof of the Four-Color Theorem, which can be utterly checkable by human mathematicians, without computer assistance. The new key idea that has permitted it is presented in the Introduction. Mathematics Subject Classification (2010). Primary 05C10; Secondary 05C15.

The Hodge theorem and Hirzebruch signature theorem form an important bridge between geometric and topological properties of compact smooth manifolds. There has been a great deal of work over the past thirty years aimed at understanding how to generalize these theorems to L2 results in the noncompact and singular settings. Early and important work was done by Atiyah, Patodi and Singer [2]. Their...