topological bf theories in 3 and 4 dimensions in this paper we discuss topological bf theories in 3 and 4 dimensions observables are associated to ordinary knots and links in 3 dimensions and to 2 knots in 4 dimensions the vacuum expectation values of such observables give a wide range of invariants here we consider mainly the 3 dimensional case where these invariants include alexander polynomials homfly polynomials and kontsevich integrals

birational characterization of abelian varieties and ordinary abelian varieties in characteristic p 0 reference epfl article 231173 url http arxiv org abs 1703 06631 record created on 2017 09 21 modified on 2017 09 21

bispectrum estimation a parametric approach higher order spectra contain information about random processes that is not contained in the ordinary power spectrum such as the degree of nonlinearity and deviations from normality estimation of the bispectrum which is a third order spectrum has been applied in various fields to obtain information regarding quadratic phase coupling among harmonic components and non gaussianness of processes existing methods of bispectrum estimation are patterned after the conventional methods of power spectrum estimation which are known to possess certain limitations the paper proposes a parametric approach to bispectrum estimation based on a non gaussian white noise driven autoregressive ar model the ar parameter estimates are obtained by solving the third order recursion equations which may be toeplitz in form but not symmetric it is shown that the method provides bispectral estimates that are far superior to the conventional estimates in terms of bispectral fidelity and that in the case of detecting phase coupling among sinusoids the method provides significantly better resolution

spectral analysis of non linear systems involving square law operations abstract this paper contains a number of useful theoretical formulas to analyze the frequency domain properties of gaussian input data passing through non linear square law systems special bispectral density functions are defined and applied that are functions of a single variable from measurements of input data and output data only results are obtained to identify the separate frequency response functions for two models of linear systems in parallel with non linear square law systems non linear coherence functions are defined from these models which determine the proportion of the output spectrum due to the non linear operations together with ordinary coherence functions a measured output spectrum for these models can be decomposed into three components representing the linear operations the non linear operations and the remaining uncorrelated noise effects this material indicates also how to analyze other types of non linear models by employing similar techniques

batalin vilkovisky quantization and the algebraic index abstract into a geometric setting we import the physical interpretation of index theorems via semi classical analysis in topological quantum field theory we develop a direct relationship between fedosov s deformation quantization of a symplectic manifold x and the batalin vilkovisky bv quantization of a one dimensional sigma model with target x this model is a quantum field theory of aksz type and is quantized rigorously using costello s homotopic theory of effective renormalization we show that fedosov s abelian connections on the weyl bundle produce solutions to the effective quantum master equation moreover bv integration produces a natural trace map on the deformation quantized algebra this formulation allows us to exploit a rigorous localization argument in quantum field theory to deduce the algebraic index theorem via semi classical analysis i e one loop feynman diagram computations

the grothendieck duality theorem via bousfield s techniques and brown representability grothendieck proved that if f x y is a proper morphism of nice schemes then rf has a right adjoint which is given as tensor product with the relative canonical bundle the original proof was by patching local data deligne proved the existence of the adjoint by a global argument and verdier showed that this global adjoint may be computed locally in this article we show that the existence of the adjoint is an immediate consequence of brown s representability theorem lit follows almost as imme diately by smashing arguments that the adjoint is given by tensor product with a dualising complex verdier s base change theorem is an easy conse quence department of mathematics university of virginia charlottesville virginia 22903 e mail address an3rqvirginia edu this content downloaded from 157 55 39 27 on wed 07 sep 2016 06 26 19 utc all use subject to http about jstor org terms

remarks on chern simons invariants the perturbative chern simons theory is studied in a finite dimensional version or assuming that the propagator satisfies certain properties as is the case e g with the propagator defined by axelrod and singer it turns out that the effective bv action is a function on cohomology with shifted degrees that solves the quantum master equation and is defined modulo certain canonical transformations that can be characterized completely out of it one obtains invariants

the multiple load method for measuring the source characteristics of time variant sources abstract a new measurement method the multiple load method for determining the source characteristics of linear time variant sources is presented the results of this measurement method are compared to the results of the two load method for a linear time invariant source the measurement methods are tested on a modified compressor the source characteristics measured by using the multiple load method gave a good prediction of the pressure at the outlet of a compressor the result was better when using the multiple load method than when using the two load method different methods have been used to study and limit the errors occurring in the measurement and calculation of the source characteristics

wheeled pro p file of batalin vilkovisky formalism using a technique of wheeled props we establish a correspondence between the homotopy theory of unimodular lie 1 bialgebras and the famous batalin vilkovisky formalism solutions of the so called quantum master equation satisfying certain boundary conditions are proven to be in 1 1 correspondence with representations of a wheeled dg prop which on the one hand is isomorphic to the cobar construction of the prop of unimodular lie 1 bialgebras and on the other hand is quasi isomorphic to the dg wheeled prop of unimodular poisson structures these results allow us to apply properadic methods for computing formulae for a homotopy transfer of a unimodular lie 1 bialgebra structure on an arbitrary complex to the associated quantum master function on its cohomology it is proven that in the category of quantum bv manifolds associated with the homotopy theory of unimodular lie 1 bialgebras quasi isomorphisms are equivalence relations it is shown that losev mnev s bf theory for unimodular lie algebras can be naturally extended to the case of unimodular lie 1 bialgebras and eventually to the case of unimodular poisson structures using a finite dimensional version of the batalin vilkovisky quantization formalism it is rigorously proven that the feynman integrals computing the effective action of this new bf theory describe precisely homotopy transfer formulae obtained within the wheeled properadic approach to the quantum master equation quantum corrections which are present in our bf model to all orders of the planck constant correspond precisely to what are often called higher massey products in the homological algebra

supersymmetry and morse theory it is shown that the morse inequalities can be obtained by consideration of a certain supersymmetric quantum mechanics hamiltonian some of the implications of modern ideas in mathematics for supersymmetric theories are discussed

nonlinear structural identification by the reverse path spectral method abstract when dealing with nonlinear dynamical systems it is important to have efficient accurate and reliable tools for estimating both the linear and nonlinear system parameters from measured data an approach for nonlinear system identification widely studied in recent years is reverse path this method is based on broad band excitation and treats the nonlinear terms as feedback forces acting on an underlying linear system parameter estimation is performed in the frequency domain using conventional multiple input multiple output or multiple input single output techniques this paper presents a generalized approach to apply the method of reverse path on continuous mechanical systems with multiple nonlinearities the method requires few spectral calculations and is therefore suitable for use in iterative processes to locate and estimate structural nonlinearities the proposed method is demonstrated in both simulations and experiments on continuous nonlinear mechanical structures the results show that the method is effective on both simulated as well as experimental data

classical bv theories on manifolds with boundary in this paper we extend the classical bv framework to gauge theories on spacetime manifolds with boundary in particular we connect the bv construction in the bulk with the bfv construction on the boundary and we develop its extension to strata of higher codimension in the case of manifolds with corners we present several examples including electrodynamics yang mills theory and topological field theories coming from the aksz construction in particular the chern simons theory the bf theory and the poisson sigma model this paper is the first step towards developing the perturbative quantization of such theories on manifolds with boundary in a way consistent with gluing

statistical errors for non linear system measurements involving square law operations abstract this paper develops normalized random error formulas for special bispectra estimates and associated frequency response function estimates in finite memory square law systems error formulas are also derived for output spectrum estimates from these non linear systems and for associated non linear coherence functions these formulas are useful to evaluate such measured non linear results as well as to design experimental programs

globally f regular and log fano varieties abstract we prove that every globally f regular variety is log fano in other words if a prime characteristic variety x is globally f regular then it admits an effective q divisor such that k x is ample and x has controlled kawamata log terminal in fact globally f regular singularities a weak form of this result can be viewed as a prime characteristic analog of de fernex and hacon s new point of view on kawamata log terminal singularities in the non q gorenstein case we also prove a converse statement in characteristic zero every log fano variety has globally f regular type our techniques apply also to f split varieties which we show to satisfy a log calabi yau condition we also prove a kawamata viehweg vanishing theorem for globally f regular pairs

polarized endomorphisms of normal projective threefolds in arbitrary characteristic let x be a projective variety over an algebraically closed field k of arbitrary characteristic p ge 0 a surjective endomorphism f of x is q polarized if f h sim qh for some ample cartier divisor h and integer q 1 suppose f is separable and x is mathbb q gorenstein and normal we show that the anti canonical divisor k x is numerically equivalent to an effective mathbb q cartier divisor strengthening slightly the conclusion of boucksom de fernex and favre duke math j 161 8 1455 1520 2012 theorem c and also covering singular varieties over an algebraically closed field of arbitrary characteristic suppose f is separable and x is normal we show that the albanese morphism of x is an algebraic fibre space and f induces polarized endomorphisms on the albanese and also the picard variety of x and k x being pseudo effective and mathbb q cartier means being a torsion mathbb q divisor let f text gal overline x rightarrow x be the galois closure of f we show that if p 5 and co prime to deg f text gal then one can run the minimal model program mmp f equivariantly after replacing f by a positive power for a mildly singular threefold x and reach a variety y with torsion canonical divisor and also with y being a quasi etale quotient of an abelian variety when dim y le 2 along the way we show that a power of f acts as a scalar multiplication on the neron severi group of x modulo torsion when x is a smooth and rationally chain connected projective variety of dimension at most three

one dimensional chern simons theory we study a one dimensional toy version of the chern simons theory we construct its simplicial version which comprises features of a low energy effective gauge theory and of a topological quantum field theory in the sense of atiyah

generic vanishing in characteristic p 0 and the characterization of ordinary abelian varieties we prove a generic vanishing type statement in positive characteristic and apply it to prove positive characteristic versions of kawamata s theorems a characterization of smooth varieties birational to ordinary abelian varieties and the surjectivity of the albanese map when the frobenius stable kodaira dimension is zero

a cellular topological field theory we present a construction of cellular bf theory in both abelian and non abelian variants on cobordisms equipped with cellular decompositions partition functions of this theory are invariant under subdivisions satisfy a version of the quantum master equation and satisfy atiyah segal type gluing formula with respect to composition of cobordisms

decomposition of wave forces into linear and non linear components abstract this paper details a methodology for analyzing non linear systems involving a square law operation with sign the analysis is applied specifically to the problem of decomposing random wave forces on an ocean structure into their inertial linear and drag non linear components a procedure is presented for identifying the individual inertial and drag force parameters based solely upon measurements of the input wave velocity and the output wave force where the wave velocity has an arbitrary spectral density function and mean value and the inertial and drag forces have an arbitrary frequency dependence and phase it is assumed only that the wave velocity is a gaussian random process experimental verifications of the analysis procedure are presented

a derived category approach to generic vanishing we prove a generic vanishing theorem for coherent sheaves on an abelian variety over an algebraically closed field k when k c this implies a conjecture of green and lazarsfeld