310,052 research outputs found

    On the Adams Spectral Sequence for R-modules

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    We discuss the Adams Spectral Sequence for R-modules based on commutative localized regular quotient ring spectra over a commutative S-algebra R in the sense of Elmendorf, Kriz, Mandell, May and Strickland. The formulation of this spectral sequence is similar to the classical case and the calculation of its E_2-term involves the cohomology of certain `brave new Hopf algebroids' E^R_*E. In working out the details we resurrect Adams' original approach to Universal Coefficient Spectral Sequences for modules over an R ring spectrum. We show that the Adams Spectral Sequence for S_R based on a commutative localized regular quotient R ring spectrum E=R/I[X^{-1}] converges to the homotopy of the E-nilpotent completion pi_*hat{L}^R_ES_R=R_*[X^{-1}]^hat_{I_*}. We also show that when the generating regular sequence of I_* is finite, hatL^R_ES_R is equivalent to L^R_ES_R, the Bousfield localization of S_R with respect to E-theory. The spectral sequence here collapses at its E_2-term but it does not have a vanishing line because of the presence of polynomial generators of positive cohomological degree. Thus only one of Bousfield's two standard convergence criteria applies here even though we have this equivalence. The details involve the construction of an I-adic tower R/I <-- R/I^2 <-- ... <-- R/I^s <-- R/I^{s+1} <-- ... whose homotopy limit is hatL^R_ES_R. We describe some examples for the motivating case R=MU.Comment: Published 7 April 2001 by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol1/agt-1-9.abs.html . Erratum added 9 May 200

    Abelian functions associated with genus three algebraic curves

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    We develop the theory of Abelian functions associated with algebraic curves. The growth in computer power and an advancement of efficient symbolic computation techniques has allowed for recent progress in this area. In this paper we focus on the genus three cases, comparing the two canonical classes of hyperelliptic and trigonal curves. We present new addition formulae, derive bases for the spaces of Abelian functions and discuss the differential equations such functions satisfy.Comment: 34 page

    Permutable entire functions and multiply connected wandering domains

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    Let f and g be permutable transcendental entire functions. We use a recent analysis of the dynamical behaviour in multiply connected wandering domains to make progress on the long standing conjecture that the Julia sets of f and g are equal; in particular, we show that J(f)=J(g) provided that neither f nor g has a simply connected wandering domain in the fast escaping set

    Iterated doubles of the Joker and their realisability

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    Let A(1)\mathcal{A}(1)^* be the subHopf algebra of the mod~22 Steenrod algebra A\mathcal{A}^* generated by Sq1\mathrm{Sq}^1 and Sq2\mathrm{Sq}^2. The \emph{Joker} is the cyclic A(1)\mathcal{A}(1)^*-module A(1)/A(1){Sq3}\mathcal{A}(1)^*/\mathcal{A}(1)^*\{\mathrm{Sq}^3\} which plays a special r\^ole in the study of A(1)\mathcal{A}(1)^*-modules. We discuss realisations of the Joker both as an A\mathcal{A}^*-module and as the cohomology of a spectrum. We also consider analogous A(n)\mathcal{A}(n)^*-modules for n2n\geq2 and prove realisability results (both stable and unstable) for n=2,3n=2,3 and non-realisability results for n4n\geq4.Comment: Minor changes and corrections. A version will appear in Homology, Homotopy and Application

    China Employment Law Update - December 2016

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    In this issue: • Government Further Signals Intent to Reduce Labour Costs for Employers • China Aims to Enhance Data Privacy Protections • Supreme People’s Court Issues Clarification on Three Employment Matters • Supreme People\u27s Court Issues Guidance Stating Attorney\u27s Fees May Be Imposed on Parties Bringing Frivolous Lawsuits • Further Clarification Issued by Various Local Authorities Regarding New Work Permit System • China and France Sign Social Security Totalization Treaty • Guangdong Province People’s Courts and Unions to Work Together in Solving Labor Dispute

    The International Trade Commission's Assessment of the Trans-Pacific Partnership: Main Findings and Implications

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    In May of 2016 the United States International Trade Commission (ITC) issued its assessment of the impact of the Trans-Pacific Partnership (TPP). This paper highlights the main findings of the ITC report and explains their derivation and implications. It also examines several issues that were explicitly excluded from analysis in the ITC report

    The Triple Bottom Line in Buffalo: Standards for Economic, Social, and Ecological Success

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    In respect to human capital, or people, the triple bottom line requires fair and beneficial business practices towards employees, the community, and the region. Such practices include offering fair salaries, safe working conditions, decent hours, healthcare, and educational opportunity. In terms of the environment, or the planet, the triple bottom line requires businesses to engage in sustainable environmental practices. Businesses aim to reduce their carbon footprint by carefully managing their energy consumption and disposal methods while also ensuring that limited resources are maintained in order to preserve the environment for subsequent generations

    The Global Employer: Showcasing New Developments for Multinational Employers

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    Baker & McKenzie’s Global Employment Practice Group is pleased to present its 54th issue of The Global Employer™ entitled “Showcasing New Developments for Multinational Employers.” This issue contains a collection of articles on legal developments from nine jurisdictions that examine changes to employment and labour laws and practices and explore developments in compensation and benefits. Included, you will find information pertaining to a new collective redundancy procedure in France aimed at providing for a more secure labor market; new measures in Spain intended to promote employment among young people under 30; the codification of requirements for the negotiation of social plans in Switzerland; effects on UK redundancy laws in light of being found in breach of EU directives; emboldened labor agency agendas in the US; a discussion from Argentina on the rights of employees and employers when it comes to monitoring in the workplace; new developments for stock option plans in Brazil; changes to the calculation of payroll taxes in Colombia; and the promotion and protection of labor rights in Peru
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