This paper examines percolation questions in a deterministic setting. In particular, I consider R, the set of elements of Z2 with greatest common divisor equal to 1, where two sites are connected if they are at distance 1. The main result of the paper proves that the infinite component has an asymptotic density. An “almost everywhere” sieve of J. Friedlander is used to obtain the result.

In this paper we extend Witten–Helffer–Sjöstrand theory from selfadjoint Laplacians based on fiber wise Hermitian structures, to non-selfadjoint Laplacians based on fiber wise non-degenerate symmetric bilinear forms. As an application we verify, up to sign, the conjecture about the comparison of the Milnor–Turaev torsion with the complex valued analytic torsion, for odd dimensional manifolds. T...

Introduction 2 1. Symmetric spectra 5 1.1. Simplicial sets 5 1.2. Symmetric spectra 6 1.3. Simplicial structure on Sp 8 1.4. Symmetric Ω-spectra 10 2. The smash product of symmetric spectra 11 2.1. Symmetric sequences 11 2.2. Symmetric spectra 14 2.3. The ordinary category of spectra 18 3. Stable homotopy theory of symmetric spectra 19 3.1. Stable equivalence 20 3.2. Model categories 26 3.3. Le...

The Friedlander–Milnor Conjecture [1] asserts that if G is a reductive algebraic group over an algebraically closed field k, then the comparison map H ét(BGk,Z/p) −→ H (BG,Z/p) is an isomorphism for all primes p not equal to the characteristic of k. Gabber’s rigidity theorem [2] implies that this map is indeed an isomorphism for the stable general linear group GL (this is due to Suslin [6] for ...

In this note we present upper bounds for the variational eigenvalues of $p$-Laplacian on smooth domains complete $n$-dimensional Riemannian manifolds and Neumann boundary conditions, compact (boundaryless) manifolds. particular, provide in conformal class a given manifold $(M,g)$ $11$ when fix metric $g$. To do so, use approach construction suitable test functions characteriza...

We investigate support schemes for infinitesimal unipotent supergroups and their representations. Our main results provide a non-cohomological description of these which generalizes the classical work Suslin, Friedlander, Bendel. As consequence, in this setting have desired features such theory, including naturality with respect to group homomorphisms, tensor product property, realizability. an...

Quinoline scaffold are found in many natural products and they exhibit remarkable biological activities like Antimalerial, antibacterial, antiasthmatic, antihypertensive, anti-inflammatory agents and antiobesity. Aryl-substituted quinolines act as ligands for 5-lipoxygenase , tyrosine kinase , leukotriene 11 and other receptors. Furthermore, polyquinolines were shown to undergo hierarchical sel...