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...

In contrast to the dozens of proteins involved in ubiquitination pathways, relatively few proteins control SUMO modification. Generating specificity and diversity in pathway outcomes may therefore rely on post-translational modification of pathway components and/or substrates. A new paper in The EMBO Journal identifies one such modification event, the acetylation of Ubc9, as a key regulatory st...

Shock tubes have been extensively used in the study of blast traumatic brain injury due to increased incidence of blast-induced neurotrauma in Iraq and Afghanistan conflicts. One of the important aspects in these studies is how to best replicate the field conditions in the laboratory which relies on reproducing blast wave profiles. Evolution of the blast wave profiles along the length of the co...