A physically natural potential energy for simple closed curves in R3 is shown to be invariant under Möbius transformations. This leads to the rapid resolution of several open problems: round circles are precisely the absolute minima for energy; there is a minimum energy threshold below which knotting cannot occur; minimizers within prime knot types exist and are regular. Finally, the number of ...

We study a problem of shape optimal design for an elliptic equation with Dirichlet boundary condition. We introduce a relaxed formulation of the problem which always admits a solution, and we find necessary conditions for optimality both for the relaxed and the original problem. Let Q be a bounded open subset of R(n > 2), let ƒ e L (Q), and let g: Q, x R —> R be a Carathéodory function (i.e. g(...

The potential of two small polyL -lysines (sPLLs), low molecular weight sPLL (LMW-L) containing 7–30 lysine residues and L18 with 18 lysine repeats, to enhance the efficiency of liposome-mediated gene transfer (GT) with cationic lipid DOCSPER [1,3-dioleoyloxy-2-(N 5 -carbamoyl-spermine)-propane] in vascular smooth muscle cells (SMCs) was investigated. Dynamic light scattering was used for deter...

EGR1 encodes a transcription factor containing three zinc-finger (ZF) DNA-binding domains of the Cys2-His2 type. It is rapidly induced by variety extracellular stimuli and involved in multiple physiological processes, including apoptosis, cell proliferation, inflammation (Li et al., 2019Li T.T. Liu M.R. Pei D.S. Friend or foe, role EGR-1 cancer.Med Oncol. 2019; 37: 7Crossref PubMed Scopus (24) ...

We construct examples of nonresolvable generalized «-manifolds, n > 6 , with arbitrary resolution obstruction, homotopy equivalent to any simply connected, closed «-manifold. We further investigate the structure of generalized manifolds and present a program for understanding their topology. By a generalized n-manifold we will mean a finite-dimensional absolute neighborhood retract X such that ...

We give a classification of the p-local stable homotopy type of BG , where G is a finite group, in purely algebraic terms. BG is determined by conjugacy classes of homomorphisms from p-groups into G . This classification greatly simplifies if G has a normal Sylow p-subgroup; the stable homotopy types then depends only on the Weyl group of the Sylow p-subgroup. If G is cyclic mod p then BG deter...

Let M be a compact connected Riemannian manifold whose sectional curvature values are all nonpositive. Let T denote the fundamental group of M. We prove that any homotopy equivalence ƒ : N —> M from a compact closed manifold TV is homotopic to a homeomorphism, provided that m > 5 where m = dim M . We show that the surgery L-group Lk+m(T, w{) is isomorphic to the set of homotopy classes of k k m...

Let P be a second-order, strictly hyperbolic differential operator on an open region Q C R n (n > 3) with smooth noncharacteristic boundary. Given a solution u G fffoc(n), s > (n + l ) /2 , to Pu = f(x,u), we discuss the propagation of microlocal H singularities in the range s < r < 2s — n/2 in the general case where the Hamilton field of p may be tangent to dT* f2\0 to arbitrarily high finite ...

We present a model for computation over the reals or an arbitrary (ordered) ring R. In this general setting, we obtain universal machines, partial recursive functions, as well as JVP-complete problems. While our theory reflects the classical over Z (e.g., the computable functions are the recursive functions) it also reflects the special mathematical character of the underlying ring R (e.g., com...

Let s/* = {l\,li, ■■■ , ln} be a line arrangement in CP2 , i.e., a collection of distinct lines in CP2 . Let L(s/ * ) be the set of all intersections of elements of A* partially ordered byX<Y&YCX.Let M{tf*) be CP2 U-af* where \Jsf* = lj{'i: !<'<"}• The central problem of the theory of arrangement of lines in CP2 is the relationship between M{stf * ) and L{s/*). Main Theorem. The topological typ...