We prove the Strengthened Hanna Neumann Conjecture. We give a more direct cohomological interpretation of the conjecture in terms of “typical” covering maps, and use graph Galois theory to “symmetrize” the conjecture. The conjecture is then related to certain kernel of a morphism of sheaves, and is implied provided these kernels are co-acyclic in the covering cohomology theory. This allows us t...

This paper describes natural decomposition of hierarchical finite element spaces, discusses a characterization of this decomposition via strengthened CBS inequality and uses this decomposition for development of hierarchical error estimates and iterative solution methods.

Many gravity load designed (GLD) reinforced concrete (RC) frames are nowadays located in seismic areas. Different strengthening methodologies have been proposed in the past; an innovative technique based on the use of composites was proposed and validated by an experimental program developed at University of Missouri-Rolla. A theoretical approach for the assessment of the subassemblage capacity...

Brooks’ Theorem states that a connected graph G of maximum degree ∆ has chromatic number at most ∆, unless G is an odd cycle or a complete graph. A result of Johansson [6] shows that if G is triangle-free, then the chromatic number drops to O(∆/ log ∆). In this paper, we derive a weak analog for the chromatic number of digraphs. We show that every (loopless) digraph D without directed cycles of...

Changes in coastal upwelling strength have been widely studied since 1990 when Bakun proposed that global warming can induce the intensification of upwelling in coastal areas. Whether present wind trends support this hypothesis remains controversial, as results of previous studies seem to depend on the study area, the length of the time series, the season, and even the database used. In this st...

The steep-walled bedrock gorges of the Greater Himalayan rivers currently lack significant stored sediment, suggesting that fluvial erosion and transport capacity outpace the supply of sediment from adjacent hillsides. Despite this appearance of sustained downcutting, such rivers can become choked with sediments and aggrade during intervals of higher precipitation. Cosmogenic dating (10Be and 2...

The improved yield strength of annealed dispersionstrengthened copper (DSC) over conventional OFE copper makes it a possible candidate for use in extremely high potential gradient particle accelerator structures where stability is of critical importance. Test brazes of such structures show that the surface of DSC is not readily wetted by conventional goldbased braze alloys used for copper. Surf...

This paper presents results of testing eccentrically loaded columns externally wrapped with two types of materials. Six cylindrical (205 mm diameter and 925 mm height) plain columns were cast and tested. Half of the columns were wrapped with GFRP and the other half with CFRP. All columns were tested by applying an axial load at 50 mm eccentricity. In each group (GFRP or CFRP wrapped) of columns...

Symbolic secrecy of exchanged keys is arguably one of the most important notions of secrecy shown with automated proof tools. It means that an adversary restricted to symbolic operations on terms can never get the entire key into its knowledge set. Cryptographic key secrecy essentially means computational indistinguishability between the real key and a random one, given the view of a much more ...