Motion of a rigid punch at a low velocity along the boundary of a viscoelastic half-plane

The contact problem of the interaction of a rigid punch with a viscoelastic half-plane is considered. The dependence of the displacement of the boundary of half-plane on the normal load applied to it is determined, and the integral equation for determining the contact pressure is derived and solved by the method of “small λ”. Distributions of contact pressures under the punch are graphically represented.     

Does a generic connection depend continuously on its curvature?

For a principal bundle with semi-simple structure group over a smooth four-dimensional base manifold, the set of connections (gauge potentials)A which are uniquely determined by their curvature (field or field strength)F is generic in the set of all potentials, endowed with the WhitneyC ^∞ topology. However, the operator taking each such fieldF to its potentialA is not continuous. Partial negative results are given concerning the existence of a smaller generic set on which this operator is continuous.     

Analysis of the low temperature fluorescence and phosphorescence spectra of p-difluorobenzene

The low temperature fluorescence spectra (4.2 K) of solid solutions of p-difluorobenzene-h₄ (pDFB-h₄) and -d₄ have been recorded and analyzed. The absence of fluorescence from vibrationally excited states at 4.2 K eliminates the sequence and “hot band” structure which complicate the analysis of the vapor fluorescence spectrum. On the basis of a comparison of our vibrational analysis with those published for the vapor phase fluorescence, several incorrect assignments in the latter have been identified. The high resolution and lack of spectral congestion obtained in the low temperature matrix isolated fluorescence spectra also allowed additional vibrational assignments to be made. These results are of added importance because of the extensive use which has been made of pDFB for radiationless relaxation studies in the vapor phase. The phosphorescence spectrum of crystalline pDFB-h₄ was observed with sufficient intensity to locate the electronic origin to make several vibrational assignments. Additionally, the zero-field splitting of the first triplet excited state was measured by optically detected magnetic resonance techniques.     

On a compromise social choice correspondence

This paper analyzes the compromise social choice correspondence derived from the τ-value of digraph games. Monotonicity of this correspondence is shown. A connection between several properties of social choice correspondences based on game theoretical solutions and game theoretical properties of the underlying solutions is given. Applications to several game theoretic solutions are provided.     

Stable Ergodicity and Frame Flows

In this note we show that all diffeomorphisms close enough to the time-one map of the frame flow on certain negatively curved manifolds are ergodic. As a simple corollary we deduce that the frame flows are ergodic for all compact manifolds with curvature pinched sufficiently close to –1, thus providing results in the case of manifolds of dimension 7 or 8 which were missing from the results of Brin and Karcher.     

Computation of Almost Split Sequences with Applications to Relatively Projective and Prinjective Modules

Let be an Artin algebra, let mod be the category of finitely generated -modules, and let Amod be a contravariantly finite and extension closed subcategory. For an indecomposable and not Ext-projective module CA, we compute the almost split sequence 0ABC0 in A from the almost split sequence 0DTrCEC0 in mod. Since the computation is particularly simple if the minimal right A-approximation of DTrC is indecomposable for all indecomposable and not Ext-projective CA, we manufacture subcategories A with the desired property using orthogonal subcategories. The method of orthogonal subcategories is applied to compute almost split sequences for relatively projective and prinjective modules.