There are known infinite families of Brieskorn homology 3-spheres which can be realized as boundaries of smooth contractible 4-manifolds. In this paper we show that smooth free periodic actions on these Brieskorn spheres do not extend smoothly over a contractible 4-manifold. We give a new infinite family of examples in which the actions extend locally linearly but not smoothly.

We consider the following Schr\"odinger-Bopp-Podolsky system in $\mathbb R^{3}$ $$\left\{ \begin{array}{c} -\varepsilon^{2} \Delta u + V(x)u \phi = f(u)\\ \varepsilon^{4} \Delta^{2}\phi 4\pi\varepsilon u^{2}\\ \end{array} \right.$$ where $\varepsilon > 0$ with $ V:\mathbb{R}^{3} \rightarrow \mathbb{R}, f:\mathbb{R} \mathbb{R}$ satisfy suitable assumptions. By using variational methods, we pr...

in this study, we introduce the classes of $phi$-strongly pseudocontractive mappings in the intermediate sense and generalized $phi$-pseudocontractive mappings in the intermediate sense and prove the existence of fixed points for those maps. the results generalise the results of several authors in literature including xiang [chang he xiang, fixed point theorem for generalized $phi$-pseudocontra...

in the 1960's noboru iwahori and hideya matsumoto, eiichi abe and kazuo suzuki, and michael stein discovered that chevalley groups $g=g(phi,r)$ over a semilocal ring admit remarkable gauss decomposition $g=tuu^-u$, where $t=t(phi,r)$ is a split maximal torus, whereas $u=u(phi,r)$ and $u^-=u^-(phi,r)$ are unipotent radicals of two opposite borel subgroups $b=b(phi,r)$ and $b^-=b^-(phi,r)$ contai...

We show that if K is a nilpotent finite complex, then ΩK can be built from spheres using fibrations and homotopy (inverse) limits. This is applied to show that if map∗(X,S ) is weakly contractible for all n, then map ∗ (X,K) is weakly contractible for any nilpotent finite complex K . AMS Classification numbers Primary: 55Q05 Secondary: 55P50

The pseudo-Brewster angle phi(pB) of minimum reflectance for p-polarized light and the principal angle phi at which incident linearly polarized light of the proper azimuth is reflected circularly polarized are considered as functions of the complex relative dielectric function epsilon of a dielectric-conductor interface over the entire complex epsilon plane. In particular, the spread of phi for...