Equivalence Principle Violation in Weakly Vainshtein-Screened Systems

Massive gravity, galileon and braneworld models that modify gravity to explain cosmic acceleration utilize the nonlinear field interactions of the Vainshtein mechanism to screen fifth forces in high density regimes. These source-dependent interactions cause apparent equivalence principle violations. In the weakly-screened regime violations can be especially prominent since the fifth forces are at near full strength. Since they can also be calculated perturbatively, we derive analytic solutions for illustrative cases: the motion of massive objects in compensated shells and voids and infall toward halos that are spherically symmetric. Using numerical techniques we show that these solutions are valid until the characteristic scale becomes comparable to the Vainshtein radius. We find a relative acceleration of more massive objects toward the center of a void and a reduction of the infall acceleration that increases with the mass ratio of the halos which can in principle be used to test the Vainshtein screening mechanism.Comment: 7 pages, 4 figure

On σ\sigma-quasinormal subgroups of finite groups

Let $G$ be a finite group and $\sigma =\{\sigma_{i} | i\in I\}$ some partition of the set of all primes $\Bbb{P}$, that is, $\sigma =\{\sigma_{i} | i\in I \}$, where $\Bbb{P}=\bigcup_{i\in I} \sigma_{i}$ and $\sigma_{i}\cap \sigma_{j}= \emptyset$ for all $i\ne j$. We say that $G$ is $\sigma$-primary if $G$ is a $\sigma _{i}$-group for some $i$. A subgroup $A$ of $G$ is said to be: ${\sigma}$-subnormal in $G$ if there is a subgroup chain $A=A_{0} \leq A_{1} \leq \cdots \leq A_{n}=G$ such that either $A_{i-1}\trianglelefteq A_{i}$ or $A_{i}/(A_{i-1})_{A_{i}}$ is $\sigma$-primary for all $i=1, \ldots, n$, modular in $G$ if the following conditions hold: (i) $\langle X, A \cap Z \rangle=\langle X, A \rangle \cap Z$ for all $X \leq G, Z \leq G$ such that $X \leq Z$, and (ii) $\langle A, Y \cap Z \rangle=\langle A, Y \rangle \cap Z$ for all $Y \leq G, Z \leq G$ such that $A \leq Z$. In this paper, a subgroup $A$ of $G$ is called $\sigma$-quasinormal in $G$ if $L$ is modular and ${\sigma}$-subnormal in $G$. We study $\sigma$-quasinormal subgroups of $G$. In particular, we prove that if a subgroup $H$ of $G$ is $\sigma$-quasinormal in $G$, then for every chief factor $H/K$ of $G$ between $H^{G}$ and $H_{G}$ the semidirect product $(H/K)\rtimes (G/C_{G}(H/K))$ is $\sigma$-primary.Comment: 9 page

Suppression of thermal conductivity in graphene nanoribbons with rough edges

We analyze numerically the thermal conductivity of carbon nanoribbons with ideal and rough edges. We demonstrate that edge disorder can lead to a suppression of thermal conductivity by several orders of magnitude. This effect is associated with the edge-induced Anderson localization and suppression of the phonon transport, and it becomes more pronounced for longer nanoribbons and low temperatures.Comment: 6 pages, 8 figure

Towards Life Long Learning: Three Models for Ubiquitous Applications

In this paper, we present three experimental proof-of-concepts: First, we demonstrate a Ubiquitous Computing Framework (UCF), which is a network of interacting technologies that support humans ubiquitously. We then present practical work based on this UCF framework: TalkingPoints, which was originally developed for use at trading fairs in order to identify each participant and company via transponder and provide specific information during and after use. Finally, we propose GARFID, a concept for using advanced technologies for teaching young children. The main outcome of this research is that the concept of UCF raises a lot of possibilities, which can bring value and benefits for end-users. When one follows the Working-is-Learning paradigm, it can be seen that the implementation of this type of technology can support Life Long Learning, thereby providing evidence that technology can benefit everybody and make life easier

Combinatorial Alphabet-Dependent Bounds for Locally Recoverable Codes

Locally recoverable (LRC) codes have recently been a focus point of research in coding theory due to their theoretical appeal and applications in distributed storage systems. In an LRC code, any erased symbol of a codeword can be recovered by accessing only a small number of other symbols. For LRC codes over a small alphabet (such as binary), the optimal rate-distance trade-off is unknown. We present several new combinatorial bounds on LRC codes including the locality-aware sphere packing and Plotkin bounds. We also develop an approach to linear programming (LP) bounds on LRC codes. The resulting LP bound gives better estimates in examples than the other upper bounds known in the literature. Further, we provide the tightest known upper bound on the rate of linear LRC codes with a given relative distance, an improvement over the previous best known bounds.Comment: To appear in IEEE Transactions on Information Theor