Discovery of Super-Li Rich Red Giants in Dwarf Spheroidal Galaxies

Stars destroy lithium (Li) in their normal evolution. The convective envelopes of evolved red giants reach temperatures of millions of K, hot enough for the 7Li(p,alpha)4He reaction to burn Li efficiently. Only about 1% of first-ascent red giants more luminous than the luminosity function bump in the red giant branch exhibit A(Li) > 1.5. Nonetheless, Li-rich red giants do exist. We present 15 Li-rich red giants--14 of which are new discoveries--among a sample of 2054 red giants in Milky Way dwarf satellite galaxies. Our sample more than doubles the number of low-mass, metal-poor ([Fe/H] <~ -0.7) Li-rich red giants, and it includes the most-metal poor Li-enhanced star known ([Fe/H] = -2.82, A(Li)_NLTE = 3.15). Because most of these stars have Li abundances larger than the universe's primordial value, the Li in these stars must have been created rather than saved from destruction. These Li-rich stars appear like other stars in the same galaxies in every measurable regard other than Li abundance. We consider the possibility that Li enrichment is a universal phase of evolution that affects all stars, and it seems rare only because it is brief.Comment: 6 pages, 3 figures, accepted to ApJ Letters, version 3 includes additional references and minor typographical change

Further results on laws of large numbers for uncertain random variables

summary:The uncertainty theory was founded by Baoding Liu to characterize uncertainty information represented by humans. Basing on uncertainty theory, Yuhan Liu created chance theory to describe the complex phenomenon, in which human uncertainty and random phenomenon coexist. In this paper, our aim is to derive some laws of large numbers (LLNs) for uncertain random variables. The first theorem proved the Etemadi type LLN for uncertain random variables being functions of pairwise independent and identically distributed random variables and uncertain variables without satisfying the conditions of regular, independent and identically distributed (IID). Two kinds of Marcinkiewicz-Zygmund type LLNs for uncertain random variables were established in the case of $p \in (0, 1)$ by the second theorem, and in the case of $p > 1$ by the third theorem, respectively. For better illustrating of LLNs for uncertain random variables, some examples were stated and explained. Compared with the existed theorems of LLNs for uncertain random variables, our theorems are the generalised results

A variable-order fractal derivative model for anomalous diffusion

This paper pays attention to develop a variable-order fractal derivative model for anomalous diffusion. Previous investigations have indicated that the medium structure, fractal dimension or porosity may change with time or space during solute transport processes, results in time or spatial dependent anomalous diffusion phenomena. Hereby, this study makes an attempt to introduce a variable-order fractal derivative diffusion model, in which the index of fractal derivative depends on temporal moment or spatial position, to characterize the previous mentioned anomalous diffusion (or transport) processes. Compared with other models, the main advantages in description and the physical explanation of new model are explored by numerical simulation. Further discussions on the dissimilitude such as computational efficiency, diffusion behavior, and heavy tail phenomena of the new model, and variable-order fractional derivative model are also offered

Cooperative caching in fog radio access networks : a graph-based approach

AbstractIn this study, cooperative caching is investigated in fog radio access networks. To maximise the offloaded traffic, a cooperative caching optimisation problem is formulated. By analysing the relationship between clustering and cooperation and utilising the solutions of the knapsack problems, the above challenging optimisation problem is transformed into a clustering subproblem and a content placement subproblem. To further reduce complexity, the authors propose an effective graph-based approach to solve the two subproblems. In the graph-based clustering approach, a node graph and a weighted graph are constructed. By setting the weights of the vertices of the weighted graph to be the incremental offloaded traffics of their corresponding complete subgraphs, the objective cluster sets can be readily obtained by using an effective greedy algorithm to search for the max-weight independent subset. In the graph-based content placement approach, a redundancy graph is constructed by removing the edges in the complete subgraphs of the node graph corresponding to the obtained cluster sets. Furthermore, they enhance the caching decisions to ensure each duplicate file is cached only once. Compared with traditional approximate solutions, their proposed graph-based approach has lower complexity. Simulation results show remarkable improvements in terms of offloaded traffic by using the proposed approach.Abstract In this study, cooperative caching is investigated in fog radio access networks. To maximise the offloaded traffic, a cooperative caching optimisation problem is formulated. By analysing the relationship between clustering and cooperation and utilising the solutions of the knapsack problems, the above challenging optimisation problem is transformed into a clustering subproblem and a content placement subproblem. To further reduce complexity, the authors propose an effective graph-based approach to solve the two subproblems. In the graph-based clustering approach, a node graph and a weighted graph are constructed. By setting the weights of the vertices of the weighted graph to be the incremental offloaded traffics of their corresponding complete subgraphs, the objective cluster sets can be readily obtained by using an effective greedy algorithm to search for the max-weight independent subset. In the graph-based content placement approach, a redundancy graph is constructed by removing the edges in the complete subgraphs of the node graph corresponding to the obtained cluster sets. Furthermore, they enhance the caching decisions to ensure each duplicate file is cached only once. Compared with traditional approximate solutions, their proposed graph-based approach has lower complexity. Simulation results show remarkable improvements in terms of offloaded traffic by using the proposed approach