“Metatext” Separated from the Main Text

“Metatext” can be either separated from the main text or placed inside it. The “metatexts” of the first type (foreword, epigraph, commentaries, footnotes, etc) are not connected syntactically with the main text, though being semantically related to it

On the Public Communication Needed to Achieve SK Capacity in the Multiterminal Source Model

The focus of this paper is on the public communication required for generating a maximal-rate secret key (SK) within the multiterminal source model of Csisz{\'a}r and Narayan. Building on the prior work of Tyagi for the two-terminal scenario, we derive a lower bound on the communication complexity, $R_{\text{SK}}$, defined to be the minimum rate of public communication needed to generate a maximal-rate SK. It is well known that the minimum rate of communication for omniscience, denoted by $R_{\text{CO}}$, is an upper bound on $R_{\text{SK}}$. For the class of pairwise independent network (PIN) models defined on uniform hypergraphs, we show that a certain "Type $\mathcal{S}$" condition, which is verifiable in polynomial time, guarantees that our lower bound on $R_{\text{SK}}$ meets the $R_{\text{CO}}$ upper bound. Thus, PIN models satisfying our condition are $R_{\text{SK}}$-maximal, meaning that the upper bound $R_{\text{SK}} \le R_{\text{CO}}$ holds with equality. This allows us to explicitly evaluate $R_{\text{SK}}$ for such PIN models. We also give several examples of PIN models that satisfy our Type $\mathcal S$ condition. Finally, we prove that for an arbitrary multiterminal source model, a stricter version of our Type $\mathcal S$ condition implies that communication from \emph{all} terminals ("omnivocality") is needed for establishing a SK of maximum rate. For three-terminal source models, the converse is also true: omnivocality is needed for generating a maximal-rate SK only if the strict Type $\mathcal S$ condition is satisfied. Counterexamples exist that show that the converse is not true in general for source models with four or more terminals.Comment: Submitted to the IEEE Transactions on Information Theory. arXiv admin note: text overlap with arXiv:1504.0062

Liouville Type Theorem For A Nonlinear Neumann Problem

Consider the following nonlinear Neumann problem $$\begin{cases} \text{div}\left(y^{a}\nabla u(x,y)\right)=0, & \text{for }(x,y)\in\mathbb{R}_{+}^{n+1}\\ \lim_{y\rightarrow0+}y^{a}\frac{\partial u}{\partial y}=-f(u), & \text{on }\partial\mathbb{R}_{+}^{n+1},\\ u\ge0 & \text{in }\mathbb{R}_{+}^{n+1}, \end{cases}$$ $a\in(-1,1)$. A Liouville type theorem and its applications are given under suitable conditions on $f$. Our tool is the famous moving plane method.Comment: This paper has been withdrawn by the author due to a poor writin

Word Containing the FFL Trigram

Where type is hand set, the type is kept in trays. Among the boxes in the lower-case trays are ones for the ligatures (letters joined on a single piece of type) ff, fi, fl, ffi and ffl. Of these, the ligature ffl always looks the newest because it is used least often. Just how infrequently is it used? When I asked the editor, he informed me that Kucera and Francis\u27s million-word sample of text published in the United States in 1962 revealed only 87 occurrences: ffl occurs, on the average, in only one word in ten thousand in running text

Spinor Field with Polynomial Nonlinearity in LRS Bianchi type-I spacetime

Within the scope of Bianchi type-I cosmological model the role of spinor field on the evolution of the Universe is investigated. In doing so we have considered a polynomial type of nonlinearity. It is found that depending on the sign of self-coupling constant the model allows either accelerated mode of expansion or oscillatory mode of evolution. Unlike general Bianchi type-I and Bianchi type $VI_0$ models in this case neither mass term nor the nonlinear term in the Lagrangian of spinor field vanish.Comment: 9 pages, 4 figures. arXiv admin note: substantial text overlap with arXiv:1409.4993; text overlap with arXiv:1507.0384