The distribution of kk-tuples of reduced residues

In 1940 Paul Erd\H{o}s made a conjecture about the distribution of reduced residues. Here we study the distribution of $k$-tuple of reduced residues.Comment: To appear in Mathematik

Transverse Plasma Waves and the Effects of Capacitive Coupling in Long Intrinsic Josephson Junctions

In this paper we investigate the excitation of longitudinal and transverse plasma waves in intrinsic Josephson junctions. We consider the outermost branch of IV characteristic (IVc) in current biased case and try to find the conditions in which plasma waves can be excited. We change the parameters of the system and get the corresponding breakpoint current at which the plasma waves start to initiate. We present specifically the modes containing only transverse waves where we can have radiation. As a result we find the range of parameters that the system can radiate.Comment: 5 pages, 6 figure

Invariance principle for tempered fractional time series models

Autoregressive tempered fractionally integrated moving average (ARTFIMA) time series is a useful model for velocity data in turbulence flows. In this paper, we obtain an invariance principle for the partial sum of an ARTFIMA process. The limiting process is called tempered Hermite process of order one, $THP^{1}$, which is well-defined for any $H>\frac{1}{2}$. When $\frac{1}{2}<H<1$, we develop the Wiener integral with respect to $THP^{1}$ to provide the sufficient condition for the convergence \begin{equation*} n^{-H}\sum_{k=0}^{+\infty}f\Big(\frac{k}{n}\Big)X^{\frac{\lambda}{n}}_{k}\rightarrow \int_{\rr}f(u)Z^{1}_{H,\lambda}(du) \end{equation*} in distribution, as $n\to\infty$, where $X_{k}$ is an ARTFIMA time series and $Z^{1}_{H,\lambda}$ is $THP^{1}$.Comment: 32 pages, 1 Figure, This new version is the replacement of the previous version "Tempered Hermite Process"; some major revisions implemented throughou

On an extension of the Landau-Gonek formula

We prove an extension of the Landau-Gonek formula. As an application we recover unconditionally some of the consequences of a pair correlation estimate that previously was known under the Riemann hypothesis. As one corollary we prove that at least two-thirds of the zeros of the zeta function are simple under a zero density hypothesis, which is weaker than the Riemann hypothesis. The results in this paper can be viewed as pair correlation estimates independent of the Riemann hypothesis.Comment: 17 pages, comments are welcom

The coloring of the regular graph of ideals

The regular graph of ideals of the commutative ring $R$, denoted by $\Gamma_{reg}(R)$, is a graph whose vertex set is the set of all non-trivial ideals of $R$ and two distinct vertices $I$ and $J$ are adjacent if and only if either $I$ contains a $J$-regular element or $J$ contains an $I$-regular element. In this paper, it is shown that for every Artinian ring $R$, the edge chromatic number of $\Gamma_{reg}(R)$ equals its maximum degree. Then a formula for the clique number of $\Gamma_{reg}(R)$ is given. Also, it is proved that for every reduced ring $R$ with $n(\geq3)$ minimal prime ideals, the edge chromatic number of $\Gamma_{reg}(R)$ is $2^{n-1}-2$. Moreover, we show that both of the clique number and vertex chromatic number of $\Gamma_{reg}(R)$ are $n-1$, for every reduced ring $R$ with $n$ minimal prime ideals.Comment: AMS-LaTeX, 11 pages with no figure

A Semantic Situation without Syntax (Non- axiomatizibility of Theories)

Here, by introducing a version of Unexpected hanging paradox first we try to open a new way and a new explanation for paradoxes, similar to liar paradox. Also, we will show that we have a semantic situation which no syntactical logical system could support it. Finally, we propose a claim in the subject of axiomatizibility. Based on this claim, having an axiomatic system for Computability Theory is not possible. In fact, the same argument shows that many other theories are non-axiomatizable. (Dare to say: General Theories of Physics and Mathematics)

Tempered Hermite process

A tempered Hermite process modifies the power law kernel in the time domain representation of a Hermite process by multiplying an exponential tempering factor $\lambda>0$ such that the process is well defined for Hurst parameter $H>\frac{1}{2}$. A tempered Hermite process is the weak convergence limit of a certain discrete chaos process.Comment: Published at http://dx.doi.org/10.15559/15-VMSTA34 in the Modern Stochastics: Theory and Applications (https://www.i-journals.org/vtxpp/VMSTA) by VTeX (http://www.vtex.lt/

A Semantic Without Syntax 1

Here, by introducing a version of "Unexpected hanging paradox" we try to open a new way and a new explanation for paradoxes, similar to liar paradox. Also, we will show that we have a semantic situation which no syntactical logical system could support that. In the end, we propose a claim as a question. Based on this claim, having an axiomatic system for computability theory is not possible. In fact we will show that the method applied here could yields us as a generalized result, some Theories like Physic is not axiomatizable.Comment: 3 page

Nash Equilibrium in Social Media

In this work, we investigate an application of a Nash equilibrium seeking algorithm in a social network. In a networked game each player (user) takes action in response to other players' actions in order to decrease (increase) his cost (profit) in the network. We assume that the players' cost functions are not necessarily dependent on the actions of all players. This is due to better mimicking the standard social media rules. A communication graph is defined for the game through which players are able to share their information with only their neighbors. We assume that the communication neighbors necessarily affect the players' cost functions while the reverse is not always true. In this game, the players are only aware of their own cost functions and actions. Thus, each of them maintains an estimate of the others' actions and share it with the neighbors to update his action and estimates.Comment: arXiv admin note: substantial text overlap with arXiv:1612.0717

A Noncommutative Residue on Tori and a Semiclassical Limit

We define a noncommutative residue for classical Euclidean pseudodifferential operators on a torus of arbitrary dimension. We prove that, up to multiplication by a constant, it is the unique trace on the algebra of classical pseudodifferential operators modulo infinitely smoothing operators. In the case of the two torus, we show that the noncommutative residue is the semiclassical limit of a noncommutative residue defined on classical pseudodifferential operators on noncommutative two tori.Comment: 10 page