6,863 research outputs found
The distribution of -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 -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
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
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,
, which is well-defined for any . When
, we develop the Wiener integral with respect to 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
, where is an ARTFIMA time series and
is .Comment: 32 pages, 1 Figure, This new version is the replacement of the
previous version "Tempered Hermite Process"; some major revisions implemented
throughou
The coloring of the regular graph of ideals
The regular graph of ideals of the commutative ring , denoted by
, is a graph whose vertex set is the set of all non-trivial
ideals of and two distinct vertices and are adjacent if and only if
either contains a -regular element or contains an -regular
element. In this paper, it is shown that for every Artinian ring , the edge
chromatic number of equals its maximum degree. Then a formula
for the clique number of is given. Also, it is proved that
for every reduced ring with minimal prime ideals, the edge
chromatic number of is . Moreover, we show that
both of the clique number and vertex chromatic number of are
, for every reduced ring with 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 such that the process is well defined for Hurst parameter
. 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
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