For vectors X, Y Î Rn, it is said that X is left matrix majorized by Y if for some row stochastic matrix R, X=RY. The relation X~LY, is defined as follows: X~LY if and only if X is left matrix majorized by Y and Y is left matrix majorized by X. A linear operator T: Rp® Rn is said to be a linear preserver of a given relation<if X<Y on Rp implies that TX<TY on Rn. The linear preservers of ~L from Rp to Rn are characterized before. In this parer we characterize the linear preservers of ~L from Rp to Rn, p³3. In fact we show that the linear preservers of ~L from Rp to Rn are the same as the linear preservers of ~L from Rp to Rn, but for p=2, they are not the same.

Let $\textbf{M}_{n,m}$ be the set of all $n$-by-$m$ real matrices, and let $\mathbb{R}^{n}$ be  the set of all $n$-by-$1$ real vectors. An $n$-by-$m$ matrix $R=[r_{ij}]$ is called g-row substochastic if $\sum_{k=1}^{m} r_{ik}\leq 1$  for all $i\     (1\leq i \leq n)$.  For $x$, $y \in \mathbb{R}^{n}$, it is said that $x$ is $\textit{sgut-majorized}$ by $y$, and we write  $ x    \prec_{sgut}y$  if there exists an $n$-by-$n$ upper triangular g-row substochastic matrix $R$ such that $x=Ry$. Define the relation $\sim_{sgut}$ as follows. $x\sim_{sgut}y$ if and only if $x$ is   sgut-majorized  by $y$ and $y$ is sgut-majorized  by $x$.  This paper characterizes all (strong)  linear preservers   of  $\sim_{sgut}$ on $\mathbb{R}^{n}$.

Let a be an orientation-preserving homeomorphism of [0,¥] onto itself with only two fixed points at 00 and ∞∞, whose restriction to R+=(0, ¥) is a diffeomorphism, and let UαUα be the isometric shift operator acting on the Lebesgue space Lp(R+) with p∈[1,∞] by the rule Uaf=( a')1/p(foa)U a f=( a ')1/p(foa). We establish criteria of the two-sided and one-sided invertibility of functional operators of the form...

This paper examines the necessity of regulating the Iranian card payments system (SHAPARAK) based on the theory of two-sided markets. The expansion of the payment card system in recent years has arisen some questions regarding the role of all kinds of costs and expenses such as interchange fees, cardholder fees, merchant fees, and network externality in balancing the market. Since there is only an interchange fee in Iran, regulation of the card payments system is necessary to assess the variables affecting this system. The data used in this study consist of 1218 observations of 29 banks from March 2016 to August 2019. The econometric method for this purpose is the fixed effects panel data model. The results indicate that the interchange fee has an essential role in balancing the Iranian card payment system market. Also, network externality makes the opportunity for balancing the market by decreasing the interchange fee and finally reducing transaction costs for acquirer banks. This policy can lower the interest rate of the bank loans because, in the Iranian card payment system, cardholders and merchants do not pay fees for transactions. So, banks try to attract clients for issuing cards and receive interchange fees as revenue to compensate for the payment network costs by the interest rate of loans. Overall, the results of the estimated model show that improving the card payments system in Iran should be regulated by related organizations.

Usually, in monitoring a proportion p, the binary observations are considered independent; however, in many real cases, there is a continuous stream of autocorrelated binary observations in which a two-state Markov chain model is applied with first-order dependence. On the other hand, the Bernoulli CUSUM control chart which is not robust to autocorrelation can be applied two-sided control chart to able to detect either increases or decreases in the process parameter. In this paper, a twosided Bernoulli-based CUSUM control chart is proposed based on a log-likelihood-ratio statistic using a Markov chain model and average run length relationship. The average run length relationship is set using the corresponding upper and lower Bernoulli CUSUM charts. Simulation studies show the superior performance of the proposed monitoring scheme. Numerical results show the superior performance of the proposed control chart.

For the power of two-sided hypothesis testing about the mean of a normal population, we derive a 100 (1-a) % confidence interval. Then by using a numerical method we will find a shortest confidence interval and consider some special cases.

This article explores the adjacency matrix of a two-sided group graph andits properties. We introduce the two-sided color group digraph to generalize the Cayley color graph and the two-sided group digraph. We alsoobtain the adjacency matrix of the latter digraph and provide a criterion fordetermining the normality of the adjacency matrix of a two-sided group graph.Moreover, we prove that if all the two-sided group digraphs of valency two fora certain group G are normal, then G is a Hamiltonian group. We also showthat if a strongly connected two-sided group digraph of valency two is normal,the corresponding group is isomorphic to the product of two groups: a cyclicgroup with either Tk,n or Hp,q, or an abelian group.

Gaussian interference known at the transmitter can be fully canceled in a Gaussian communication channel employing dirty paper coding, as Costa shows, when interference is independent of the channel noise and when the channel input designed independently of the interference. In this paper, a new and general version of the Gaussian channel in presence of two-sided state information correlated to the channel input and noise is considered. Determining a general achievable rate for the channel and obtaining the capacity in a non-limiting case, we try to analyze and solve the Gaussian version of the Cover-Chiang theorem mathematically and information-theoretically. Our capacity theorem, while including all previous theorems as its special cases, explains situations that can not be analyzed by them; for example, the effect of the correlation between the side information and the channel input on the capacity of the channel that can not be analyzed with Costa’ s ― writing on dirty paper" theorem. Meanwhile, we try to exemplify the concept of ― cognition" of the transmitter or the receiver on a variable (here, the channel noise) with the information-theoretic concept of ― side information" correlated to that variable and known at the transmitter or at the receiver. According to our theorem, the channel capacity is an increasing function of the mutual information of the side information and the channel noise.