For vectors $X, Yin mathbb{R}^{n}$, we say $X$ is left matrix majorized by $Y$ and write $X prec_{ell} Y$ if for some row stochastic matrix $R, ~X=RY.$ Also, we write $Xsim_{ell}Y,$ when $Xprec_{ell}Yprec_{ell}X.$ A linear operator $Tcolon mathbb{R}^{p}to mathbb{R}^{n}$ is said to be a linear preserver of a given relation $prec$ if $Xprec Y$ on $mathbb{R}^{p}$ implies that $TXprec TY$ on $mathb...

The valuation of insurance liabilities has traditionally been dealt with by actuaries, who closely monitored underlying illiquid features, assumed a long-term perspective, and exercised their own subjective, expert judgment. However, the new EU regulatory regime Solvency II (S2) come to require market-consistent supplemented risk-sensitive capital. This is considered an unwanted shift towards s...

With the rapid development of wireless communication technologies, mobile networks will enable users to use personal mobile devices to access various network information services at anytime and anyplace. Recently, Lu et al. proposed a dynamic ID based mutual authentication and key agreement scheme using elliptic curve cryptography (ECC) which attempts to support better security properties and r...

Life Buoy, also known as a life preserver, is crucial safety tool on board any marine ships. The most common and conventional lifesaver operated manually to save people from drowning, yet this method poses risk for both the victim rescuer. Hence, with help of current technology, smart lifebuoy has been developed, whereby rescuer just operates using remote control. Yet, existing buoy system foun...

in this study, the nonlinear optical properties and optical limiting performance of the silver nanoparticles (agnps) in distilled water are investigated. the nonlinear absorption coefficient of the colloid is measured by the z-scan technique. the optical limiting behavior of the agnp suspension is investigated under exposure to nanosecond laser pulses at 532 nm. the results show that nonlinear ...

this paper proposes a three-step method for solving nonlinear volterra integralequations system. the proposed method convents the system to a (3 × 3)nonlinear block system and then by solving this nonlinear system we ndapproximate solution of nonlinear volterra integral equations system. to showthe advantages of our method some numerical examples are presented.

This paper introduces an inequality on vectors in $mathbb{R}^n$ which compares vectors in $mathbb{R}^n$ based on the $p$-norm of their projections on $mathbb{R}^k$ ($kleq n$). For $p>0$, we say $x$ is $d$-projectionally less than or equal to $y$ with respect to $p$-norm if $sum_{i=1}^kvert x_ivert^p$ is less than or equal to $ sum_{i=1}^kvert y_ivert^p$, for every $dleq kleq n$. For...

for vectors x, y ∈ rn, it is said that x is left matrix majorizedby y if for some row stochastic matrix r; x = ry. the relationx ∼` y, is defined as follows: x ∼` y if and only if x is leftmatrix majorized by y and y is left matrix majorized by x. alinear operator t : rp → rn is said to be a linear preserver ofa given relation ≺ if x ≺ y on rp implies that t x ≺ ty onrn. the linear preservers o...