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Register a new userConsimilarity and quaternion matrix equations $AX-hat{X}B=C$, $X-Ahat{X}B=C$
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L.Huang [Linear Algebra Appl. 331 (2001) 21-30] gave a canonical form of a quaternion matrix $A$ with respect to consimilarity transformations $tilde{S}^{-1}AS$ in which $S$ is a nonsingular quaternion matrix and $tilde{h}:=a-bi+cj-dk$ for each quaternion $h=a+bi+cj+dk$. We give an analogous canonical form of a quaternion matrix with respect to consimilarity transformations $hat{S}^{-1}AS$ in which $hmapstohat{h}$ is an arbitrary involutive automorphism of the skew field of quaternions. We apply the obtained canonical form to the quaternion matrix equations $AX-hat{X}B=C$ and $X-Ahat{X}B=C$.
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The matrix equation $AX-XB=C$ has a solution if and only if the matrices [A&C0&B] and [A &00 & B] are similar. This criterion was proved over a field by W.E. Roth (1952) and over the skew field of quaternions by Huang Liping (1996). H.K. Wimmer (1988) obtained an analogous criterion for the matrix equation $X-AXB=C$ over a field. We extend these criteria to the matrix equations $AX-widehat XB=C$ and $X-Awidehat XB=C$ over the skew field of quaternions with a fixed involutive automorphism $qmapsto hat q$.
We have synthesized bulk Mg(B$_{1-x}$C$_x$)$_2$ from a mixture of elemental Mg, B, and the binary compound B$_4$C. Carbon incorporation was dramatically improved by a two step reaction process at an elevated temperature of 1200 $^o$C. This reaction process results in a solubility limit near x$sim$0.07. We found that impurities in the starting B cause an additive suppression of T$_c$. We combine these data with T$_c$ and H$_{c2}$(T=0) data from CVD wires as well as plasma spray synthesized powders and present a unifying H$_{c2}$ and T$_c$ versus x plot.
We present first-principles density functional theory (DFT) investigations of mechanical, thermodynamic and optical properties of synthesized inverse-perovskites Sc3InX (X = B, C, N). The elastic constants at zero pressure and temperature are calculated and the anisotropic behavior of the compounds is illustrated. All the three materials are shown to be brittle in nature. The computed Peierls stress, approximately 3 to 5 times larger than of a selection of MAX phases, show that dislocation movement may follow but with much reduced occurrences compared to these MAX phases. The Mulliken bonding population and charge density maps show stronger covalency between Sc and X atoms compared with Sc-Sc bond. The Vickers hardness values of Sc3InX are predicted to be between 3.03 and 3.88 GPa. The Fermi surfaces of Sc3InX contain both hole- and electron-like topology which changes as one replaces B with C or N. The bulk modulus, specific heats, thermal expansion coefficient, and Debye temperature are calculated as a function both temperature and pressure using the quasi-harmonic Debye model with phononic effects. The results so obtained are analysed in comparison to the characteristics of other related compounds. Moreover optical functions are calculated and discussed for the first time. The reflectivity is found to be high in the IR-UV regions up to ~ 10.7 eV (Sc3InB, Sc3InC) and 12.3 eV (Sc3InN), thus showing promise as good coating materials. Keywords: Sc3InX, Mechanical properties; Fermi surface; Quasi-harmonic Debye model; Thermodynamic properties; Optical properties
We have performed fully-kinetic simulations of X-B and O-X-B mode conversion in one and two dimensional setups using the PIC code EPOCH. We have recovered the linear dispersion relation for electron Bernstein waves by employing relatively low amplitude incoming waves. The setups presented here can be used to study non-linear regimes of X-B and O-X-B mode conversion.
Using the data sample of 711 fb$^{-1}$ of $Upsilon(4S)$ on-resonance data taken by the Belle detector at the KEKB asymmetric-energy electron-positron collider, we present the first measurements of branching fractions of the decays $B^{-} to bar{Lambda}_{c}^{-} Xi_{c}^{0}$, $B^{-} to bar{Lambda}_{c}^{-} Xi_{c}(2645)^{0}$, and $B^{-} to bar{Lambda}_{c}^{-} Xi_{c}(2790)^{0} $. The signal yields for these decays are extracted from the recoil mass spectrum of the system recoiling against $bar{Lambda}_{c}^{-}$ baryons in selected $B^-$ candidates. The branching fraction of $B^{-} to bar{Lambda}_{c}^{-} Xi_{c}(2790)^{0}$ is measured to be $ (1.1 pm 0.4 pm 0.2)times 10^{-3}$, where the first uncertainty is statistical and the second systematic. The 90% credibility level upper limits on ${cal B}(B^{-} to bar{Lambda}_{c}^{-} Xi_{c}^{0})$ and ${cal B}(B^{-} to bar{Lambda}_{c}^{-} Xi_{c}(2645)^{0})$ are determined to be $6.5times 10^{-4}$ and $7.9times 10^{-4}$, respectively.
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