CsCl-type compounds in binary alloys of rare-earth metals with gold and silver

In binary alloys of silver with Sm, Tb, Ho, and Tm, and of gold with Y, Pr, Nd, Sm, Gd, Tb, Dy, Ho, Er, and Tm, intermediate phases containing stoichiometric proportions of the two metals were found to crystallize into the CsCl (B2)-type structure. The lattice parameters of these phases are reported and a correlation has been found between these lattice parameters and the trivalent ionic radii of the rare-earth metals

On the Classical W4(2)W_{4}^{(2)} Algebra

We consider the classical \w42 algebra from the integrable system viewpoint. The integrable evolution equations associated with the \w42 algebra are constructed and the Miura maps , consequently modifications, are presented. Modifying the Miura maps, we give a free field realization the classical \w42 algebra. We also construct the Toda type integrable systems for it.Comment: 14 pages, latex, no figure

Solar meridional circulation from twenty-one years of SOHO/MDI and SDO/HMI observations: Helioseismic travel times and forward modeling in the ray approximation

The south-north travel-time differences are measured by applying time-distance helioseismology to the MDI and HMI medium-degree Dopplergrams covering May 1996-April 2017. Our data analysis corrects for several sources of systematic effects: P-angle error, surface magnetic field effects, and center-to-limb variations. An interpretation of the travel-time measurements is obtained using a forward-modeling approach in the ray approximation. The travel-time differences are similar in the southern hemisphere for cycles 23 and 24. However, they differ in the northern hemisphere between cycles 23 and 24. Except for cycle 24's northern hemisphere, the measurements favor a single-cell meridional circulation model where the poleward flows persist down to $\sim$0.8 $R_\odot$, accompanied by local inflows toward the activity belts in the near-surface layers. Cycle 24's northern hemisphere is anomalous: travel-time differences are significantly smaller when travel distances are greater than 20$^\circ$. This asymmetry between northern and southern hemispheres during cycle 24 was not present in previous measurements (e.g., Rajaguru & Antia 2015), which assumed a different P-angle error correction where south-north travel-time differences are shifted to zero at the equator for all travel distances. In our measurements, the travel-time differences at the equator are zero for travel distances less than $\sim$30$^\circ$, but they do not vanish for larger travel distances. This equatorial offset for large travel distances need not be interpreted as a deep cross-equator flow; it could be due to the presence of asymmetrical local flows at the surface near the end points of the acoustic ray paths.Comment: accepted for publication in A&

Improved Approximation Algorithms for Computing k Disjoint Paths Subject to Two Constraints

For a given graph $G$ with positive integral cost and delay on edges, distinct vertices $s$ and $t$, cost bound $C\in Z^{+}$ and delay bound $D\in Z^{+}$, the $k$ bi-constraint path ($k$BCP) problem is to compute $k$ disjoint $st$-paths subject to $C$ and $D$. This problem is known NP-hard, even when $k=1$ \cite{garey1979computers}. This paper first gives a simple approximation algorithm with factor-$(2,2)$, i.e. the algorithm computes a solution with delay and cost bounded by $2*D$ and $2*C$ respectively. Later, a novel improved approximation algorithm with ratio $(1+\beta,\,\max\{2,\,1+\ln\frac{1}{\beta}\})$ is developed by constructing interesting auxiliary graphs and employing the cycle cancellation method. As a consequence, we can obtain a factor-$(1.369,\,2)$ approximation algorithm by setting $1+\ln\frac{1}{\beta}=2$ and a factor-$(1.567,\,1.567)$ algorithm by setting $1+\beta=1+\ln\frac{1}{\beta}$. Besides, by setting $\beta=0$, an approximation algorithm with ratio $(1,\, O(\ln n))$, i.e. an algorithm with only a single factor ratio $O(\ln n)$ on cost, can be immediately obtained. To the best of our knowledge, this is the first non-trivial approximation algorithm for the $k$BCP problem that strictly obeys the delay constraint.Comment: 12 page

The Color-Octet intrinsic charm in η′\eta^\prime and B→η′XB\to \eta^\prime X decays

Color-octet mechanism for the decay B\to \eta^\prime X is proposed to explain the large branching ratio of Br(B\to \eta^\prime X)\sim 1\times 10^{-3} recently announced by CLEO. We argue that the inclusive \eta^\prime production in B decays may dominantly come from the Cabbibo favored b\to (\bar c c)_8s process where \bar c c pair is in a color-octet configuration, and followed by the nonperturbative transition (\bar c c)_8\to \eta^\prime X. The color-octet intrinsic charm component in the higher Fock states of \eta^\prime is crucial and is induced by the strong coupling of \eta^\prime to gluons via QCD axial anomaly.Comment: 9 pages, RevTex, 1 PS figur