In [13], Migliore–Miró-Roig–Nagel show that the Weak Lefschetz property can fail for an ideal I ⊆ K[x1, . . . , x4] generated by powers of linear forms. This is in contrast to the analogous situation in K[x1, x2, x3], where WLP always holds [16]. We use the inverse system dictionary to connect I to an ideal of fat points, and show that failure of WLP for powers of linear forms is connected to t...

in this paper, we introduce a method by which we can find a close connection between the set of prime $z$-ideals of $c(x)$ and the same of $c(y)$, for some special subset $y$ of $x$. for instance, if $y=coz(f)$ for some $fin c(x)$, then there exists a one-to-one correspondence between the set of prime $z$-ideals of $c(y)$ and the set of prime $z$-ideals of $c(x)$ not containing $f$. moreover, c...

[1] One difficulty for ocean modeling is the lack of velocity data for specifying the initial condition. Diagnostic initialization is widely used; it integrates the model from known temperature (Tc) and salinity (Sc) and zero velocity fields while holding (Tc, Sc) unchanged. After a period (around 30 days) of the diagnostic run, the velocity field (Vc) is established, and (Tc, Sc, Vc) fields ar...

We determine the distribution of circumstellar disk masses in the young (∼ 0.3 Myr) cluster NGC 2024 by imaging a 2. 5×2. 5 region in λ3mm continuum emission to an RMS noise level of ∼ 0.75 mJy beam with the Owens Valley Millimeter Array. The mosaic encompasses 147 K-band sources as well as the molecular ridge seen previously in dust continuum emission. We detect 10 point-like sources in λ3mm c...