Hilbert polynomials of j-transforms

We study transformations of finite modules over Noetherian local rings that attach to a module $M$ a graded module $H^{0}_{\mathfrak{m}}( \mathrm{gr}_{I}(M))$ defined via partial systems of parameters of $M$. Despite the generality of the process, which are called $\mathbf{j}$-transforms, in numerous cases they have interesting cohomological properties. We focus on deriving the Hilbert functions of $\mathbf{j}$-transforms and studying the significance of the vanishing of some of its coefficients.Comment: This manuscript has been submitted to a journa

Variation of Hilbert Coefficients

For a Noetherian local ring (\RR, \m), the first two Hilbert coefficients, $e_0$ and $e_1$, of the $I$-adic filtration of an \m-primary ideal $I$ are known to code for properties of \RR, of the blowup of \spec(\RR) along $V(I)$, and even of their normalizations. We give estimations for these coefficients when $I$ is enlarged (in the case of $e_1$ in the same integral closure class) for general Noetherian local rings

Dilepton asymmetries at BB factories in search of ΔB=−ΔQ\Delta B =- \Delta Q transitions

In order to detect the possible presence of $\Delta B = - \Delta Q$ amplitudes in neutral $B$ meson decays, we consider the measurement of decay time asymmetries involving like-sign dilepton events at the $B$ factories.Comment: 5 pages, latex, no fig

Variation of the first Hilbert coefficients of parameters with a common integral closure

A problem posed by Wolmer V. Vasconcelos on the variation of the first Hilbert coefficients of parameter ideals with a common integral closure in a local ring is studied. Affirmative answers are given and counterexamples are explored as well

Reading The Gruffalo in Another Language: Assessing Non-Graded Children’s Picture Books for Extensive Reading

Article信州大学総合人間科学研究 17 : 92-104, (2023)departmental bulletin pape

Origin for the enhanced copper spin echo decay rate in the pseudogap regime of the multilayer high-T_c cuprates

We report measurements of the anisotropy of the spin echo decay for the inner layer Cu site of the triple layer cuprate, Hg_0.8Re_0.2Ba_2Ca_2Cu_3O_8 (T_c=126 K) in the pseudogap T regime below T_pg ~ 170 K and the corresponding analysis for their interpretation. As the field alignment is varied, the shape of the decay curve changes from Gaussian (H_0 \parallel c) to single exponential (H_0 \perp c). The latter characterizes the decay caused by the fluctuations of adjacent Cu nuclear spins caused by their interactions with electron spins. The angular dependence of the second moment (T_{2M}^{-2} \equiv ) deduced from the decay curves indicates that T_{2M}^{-2} for H_0 \parallel c, which is identical to T_{2G}^{-2} (T_{2G} is the Gaussian component), is substantially enhanced, as seen in the pseudogap regime of the bilayer systems. Comparison of T_{2M}^{-2} between H_0 \parallel c and H_0 \perp c indicates that this enhancement is caused by electron spin correlations between the inner and the outer CuO_2 layers. These results provide the answer to the long-standing controversy regarding the opposite T dependences of (T_1T)^{-1} and T_{2G}^{-2} in the pseudogap regime of bi- and trilayer systems.Comment: 4 pages, 4 figure

[Ultra] Luminous Infrared Galaxies selected at 90 μ\mum in the AKARI deep field: a study of AGN types contributing to their infrared emission

The aim of this work is to characterize physical properties of Ultra Luminous Infrared Galaxies (ULIRGs) and Luminous Infrared Galaxies (LIRGs) detected in the far-infrared (FIR) 90um band in the AKARI Deep Field-South (ADF-S) survey. In particular, we want to estimate the AGN contribution to the [U]LIRGs' infrared emission and which types of AGNs are related to their activity. We examined 69 galaxies at z>0.05 detected at 90um by the AKARI satellite in the ADF-S, with optical counterparts and spectral coverage from the ultraviolet to the FIR. We used two independent spectral energy distribution fitting codes: one fitting the SED from FIR to FUV (CIGALE) and gray-body + power spectrum fit for the infrared part of the spectra (CMCIRSED) in order to identify a subsample of [U]LIRGs, and to estimate their properties. Based on the CIGALE SED fitting, we have found that [U]LIRGs selected at the 90um AKARI band compose ~56% of our sample (we found 17 ULIRGs and 22 LIRGs, spanning over the redshift range 0.06<z<1.23). Their physical parameters, such as stellar mass, star formation rate (SFR), and specific SFR are consistent with the ones found for other samples selected at IR wavelengths. We have detected a significant AGN contribution to the MIR luminosity for 63% of LIRGs and ULIRGs. Our LIRGs contain Type 1, Type 2, and intermediate types of AGN, whereas for ULIRGs, a majority (more than 50%) of AGN emission originates from Type 2 AGNs. The temperature--luminosity and temperature--mass relations for the dust component of ADF--S LIRGs and ULIRGs indicate that these relations are shaped by the dust mass and not by the increased dust heating. We conclude that LIRGs contain Type 1, Type 2, and intermediate types of AGNs, with an AGN contribution to the MIR emission at the median level of 13+/-3%, whereas the majority of ULIRGs contain Type 2 AGNs, with a median AGN fraction equal to 19+/-8%.Comment: 24 pages, 21 figures, accepted for publication in Astronomy & Astrophysic

Integrable magnetic geodesic flows on Lie groups

Right-invariant geodesic flows on manifolds of Lie groups associated with 2-cocycles of corresponding Lie algebras are discussed. Algebra of integrals of motion for magnetic geodesic flows is considered and necessary and sufficient condition of integrability in quadratures is formulated. Canonic forms for 2-cocycles of all 4-dimensional Lie algebras are given and integrable cases among them are separated.Comment: 16 page