A note on Newton non-degeneracy of mixed weighted homogeneous polynomials

A mixed polynomial $f(\boldsymbol{z}, \bar{\boldsymbol{z}})$ is called a mixed weighted homogeneous polynomial (Definition 5) if it is both radially and polar weighted homogeneous. Let $f$ be a mixed weighted homogeneous polynomial with respect to a strictly positive radial weight vector $P$ and a polar weight vector $Q$. Suppose that $f$ is Newton non-degenerate over a compact face $\Delta(P)$ and polar weighted homogeneous of non-zero polar degree with respect to $Q$. Then $f : {{\mathbb{C}}^*}^n \to \mathbb{C}$ has no mixed critical points. Moreover, under the assumption $f^{-1}(0) \cap {{\mathbb{C}}^*}^n \neq \emptyset$, $f : {{\mathbb{C}}^*}^n \to \mathbb{C}$ is surjective. In other words, in this situation, Newton non-degeneracy over a compact face $\Delta(P)$ implies strong Newton non-degeneracy over $\Delta(P)$ (Proposition 10). With this fact as a starting point, we investigate the sets $f^{-1}(0) \cap {{\mathbb{C}}^*}^n$, and show the existence of a collection of mixed weighted homogeneous polynomials $f = f_{\Delta (P)}$ of non-zero polar degree which satisfy $\dim \Delta (P) \geq 1$ and $f^{-1}(0) \cap {{\mathbb{C}}^*}^n = \emptyset$ (Theorem 11). We also give an example of convenient mixed function germs of mixed weighted homogeneous face type which are not true non-degenerate (Definition 14).Comment: 11 page

Localization of Liv2 as an Immature Hepatocyte Marker in EB Outgrowth

The objective of this study was to establish Liv2, a surface marker of mouse immature hepatocytes (hepatoblasts), as a selection tool for embryonic stem (ES) cell–derived immature hepatocytes by acquiring basic data on Liv2 in normal mouse embryos and by confirming Liv2 expression in mouse ES-derived cells. The estimated molecular weight of Liv2 was 4045 kDa, and immunoreactivity was definitively detected in the cell membrane of fetal hepatocytes on embryonic day (E) 9.5, declined gradually until E12.5, and subsequently became undetectable. Liv2 was localized on and close to the cell membrane. Embryoid bodies (EB) were formed from mouse ES cells whose undifferentiated state was confirmed with immunostaining of Nanog by the hanging drop method. A few Liv2-positive cells occurred as a cluster in EB outgrowth on day 7, but only some of these were albumin (ALB)-positive on day 13. These cells had the same pattern of immunoreactivity, i.e., localization on the cell membrane, as immature hepatocytes in the developing liver, although there were other types of cells with a different pattern of immunoreactivity that were seen only as a granular pattern in the cytoplasm and without ALB or the neuronal marker nestin. These results suggest that Liv2 may be useful as a surface marker for immature hepatocytes derived from ES cells. This application would allow for the sole selection of immature hepatocytes and provide a useful tool for regenerative medicine

An Autopsy Case of Anaplastic Pancreatic Ductal Carcinoma (Spindle Cell Type) Multiple Onset in the Pancreas

This is a case of a 75-year-old man who was diagnosed with anaplastic pancreatic ductal carcinoma (spindle cell type). His image findings showed pancreatic head cysts and pancreatic head, body, and tail tumors respectively. EUS-FNA was performed to the pancreatic head and pancreatic body tumors, and the same high atypical type cells suspected of cancer were obtained from either specimen, and finally total pancreatectomy was performed. On the specimen, there were 4 lesions in the pancreas; histology showed that the same anaplastic pancreatic ductal carcinoma (spindle cell type) was obtained from the pancreatic head cyst and the pancreatic tumors

Orbital forcing and evolution of the Southern African Monsoon from late Miocene to early Pliocene

The late Miocene-early Pliocene (7.4-4.5 Ma) is a key interval in Earth's history where intense reorganization of atmospheric and ocean circulation occurred within a global cooling scenario. The Southern African monsoon (SAFM) potentially played an important role in climate systems variability during this interval. However, the dynamics of this important atmospheric system is poorly understood due to the scarcity of continuous records. Here, we present an exceptional continuous late Miocene to early Pliocene reconstruction of SAFM based on elemental geochemistry (Ca/Ti and Si/K ratios), stable isotope geochemistry (δ18O and δ13C recorded in the planktonic foraminifera Orbulina universa), and marine sediment grain size data from the International Ocean Discovery Program (IODP) Site U1476 located at the entrance of the Mozambique Channel. Spectral characteristics of the Si/K ratio (fluvial input) was used to identify the main orbital forcing controlling SAFM. Precession cycles governed precipitation from 7.4 to ∼6.9 Ma and during the early Pliocene. From ∼6.9 to ∼5.9 Ma, the precession and long eccentricity cycles drove the SAFM. The major Antarctic ice sheet expansion across this interval appear to influence the isotopic records of O. universa imprinting its long-term variability signal as a response to the ocean and atmospheric reorganization. Precession cycles markedly weakened from 5.9 to 5.3 Ma, almost the same period when the Mediterranean Outflow Water ceased. These findings highlight important teleconnections among the SAFM, Mediterranean Sea, and other tropical regions

A reference time scale for Site U1385 (Shackleton Site) on the SW Iberian Margin

We produced a composite depth scale and chronology for Site U1385 on the SW Iberian Margin. Using log(Ca/Ti) measured by core scanning XRF at 1-cm resolution in all holes, a composite section was constructed to 166.5 meters composite depth (mcd) that corrects for stretching and squeezing in each core. Oxygen isotopes of benthic foraminifera were correlated to a stacked δ^18O reference signal (LR04) to produce an oxygen isotope stratigraphy and age model. Variations in sediment color contain very strong precession signals at Site U1385, and the amplitude modulation of these cycles provides a powerful tool for developing an orbitally-tuned age model. We tuned the U1385 record by correlating peaks in L* to the local summer insolation maxima at 37^oN. The benthic δ^18O record of Site U1385, when placed on the tuned age model, generally agrees with other time scales within their respective chronologic uncertainties. The age model is transferred to down-core data to produce a continuous time series of log(Ca/Ti) that reflect relative changes of biogenic carbonate and detrital sediment. Biogenic carbonate increases during interglacial and interstadial climate states and decreases during glacial and stadial periods. Much of the variance in the log(Ca/Ti) is explained by a linear combination of orbital frequencies (precession, tilt and eccentricity), whereas the residual signal reflects suborbital climate variability. The strong correlation between suborbital log(Ca/Ti) variability and Greenland temperature over the last glacial cycle at Site U1385 suggests that this signal can be used as a proxy for millennial-scale climate variability over the past 1.5 Ma. Millennial climate variability, as expressed by log(Ca/Ti) at Site U1385, was a persistent feature of glacial climates over the past 1.5 Ma, including glacial periods of the early Pleistocene (‘41-kyr world’) when boundary conditions differed significantly from those of the late Pleistocene (‘100-kyr world’). Suborbital variability was suppressed during interglacial stages and enhanced during glacial periods, especially when benthic δ^18O surpassed ~ 3.3-3.5‰. Each glacial inception was marked by appearance of strong millennial variability and each deglaciation was preceded by a terminal stadial event. Suborbital variability may be a symptomatic feature of glacial climate or, alternatively, may play a more active role in the inception and/or termination of glacial cycles.This research was supported by the Natural Environmental Research Council Grant NE/K005804/1 to DH and LS and NE/J017922/1 to DH.This is the final version of the article. It first appeared from Elsevier via http://dx.doi.org/10.1016/j.gloplacha.2015.07.00

Onset of Mediterranean outflow into the North Atlantic

Sediments cored along the southwestern Iberian margin during Integrated Ocean Drilling Program Expedition 339 provide constraints on Mediterranean Outflow Water (MOW) circulation patterns from the Pliocene epoch to the present day. After the Strait of Gibraltar opened (5.33 million years ago), a limited volume of MOW entered the Atlantic. Depositional hiatuses indicate erosion by bottom currents related to higher volumes of MOW circulating into the North Atlantic, beginning in the late Pliocene. The hiatuses coincide with regional tectonic events and changes in global thermohaline circulation (THC). This suggests that MOW influenced Atlantic Meridional Overturning Circulation (AMOC), THC, and climatic shifts by contributing a component of warm, saline water to northern latitudes while in turn being influenced by plate tectonics

A reference time scale for Site U1385 (Shackleton Site) on the SW Iberian Margin

Variations in sediment color contain very strong precession signals at Site U1385, and the amplitude modulation of these cycles provides a powerful tool for developing an orbitally-tuned age model. We tuned the U1385 record by correlating peaks in L* to the local summer insolation maxima at 37°N. The benthic δ18O record of Site U1385, when placed on the tuned age model, generally agrees with other time scales within their respective chronologic uncertainties. The age model is transferred to down-core data to produce a continuous time series of log(Ca/Ti) that reflect relative changes of biogenic carbonate and detrital sediment. Biogenic carbonate increases during interglacial and interstadial climate states and decreases during glacial and stadial periods. Much of the variance in the log(Ca/Ti) is explained by a linear combination of orbital frequencies (precession, tilt and eccentricity), whereas the residual signal reflects suborbital climate variability. The strong correlation between suborbital log(Ca/Ti) variability and Greenland temperature over the last glacial cycle at Site U1385 suggests that this signal can be used as a proxy for millennial-scale climate variability over the past 1.5 Ma. Millennial climate variability, as expressed by log(Ca/Ti) at Site U1385, was a persistent feature of glacial climates over the past 1.5 Ma, including glacial periods of the early Pleistocene (‘41-kyr world’) when boundary conditions differed significantly from those of the late Pleistocene (‘100-kyr world’). Suborbital variability was suppressed during interglacial stages and enhanced during glacial periods, especially when benthic δ18O surpassed ~ 3.3–3.5‰. Each glacial inception was marked by appearance of strong millennial variability and each deglaciation was preceded by a terminal stadial event. Suborbital variability may be a symptomatic feature of glacial climate or, alternatively, may play a more active role in the inception and/or termination of glacial cycles

Theory of hard photoproduction

The present theoretical knowledge about photons and hard photoproduction processes, i.e. the production of jets, light and heavy hadrons, quarkonia, and prompt photons in photon-photon and photon-hadron collisions, is reviewed. Virtual and polarized photons and prompt photon production in hadron collisions are also discussed. The most important leading and next-to-leading order QCD results are compiled in analytic form. A large variety of numerical predictions is compared to data from TRISTAN, LEP, and HERA and extended to future electron and muon colliders. The sources of all relevant results are collected in a rich bibliography.Comment: Habilitationsschrift, scheduled for publication in Rev. Mod. Phys., 126 pages, 61 figure