Hopf algebras of dimension 2p^2

Let H be a non-semisimple Hopf algebra of dimension 2p^2 over an algebraically closed field of characteristic zero, where p is an odd prime. We prove that H or H^* is pointed, which completes the classification for Hopf algebras of these dimensions.Comment: 16pp Latex; Corrected typos and added references; Made a correction to the proof of Lemma 2.2 in the version (V1

Dalton State College APEX Calculus

This text for Analytic Geometry and Calculus I, II, and III is a Dalton State College remix of APEX Calculus 3.0. The text was created through a Round Six ALG Textbook Transformation Grant. Topics covered in this text include: Limits Derivatives Integration Antidifferentiation Sequences Vectors Files can also be downloaded on the Dalton State College GitHub: https://github.com/DaltonStateCollege/calculus-text/blob/master/Calculus.pdf Accessible files with optical character recognition (OCR) and auto-tagging provided by the Center for Inclusive Design and Innovation.https://oer.galileo.usg.edu/mathematics-textbooks/1016/thumbnail.jp

Analytic Geometry and Calculus I, II, & III (Dalton)

This Grants Collection for Analytic Geometry and Calculus I, II, & III was created under a Round Six ALG Textbook Transformation Grant. Affordable Learning Georgia Grants Collections are intended to provide faculty with the frameworks to quickly implement or revise the same materials as a Textbook Transformation Grants team, along with the aims and lessons learned from project teams during the implementation process. Documents are in .pdf format, with a separate .docx (Word) version available for download. Each collection contains the following materials: Linked Syllabus Initial Proposal Final Reporthttps://oer.galileo.usg.edu/mathematics-collections/1024/thumbnail.jp

Massive calcium–activated endocytosis without involvement of classical endocytic proteins

We describe rapid massive endocytosis (MEND) of >50% of the plasmalemma in baby hamster kidney (BHK) and HEK293 cells in response to large Ca transients. Constitutively expressed Na/Ca exchangers (NCX1) are used to generate Ca transients, whereas capacitance recording and a membrane tracer dye, FM 4–64, are used to monitor endocytosis. With high cytoplasmic adenosine triphosphate (ATP; >5 mM), Ca influx causes exocytosis followed by MEND. Without ATP, Ca transients cause only exocytosis. MEND can then be initiated by pipette perfusion of ATP, and multiple results indicate that ATP acts via phosphatidylinositol-bis 4,5-phosphate (PIP2) synthesis: PIP2 substitutes for ATP to induce MEND. ATP-activated MEND is blocked by an inositol 5-phosphatase and by guanosine 5′-[γ-thio]triphosphate (GTPγS). Block by GTPγS is overcome by the phospholipase C inhibitor, U73122, and PIP2 induces MEND in the presence of GTPγS. MEND can occur in the absence of ATP and PIP2 when cytoplasmic free Ca is clamped to 10 µM or more by Ca-buffered solutions. ATP-independent MEND occurs within seconds during Ca transients when cytoplasmic solutions contain polyamines (e.g., spermidine) or the membrane is enriched in cholesterol. Although PIP2 and cholesterol can induce MEND minutes after Ca transients have subsided, polyamines must be present during Ca transients. MEND can reverse over minutes in an ATP-dependent fashion. It is blocked by brief β-methylcyclodextrin treatments, and tests for involvement of clathrin, dynamins, calcineurin, and actin cytoskeleton were negative. Therefore, we turned to the roles of lipids. Bacterial sphingomyelinases (SMases) cause similar MEND responses within seconds, suggesting that ceramide may be important. However, Ca-activated MEND is not blocked by reagents that inhibit SMases. MEND is abolished by the alkylating phospholipase A2 inhibitor, bromoenol lactone, whereas exocytosis remains robust, and Ca influx causes MEND in cardiac myocytes without preceding exocytosis. Thus, exocytosis is not prerequisite for MEND. From these results and two companion studies, we suggest that Ca promotes the formation of membrane domains that spontaneously vesiculate to the cytoplasmic side

Mechanistic analysis of massive endocytosis in relation to functionally defined surface membrane domains

A large fraction of endocytosis in eukaryotic cells occurs without adaptors or dynamins. Here, we present evidence for the involvement of lipid domains in massive endocytosis (MEND) activated by both large Ca transients and amphipathic compounds in baby hamster kidney and HEK293 cells. First, we demonstrate functional coupling of the two MEND types. Ca transients can strongly facilitate detergent-activated MEND. Conversely, an amphipath with dual alkyl chains, ditridecylphthalate, is without effect in the absence of Ca transients but induces MEND to occur within seconds during Ca transients. Ca transients, like amphipaths, enhance the extraction of lipids from cells by β-cyclodextrins. Second, we demonstrate that electrical and/or optical signals generated by selected membrane probes are nearly insensitive to MEND, suggesting that those probes segregate into membrane domains that are not taken up by MEND. Triphenylphosphoniums are increasingly excluded from domains that internalize as the carbon chain length increases from 4 to 12. The small cationic membrane dye, FM 4–64, binds well to domains that internalize, whereas a closely related dye with a larger hydrophobic moiety, di-4-ANEPPDHQ (ANEPPDHQ) is excluded. Multiple carrier-type ionophores and a small amphipathic anion, niflumic acid, are also excluded. Probes with modest MEND sensitivity include the hydrophobic anion, dipicrylamine, carbonyl cyanide m-chlorophenylhydrazone, and NBD-phosphatidylethanolamine. Third, we demonstrate that large Ca transients can strongly enhance the extracellular binding of several membrane probes, monitored electrically or optically, consistent with a more disordered membrane with more amphipath-binding sites. Fluorescence shifts of ANEPPDHQ report increased disorder of the extracellular monolayer after large Ca transients, consistent with an increased propensity of the membrane to phase separate and vesiculate. Collectively, the results indicate that >50% of the outer monolayer is ordered and can be selectively internalized during MEND responses initiated by two very different cell perturbations

Massive endocytosis driven by lipidic forces originating in the outer plasmalemmal monolayer: a new approach to membrane recycling and lipid domains

The roles that lipids play in endocytosis are the subject of debate. Using electrical and imaging methods, we describe massive endocytosis (MEND) in baby hamster kidney (BHK) and HEK293 cells when the outer plasma membrane monolayer is perturbed by the nonionic detergents, Triton X-100 (TX100) and NP-40. Some alkane detergents, the amphipathic drugs, edelfosine and tamoxifen, and the phospholipase inhibitor, U73122, are also effective. Uptake of the membrane tracer, FM 4–64, into vesicles and loss of reversible FM 4–64 binding confirm that 40–75% of the cell surface is internalized. Ongoing MEND stops in 2–4 s when amphipaths are removed, and amphipaths are without effect from the cytoplasmic side. Thus, expansion of the outer monolayer is critical. As found for Ca-activated MEND, vesicles formed are <100 nm in diameter, membrane ruffles are lost, and β-cyclodextrin treatments are inhibitory. However, amphipath-activated MEND does not require Ca transients, adenosine triphosphate (ATP) hydrolysis, G protein cycling, dynamins, or actin cytoskeleton remodeling. With elevated cytoplasmic ATP (>5 mM), MEND can reverse completely and be repeated multiple times in BHK and HEK293 cells, but not cardiac myocytes. Reversal is blocked by N-ethylmaleimide and a nitric oxide donor, nitroprusside. Constitutively expressed Na/Ca exchangers internalize roughly in proportion to surface membrane, whereas Na/K pump activities decrease over-proportionally. Sodium dodecyl sulfate and dodecylglucoside do not cause MEND during their application, but MEND occurs rapidly when they are removed. As monitored capacitively, the binding of these detergents decreases with MEND, whereas TX100 binding does not decrease. In summary, nonionic detergents can fractionate the plasma membrane in vivo, and vesicles formed connect immediately to physiological membrane-trafficking mechanisms. We suggest that lateral and transbilayer inhomogeneities of the plasma membrane provide potential energies that, when unbridled by triggers, can drive endocytosis by lipidic forces

The Habitable Exoplanet Observatory (HabEx) Mission Concept Study Final Report

The Habitable Exoplanet Observatory, or HabEx, has been designed to be the Great Observatory of the 2030s. For the first time in human history, technologies have matured sufficiently to enable an affordable space-based telescope mission capable of discovering and characterizing Earthlike planets orbiting nearby bright sunlike stars in order to search for signs of habitability and biosignatures. Such a mission can also be equipped with instrumentation that will enable broad and exciting general astrophysics and planetary science not possible from current or planned facilities. HabEx is a space telescope with unique imaging and multi-object spectroscopic capabilities at wavelengths ranging from ultraviolet (UV) to near-IR. These capabilities allow for a broad suite of compelling science that cuts across the entire NASA astrophysics portfolio. HabEx has three primary science goals: (1) Seek out nearby worlds and explore their habitability; (2) Map out nearby planetary systems and understand the diversity of the worlds they contain; (3) Enable new explorations of astrophysical systems from our own solar system to external galaxies by extending our reach in the UV through near-IR. This Great Observatory science will be selected through a competed GO program, and will account for about 50% of the HabEx primary mission. The preferred HabEx architecture is a 4m, monolithic, off-axis telescope that is diffraction-limited at 0.4 microns and is in an L2 orbit. HabEx employs two starlight suppression systems: a coronagraph and a starshade, each with their own dedicated instrument

The Habitable Exoplanet Observatory (HabEx) Mission Concept Study Final Report

The Habitable Exoplanet Observatory, or HabEx, has been designed to be the Great Observatory of the 2030s. For the first time in human history, technologies have matured sufficiently to enable an affordable space-based telescope mission capable of discovering and characterizing Earthlike planets orbiting nearby bright sunlike stars in order to search for signs of habitability and biosignatures. Such a mission can also be equipped with instrumentation that will enable broad and exciting general astrophysics and planetary science not possible from current or planned facilities. HabEx is a space telescope with unique imaging and multi-object spectroscopic capabilities at wavelengths ranging from ultraviolet (UV) to near-IR. These capabilities allow for a broad suite of compelling science that cuts across the entire NASA astrophysics portfolio. HabEx has three primary science goals: (1) Seek out nearby worlds and explore their habitability; (2) Map out nearby planetary systems and understand the diversity of the worlds they contain; (3) Enable new explorations of astrophysical systems from our own solar system to external galaxies by extending our reach in the UV through near-IR. This Great Observatory science will be selected through a competed GO program, and will account for about 50% of the HabEx primary mission. The preferred HabEx architecture is a 4m, monolithic, off-axis telescope that is diffraction-limited at 0.4 microns and is in an L2 orbit. HabEx employs two starlight suppression systems: a coronagraph and a starshade, each with their own dedicated instrument.Comment: Full report: 498 pages. Executive Summary: 14 pages. More information about HabEx can be found here: https://www.jpl.nasa.gov/habex