The Space of Differences of Convex Functions on [0, 1]

∗Participant in Workshop in Linear Analysis and Probability, Texas A & M University, College Station, Texas, 2000. Research partially supported by the Edmund Landau Center for Research in Mathematical Analysis and related areas, sponsored by Minerva Foundation (Germany).The space K[0, 1] of differences of convex functions on the closed interval [0, 1] is investigated as a dual Banach space. It is proved that a continuous function f on [0, 1] belongs to K[0, 1

Topological regluing of rational functions

Regluing is a topological operation that helps to construct topological models for rational functions on the boundaries of certain hyperbolic components. It also has a holomorphic interpretation, with the flavor of infinite dimensional Thurston--Teichm\"uller theory. We will discuss a topological theory of regluing, and trace a direction in which a holomorphic theory can develop.Comment: 38 page

Factorization of operators through subspaces of L-1-spaces

[EN] We analyze domination properties and factorization of operators in Banach spaces through subspaces of L1-spaces. Using vector measure integration and extending classical arguments based on scalar integral bounds, we provide characterizations of operators factoring through subspaces of L1-spaces of finite measures. Some special cases involving positivity and compactness of the operators are considered.Research supported by MINECO/FEDER under projects MTM2014-53009-P (J.M Calabuig), MTM2014-54182-P (J. Rodriguez) and MTM2012-36740-C02-02 (E. A. Sanchez-Perez).Calabuig, JM.; Rodríguez, J.; Sánchez Pérez, EA. (2017). Factorization of operators through subspaces of L-1-spaces. Journal of the Australian Mathematical Society. 103(3):313-328. https://doi.org/10.1017/S1446788716000513S3133281033Lindenstrauss, J., & Tzafriri, L. (1979). Classical Banach Spaces II. doi:10.1007/978-3-662-35347-9Pisier, G. (1986). Factorization of Linear Operators and Geometry of Banach Spaces. CBMS Regional Conference Series in Mathematics. doi:10.1090/cbms/060Okada, S., Ricker, W. J., & Sánchez Pérez, E. A. (2008). Optimal Domain and Integral Extension of Operators. doi:10.1007/978-3-7643-8648-1Lacey, H. E. (1974). The Isometric Theory of Classical Banach Spaces. doi:10.1007/978-3-642-65762-7Fernández, A., Mayoral, F., Naranjo, F., Sáez, C., & Sánchez-Pérez, E. A. (2005). Vector measure Maurey–Rosenthal-type factorizations and ℓ-sums of L1-spaces. Journal of Functional Analysis, 220(2), 460-485. doi:10.1016/j.jfa.2004.06.010Juan, M. A., & Sánchez Pérez, E. A. (2013). Maurey-Rosenthal domination for abstract Banach lattices. Journal of Inequalities and Applications, 2013(1). doi:10.1186/1029-242x-2013-213Avilés, A., Cabello Sánchez, F., Castillo, J. M. F., González, M., & Moreno, Y. (2013). On separably injective Banach spaces. Advances in Mathematics, 234, 192-216. doi:10.1016/j.aim.2012.10.013Defant, A., & Sánchez Pérez, E. A. (2004). Maurey–Rosenthal factorization of positive operators and convexity. Journal of Mathematical Analysis and Applications, 297(2), 771-790. doi:10.1016/j.jmaa.2004.04.047DEFANT, A., & PÉREZ, E. A. S. (2009). Domination of operators on function spaces. Mathematical Proceedings of the Cambridge Philosophical Society, 146(1), 57-66. doi:10.1017/s0305004108001734Bartle, R. G., Dunford, N., & Schwartz, J. (1955). Weak Compactness and Vector Measures. Canadian Journal of Mathematics, 7, 289-305. doi:10.4153/cjm-1955-032-1Rosenthal, H. P. (1974). A Characterization of Banach Spaces Containing l1. Proceedings of the National Academy of Sciences, 71(6), 2411-2413. doi:10.1073/pnas.71.6.2411Diestel, J., Jarchow, H., & Tonge, A. (1995). Absolutely Summing Operators. doi:10.1017/cbo9780511526138Rueda, P., & Sánchez-Pérez, E. A. (2015). Compactness in spaces of p-integrable functions with respect to a vector measure. Topological Methods in Nonlinear Analysis, 45(2), 641. doi:10.12775/tmna.2015.030Rosenthal, H. P. (1973). On Subspaces of L p. The Annals of Mathematics, 97(2), 344. doi:10.2307/1970850Diestel, J., & Uhl, J. (1977). Vector Measures. Mathematical Surveys and Monographs. doi:10.1090/surv/015[16] M. Mastyło and E. A. Sánchez-Pérez , ‘Factorization of operators through Orlicz spaces’, Bull. Malays. Math. Sci. Soc. doi:10.1007/s40840-015-0158-5, to appear.Calabuig, J. M., Lajara, S., Rodríguez, J., & Sánchez-Pérez, E. A. (2014). Compactness in L1of a vector measure. Studia Mathematica, 225(3), 259-282. doi:10.4064/sm225-3-6Defant, A. (2001). Positivity, 5(2), 153-175. doi:10.1023/a:1011466509838Fabian, M., Habala, P., Hájek, P., Montesinos, V., & Zizler, V. (2011). Banach Space Theory. CMS Books in Mathematics. doi:10.1007/978-1-4419-7515-

Continuous selections of multivalued mappings

This survey covers in our opinion the most important results in the theory of continuous selections of multivalued mappings (approximately) from 2002 through 2012. It extends and continues our previous such survey which appeared in Recent Progress in General Topology, II, which was published in 2002. In comparison, our present survey considers more restricted and specific areas of mathematics. Note that we do not consider the theory of selectors (i.e. continuous choices of elements from subsets of topological spaces) since this topics is covered by another survey in this volume

“cAMP Sponge”: A Buffer for Cyclic Adenosine 3′, 5′-Monophosphate

Background: While intracellular buffers are widely used to study calcium signaling, no such tool exists for the other major second messenger, cyclic AMP (cAMP). Methods/Principal Findings: Here we describe a genetically encoded buffer for cAMP based on the high-affinity cAMP-binding carboxy-terminus of the regulatory subunit $RI\beta$ of protein kinase A (PKA). Addition of targeting sequences permitted localization of this fragment to the extra-nuclear compartment, while tagging with mCherry allowed quantification of its expression at the single cell level. This construct (named “cAMP sponge”) was shown to selectively bind cAMP in vitro. Its expression significantly suppressed agonist-induced cAMP signals and the downstream activation of PKA within the cytosol as measured by FRET-based sensors in single living cells. Point mutations in the cAMP-binding domains of the construct rendered the chimera unable to bind cAMP in vitro or in situ. Cyclic AMP sponge was fruitfully applied to examine feedback regulation of gap junction-mediated transfer of cAMP in epithelial cell couplets. Conclusions: This newest member of the cAMP toolbox has the potential to reveal unique biological functions of cAMP, including insight into the functional significance of compartmentalized signaling events

Separably injective C*-algebras

We show that a C*-algebra is a $1$-separably injective Banach space if, and only if, it is linearly isometric to the Banach space $C_0(\Omega)$ of complex continuous functions vanishing at infinity on a substonean locally compact Hausdorff space $\Omega$

Somatic ‘Soluble’ Adenylyl Cyclase Isoforms Are Unaffected in Sacytm1Lex/Sacytm1Lex ‘Knockout’ Mice

BACKGROUND: Mammalian Soluble adenylyl cyclase (sAC, Adcy10, or Sacy) represents a source of the second messenger cAMP distinct from the widely studied, G protein-regulated transmembrane adenylyl cyclases. Genetic deletion of the second through fourth coding exons in Sacy(tm1Lex)/Sacy(tm1Lex) knockout mice results in a male sterile phenotype. The absence of any major somatic phenotype is inconsistent with the variety of somatic functions identified for sAC using pharmacological inhibitors and RNA interference. PRINCIPAL FINDINGS: We now use immunological and molecular biological methods to demonstrate that somatic tissues express a previously unknown isoform of sAC, which utilizes a unique start site, and which 'escapes' the design of the Sacy(tm1Lex) knockout allele. CONCLUSIONS/SIGNIFICANCE: These studies reveal increased complexity at the sAC locus, and they suggest that the known isoforms of sAC play a unique function in male germ cells

Phosphodiesterase 10A Upregulation Contributes to Pulmonary Vascular Remodeling

Phosphodiesterases (PDEs) modulate the cellular proliferation involved in the pathophysiology of pulmonary hypertension (PH) by hydrolyzing cAMP and cGMP. The present study was designed to determine whether any of the recently identified PDEs (PDE7-PDE11) contribute to progressive pulmonary vascular remodeling in PH. All in vitro experiments were performed with lung tissue or pulmonary arterial smooth muscle cells (PASMCs) obtained from control rats or monocrotaline (MCT)-induced pulmonary hypertensive (MCT-PH) rats, and we examined the effects of the PDE10 inhibitor papaverine (Pap) and specific small interfering RNA (siRNA). In addition, papaverine was administrated to MCT-induced PH rats from day 21 to day 35 by continuous intravenous infusion to examine the in vivo effects of PDE10A inhibition. We found that PDE10A was predominantly present in the lung vasculature, and the mRNA, protein, and activity levels of PDE10A were all significantly increased in MCT PASMCs compared with control PASMCs. Papaverine and PDE10A siRNA induced an accumulation of intracellular cAMP, activated cAMP response element binding protein and attenuated PASMC proliferation. Intravenous infusion of papaverine in MCT-PH rats resulted in a 40%–50% attenuation of the effects on pulmonary hypertensive hemodynamic parameters and pulmonary vascular remodeling. The present study is the first to demonstrate a central role of PDE10A in progressive pulmonary vascular remodeling, and the results suggest a novel therapeutic approach for the treatment of PH

The effect on survival of continuing chemotherapy to near death

<p>Abstract</p> <p>Background</p> <p>Overuse of anti-cancer therapy is an important quality-of-care issue. An aggressive approach to treatment can have negative effects on quality of life and cost, but its effect on survival is not well-defined.</p> <p>Methods</p> <p>Using the Surveillance, Epidemiology, and End Results-Medicare database, we identified 7,879 Medicare-enrolled patients aged 65 or older who died after having survived at least 3 months after diagnosis of advanced non-small cell lung cancer (NSCLC) between 1991 and 1999. We used Cox proportional hazards regression analysis, propensity scores, and instrumental variable analysis (IVA) to compare survival among patients who never received chemotherapy (n = 4,345), those who received standard chemotherapy but not within two weeks prior to death (n = 3,235), and those who were still receiving chemotherapy within 14 days of death (n = 299). Geographic variation in the application of chemotherapy was used as the instrument for IVA.</p> <p>Results</p> <p>Receipt of chemotherapy was associated with a 2-month improvement in overall survival. However, based on three different statistical approaches, no additional survival benefit was evident from continuing chemotherapy within 14 days of death. Moreover, patients receiving chemotherapy near the end of life were much less likely to enter hospice (81% versus 51% with no chemotherapy and 52% with standard chemotherapy, P < 0.001), or were more likely to be admitted within only 3 days of death.</p> <p>Conclusions</p> <p>Continuing chemotherapy for advanced NSCLC until very near death is associated with a decreased likelihood of receiving hospice care but not prolonged survival. Oncologists should strive to discontinue chemotherapy as death approaches and encourage patients to enroll in hospice for better end-of-life palliative care.</p