32 research outputs found

    Well-posedness for degenerate third order equations with delay and applications to inverse problems

    Get PDF
    [EN] In this paper, we study well-posedness for the following third-order in time equation with delay <disp-formula idoperators defined on a Banach space X with domains D(A) and D(B) such that t)is the state function taking values in X and u(t): (-, 0] X defined as u(t)() = u(t+) for < 0 belongs to an appropriate phase space where F and G are bounded linear operators. Using operator-valued Fourier multiplier techniques we provide optimal conditions for well-posedness of equation (0.1) in periodic Lebesgue-Bochner spaces Lp(T,X), periodic Besov spaces Bp,qs(T,X) and periodic Triebel-Lizorkin spaces Fp,qs(T,X). A novel application to an inverse problem is given.The first, second and third authors have been supported by MEC, grant MTM2016-75963-P. The second author has been supported by AICO/2016/30. The fourth author has been supported by MEC, grant MTM2015-65825-P.Conejero, JA.; Lizama, C.; Murillo-Arcila, M.; Seoane Sepúlveda, JB. (2019). Well-posedness for degenerate third order equations with delay and applications to inverse problems. Israel Journal of Mathematics. 229(1):219-254. https://doi.org/10.1007/s11856-018-1796-8S2192542291K. Abbaoui and Y. Cherruault, New ideas for solving identification and optimal control problems related to biomedical systems, International Journal of Biomedical Computing 36 (1994), 181–186.M. Al Horani and A. Favini, Perturbation method for first- and complete second-order differential equations, Journal of Optimization Theory and Applications 166 (2015), 949–967.H. Amann, Operator-valued Fourier multipliers, vector-valued Besov spaces, and applications, Mathematische Nachrichten 186 (1997), 5–56.U. A. Anufrieva, A degenerate Cauchy problem for a second-order equation. A wellposedness criterion, Differentsial’nye Uravneniya 34 (1998), 1131–1133; English translation: Differential Equations 34 (1999), 1135–1137.W. Arendt and S. Bu, The operator-valued Marcinkiewicz multiplier theorem and maximal regularity, Mathematische Zeitschrift 240 (2002), 311–343.W. Arendt and S. Bu, Operator-valued Fourier multipliers on periodic Besov spaces and applications, Proceedings of the Edinburgh Mathematical Society 47 (2004), 15–33.W. Arendt, C. Batty and S. Bu, Fourier multipliers for Holder continuous functions and maximal regularity, Studia Mathematica 160 (2004), 23–51.V. Barbu and A. Favini, Periodic problems for degenerate differential equations, Rendiconti dell’Istituto di Matematica dell’Università di Trieste 28 (1996), 29–57.A. Bátkai and S. Piazzera, Semigroups for Delay Equations, Research Notes in Mathematics, Vol. 10, A K Peters, Wellesley, MA, 2005.S. Bu, Well-posedness of second order degenerate differential equations in vector-valued function spaces, Studia Mathematica 214 (2013), 1–16.S. Bu and G. Cai, Periodic solutions of third-order degenerate differential equations in vector-valued functional spaces, Israel Journal of Mathematics 212 (2016), 163–188.S. Bu and G. Cai, Well-posedness of second-order degenerate differential equations with finite delay in vector-valued function spaces, Pacific Journal of Mathematics 288 (2017), 27–46.S. Bu and Y. Fang, Periodic solutions of delay equations in Besov spaces and Triebel–Lizorkin spaces, Taiwanese Journal of Mathematics 13 (2009), 1063–1076.S. Bu and J. Kim, Operator-valued Fourier multipliers on periodic Triebel spaces, Acta Mathematica Sinica 21 (2005), 1049–1056.G. Cai and S. Bu, Well-posedness of second order degenerate integro-differential equations with infinite delay in vector-valued function spaces, Mathematische Nachrichten 289 (2016), 436–451.R. Chill and S. Srivastava, Lp-maximal regularity for second order Cauchy problems, Mathematische Zeitschrift 251 (2005), 751–781.R. Denk, M. Hieber and J. Prüss, R-boundedness, Fourier multipliers and problems of elliptic and parabolic type, Memoirs of the American Mathematical Society 166 (2003).O. Diekmann, S. A. van Giles, S. M. Verduyn Lunel and H.-O. Walther, Delay Equations, Applied Mathematical Sciences, Vol. 110, Springer, New York, 1995.K. J. Engel and R. Nagel, One-Parameter Semigroups for Linear Evolution Equations, Graduate Texts in Mathematics, Vol. 194, Springer, New York, 2000.M. Fabrizio, A. Favini and G. Marinoschi, An optimal control problem for a singular system of solid liquid phase-transition, Numerical Functional Analysis and Optimization 31 (2010), 989–1022.A. Favini and G. Marinoschi, Periodic behavior for a degenerate fast diffusion equation, Journal of Mathematical Analysis and Applications 351 (2009), 509–521.A. Favini and G. Marinoschi, Identification of the time derivative coefficients in a fast diffusion degenerate equation, Journal of Optimization Theory and Applications 145 (2010), 249–269.A. Favini and A. Yagi, Degenerate differential equations in Banach spaces, Monographs and Textbooks in Pure and Applied Mathematics, Vol. 215, Marcel Dekker, New York, 1999.X. L. Fu and M. Li, Maximal regularity of second-order evolution equations with infinite delay in Banach spaces, Studia Mathematica 224 (2014), 199–219.G. C. Gorain, Boundary stabilization of nonlinear vibrations of a flexible structure in a bounded domain in Rn, Journal of Mathematical Analysis and Applications 319 (2006), 635–650.P. Grisvard, Équations différentielles abstraites, Annales Scientifiques de l’école Normale Superieure 2 (1969), 311–395.J. K. Hale and W. Huang, Global geometry of the stable regions for two delay differential equations, Journal of Mathematical Analysis and Applications 178 (1993), 344–362.Y. Hino, S. Murakami and T. Naito, Functional Differential Equations with Infinite Delay, Lecture Notes in Mathematics, Vol. 1473, Springer, Berlin, 1991.B. Kaltenbacher, I. Lasiecka and M. Pospieszalska, Well-posedness and exponential decay of the energy in the nonlinear Moore-Gibson-Thomson equation arising in high intensity ultrasound, Mathematical Models & Methods in Applied Sciences 22 (2012), 1250035.V. Keyantuo and C. Lizama, Fourier multipliers and integro-differential equations in Banach spaces, Journal of the London Mathematical Society 69 (2004), 737–750.V. Keyantuo and C. Lizama, Maximal regularity for a class of integro-differential equations with infinite delay in Banach spaces, Studia Mathematica 168 (2005), 25–50.V. Keyantuo, C. Lizama and V. Poblete, Periodic solutions of integro-differential euations in vector-valued function spaces, Journal of Differential Equations 246 (2009), 1007–1037.C. Lizama, Fourier multipliers and periodic solutions of delay equations in Banach spaces, Journal of Mathematical Analysis and Applications 324 (2006), 921–933.C. Lizama and V. Poblete, Maximal regularity of delay equations in Banach spaces, Studia Mathematica 175 (2006), 91–102.C. Lizama and R. Ponce, Periodic solutions of degenerate differential equations in vector valued function spaces, Studia Mathematica 202 (2011), 49–63.C. Lizama and R. Ponce, Maximal regularity for degenerate differential equations with infinite delay in periodic vector-valued function spaces, Proceedings of the Edinburgh Mathematical Society 56 (2013), 853–871.R. Marchand, T. Mcdevitt and R. Triggiani, An abstract semigroup approach to the third-order Moore–Gibson–Thompson partial differential equation arising in highintensity ultrasound: structural decomposition, spectral analysis, exponential stability, Mathematical Methods in the Applied Sciences 35 (2012), 1896–1929.V. Poblete, Solutions of second-order integro-differential equations on periodic Besov spaces, Proceedings of the Edinburgh Mathematical Society 50 (2007), 477–492.V. Poblete and J. C. Pozo, Periodic solutions of an abstract third-order differential equation, Studia Mathematica 215 (2013), 195–219.J. Prüss, Evolutionary Integral Equations and Applications, Monographs in Mathematics, Vol. 87, Birkhäuser, Heidelberg, 1993.G. A. Sviridyuk and V. E. Fedorov, Linear Sobolev type Equations and Degenerate Semigroups of Operators, Inverse and Ill-posed Problems Series, VSP, Utrecht, 2003.L. Weis, Operator-valued Fourier multiplier theorems and maximal Lp-regularity, Mathematische Annalen 319 (2001), 735–758

    MFGE8 links absorption of dietary fatty acids with catabolism of enterocyte lipid stores through HNF4γ-dependent transcription of CES enzymes

    Get PDF
    Enterocytes modulate the extent of postprandial lipemia by storing dietary fats in cytoplasmic lipid droplets (cLDs). We have previously shown that the integrin ligand MFGE8 links absorption of dietary fats with activation of triglyceride (TG) hydrolases that catabolize cLDs for chylomicron production. Here, we identify CES1D as the key hydrolase downstream of the MFGE8-αvβ5 integrin pathway that regulates catabolism of diet-derived cLDs. Mfge8 knockout (KO) enterocytes have reduced CES1D transcript and protein levels and reduced protein levels of the transcription factor HNF4γ. Both Ces1d and Hnf4γ KO mice have decreased enterocyte TG hydrolase activity coupled with retention of TG in cLDs. Mechanistically, MFGE8-dependent fatty acid uptake through CD36 stabilizes HNF4γ protein level; HNF4γ then increases Ces1d transcription. Our work identifies a regulatory network that regulates the severity of postprandial lipemia by linking dietary fat absorption with protein stabilization of a transcription factor that increases expression of hydrolases responsible for catabolizing diet-derived cLDs

    Effects of Anacetrapib in Patients with Atherosclerotic Vascular Disease

    Get PDF
    BACKGROUND: Patients with atherosclerotic vascular disease remain at high risk for cardiovascular events despite effective statin-based treatment of low-density lipoprotein (LDL) cholesterol levels. The inhibition of cholesteryl ester transfer protein (CETP) by anacetrapib reduces LDL cholesterol levels and increases high-density lipoprotein (HDL) cholesterol levels. However, trials of other CETP inhibitors have shown neutral or adverse effects on cardiovascular outcomes. METHODS: We conducted a randomized, double-blind, placebo-controlled trial involving 30,449 adults with atherosclerotic vascular disease who were receiving intensive atorvastatin therapy and who had a mean LDL cholesterol level of 61 mg per deciliter (1.58 mmol per liter), a mean non-HDL cholesterol level of 92 mg per deciliter (2.38 mmol per liter), and a mean HDL cholesterol level of 40 mg per deciliter (1.03 mmol per liter). The patients were assigned to receive either 100 mg of anacetrapib once daily (15,225 patients) or matching placebo (15,224 patients). The primary outcome was the first major coronary event, a composite of coronary death, myocardial infarction, or coronary revascularization. RESULTS: During the median follow-up period of 4.1 years, the primary outcome occurred in significantly fewer patients in the anacetrapib group than in the placebo group (1640 of 15,225 patients [10.8%] vs. 1803 of 15,224 patients [11.8%]; rate ratio, 0.91; 95% confidence interval, 0.85 to 0.97; P=0.004). The relative difference in risk was similar across multiple prespecified subgroups. At the trial midpoint, the mean level of HDL cholesterol was higher by 43 mg per deciliter (1.12 mmol per liter) in the anacetrapib group than in the placebo group (a relative difference of 104%), and the mean level of non-HDL cholesterol was lower by 17 mg per deciliter (0.44 mmol per liter), a relative difference of -18%. There were no significant between-group differences in the risk of death, cancer, or other serious adverse events. CONCLUSIONS: Among patients with atherosclerotic vascular disease who were receiving intensive statin therapy, the use of anacetrapib resulted in a lower incidence of major coronary events than the use of placebo. (Funded by Merck and others; Current Controlled Trials number, ISRCTN48678192 ; ClinicalTrials.gov number, NCT01252953 ; and EudraCT number, 2010-023467-18 .)

    Cell cycle dynamics and complement expression distinguishes mature haematopoietic subsets arising from hemogenic endothelium

    No full text
    <p>The emergence of haematopoietic stem and progenitor cells (HSPCs) from hemogenic endothelium results in the formation of sizeable HSPC clusters attached to the vascular wall. We evaluate the cell cycle and proliferation of HSPCs involved in cluster formation, as well as the molecular signatures from their initial appearance to the point when cluster cells are capable of adult engraftment (definitive HSCs). We uncover a non-clonal origin of HSPC clusters with differing cell cycle, migration, and cell signaling attributes. In addition, we find that the complement cascade is highly enriched in mature HSPC clusters, possibly delineating a new role for this pathway in engraftment.</p

    AGPAT2 is essential for postnatal development and maintenance of white and brown adipose tissue

    No full text
    Objective: Characterize the cellular and molecular events responsible for lipodystrophy in AGPAT2 deficient mice. Methods: Adipose tissue and differentiated MEF were assessed using light and electron microscopy, followed by protein (immunoblots) and mRNA analysis (qPCR). Phospholipid profiling was determined by electrospray ionization tandem mass spectrometry (ESI-MS/MS). Results: In contrast to adult Agpat2−/− mice, fetuses and newborn Agpat2−/− mice have normal mass of white and brown adipose tissue. Loss of both the adipose tissue depots occurs during the first week of postnatal life as a consequence of adipocyte death and inflammatory infiltration of the adipose tissue. At the ultrastructural level, adipose tissue of newborn Agpat2−/− mice is virtually devoid of caveolae and has abnormal mitochondria and lipid droplets. Autophagic structures are also abundant. Consistent with these findings, differentiated Agpat2−/− mouse embryonic fibroblasts (MEFs) also have impaired adipogenesis, characterized by a lower number of lipid-laden cells and ultrastructural abnormalities in lipid droplets, mitochondria and plasma membrane. Overexpression of PPARγ, the master regulator of adipogenesis, increased the number of Agpat2−/− MEFs that differentiated into adipocyte-like cells but did not prevent morphological abnormalities and cell death. Furthermore, differentiated Agpat2−/− MEFs have abnormal phospholipid compositions with 3-fold increased levels of phosphatidic acid. Conclusion: We conclude that lipodystrophy in Agpat2−/− mice results from postnatal cell death of adipose tissue in association with acute local inflammation. It is possible that AGPAT2 deficient adipocytes have an altered lipid filling or a reduced capacity to adapt the massive lipid availability associated with postnatal feeding. Keywords: AGPAT2, Adipose tissue, Adipogenesis, Phospholipid, Lipodystroph

    Internet learning resources to improve students’ listening comprehension

    No full text
    BackgroundNon-integrating episomal vectors have become an important tool for induced pluripotent stem cell reprogramming. The episomal vectors carrying the "Yamanaka reprogramming factors" (Oct4, Klf, Sox2, and L-Myc + Lin28) are critical tools for non-integrating reprogramming of cells to a pluripotent state. However, the reprogramming process remains highly stochastic, and is hampered by an inability to easily identify clones that carry the episomal vectors.MethodsWe modified the original set of vectors to express spectrally separable fluorescent proteins to allow for enrichment of transfected cells. The vectors were then tested against the standard original vectors for reprogramming efficiency and for the ability to enrich for stoichiometric ratios of factors.ResultsThe reengineered vectors allow for cell sorting based on reprogramming factor expression. We show that these vectors can assist in tracking episomal expression in individual cells and can select the reprogramming factor dosage.ConclusionsTogether, these modified vectors are a useful tool for understanding the reprogramming process and improving induced pluripotent stem cell isolation efficiency
    corecore