A Numerical anlysis of Resin Transfer Molding

The aim of this work is to study a mathematical model, based on the pseudo-concentration function model, for the filling of shallow molds with polymers. The proposed model is 2-D, the chemical reactivity of the fluid is accounted with the conversion rate satisfying a Kamal-Sourour model, and the temperature is not considered. We prove the existence of a solution of the proposed mathematical model.The aim of this work is to study a mathematical model, based on the pseudo-concentration function model, for the filling of shallow molds with polymers. The proposed model is 2-D, the chemical reactivity of the fluid is accounted with the conversion rate satisfying a Kamal-Sourour model, and the temperature is not considered. We prove the existence of a solution of the proposed mathematical model

Numerical approximation of an identification problem in porous media

When the ground is accidentally polluted with a volatile organic contaminant, it is important to know the amount of this contaminant in liquid form, in this paper it is shown that the concentration in the liquid phase of the volatile organic contaminant can be identified by analyzing the gaseous phase and using inverse problem. In order to do that we consider an inverse problem.When the ground is accidentally polluted with a volatile organic contaminant, it is important to know the amount of this contaminant in liquid form, in this paper it is shown that the concentration in the liquid phase of the volatile organic contaminant can be identified by analyzing the gaseous phase and using inverse problem. In order to do that we consider an inverse problem

Duals of variable exponent Hörmander spaces (0<p−≤p+≤10< p^- \le p^+ \le 1) and some applications

In this paper we characterize the dual \bigl(\B^c_{p(\cdot)} (\Omega) \bigr)' of the variable exponent H\"or\-man\-der space \B^c_{p(\cdot)} (\Omega) when the exponent $p(\cdot)$ satisfies the conditions $0 < p^- \le p^+ \le 1$, the Hardy-Littlewood maximal operator $M$ is bounded on $L_{p(\cdot)/p_0}$ for some $0 < p_0 < p^-$ and $\Omega$ is an open set in $\R^n$. It is shown that the dual \bigl(\B^c_{p(\cdot)} (\Omega) \bigr)' is isomorphic to the H\"ormander space \B^{\mathrm{loc}}_\infty (\Omega) (this is the $p^+ \le 1$ counterpart of the isomorphism \bigl(\B^c_{p(\cdot)} (\Omega) \bigr)' \simeq \B^{\mathrm{loc}}_{\widetilde{p'(\cdot)}} (\Omega), $1 < p^- \le p^+ < \infty$, recently proved by the authors) and hence the representation theorem \bigl( \B^c_{p(\cdot)} (\Omega) \bigr)' \simeq l^{\N}_\infty is obtained. Our proof relies heavily on the properties of the Banach envelopes of the steps of \B^c_{p(\cdot)} (\Omega) and on the extrapolation theorems in the variable Lebesgue spaces of entire analytic functions obtained in a precedent paper. Other results for $p(\cdot) \equiv p$, $0 < p < 1$, are also given (e.g. \B^c_p (\Omega) does not contain any infinite-dimensional $q$-Banach subspace with $p < q \le 1$ or the quasi-Banach space \B_p \cap \E'(Q) contains a copy of $l_p$ when $Q$ is a cube in $\R^n$). Finally, a question on complex interpolation (in the sense of Kalton) of variable exponent H\"ormander spaces is proposed.J. Motos is partially supported by grant MTM2011-23164 from the Spanish Ministry of Science and Innovation. The authors wish to thank the referees for the careful reading of the manuscript and for many helpful suggestions and remarks that improved the exposition. In particular, the remark immediately following Theorem 2.1 and the Question 2 were motivated by the comments of one of them.Motos Izquierdo, J.; Planells Gilabert, MJ.; Talavera Usano, CF. (2015). Duals of variable exponent Hörmander spaces ($0< p^- \le p^+ \le 1$) and some applications. Revista- Real Academia de Ciencias Exactas Fisicas Y Naturales Serie a Matematicas. 109(2):657-668. https://doi.org/10.1007/s13398-014-0209-zS6576681092Aboulaich, R., Meskine, D., Souissi, A.: New diffussion models in image processing. Comput. Math. Appl. 56(4), 874–882 (2008)Acerbi, E., Mingione, G.: Regularity results for stationary electro-rheological fluids. Arch. Ration. Mech. Anal. 164(3), 213–259 (2002)Bastero, J.: $$l^q$$ l q -subspaces of stable $$p$$ p -Banach spaces, $$0 < p \le 1$$ 0 < p ≤ 1 . Arch. Math. (Basel) 40, 538–544 (1983)Boas, R.P.: Entire functions. Academic Press, London (1954)Boza, S.: Espacios de Hardy discretos y acotación de operadores. Dissertation, Universitat de Barcelona (1998)Cruz-Uribe, D., Fiorenza, A.: Variable Lebesgue spaces, foundations and harmonic analysis. Birkhäuser, Basel (2013)Cruz-Uribe, D.: SFO, A. Fiorenza, J. M. Martell, C. Pérez: The boundedness of classical operators on variable $$L^p$$ L p spaces. Ann. Acad. Sci. Fenn. Math. 31, 239–264 (2006)Diening, L., Harjulehto, P., Hästö, P., Růžička, M.: Lebesgue and sobolev spaces with variable exponents. lecture notes in mathematics, vol. 2007. Springer, Berlin, Heidelberg (2011)Hörmander, L.: The analysis of linear partial operators II, Grundlehren 257. Springer, Berlin, Heidelberg (1983)Hörmander, L.: The analysis of linear partial operators I, Grundlehren 256. Springer, Berlin, Heidelberg (1983)Kalton, N.J., Peck, N.T., Roberts, J.W.: An $$F$$ F -space sampler, London Mathematical Society Lecture Notes, vol. 89. Cambridge University Press, Cambridge (1985)Kalton, N.J.: Banach envelopes of non-locally convex spaces. Canad. J. Math. 38(1), 65–86 (1986)Kalton, N.J., Mitrea, M.: Stability results on interpolation scales of quasi-Banach spaces and applications. Trans. Am. Math. Soc. 350(10), 3903–3922 (1998)Kalton, N.J.: Quasi-Banach spaces, Handbook of the Geometry of Banach Spaces, vol. 2. In: Johnson, W.B., Lindenstrauss, J. (eds.), pp. 1099–1130. Elsevier, Amsterdam (2003)Köthe, G.: Topological vector spaces I. Springer, Berlin, Heidelberg (1969)Motos, J., Planells, M.J., Talavera, C.F.: On variable exponent Lebesgue spaces of entire analytic functions. J. Math. Anal. Appl. 388, 775–787 (2012)Motos, J., Planells, M.J., Talavera, C.F.: A note on variable exponent Hörmander spaces. Mediterr. J. Math. 10, 1419–1434 (2013)Stiles, W.J.: Some properties of $$l_p$$ l p , $$0 < p < 1$$ 0 < p < 1 . Studia Math. 42, 109–119 (1972)Triebel, H.: Theory of function spaces. Birkhäuser, Basel (1983)Vogt, D.: Sequence space representations of spaces of test functions and distributions. In: Zapata, G.I. (ed.) Functional analysis, holomorphy and approximation theory, Lecture Notes in Pure and Applied Mathematics, vol. 83, pp. 405–443 (1983

Caveolins/caveolae protect adipocytes from fatty acid-mediated lipotoxicity

Mice and humans lacking functional caveolae are dyslipidemic and have reduced fat stores and smaller fat cells. To test the role of caveolins/caveolae in maintaining lipid stores and adipocyte integrity, we compared lipolysis in caveolin-1 (Cav1)-null fat cells to that in cells reconstituted for caveolae by caveolin-1 re-expression. We find that the Cav1-null cells have a modestly enhanced rate of lipolysis and reduced cellular integrity compared with reconstituted cells as determined by the release of lipid metabolites and lactic dehydrogenase, respectively, into the media. There are no apparent differences in the levels of lipolytic enzymes or hormonally stimulated phosphorylation events in the two cell lines. In addition, acute fasting, which dramatically raises circulating fatty acid levels in vivo, causes a significant upregulation of caveolar protein constituents. These results are consistent with the hypothesis that caveolae protect fat cells from the lipotoxic effects of elevated levels fatty acids, which are weak detergents at physiological pH, by virtue of the property of caveolae to form detergentresistant membrane domains

MURC/Cavin-4 and cavin family members form tissue-specific caveolar complexes

Polymerase I and transcript release factor (PTRF)/Cavin is a cytoplasmic protein whose expression is obligatory for caveola formation. Using biochemistry and fluorescence resonance energy transfer–based approaches, we now show that a family of related proteins, PTRF/Cavin-1, serum deprivation response (SDR)/Cavin-2, SDR-related gene product that binds to C kinase (SRBC)/Cavin-3, and muscle-restricted coiled-coil protein (MURC)/Cavin-4, forms a multiprotein complex that associates with caveolae. This complex can constitutively assemble in the cytosol and associate with caveolin at plasma membrane caveolae. Cavin-1, but not other cavins, can induce caveola formation in a heterologous system and is required for the recruitment of the cavin complex to caveolae. The tissue-restricted expression of cavins suggests that caveolae may perform tissue-specific functions regulated by the composition of the cavin complex. Cavin-4 is expressed predominantly in muscle, and its distribution is perturbed in human muscle disease associated with Caveolin-3 dysfunction, identifying Cavin-4 as a novel muscle disease candidate caveolar protein

Fatal Cardiac Arrhythmia and Long-QT Syndrome in a New Form of Congenital Generalized Lipodystrophy with Muscle Rippling (CGL4) Due to PTRF-CAVIN Mutations

We investigated eight families with a novel subtype of congenital generalized lipodystrophy (CGL4) of whom five members had died from sudden cardiac death during their teenage years. ECG studies revealed features of long-QT syndrome, bradycardia, as well as supraventricular and ventricular tachycardias. Further symptoms comprised myopathy with muscle rippling, skeletal as well as smooth-muscle hypertrophy, leading to impaired gastrointestinal motility and hypertrophic pyloric stenosis in some children. Additionally, we found impaired bone formation with osteopenia, osteoporosis, and atlanto-axial instability. Homozygosity mapping located the gene within 2 Mbp on chromosome 17. Prioritization of 74 candidate genes with GeneDistiller for high expression in muscle and adipocytes suggested PTRF-CAVIN (Polymerase I and transcript release factor/Cavin) as the most probable candidate leading to the detection of homozygous mutations (c.160delG, c.362dupT). PTRF-CAVIN is essential for caveolae biogenesis. These cholesterol-rich plasmalemmal vesicles are involved in signal-transduction and vesicular trafficking and reside primarily on adipocytes, myocytes, and osteoblasts. Absence of PTRF-CAVIN did not influence abundance of its binding partner caveolin-1 and caveolin-3. In patient fibroblasts, however, caveolin-1 failed to localize toward the cell surface and electron microscopy revealed reduction of caveolae to less than 3%. Transfection of full-length PTRF-CAVIN reestablished the presence of caveolae. The loss of caveolae was confirmed by Atomic Force Microscopy (AFM) in combination with fluorescent imaging. PTRF-CAVIN deficiency thus presents the phenotypic spectrum caused by a quintessential lack of functional caveolae

Cholesterol Depletion in Adipocytes Causes Caveolae Collapse Concomitant with Proteosomal Degradation of Cavin-2 in a Switch-Like Fashion

Caveolae, little caves of cell surfaces, are enriched in cholesterol, a certain level of which is required for their structural integrity. Here we show in adipocytes that cavin-2, a peripheral membrane protein and one of 3 cavin isoforms present in caveolae from non-muscle tissue, is degraded upon cholesterol depletion in a rapid fashion resulting in collapse of caveolae. We exposed 3T3-L1 adipocytes to the cholesterol depleting agent methyl-β-cyclodextrin, which results in a sudden and extensive degradation of cavin-2 by the proteasome and a concomitant movement of cavin-1 from the plasma membrane to the cytosol along with loss of caveolae. The recovery of cavin-2 at the plasma membrane is cholesterol-dependent and is required for the return of cavin-1 from the cytosol to the cell surface and caveolae restoration. Expression of shRNA directed against cavin-2 also results in a cytosolic distribution of cavin-1 and loss of caveolae. Taken together, these data demonstrate that cavin-2 functions as a cholesterol responsive component of caveolae that is required for cavin-1 localization to the plasma membrane, and caveolae structural integrity

Histone Variants and Their Post-Translational Modifications in Primary Human Fat Cells

Epigenetic changes related to human disease cannot be fully addressed by studies of cells from cultures or from other mammals. We isolated human fat cells from subcutaneous abdominal fat tissue of female subjects and extracted histones from either purified nuclei or intact cells. Direct acid extraction of whole adipocytes was more efficient, yielding about 100 µg of protein with histone content of 60% –70% from 10 mL of fat cells. Differential proteolysis of the protein extracts by trypsin or ArgC-protease followed by nanoLC/MS/MS with alternating CID/ETD peptide sequencing identified 19 histone variants. Four variants were found at the protein level for the first time; particularly HIST2H4B was identified besides the only H4 isoform earlier known to be expressed in humans. Three of the found H2A potentially organize small nucleosomes in transcriptionally active chromatin, while two H2AFY variants inactivate X chromosome in female cells. HIST1H2BA and three of the identified H1 variants had earlier been described only as oocyte or testis specific histones. H2AFX and H2AFY revealed differential and variable N-terminal processing. Out of 78 histone modifications by acetylation/trimethylation, methylation, dimethylation, phosphorylation and ubiquitination, identified from six subjects, 68 were found for the first time. Only 23 of these modifications were detected in two or more subjects, while all the others were individual specific. The direct acid extraction of adipocytes allows for personal epigenetic analyses of human fat tissue, for profiling of histone modifications related to obesity, diabetes and metabolic syndrome, as well as for selection of individual medical treatments