Completability and optimal factorization norms in tensor products of Banach function spaces

[EN] Given s-finite measure spaces ( 1, 1, mu 1) and ( 2, 2, mu 2), we consider Banach spaces X1(mu 1) and X2(mu 2), consisting of L0(mu 1) and L0(mu 2) measurable functions respectively, and study when the completion of the simple tensors in the projective tensor product X1(mu 1). p X2(mu 2) is continuously included in the metric space of measurable functions L0(mu 1. mu 2). In particular, we prove that the elements of the completion of the projective tensor product of L p-spaces are measurable functions with respect to the product measure. Assuming certain conditions, we finally showthat given a bounded linear operator T : X1(mu 1). p X2(mu 2). E (where E is a Banach space), a norm can be found for T to be bounded, which is ` minimal' with respect to a given property (2-rectangularity). The same technique may work for the case of n-spaces.J. M. Calabuig and M. Fernandez-Unzueta were supported by Ministerio de Economia, Industria y Competitividad (Spain) under project MTM2014-53009-P. M. Fernandez-Unzueta was also suported by CONACyT 284110. F. Galaz-Fontes was supported by Ministerio de Ciencia e Innovacion (Spain) and FEDER under project MTM2009-14483-C02-01. E. A. Sanchez Perez was supported by Ministerio de Economia, Industria y Competitividad (Spain) and FEDER under project MTM2016-77054-C2-1-P.Calabuig, JM.; Fernández-Unzueta, M.; Galaz-Fontes, F.; Sánchez Pérez, EA. (2019). Completability and optimal factorization norms in tensor products of Banach function spaces. Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas. 113(4):3513-3530. https://doi.org/10.1007/s13398-019-00711-7S351335301134Abramovich, Y.A., Aliprantis, C.D.: An invitation to operator theory. Graduate Studies in Mathematics, Vol 50, AMS (2002)Bennett, C., Sharpley, R.: Interpolation of Operators. Academic Press, Boston (1988)Bu, Q., Buskes, G., Kusraev, A.G.: Bilinear maps on products of vector lattices: a survey. In: Boulabiar, K., Buskes, G., Triki, A. (eds.) Positivity-Trends in Mathematics. Birkhäser Verlag AG, Basel, pp. 97–26 (2007)Buskes, G., Van Rooij, A.: Bounded variation and tensor products of Banach lattices. Positivity 7, 47–59 (2003)Calabuig, J.M., Fernández-Unzueta, M., Galaz-Fontes, F., Sánchez-Pérez, E.A.: Extending and factorizing bounded bilinear maps defined on order continuous Banach function spaces. RACSAM 108(2), 353–367 (2014)Calabuig, J.M., Fernández-Unzueta, M., Galaz-Fontes, F., Sánchez-Pérez, E.A.: Equivalent norms in a Banach function space and the subsequence property. J. Korean Math. Soc. https://doi.org/10.4134/JKMS.j180682Curbera, G.P., Ricker, W.J.: Optimal domains for kernel operators via interpolation. Math. Nachr. 244, 47–63 (2002)Curbera, G.P., Ricker, W.J.: Vector measures, integration and applications. In: Positivity. Birkhäuser Basel, pp. 127–160 (2007)Gil de Lamadrid, J.: Uniform cross norms and tensor products. J. Duke Math. 32, 797–803 (1965)Dunford, N., Schwartz, J.: Linear Operators, Part I: General Theory. Interscience Publishers Inc., New York (1958)Fremlin, D.H.: Tensor products of Archimedean vector lattices. Am. J. Math. 94(3), 777–798 (1972)Fremlin, D.H.: Tensor products of Banach lattices. Math. Ann. 211(2), 87–106 (1974)Yew, K.L.: Completely $$p$$-summing maps on the operator Hilbert space OH. J. Funct. Anal. 255, 1362–1402 (2008)Kwapien, S., Pelczynski, A.: The main triangle projection in matrix spaces and its applications. Stud. Math. 34(1), 43–68 (1970)Lindenstrauss, J., Tzafriri, L.: Classical Banach spaces II. Springer, Berlin (1979)Luxemburg, W.A.J., Zaanen, A.C.: Riesz Spaces I. North-Holland Publishing Company, Amsterdam (1971)Milman, M.: Some new function spaces and their tensor products. Depto. de Matemática, Facultad de Ciencias, U. de los Andes, Mérida, Venezuela (1978)Okada, S., Ricker, W.J., Sánchez Pérez, E.A.: Optimal domain and integral extension of operators acting in function spaces. Oper. Theory Adv. Appl., vol. 180. Birkhäuser, Basel (2008)Schep, A.R.: Factorization of positive multilinear maps. Illinois J. Math. 579–591 (1984)Zaanen, A.C.: Integration. North-Holland Publishing Company, Amsterdam-New York (1967)Zaanen, A.C.: Riesz Spaces II. North-Holland Publishing Company, Amsterdam (1983

Phenotypic and genotypic differences between Indian and Scandinavian women with gestational diabetes mellitus

Objective Gestational diabetes mellitus (GDM) is a transient form of diabetes characterized by impaired insulin secretion and action during pregnancy. Population-based differences in prevalence exist which could be explained by phenotypic and genetic differences. The aim of this study was to examine these differences in pregnant women from Punjab, India and Scandinavia. Methods Eighty-five GDM/T2D loci in European and/or Indian populations from previous studies were assessed for association with GDM based on Swedish GDM criteria in 4018 Punjabi Indian and 507 Swedish pregnant women. Selected loci were replicated in Scandinavian cohorts, Radiel (N = 398, Finnish) and STORK/STORK-G (N = 780, Norwegian). Results Punjabi Indian women had higher GDM prevalence, lower insulin secretion and better insulin sensitivity than Swedish women. There were significant frequency differences of GDM/T2D risk alleles between both populations. rs7178572 at HMG20A, previously associated with GDM in South Indian and European women, was replicated in North Indian women. The T2D risk SNP rs11605924 in the CRY2 gene was associated with increased GDM risk in Scandinavian but decreased GDM risk in Punjabi Indian women. No other overlap was seen between GDM loci in both populations. Conclusions Gestational diabetes mellitus is more common in Indian than Swedish women, which partially can be attributed to differences in insulin secretion and action. There was marked heterogeneity in the GDM phenotypes between the populations which could only partially be explained by genetic differences.Peer reviewe

Effect of controlled and uncontrolled cooling rate on motility parameters of cryopreserved ram spermatozoa

<p>Abstract</p> <p>Background</p> <p>Ram spermatozoa are sensitive to extreme changes in temperature during the freeze-thaw process. The degree of damage depends on a combined effect of various factors including freezing temperature. The aim of this study was to determine the effects of two cooling method (controlled-rate and uncontrolled-rate) on pre-freezing and post-thaw sperm motility parameters.</p> <p>Results</p> <p>Ejaculates were collected using the artificial vagina from four Chal rams and three replicates of the ejaculates were diluted with a Tris-based extender and packed in 0.25 ml straws. Then, sample processed according to the two methods. Method 1: straws cooled from 37 to 5°C, at a liner rate of -0.3°C/min in a controlled-rate cooling machine (custom-built) and equilibrated at 5°C for 80 min, then the straws were frozen at rate of -0.3°C/min from 5°C to -10°C and -25°C/min from -10°C to -150°C and plunged into liquid nitrogen for storage. Method 2: straws were transferred to refrigerator and maintained at 5°C for 3 h, then the straws were frozen in liquid nitrogen vapor, 4 cm above the liquid nitrogen for 15 min and plunged into liquid nitrogen. Computer-assisted sperm motility analysis was used to analyze sperm motion characteristics.</p> <p>Conclusions</p> <p>Controlled rate of freezing (Method 1) significantly improve the pre-freezing and post-thaw total and progressive motility compared to uncontrolled rate (Method 2). In specific kinetic parameters, Method 1 gives significantly higher value for VSL and VCL in comparison with Method 2. There are no significant differences between the two methods for VAP and LIN. In conclusion, controlled rate of cooling conferred better cryopreserving ability to ram spermatozoa compared to uncontrolled rate of cooling prior to programmable freezing.</p

Metastatic breast carcinoma of the coracoid process: two case reports

<p>Abstract</p> <p>Background</p> <p>The coracoid process of the scapula is a rare site of involvement for metastatic disease or for primary tumors. We are unaware of any reports in the literature of pathologic coracoid process fractures and only one report of metastatic disease to the coracoid.</p> <p>Methods and Results</p> <p>In this case report, we present two cases with metastatic breast carcinoma of the coracoid process, one of which presented with a pathologic fracture of the coracoid.</p> <p>Conclusions</p> <p>An orthopaedic surgeon must be aware of the potential for metastatic disease to the coracoid as they may be the first medical provider to encounter evidence of malignant disease.</p

Different Conformations of Phosphatase and Tensin Homolog, Deleted on Chromosome 10 (PTEN) Protein within the Nucleus and Cytoplasm of Neurons

PTEN is a critical gene involved in the regulation of many cellular processes. The product of this gene has dual phosphatase activity and is able to dephosphorylate the 5′ end of the phosphatidylinositol (3,4,5)-trisphosphate. Within the cellular nucleus, this protein has been associated with regulation of the expression of many genes, although the mechanism of this regulation remains unclear. In this paper, two specific oligonucleotide aptamers were developed and selected, using the SELEX procedure, according to their ability to detect the PTEN protein in different subcellular compartments of neurons. While one aptamer was able to detect PTEN in the nucleus, the other recognized PTEN in the cytoplasm. The recognition pattern of PTEN by both aptamers was confirmed using antibodies in western blots of the proteins purified from mouse cerebellar homogenates and subcellular fractions. Additionally, we demonstrated that the two aptamers recognized different epitopes of the target peptide. The results presented here could not be fully explained by the canonical phosphatase structure of PTEN, suggesting the existence of different conformations of phosphatase in the nucleus and the cytoplasm

The Evolution of Compact Binary Star Systems

We review the formation and evolution of compact binary stars consisting of white dwarfs (WDs), neutron stars (NSs), and black holes (BHs). Binary NSs and BHs are thought to be the primary astrophysical sources of gravitational waves (GWs) within the frequency band of ground-based detectors, while compact binaries of WDs are important sources of GWs at lower frequencies to be covered by space interferometers (LISA). Major uncertainties in the current understanding of properties of NSs and BHs most relevant to the GW studies are discussed, including the treatment of the natal kicks which compact stellar remnants acquire during the core collapse of massive stars and the common envelope phase of binary evolution. We discuss the coalescence rates of binary NSs and BHs and prospects for their detections, the formation and evolution of binary WDs and their observational manifestations. Special attention is given to AM CVn-stars -- compact binaries in which the Roche lobe is filled by another WD or a low-mass partially degenerate helium-star, as these stars are thought to be the best LISA verification binary GW sources.Comment: 105 pages, 18 figure

Cytotoxic and apoptotic evaluations of marine bacteria isolated from brine-seawater interface of the Red Sea.

BACKGROUND: High salinity and temperature combined with presence of heavy metals and low oxygen renders deep-sea anoxic brines of the Red Sea as one of the most extreme environments on Earth. The ability to adapt and survive in these extreme environments makes inhabiting bacteria interesting candidates for the search of novel bioactive molecules. METHODS: Total 20 i.e. lipophilic (chloroform) and hydrophilic (70% ethanol) extracts of marine bacteria isolated from brine-seawater interface of the Red Sea were tested for cytotoxic and apoptotic activity against three human cancer cell lines, i.e. HeLa (cervical carcinoma), MCF-7 (Breast Adenocarcinoma) and DU145 (Prostate carcinoma). RESULTS: Among these, twelve extracts were found to be very active after 24 hours of treatment, which were further evaluated for their cytotoxic and apoptotic effects at 48 hr. The extracts from the isolates P1-37B and P3-37A (Halomonas) and P1-17B (Sulfitobacter) have been found to be the most potent against tested cancer cell lines. CONCLUSION: Overall, bacterial isolates from the Red Sea displayed promising results and can be explored further to find novel drug-like molecules. The cell line specific activity of the extracts may be attributed to the presence of different polarity compounds or the cancer type i.e. biological differences in cell lines and different mechanisms of action of programmed cell death prevalent in different cancer cell lines

AAPS Workshop Report: Strategies to Address Therapeutic Protein–Drug Interactions during Clinical Development

Therapeutic proteins (TPs) are increasingly combined with small molecules and/or with other TPs. However preclinical tools and in vitro test systems for assessing drug interaction potential of TPs such as monoclonal antibodies, cytokines and cytokine modulators are limited. Published data suggests that clinically relevant TP-drug interactions (TP-DI) are likely from overlap in mechanisms of action, alteration in target and/or drug-disease interaction. Clinical drug interaction studies are not routinely conducted for TPs because of the logistical constraints in study design to address pharmacokinetic (PK)- and pharmacodynamic (PD)-based interactions. Different pharmaceutical companies have developed their respective question- and/or risk-based approaches for TP-DI based on the TP mechanism of action as well as patient population. During the workshop both company strategies and regulatory perspectives were discussed in depth using case studies; knowledge gaps and best practices were subsequently identified and discussed. Understanding the functional role of target, target expression and their downstream consequences were identified as important for assessing the potential for a TP-DI. Therefore, a question-and/or risk-based approach based upon the mechanism of action and patient population was proposed as a reasonable TP-DI strategy. This field continues to evolve as companies generate additional preclinical and clinical data to improve their understanding of possible mechanisms for drug interactions. Regulatory agencies are in the process of updating their recommendations to sponsors regarding the conduct of in vitro and in vivo interaction studies for new drug applications (NDAs) and biologics license applications (BLAs)