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Abstract In this article, we study the Lipschitz Geometry at infinity of complex analytic sets and we obtain results on algebraicity of analytic sets and on Bernstein’s problem. Moser’s Bernstein Theorem says that a minimal hype...
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Abstract In this article, we study the Lipschitz Geometry at infinity of complex analytic sets and we obtain results on algebraicity of analytic sets and on Bernstein’s problem. Moser’s Bernstein Theorem says that a minimal hypersurface which is a graph of an entire Lipschitz function must be a hyperplane. H. B. Lawson, Jr. and R. Osserman presented examples showing that an analogous result for arbitrary codimension is not true. In this article, we prove a complex parametric version of Moser’s Bernstein Theorem. More precisely, we prove that any entire complex analytic set in Cn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {C}^n$$\end{document} which is Lipschitz regular at infinity must be an affine linear subspace of Cn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {C}^n$$\end{document}. In particular, a complex analytic set which is a graph of an entire Lipschitz function must be affine linear subspace. That result comes as a consequence of the following characterization of algebraic sets, which is also proved here: if X and Y are entire complex analytic sets which are bi-Lipschitz homeomorphic at infinity then X is a complex algebraic set if and only if Y is a complex algebraic set too. Thus, an entire complex analytic set is a complex algebraic set if and only if it is bi-Lipschitz homeomorphic at infinity to a complex algebraic set. No restrictions on the singular set, dimension nor codimension are required in the results proved here.
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Something that came across the table during one of our meetings was how we could promote our Society. Do we start up as a Morris Dance group and rattle our stuff in front of Research facilities or University faculties knowing that...
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Something that came across the table during one of our meetings was how we could promote our Society. Do we start up as a Morris Dance group and rattle our stuff in front of Research facilities or University faculties knowing that we would get strange looks hashing long necked glass vessels over our heads; or should we invest in some lee shirts with some form of promotion on them, as glass might gel in our eyes from some poor timing during the dance routines. The lee shirts won out and these will be available to purchase at the next Symposium. which I now believe is in full swing and ready to rock and roll.
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New Year wishes are great for sharing joy and hope for the New Year with friends and family. Whether you had a bottle of champagne set aside to ring in 2023, or a planner full of new goals and resolutions. The start of each New Ye...
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New Year wishes are great for sharing joy and hope for the New Year with friends and family. Whether you had a bottle of champagne set aside to ring in 2023, or a planner full of new goals and resolutions. The start of each New Year is a time to reflect on the year just past and make plans. It holds a special magic, with a promise of new opportunities and the possibility to change our lives for the better. It's also a great time to bond over old memories as you endeavour to make more. Some of us have had a difficult year with illness, loss, grief, uncertain employment, and isolation due to Covid-19 or to other circumstances in our lives. New Years can be a reset and a fresh start to re-focus on your hopes and dreams. 2022 turned out to be a good year for the Society. For the first time since 2017 the Society held a full Symposium. The main aim was to make the Symposium a financial success to ensure the continuation of the Journal. I'm happy to say this was achieved and the Society can look forward to holding a Symposium in 2023.
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Purpose How a micro-founded discipline such as economics could deal with the increasing global economic reality? This question has been asked frequently since the last economic crisis that appeared in 2008. In this challenging con...
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Purpose How a micro-founded discipline such as economics could deal with the increasing global economic reality? This question has been asked frequently since the last economic crisis that appeared in 2008. In this challenging context, some commentators have turned their attention to a new area of knowledge coming from physics: econophysics which mainly focuses on a macro-analysis of economic systems. By showing that concepts used by econophysicists are consistent with an existing economic knowledge (developed by J.S. Mill), the purpose of this paper is to claim that an interdisciplinary perspective is possible between these two communities. Design/methodology/approach The authors propose a historical and conceptual analysis of the key concept of emergence to emphasize the potential bridge between econophysics and economics. Findings Six methodological arguments will be developed in order to show the existence of conceptual bridges as a necessary condition for the elaboration of a common language between economists and econophysics which would not be superfluous, in this challenging context, to clarify the growing complexity of economic phenomena. Originality/value Although the economics and econophysics study same the complex economic phenomena, very few collaborations exist between them. This paper paves a conceptual/methodological path for more collaboration between the two fields.
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Magnetite nanoparticles were precipitated by the classic Massart's method in a 2.5 L stirred tank reactor where the injection of reagent solutions was effectuated by different micro-mixers (T-tube and Hartridge-Roughton rapid mixi...
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Magnetite nanoparticles were precipitated by the classic Massart's method in a 2.5 L stirred tank reactor where the injection of reagent solutions was effectuated by different micro-mixers (T-tube and Hartridge-Roughton rapid mixing devices). The specific surface area, the average particle size and the particle size distribution were highly influenced by changing operating parameters. Laser Diffraction, BET adsorption, Energy-Dispersive X-ray Spectroscopy (EDX), Raman spectroscopy and Transmission Electron Microscopy (TEM) were used for characterizing magnetite nanoparticles. Especially, Hartridge-Roughton micromixer appears to be the most efficient mixing device for producing magnetite nanoparticles. The average particle size of magnetite nanoparticles prepared by Hartridge-Roughton rapid mixing device was less than 10 nm and the EDX and Raman spectroscopy shows that the particle purity is quite high.
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Abstract Since 2015, concentration–QTc?(C–QTc) analysis has been used to exclude the possibility that a drug has a concerning effect on the QTc interval. This has enabled the replacement of the designated thorough QT (TQT) study...
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Abstract Since 2015, concentration–QTc?(C–QTc) analysis has been used to exclude the possibility that a drug has a concerning effect on the QTc interval. This has enabled the replacement of the designated thorough QT (TQT) study with serial electrocardiograms (ECGs) in routine clinical pharmacology studies, such as the first‐in‐human (FIH) study. The E14 revision?has led to an increased proportion of FIH studies with the added objective of QT evaluation, with the intention of replacing the TQT study. With the more recent revision of the S7B/E14 Q&A document in February 2022, nonclinical assays/studies can be brought into the process of regulatory decisions at the time of marketing application. If the hERG (human ether‐a‐go‐go‐related gene) and the non‐rodent in?vivo study are conducted according to the described best practices and are negative, the previous requirement that a QTc effect of >10?milliseconds must be excluded in healthy subjects at plasma concentrations 2‐fold above what can be seen in patients can be reduced to covering the concentrations seen in patients. For drugs that cannot be safely given in high doses to healthy subjects, ECG evaluation is often performed at the therapeutic dose in patients. If a QTc effect of >10?milliseconds can be excluded, an argument can be made that the drug should be considered as having a low likelihood of proarrhythmic effects due to delayedrepolarization, if supported by negative best practices hERG and in vivo studies. In this article, we describe what clinicians involved in early clinical development need to understand in terms of the hERG and in?vivo studies to determine whether these meet best practices and therefore can be used in an integrated clinical/nonclinical QT/QTc risk assessment.
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A simple single-tube duplex-PCR assay was optimized for rapid and sensitive detection and differentiation of Brucella abortus (B.abortus) S19 vaccine strain from other Brucella spp.(B.abortus 544,B abortus S99,B.melitensis 16M,B.s...
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A simple single-tube duplex-PCR assay was optimized for rapid and sensitive detection and differentiation of Brucella abortus (B.abortus) S19 vaccine strain from other Brucella spp.(B.abortus 544,B abortus S99,B.melitensis 16M,B.suis).This assay was optimized using two primer pairs that were designed, one targeting genus specific multicopy IS711 and another eryC for the development of the duplex-PCR assay. Specificity of the assay was assessed using DNA templates from various Brucella species (B.abortus, B.melitensis, B.suis) and non Brucella bacteria like Staphylococcus aureus, Proteus vulgaris, Pasteurella multocida, Pseudomonas aeruginosa, Citrobacter freundii, E. coli, Salmonella enteritidis, Campylobacter jejuni and Listeria monocytogenes. The assay was also evaluated on spiked milk samples with known B.abortus cultures. The assay was able to detect up to 2.47 x 10(3)CFU of B. abortus S99 organism in spiked milk sample. The assay was further validated in 53 clinical specimens (aborted foetal stomach content). Results confirm that Single tube duplex-PCR assay was useful for early and rapid detection and differentiation of B. abortus vaccine strain S19 from other Brucella spp in milk as well as in clinical specimen.
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