9 results
Evaluation of a modified paediatric early warning score for children with congenital heart disease
- Simone Commotio, Nicolas Leister, Christoph Menzel, Christoph Ulrichs, Wolfgang A. Wetsch, Mathias Emmel, Uwe Trieschmann
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- Journal:
- Cardiology in the Young / Volume 34 / Issue 3 / March 2024
- Published online by Cambridge University Press:
- 11 September 2023, pp. 637-642
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Background:
Paediatric early warning score systems are used for early detection of clinical deterioration of patients in paediatric wards. Several paediatric early warning scores have been developed, but most of them are not suitable for children with cyanotic CHD who are adapted to lower arterial oxygen saturation.
Aim:The present study compared the original paediatric early warning system of the Royal College of Physicians of Ireland with a modification for children with cyanotic CHD.
Design:Retrospective single-centre study in a paediatric cardiology intermediate care unit at a German university hospital.
Results:The distribution of recorded values showed a significant shift towards higher score values in patients with cyanotic CHD (p < 0.001) using the original score, but not with the modification. An analysis of sensitivity and specificity for the factor “requirement of action” showed an area under the receiver operating characteristic for non-cyanotic patients of 0.908 (95% CI 0.862–0.954). For patients with cyanotic CHD, using the original score, the area under the receiver operating characteristic was reduced to 0.731 (95% CI 0.637–0.824, p = 0.001) compared to 0.862 (95% CI 0.809–0.915, p = 0.207), when the modified score was used. Using the critical threshold of scores ≥ 4 in patients with cyanotic CHD, sensitivity and specificity for the modified score was higher than for the original (sensitivity 78.8 versus 72.7%, specificity 78.2 versus 58.4%).
Conclusion:The modified score is a uniform scoring system for identifying clinical deterioration, which can be used in children with and without cyanotic CHD.
Human metapneumovirus infection in the cardiac paediatric ICU before and during COVID-19 pandemic: a retrospective cohort analysis
- Nicolas Leister, Simone Commotio, Christoph Menzel, Sirin Yücetepe, Christoph Ulrichs, Stefanie Wendt, Christoph Dedden, Uwe Trieschmann, Tobias Hannes
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- Journal:
- Cardiology in the Young / Volume 33 / Issue 9 / September 2023
- Published online by Cambridge University Press:
- 03 August 2022, pp. 1517-1522
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Introduction:
This study investigates the hygiene standards in the context of the COVID-19 pandemic and their impact on the perioperative incidence of human metapneumovirus as well as the typical symptom burden of human metapneumovirus-infected children with CHDs.
Materials and methods:Between March 2018 and July 2021, all patients of a cardiac paediatric ICU of a German university hospital were included in this retrospective cohort analysis.
Results:A total of 589 patients with CHD were included in the analysis. Three hundred and fifty-two patients (148 females and 204 males) were admitted before the introduction of social distancing and face masks between March 2018 and 15 April 2020 (cohort A). Two hundred and thirty-seven patients (118 females and 119 males) were admitted after the introduction between April 16 and July 2021 (cohort B). In cohort A, human metapneumovirus was detected in 11 out of 352 patients (3.1%) during their stay at cardiac paediatric ICU. In cohort B, one patient out of 237 (0.4%) tested positive for human metapneumovirus. Patients who tested positive for human metapneumovirus stayed in cardiac paediatric ICU for a median of 17.5 days (range, 2–45 days). Patients without a detected human metapneumovirus infection stayed in the cardiac paediatric ICU for a median of 4 days (range, 0.5–114 days). Nine out of 12 (75%) human metapneumovirus-positive patients showed atelectasis.
Conclusion:Perioperative human metapneumovirus infections prolong cardiac paediatric ICU stay in children with CHD. In affected patients, pulmonary impairment with typical symptoms appears. Under certain circumstances, a complication-rich perioperative infection with human metapneumovirus could be prevented in paediatric cardiac high-risk patients by prophylactic hygiene intervention.
RACHS-1 score as predictive factor for postoperative ventilation time in children with congenital heart disease
- Luisa Geier, Christoph Menzel, Ingo Germund, Uwe Trieschmann
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- Journal:
- Cardiology in the Young / Volume 30 / Issue 2 / February 2020
- Published online by Cambridge University Press:
- 17 January 2020, pp. 213-218
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Background:
Congenital heart disease is the most frequent malformation in newborns. The postoperative mortality of these patients can be assessed with the Risk Adjustment in Congenital Heart Surgery-1 (RACHS-1) score. This study evaluates whether the RACHS-1 score can also be used as a predictor for the length of postoperative ventilation and what is the influence of age.
Material and Methods:In a retrospective study over the period from 2007 to 2013, all patient records were evaluated: 598 children with congenital heart disease and cardiac surgery were identified and 39 patients have been excluded because of additional comorbidities. For evaluation of mortality, 559 patients could be analysed, after exclusion of 39 deceased patients, 520 cases remained for analysis of postoperative ventilation.
Results:Overall mortality was 7% with a dependency on RACHS-1 categories. The median length of postoperative ventilation rose according to the RACHS-1 categories: RACHS-1 category 1: 9 hours (interquartile range (IQR) 7–13 hours), category 2: 30 hours (IQR 12–85 hours), category 4: 58 hours (IQR 13–135 hours), category 4: 71 hours (IQR 29–165 hours), and category 6: 189 hours (IQR 127–277 hours). Some of the RACHS-1 subgroups differed significantly from the categories, especially the repair of tetralogy of Fallot with a longer ventilation time and strong variability. Younger age was an independent factor for longer postoperative ventilation.
Conclusion:RACHS-1 is a good predictor for the length of postoperative ventilation after cardiac surgery with the exception of some subgroups. Younger age is another independent factor for longer postoperative ventilation. These data provide better insight into ventilation times and allow better planning of operations in terms of available intensive care beds.
Frege Numbers and the Relativity Argument
- Christopher Menzel
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- Journal:
- Canadian Journal of Philosophy / Volume 18 / Issue 1 / March 1988
- Published online by Cambridge University Press:
- 01 January 2020, pp. 87-98
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Textual and historical subtleties aside, let's call the idea that numbers are properties (or classes) of equinumerous sets ‘the Fregean thesis.’ In a recent paper, Palle Yourgrau claims to have found a decisive refutation of this thesis. More surprising still, he claims in addition that the essence of this refutation is found in the Grundlagen itself – the very masterpiece in which Frege first proffered his thesis. My intention in this note is to evaluate these claims, and along the way to shed some light on relevant passages of the Grundlagen. I will argue that Yourgrau does not make his case.
The arguments with which we are concerned are found in the last three sections of Yourgrau's paper. A pervasive difficulty in these sections is that it is not clear exactly what Yourgrau is arguing against. The stated object of his attack is the Fregean thesis (d. 581-6), a thesis about what numbers are; however, instead of a frontal assault, his strategy is to embark on a foray into the ill-defined issue of what it is that numbers number (586ff.), where, roughly speaking, a number n numbers an object x just in case n can be legitimately assigned to x. The reason for this shift in emphasis appears to be rooted in a misconception. As we’ll see in more detail shortly, Yourgrau's argument against the Fregean thesis is based on an extension of a well known argument of Frege's found in §§22-3 of the Grundlagen, which Glenn Kessler has tagged the ‘relativity argument,’ (henceforth ‘RA’). According to Yourgrau, this is an argument ‘to the effect that what is literally numbered cannot simply be concrete objects’ (586). This is incorrect. Frege himself clarifies the point of the argument in §21 with the following preface:
In language, numbers (i.e., numerals] most commonly appear in adjectival form and attributive construction in the same sort of way as the words "hard" or "heavy" or "red," which have for their meanings properties of external things. It is natural to ask whether we must think of the individual numbers too as such properties, and whether, accordingly, the concept of number can be classed along with that, say, of color.
Contributors
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- By Mitchell Aboulafia, Frederick Adams, Marilyn McCord Adams, Robert M. Adams, Laird Addis, James W. Allard, David Allison, William P. Alston, Karl Ameriks, C. Anthony Anderson, David Leech Anderson, Lanier Anderson, Roger Ariew, David Armstrong, Denis G. Arnold, E. J. Ashworth, Margaret Atherton, Robin Attfield, Bruce Aune, Edward Wilson Averill, Jody Azzouni, Kent Bach, Andrew Bailey, Lynne Rudder Baker, Thomas R. Baldwin, Jon Barwise, George Bealer, William Bechtel, Lawrence C. Becker, Mark A. Bedau, Ernst Behler, José A. Benardete, Ermanno Bencivenga, Jan Berg, Michael Bergmann, Robert L. Bernasconi, Sven Bernecker, Bernard Berofsky, Rod Bertolet, Charles J. Beyer, Christian Beyer, Joseph Bien, Joseph Bien, Peg Birmingham, Ivan Boh, James Bohman, Daniel Bonevac, Laurence BonJour, William J. Bouwsma, Raymond D. Bradley, Myles Brand, Richard B. Brandt, Michael E. Bratman, Stephen E. Braude, Daniel Breazeale, Angela Breitenbach, Jason Bridges, David O. Brink, Gordon G. Brittan, Justin Broackes, Dan W. Brock, Aaron Bronfman, Jeffrey E. Brower, Bartosz Brozek, Anthony Brueckner, Jeffrey Bub, Lara Buchak, Otavio Bueno, Ann E. Bumpus, Robert W. Burch, John Burgess, Arthur W. Burks, Panayot Butchvarov, Robert E. Butts, Marina Bykova, Patrick Byrne, David Carr, Noël Carroll, Edward S. Casey, Victor Caston, Victor Caston, Albert Casullo, Robert L. Causey, Alan K. L. Chan, Ruth Chang, Deen K. Chatterjee, Andrew Chignell, Roderick M. Chisholm, Kelly J. Clark, E. J. Coffman, Robin Collins, Brian P. Copenhaver, John Corcoran, John Cottingham, Roger Crisp, Frederick J. Crosson, Antonio S. Cua, Phillip D. Cummins, Martin Curd, Adam Cureton, Andrew Cutrofello, Stephen Darwall, Paul Sheldon Davies, Wayne A. Davis, Timothy Joseph Day, Claudio de Almeida, Mario De Caro, Mario De Caro, John Deigh, C. F. Delaney, Daniel C. Dennett, Michael R. DePaul, Michael Detlefsen, Daniel Trent Devereux, Philip E. Devine, John M. Dillon, Martin C. Dillon, Robert DiSalle, Mary Domski, Alan Donagan, Paul Draper, Fred Dretske, Mircea Dumitru, Wilhelm Dupré, Gerald Dworkin, John Earman, Ellery Eells, Catherine Z. Elgin, Berent Enç, Ronald P. Endicott, Edward Erwin, John Etchemendy, C. Stephen Evans, Susan L. Feagin, Solomon Feferman, Richard Feldman, Arthur Fine, Maurice A. Finocchiaro, William FitzPatrick, Richard E. Flathman, Gvozden Flego, Richard Foley, Graeme Forbes, Rainer Forst, Malcolm R. Forster, Daniel Fouke, Patrick Francken, Samuel Freeman, Elizabeth Fricker, Miranda Fricker, Michael Friedman, Michael Fuerstein, Richard A. Fumerton, Alan Gabbey, Pieranna Garavaso, Daniel Garber, Jorge L. A. Garcia, Robert K. Garcia, Don Garrett, Philip Gasper, Gerald Gaus, Berys Gaut, Bernard Gert, Roger F. Gibson, Cody Gilmore, Carl Ginet, Alan H. Goldman, Alvin I. Goldman, Alfonso Gömez-Lobo, Lenn E. Goodman, Robert M. Gordon, Stefan Gosepath, Jorge J. E. Gracia, Daniel W. Graham, George A. Graham, Peter J. Graham, Richard E. Grandy, I. Grattan-Guinness, John Greco, Philip T. Grier, Nicholas Griffin, Nicholas Griffin, David A. Griffiths, Paul J. Griffiths, Stephen R. Grimm, Charles L. Griswold, Charles B. Guignon, Pete A. Y. Gunter, Dimitri Gutas, Gary Gutting, Paul Guyer, Kwame Gyekye, Oscar A. Haac, Raul Hakli, Raul Hakli, Michael Hallett, Edward C. Halper, Jean Hampton, R. James Hankinson, K. R. Hanley, Russell Hardin, Robert M. Harnish, William Harper, David Harrah, Kevin Hart, Ali Hasan, William Hasker, John Haugeland, Roger Hausheer, William Heald, Peter Heath, Richard Heck, John F. Heil, Vincent F. Hendricks, Stephen Hetherington, Francis Heylighen, Kathleen Marie Higgins, Risto Hilpinen, Harold T. Hodes, Joshua Hoffman, Alan Holland, Robert L. Holmes, Richard Holton, Brad W. Hooker, Terence E. Horgan, Tamara Horowitz, Paul Horwich, Vittorio Hösle, Paul Hoβfeld, Daniel Howard-Snyder, Frances Howard-Snyder, Anne Hudson, Deal W. Hudson, Carl A. Huffman, David L. Hull, Patricia Huntington, Thomas Hurka, Paul Hurley, Rosalind Hursthouse, Guillermo Hurtado, Ronald E. Hustwit, Sarah Hutton, Jonathan Jenkins Ichikawa, Harry A. Ide, David Ingram, Philip J. Ivanhoe, Alfred L. Ivry, Frank Jackson, Dale Jacquette, Joseph Jedwab, Richard Jeffrey, David Alan Johnson, Edward Johnson, Mark D. Jordan, Richard Joyce, Hwa Yol Jung, Robert Hillary Kane, Tomis Kapitan, Jacquelyn Ann K. Kegley, James A. Keller, Ralph Kennedy, Sergei Khoruzhii, Jaegwon Kim, Yersu Kim, Nathan L. King, Patricia Kitcher, Peter D. Klein, E. D. Klemke, Virginia Klenk, George L. Kline, Christian Klotz, Simo Knuuttila, Joseph J. Kockelmans, Konstantin Kolenda, Sebastian Tomasz Kołodziejczyk, Isaac Kramnick, Richard Kraut, Fred Kroon, Manfred Kuehn, Steven T. Kuhn, Henry E. Kyburg, John Lachs, Jennifer Lackey, Stephen E. Lahey, Andrea Lavazza, Thomas H. Leahey, Joo Heung Lee, Keith Lehrer, Dorothy Leland, Noah M. Lemos, Ernest LePore, Sarah-Jane Leslie, Isaac Levi, Andrew Levine, Alan E. Lewis, Daniel E. Little, Shu-hsien Liu, Shu-hsien Liu, Alan K. L. Chan, Brian Loar, Lawrence B. Lombard, John Longeway, Dominic McIver Lopes, Michael J. Loux, E. J. Lowe, Steven Luper, Eugene C. Luschei, William G. Lycan, David Lyons, David Macarthur, Danielle Macbeth, Scott MacDonald, Jacob L. Mackey, Louis H. Mackey, Penelope Mackie, Edward H. Madden, Penelope Maddy, G. B. Madison, Bernd Magnus, Pekka Mäkelä, Rudolf A. Makkreel, David Manley, William E. Mann (W.E.M.), Vladimir Marchenkov, Peter Markie, Jean-Pierre Marquis, Ausonio Marras, Mike W. Martin, A. P. Martinich, William L. McBride, David McCabe, Storrs McCall, Hugh J. McCann, Robert N. McCauley, John J. McDermott, Sarah McGrath, Ralph McInerny, Daniel J. McKaughan, Thomas McKay, Michael McKinsey, Brian P. McLaughlin, Ernan McMullin, Anthonie Meijers, Jack W. Meiland, William Jason Melanson, Alfred R. Mele, Joseph R. Mendola, Christopher Menzel, Michael J. Meyer, Christian B. Miller, David W. Miller, Peter Millican, Robert N. Minor, Phillip Mitsis, James A. Montmarquet, Michael S. Moore, Tim Moore, Benjamin Morison, Donald R. Morrison, Stephen J. Morse, Paul K. Moser, Alexander P. D. Mourelatos, Ian Mueller, James Bernard Murphy, Mark C. Murphy, Steven Nadler, Jan Narveson, Alan Nelson, Jerome Neu, Samuel Newlands, Kai Nielsen, Ilkka Niiniluoto, Carlos G. Noreña, Calvin G. Normore, David Fate Norton, Nikolaj Nottelmann, Donald Nute, David S. Oderberg, Steve Odin, Michael O’Rourke, Willard G. Oxtoby, Heinz Paetzold, George S. Pappas, Anthony J. Parel, Lydia Patton, R. P. Peerenboom, Francis Jeffry Pelletier, Adriaan T. Peperzak, Derk Pereboom, Jaroslav Peregrin, Glen Pettigrove, Philip Pettit, Edmund L. Pincoffs, Andrew Pinsent, Robert B. Pippin, Alvin Plantinga, Louis P. Pojman, Richard H. Popkin, John F. Post, Carl J. Posy, William J. Prior, Richard Purtill, Michael Quante, Philip L. Quinn, Philip L. Quinn, Elizabeth S. Radcliffe, Diana Raffman, Gerard Raulet, Stephen L. Read, Andrews Reath, Andrew Reisner, Nicholas Rescher, Henry S. Richardson, Robert C. Richardson, Thomas Ricketts, Wayne D. Riggs, Mark Roberts, Robert C. Roberts, Luke Robinson, Alexander Rosenberg, Gary Rosenkranz, Bernice Glatzer Rosenthal, Adina L. Roskies, William L. Rowe, T. M. Rudavsky, Michael Ruse, Bruce Russell, Lilly-Marlene Russow, Dan Ryder, R. M. Sainsbury, Joseph Salerno, Nathan Salmon, Wesley C. Salmon, Constantine Sandis, David H. Sanford, Marco Santambrogio, David Sapire, Ruth A. Saunders, Geoffrey Sayre-McCord, Charles Sayward, James P. Scanlan, Richard Schacht, Tamar Schapiro, Frederick F. Schmitt, Jerome B. Schneewind, Calvin O. Schrag, Alan D. Schrift, George F. Schumm, Jean-Loup Seban, David N. Sedley, Kenneth Seeskin, Krister Segerberg, Charlene Haddock Seigfried, Dennis M. Senchuk, James F. Sennett, William Lad Sessions, Stewart Shapiro, Tommie Shelby, Donald W. Sherburne, Christopher Shields, Roger A. Shiner, Sydney Shoemaker, Robert K. Shope, Kwong-loi Shun, Wilfried Sieg, A. John Simmons, Robert L. Simon, Marcus G. Singer, Georgette Sinkler, Walter Sinnott-Armstrong, Matti T. Sintonen, Lawrence Sklar, Brian Skyrms, Robert C. Sleigh, Michael Anthony Slote, Hans Sluga, Barry Smith, Michael Smith, Robin Smith, Robert Sokolowski, Robert C. Solomon, Marta Soniewicka, Philip Soper, Ernest Sosa, Nicholas Southwood, Paul Vincent Spade, T. L. S. Sprigge, Eric O. Springsted, George J. Stack, Rebecca Stangl, Jason Stanley, Florian Steinberger, Sören Stenlund, Christopher Stephens, James P. Sterba, Josef Stern, Matthias Steup, M. A. Stewart, Leopold Stubenberg, Edith Dudley Sulla, Frederick Suppe, Jere Paul Surber, David George Sussman, Sigrún Svavarsdóttir, Zeno G. Swijtink, Richard Swinburne, Charles C. Taliaferro, Robert B. Talisse, John Tasioulas, Paul Teller, Larry S. Temkin, Mark Textor, H. S. Thayer, Peter Thielke, Alan Thomas, Amie L. Thomasson, Katherine Thomson-Jones, Joshua C. Thurow, Vzalerie Tiberius, Terrence N. Tice, Paul Tidman, Mark C. Timmons, William Tolhurst, James E. Tomberlin, Rosemarie Tong, Lawrence Torcello, Kelly Trogdon, J. D. Trout, Robert E. Tully, Raimo Tuomela, John Turri, Martin M. Tweedale, Thomas Uebel, Jennifer Uleman, James Van Cleve, Harry van der Linden, Peter van Inwagen, Bryan W. Van Norden, René van Woudenberg, Donald Phillip Verene, Samantha Vice, Thomas Vinci, Donald Wayne Viney, Barbara Von Eckardt, Peter B. M. Vranas, Steven J. Wagner, William J. Wainwright, Paul E. Walker, Robert E. Wall, Craig Walton, Douglas Walton, Eric Watkins, Richard A. Watson, Michael V. Wedin, Rudolph H. Weingartner, Paul Weirich, Paul J. Weithman, Carl Wellman, Howard Wettstein, Samuel C. Wheeler, Stephen A. White, Jennifer Whiting, Edward R. Wierenga, Michael Williams, Fred Wilson, W. Kent Wilson, Kenneth P. Winkler, John F. Wippel, Jan Woleński, Allan B. Wolter, Nicholas P. Wolterstorff, Rega Wood, W. Jay Wood, Paul Woodruff, Alison Wylie, Gideon Yaffe, Takashi Yagisawa, Yutaka Yamamoto, Keith E. Yandell, Xiaomei Yang, Dean Zimmerman, Günter Zoller, Catherine Zuckert, Michael Zuckert, Jack A. Zupko (J.A.Z.)
- Edited by Robert Audi, University of Notre Dame, Indiana
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- The Cambridge Dictionary of Philosophy
- Published online:
- 05 August 2015
- Print publication:
- 27 April 2015, pp ix-xxx
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- By Sefanja Achterberg, James A. Adams, Angelika Alonso, Bettina Anders, Ana Patrícia Antunes, Johannes Binder, Manuel Bolognese, Louis R. Caplan, Paolo Costa, Sofie De Blauwe, Exuperio Díez-Tejedor, Philipp Eisele, Alex Förster, Blanca Fuentes, Ruth Geraldes, Martin Griebe, Valentin Held, Gregory Helsen, Michael G. Hennerici, Eva Hornberger, Micha Kablau, L. Jaap Kappelle, Rolf Kern, Patricia Martínez-Sánchez, Tilman Menzel, Nadja Meyer, Caroline Ottomeyer, Suzanne Persoon, Alessandro Pezzini, Miriam M. Pfeiffer, Björn Reuter, Katlijn Schotsmans, Christopher Schwarzbach, Markus Stürmlinger, Kristina Szabo, Tiago Teodoro, Ralph Werner, Johannes C. Wöhrle, Marc Wolf
- Edited by Michael G. Hennerici, Ruprecht-Karls-Universität Heidelberg, Germany, Rolf Kern, Ruprecht-Karls-Universität Heidelberg, Germany, Louis R. Caplan, Kristina Szabo, Ruprecht-Karls-Universität Heidelberg, Germany
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- More Case Studies in Stroke
- Published online:
- 05 June 2014
- Print publication:
- 15 May 2014, pp ix-xii
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Analysis of a folded reflect-array antenna using particle swarm optimization
- Sabine Dieter, Christoph Fischer, Wolfgang Menzel
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- International Journal of Microwave and Wireless Technologies / Volume 3 / Issue 3 / June 2011
- Published online by Cambridge University Press:
- 19 April 2011, pp. 267-272
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In this paper, a method for design and optimization of folded reflect-array antennas is proposed based on particleswarm optimization (PSO). In addition to such a powerful optimization algorithm, two further requirements have to be fulfilled. The first one is a good and fast algorithm for the exact prognosis of the far-field radiation diagram, resulting from a specific element configuration on the reflector. Additionally, a good choice of the fitness function for the evaluation of the resulting radiation diagrams is necessary. In both, reflect-array-related aspects such as phase truncation, reflection losses, and cell discontinuities have to be considered. Antenna optimization based on this technique is presented in this paper at the example of two 77 GHz folded reflect-array antennas. The efficiency of this approach is demonstrated with these examples, and the results are verified by measurement, showing an excellent agreement with the specifications of the diagram masks. The implemented tool, including a realistic antenna diagram preview, allows the investigation of the design parameters’ influence on the antenna performance, such as illumination amplitude, high substrate losses, and phase truncation.
Edward N. Zalta. Intensional logic and the metaphysics of intentionality. Bradford books. The MIT Press, Cambridge, Mass., and London, 1988, xiii + 256 pp.
- Christopher Menzel
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- Journal:
- The Journal of Symbolic Logic / Volume 57 / Issue 3 / September 1992
- Published online by Cambridge University Press:
- 12 March 2014, pp. 1146-1150
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- September 1992
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Structuralism and Conceptual Change in Mathematics
- Christopher Menzel
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- PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association / Volume 1990 / Issue 2 / 1990
- Published online by Cambridge University Press:
- 31 January 2023, pp. 397-401
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- 1990
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Professor Grosholz packs a lot into her interesting and suggestive paper “Formal Unities and Real Individuals” (Grosholz 1990b). In the limited space available I can comment briefly on its several parts, or direct more substantive comments at a single issue. I will opt for the latter; specifically, I want to address her critique of mathematical structuralism, as found especially in the writings of Michael Resnik.
I begin with a brief, hence necessarily caricatured, summary of Resnik’s influential view. According to structuralism, the subject matter of a mathematical theory is a given pattern, or structure, and the objects of the theory are intrinsically unstructured points, or positions, within that pattern. Mathematical objects thus have no identity, and no intrinsic features, outside of the patterns in which they occur. Hence, they cannot be given in isolation but only in their role within an antecedently given pattern, and are distinguishable from one another only in virtue of the relations they bear to one another in the pattern (see, e.g., Resnik (1981)).