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233 results on '"Wolfram, D."'

1. Change of Basis from Bernstein to Zernike

Author

Wolfram, D. A.

Subjects
Mathematics - Classical Analysis and ODEs, Primary 15A03, Secondary 20N02, 33C45, 20L05
Abstract

We increase the scope of previous work on change of basis between finite bases of polynomials by defining ascending and descending bases and introducing three techniques for defining them from known ones. The minimum degrees of polynomials in an ascending basis can increase such as with bases of Bernstein and Zernike Radial polynomials. They have applications in computer-aided design and optics. We give coefficient functions for mappings from the monomials to descending bases of Bernstein polynomials, and ascending ones of Zernike Radial polynomials and prove their correctness. Allowing for parity, we define eight general change of basis matrices and the related equations for composing their coefficient functions. A main example is the change of basis from shifted Legendre polynomials to Bernstein polynomials considered by R Farouki [7]. The analysis enables us to find a more general hypergeometric function for the coefficient function, and recurrences for finding coefficient functions by matrix row and column. We show the column coefficient functions are equivalent to the Lagrange interpolation polynomials of their elements. We also provide a solution to an open problem [7] by showing there is no general closed form expression for the coefficient function from Gosper's Algorithm. Truncation, alternation and superposition increase the scope further. Alternation enables, for example, a change of basis between Bernstein and Zernike Radial polynomials. A summary shows that the groupoid of change of basis matrices is a small category, and triangular and alternating change of basis matrices are morphisms in full subcategories of it. Truncation is a covariant functor., Comment: 77 pages

Published
2022

2. Change of Basis between Classical Orthogonal Polynomials

Author

Wolfram, D. A.

Subjects
Mathematics - Classical Analysis and ODEs, Mathematics - Rings and Algebras, 33C45 (Primary) 15A03, 20N02 (Secondary)
Abstract

Classical orthogonal polynomials have widespread applications including in numerical integration, solving differential equations, and interpolation. Changing basis between classical orthogonal polynomials can affect the convergence, accuracy, and stability of solutions. We provide a general method for changing basis between any pair of classical orthogonal polynomials by using algebraic expressions called coefficient functions that evaluate to connection coefficients. The method builds directly on previous work on the change of basis groupoid. The scope has fifteen kinds of classical orthogonal polynomials including the classes of Jacobi, Gegenbauer and generalized Laguerre polynomials. The method involves the mappings to and from the monomials for these polynomial bases. Sixteen coefficient functions appear to be new for polynomials that do not have definite parity. We derive the remainder from seven sources in the literature. We give a complete summary of thirty coefficient functions. This enables change of basis to be defined algebraically and uniformly between any pair of classical orthogonal polynomial bases by using a vector dot product to compose two coefficient functions to give a third. A definition of Jacobi polynomials uses a basis of shifted monomials. We find a key new mapping between the monomials and Jacobi polynomials by using a general mapping between shifted monomials and monomials. It yields new mappings for the Chebyshev polynomials of the third and fourth kinds and their shifted versions., Comment: 25 pages

Published
2021

3. The Change of Basis Groupoid

Author

Wolfram, D. A.

Subjects
Mathematics - Rings and Algebras, Primary 15A03, Secondary 20N02, 33C45
Abstract

We show that the change of basis matrices of a set of $m$ bases of a finite vector space is a connected groupoid of order $m^2$. We define a general method to express the elements of change of basis matrices as algebraic expressions using optimizations of evaluations of vector dot products. Examples are given with orthogonal polynomials., Comment: 23 pages

Published
2021

4. Factoring Variants of Chebyshev Polynomials with Minimal Polynomials of $\cos(\frac{2\pi}{d})$

Author

Wolfram, D. A.

Subjects
Mathematics - Classical Analysis and ODEs, Mathematics - Rings and Algebras, Primary 12E10, Secondary 12D05
Abstract

We solve the problem of factoring polynomials $V_n(x) \pm 1$ and $W_n(x) \pm 1$ where $V_n(x)$ and $W_n(x)$ are Chebyshev polynomials of the third and fourth kinds. The method of proof is based on previous work by Wolfram [12] for factoring variants of Chebyshev polynomials of the first and second kinds, $T_n(x) \pm 1$ and $U_n(x) \pm 1$. We also show that, in general, there are no factorizations of variants of Chebyshev polynomials of the fifth and sixth kinds, $X_n(x) \pm 1$ and $Y_n(x) \pm 1$ using minimal polynomials of $\cos(\frac{2\pi}{d})$., Comment: 9 pages

Published
2021
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5. INVERSE CONNECTION FORMULAE FOR GENERALISED BESSEL POLYNOMIALS.

Author

WOLFRAM, D. A.

Subjects
*INVERSE problems, *POLYNOMIALS, *PROBLEM solving
Abstract

We solve the problem of finding the inverse connection formulae for the generalised Bessel polynomials and their reciprocals, the reverse generalised Bessel polynomials. The connection formulae express monomials in terms of the generalised Bessel polynomials. They enable formulae for the elements of change of basis matrices for both kinds of generalised Bessel polynomials to be derived and proved correct directly. [ABSTRACT FROM AUTHOR]

Published
2024
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8. Historie und Indikationen

Author

Djedovic, G., Wolfram, D., Zimmermann, R. F., Pierer, G., Kneser, Ulrich, editor, Horch, Raymund E., editor, and Lehnhardt, Marcus, editor

Published
2016
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14. Soil science within German cities

Author

Burghardt, Wolfgang, primary, Kneib, Wolfram D., additional, Höke, Silke, additional, Lehmann, Andreas, additional, Makowsky, Lutz, additional, Kocher, Birgit, additional, and Steinweg, Bernd, additional

Published
2022
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15. Soil science within German cities

Author

Burghardt, Wolfgang, Kneib, Wolfram D., Höke, Silke, Lehmann, Andreas, Makowsky, Lutz, Kocher, Birgit, and Steinweg, Bernd

Subjects
Biologie
Published
2022

16. Unification and matching modulo nilpotence

Author

Guo, Qing, Narendran, Paliath, Wolfram, D. A., Goos, G., editor, Hartmanis, J., editor, van Leeuwen, J., editor, Carbonell, Jaime G., editor, Siekmann, Jörg, editor, McRobbie, M. A., editor, and Slaney, J. K., editor

Published
1996
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22. Rewriting, and equational unification: the higher-order cases

Author

Wolfram, D. A., Goos, G., editor, Hartmanis, J., editor, Barstow, D., editor, Brauer, W., editor, Brinch Hansen, P., editor, Gries, D., editor, Luckham, D., editor, Moler, C., editor, Pnueli, A., editor, Seegmüller, G., editor, Stoer, J., editor, Wirth, N., editor, and Book, Ronald V., editor

Published
1991
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41. Scaled momentum distributions for K S 0 and ∧/∧ in DIS at HERA

Author

Abramowicz, Halina, Abt, Iris, Adamczyk, Leszek, Adamus, Marek, Aggarwal, Ritu, Antonelli, Stefano, Antonioli, Pietro, Antonov, Alexei A., Arneodo, Michele, Aushev, Volodymyr E., Aushev, Y., Bachynska, O., Bamberger, Andreas, Barakbaev, A. N., Barbagli, G., Bári, Gergely, Barreiro, Fernando, Bartosik, N., Bartsch, D., Basile, Maurizio, Behnke, Olaf, Behr, Jörg, Behrens, Ulf, Bellagamba, Lorenzo, Bertolin, Alessandro, Bhadra, Sampa, Bindi, Marcello, Blohm, C., Bokhonov, V., Bołd, Tomasz, Bondarenko, K., Boos, E. G., Borras, Kerstin, Boscherini, Davide, Bot, D., Brock, Ian C., Brownson, Eric, Brugnera, Riccardo, Brümmer, Nichol C., Bruni, Alessia, Bruni, Graziano, Brzozowska, Beata, Bussey, Peter J., Bylsma, B. G., Caldwell, Allen C., Capua, M., Carlin, Roberto, Catterall, C. D., Chekanov, S. V., Chwastowski, Janusz J., Ciborowski, Jacek, Ciesielski, Robert, Cifarelli, Luisa, Cindolo, Federico, Contin, Andrea, Cooper-Sarkar, Amanda M., Coppola, Nicola, Corradi, Massimo, Corriveau, François, Costa, Mario J., D'Agostini, Giulio, Dal Corso, Flavio, Del Peso, J., Dementiev, R. K., De Pasquale, Salvatore, Derrick, Mark, Devenish, Robin C E, Dobur, Didar, Dolgoshein, Boris A., Dolinska, Ganna, Doyle, Anthony T., Drugakov, V., Durkin, Louis S., Dusini, S., Eisenberg, Yehuda, Ermolov., P. F., Eskreys, A. W., Fang, Shuangshi, Fazio, Salvatore, Ferrando, James, Ferrero, Mauro I., Figiel, Jan, Forrest, Matthew, Foster, Brian, Gach, Grzegorz P., Galas, Anna I., Gallo, Elisabetta, Garfagnini, Alberto, Geiser, Achim, Gialas, Ioannis, Gladilin, Leonid K., Gladkov, Daniil, Glasman, Claudia J., Gogota, O., Golubkov, Yu A., Göttlicher, Peter, Grabowska-Bo, I., Grebenyuk, Julia, Gregor, Ingrid Maria, Grigorescu, Gabriela, Grzelak, Grzegorz, Gueta, O., Guzik, M., Gwenlan, Claire, Haas, Tobias, Hain, W., Hamatsu, Ryosuke, Hart, John C., Hartmann, Hans Jörg, Hartner, G., Hilger, Erwin, Hochman, Don, Hori, R., Horton, K., Hüttmann, Antje, Ibrahim, Zainol Abidin, Iga, Yasunobu, Ingbir, Ronen, Ishitsuka, Masaki, Jakob, H. P., Januschek, Friederike, Jones, T. W., Jüngst, M., Kadenko, Igor M., Kahle, Benjamin, Kananov, S., Kanno, Takayuki, Karshon, Uri, Karstens, Falk, Katkov, Igor I., Kaur, Manjit, Kaur, Prabhdeep, Keramidas, Avraam A., Khein, Lev A., Kim, Jihyun, Kisielewska, Danuta, Kitamura, Shoichi, Klanner, Robert, Klein, Uta, Koffeman, Els N., Kooijman, Paul M., Korol, Korzhavina, Irina A., Kotański, A., Kötz, Ulrich, Kowalski, Henryk, Kuprash, Oleg E., Kuze, Masahiro, Lee, Albert, Levchenko, Boris B., Levy, Aharon, Libov, Vladyslav, Limentani, Sylvia, Ling, T. Y., Lisovyi, Mykhailo, Łobodzińska, Ewelina Maria, Lohmann, Wolfgang, Löhr, Bernd, Lohrmann, Erich, Long, Kenneth, Longhin, Andrea, Lontkovskyi, Denys I., Lukina, Ou Yu, Maeda, Jouji, Magill, Stephen R., Makarenko, Irina V., Malka, Janusz, Mankel, Rainer, Margotti, Anselmo, Marini, Giuseppe P., Martin, John F., Mastroberardino, A., Mattingly, M. C K, Melzer-Pellmann, Isabell Alissandra, Mergelmeyer, Sebastian, Miglioranzi, Silvia, Mohamad Idris, F., Monaco, Vincenzo, Montanari, Andrea, Morris, John D., Mujkic, Kenan, Musgrave, B., Nagano, Kunihiro, Namsoo, Tim A., Nania, Rosario, Nigro, Andrea, Ning, Y., Nobe, Takuya, Noor, U., Notz, Dieter, Nowak, Roman J., Nuncio-Quiroz, A. E., Oh, B. Y., Okazaki, Noriaki, Oliver, Katie, Olkiewicz, Krystyna, Onishchuk, Yu M., Papageorgiu, K., Parenti, Andrea, Paul, Ewald, Pawlak, J. M., Pawlik, Barbara, Pelfer, Pier Giovanni, Pellegrino, Antonio R., Perlański, Wojciech, Perrey, Hanno, Piotrzkowski, Krzysztof, Pluciński, Pawel, Pokrovskiy, N. S., Polini, Alessandro, Proskuryakov, Alexander S., Przybycień, Mariusz B., Raval, Amita, Reeder, D. D., Reisert, Burkard, Ren, Zhongliang, Repond, José, Ri, Y. D., Robertson, Ashley I., Roloff, Philipp, Rubinsky, I. A., Ruspa, Marta, Sacchi, Roberto, Salii, Andrii, Samson, Ursula, Sartorelli, Gabriella, Savin, Alexander A., Saxon, David H., Schioppa, Marco, Schlenstedt, Stefan, Schleper, Peter, Schmidke, William B., Schneekloth, U., Schönberg, Verena, Schörner-Sadenius, Thomas, Schwartz, Joshua David, Sciulli, Frank J., Shcheglova, Lydia M., Shehzadi, R., Shimizu, Shima, Singh, Inderpal J., Skillicorn, Ian O., Słomiński, Wojciech, Smith, Wesley H., Sola, Valentina, Solano, Ada, Son, Dongchul, Sosnovtsev, V. V., Spiridonov, A., Stadie, Hartmut, Stanco, Luca, Stern, Amir, Stewart, T. P., Stifutkin, A. A., Stopa, P., Suchkov, S. I., Susinno, G. C., Suszycki, Leszek, Sztuk-Dambietz, Jolanta, Szuba, Dorota, Szuba, J., Tapper, A. D., Tassi, Enrico, Terrón, Juan M., Theedt, T., Tiecke., H. G J M, Tokushuku, Katsuo, Tomalak, O., Tomaszewska, Justyna, Tsurugai, Takashi, Turcato, Monica, Tymieniecka, Teresa, Vázquez., Manuel M., Verbytskyi, Andrii, Viazlo, O., Vlasov, Nikolai N., Volynets, G. V., Walczak, Roman, Wan Abdullah, Wan Ahmad Tajuddin Bin, Whitmore, J. J., Wiggers, Lisbeth W., Wing, Matthew, Własenko, Michał, Wolf, Günter K., Wolfe, H., Wrona, K., Yagües-Molina, A. G., Yamada, Satoru, Yamazaki, Yasunori, Yoshida, Rik, Youngman, Christopher, Zarnecki, Aleksander Filip, Zawiejski, Leszek, Zenaiev, Oleksandr, Zeuner, Wolfram D., Zhautykov, B. O., Zhmak, N., Zhou, C., Zichichi, Antonino, Zolkapli, Zukhaimira, Zolko, M., Zotkin, D. S., and UAM. Departamento de Física Teórica

Subjects
Lepton-nucleon scattering, High Energy Physics::Phenomenology, Física, High Energy Physics::Experiment, Nuclear Experiment
Abstract

Journal of High Energy Physics 2012. 3 (2012): 020 reproduced by permission of Scuola Internazionale Superiore di Studi Avanzati (SISSA), Scaled momentum distributions for the strange hadrons KS0 and Λ/Λ were measured in deep inelastic ep scattering with the ZEUS detector at HERA using an integrated luminosity of 330 pb-1. The evolution of these distribuitions with the photon virtuality, Q2, was studied in the kinematic region 10 < Q2 < 40000 GeV2 and 0.001 < x < 0.75, where x is the Bjorken scaling variable. Clear scaling violations are observed. Predictions based on different approaches to fragmentation were compared to the measurements. Leading-logarithm parton-shower Monte Carlo calculations interfaced to the Lund string fragmentation model describe the data reasonably well in the whole range measured. Next- to-leading-order QCD calculations based on fragmentation functions, FFs, extracted from e+e- data alone, fail to describe the measurements. The calculations based on FFs extracted from a global analysis including e+e-, ep and pp data give an improved description. The measurements presented in this paper have the potential to further constrain the FFs of quarks, anti-quarks and gluons yielding KS 0 and Λ/ Λ̄ strange hadrons., We thank the DESY Directorate for their strong support and encouragement. The remarkable achievements of the HERA machine group were essential for the successful completion of this work and are greatly appreciated. We are grateful for the support of the DESY computing and network services

Published
2012

42. Komplikationen beim Einsatz von Fillern – Wann ist die chirurgische Intervention notwendig?

Author

Wolfram, D, Tzankov, A, and Piza-Katzer, H

Subjects
ddc: 610, 610 Medical sciences, Medicine
Abstract

Einleitung: Filler-Substanzen werden zur Korrektur des altersbedingten Volumenmangels im Gesicht eingesetzt. Aktuell ist eine Vielzahl an unterschiedlichen Fillern am Markt, wobei diese Produkte zumeist als atoxische, nicht-immunogene und relative harmlose Alternativen zu chirurgischen „Anti[for full text, please go to the a.m. URL], 49. Jahrestagung der Österreichischen Gesellschaft für Plastische, Ästhetische und Rekonstruktive Chirurgie (ÖGPÄRC), 42. Jahrestagung der Deutschen Gesellschaft der Plastischen, Rekonstruktiven und Ästhetischen Chirurgen (DGPRÄC), 16. Jahrestagung der Vereinigung der Deutschen Ästhetisch-Plastischen Chirurgen (VDÄPC)

Published
2011
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43. Insights from computational modeling in inflammation and acute rejection in limb transplantation

Author

Wolfram, D, Starzl, R, Hackl, H, Barclay, D, Hautz, T, Zelger, B, Brandacher, G, Lee, WPA, Eberhart, N, Vodovotz, Y, Pratschke, J, Pierer, G, Schneeberger, S, Wolfram, D, Starzl, R, Hackl, H, Barclay, D, Hautz, T, Zelger, B, Brandacher, G, Lee, WPA, Eberhart, N, Vodovotz, Y, Pratschke, J, Pierer, G, and Schneeberger, S

Abstract

Acute skin rejection in vascularized composite allotransplantation (VCA) is the major obstacle for wider adoption in clinical practice. This study utilized computational modeling to identify biomarkers for diagnosis and targets for treatment of skin rejection. Protein levels of 14 inflammatory mediators in skin and muscle biopsies from syngeneic grafts [n = 10], allogeneic transplants without immunosuppression [n = 10] and allografts treated with tacrolimus [n = 10] were assessed by multiplexed analysis technology. Hierarchical Clustering Analysis, Principal Component Analysis, Random Forest Classification and Multinomial Logistic Regression models were used to segregate experimental groups. Based on Random Forest Classification, Multinomial Logistic Regression and Hierarchical Clustering Analysis models, IL-4, TNF-α and IL-12p70 were the best predictors of skin rejection and identified rejection well in advance of histopathological alterations. TNF-α and IL-12p70 were the best predictors of muscle rejection and also preceded histopathological alterations. Principal Component Analysis identified IL-1α, IL-18, IL-1β, and IL-4 as principal drivers of transplant rejection. Thus, inflammatory patterns associated with rejection are specific for the individual tissue and may be superior for early detection and targeted treatment of rejection. © 2014 Wolfram et al.

Published
2014

48. Besonderheiten des Managements von Kongresszentren

Author

Ralf G. Kleinhenz and Wolfram D. Svoboda

Abstract

Spricht man von den gangigen Veranstaltungstypen auf deutschen Messe- und Kongressplatzen, so wird haufig zwischen drei Veranstaltungsgattungen unterschieden: Messen, Kongresse und sonstige Veranstaltungen/Events. Letztere bilden eine Art Sammelbegriff fur jene Veranstaltungen, die sich nicht eindeutig in den beiden ersten Kategorien abbilden lassen. Als Beispiele konnen v. a. Firmenveranstaltungen genannt werden, die entweder ihren Schwerpunkt z. B. in der Prasentation von Produkten oder Dienstleistungen haben oder schlichtweg Mischformen zwischen Messen und Kongressen sind. Hierzu zahlen viele Veranstaltungen aus der IT- und Kommunikationsbranche. Diese Dreiteilung des Veranstaltungsgeschafts greift, insbesondere bei den in diesem Beitrag im Zentrum stehenden Kongresszentren, zu kurz. Vielmehr ist es sinnvoller, die Unterscheidung grundsatzlich danach vorzunehmen, wer die Rolle des Veranstalters innehat. Konsequenterweise kommt dabei die Unterscheidung in Eigen- und Gastveranstaltungen zum Tragen.

Published
2003
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