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(2015-10-19)  -  Schellenberg et al.: J Forensic Sci.  -  2007 Jul;52(4):954-956.  -  TUDelft Subscription  

(2015-05-27)  -  MARTIN, WILLIAM F.: Protecting Personnel at Hazardous Waste Sites.  EBook at UUtrecht  -  Full Text  

(2015-05-27)  -  Williams, J. G. P.: Medical Aspects of Sport and Physical Fitness: The Commonwealth and International Library: Physical Education, Health and Recreation Division.
                         EBook at UUtrecht  -  Full Text  

(2014-04-29)  -  S. Krenk: A vector format for conservative time integration of rotations.
In Multibody Dynamics 2007, ECCOMAS Thematic Conference, Milan, Italy, 1–12, 2007

Quaestiones Mathematicae, Volume 17, Issue 1, 1994  -  pp 67-81  -  doi: 10.1080/16073606.1994.9632218
No electronic and paper subscriptions at TUDelft, nor at UUtrecht

Abstract: For commutative Banach algebras B and I and a continuous representation π: B → M(I), where M(I) are those bounded linear operators T: I → I that satisfy T(ij) = iT(j) for all i,j in I, the direct sum B I can be made into a commutative Banach algebra which contains B and I as respectively a closed subalgebra and a closed ideal. This algebra is called the semidirect product of B and I. Some topological aspects of the character space of a semidirect product are described. Furthermore, decompositions of commutative Banach algebras into the direct sum of a subalgebra and a principal ideal are investigated.

(2010-09-30)  -  Bertram Kostant: The principle of triality and a distinguished unitary representation of SO(4, 4).
Geometric methods in Theoretical Physics, K. Bleuler and M. Werner (eds), Kluwer Academic Publishers, 1988, 65-108  

(2010-09-30)  -  The Coxeter Element and the structure of the exceptional Lie groups. Colloquium Lectures of the AMS, note available from the AMS

(2010-09-30)  -  Alexandre Grothendieck: Résumé de la théorie métrique des produits tensoriels topologiques. Boletin de Sociedade de Matematica de Sao-Paulo, number 8, 1956, 1-19

Successful 2015-05-11  -   (2015-03-29)  -  Jin-su Ahn, Won-jee Chung, Chang-doo Jung: Realization of orientation interpolation of 6-axis articulated robot using quaternion.
in Journal of Central South University, December 2012, Volume 19, Issue 12, pp 3407-3414
Electronic subscription at Library TUDelft  

Abstract: In general, the orientation interpolation of industrial robots has been done based on Euler angle system which can result in singular point (so-called Gimbal Lock). However, quaternion interpolation has the advantage of natural (specifically smooth) orientation interpolation without Gimbal Lock.

This work presents the application of quaternion interpolation, specifically Spherical Linear IntERPolation (SLERP), to the orientation control of the 6-axis articulated robot (RS2) using LabVIEW and RecurDyn.

For the comparison of SLERP with linear Euler interpolation in the view of smooth movement (profile) of joint angles (torques), the two methods are dynamically simulated on RS2 by using both LabVIEW and RecurDyn.

Finally, our original work, specifically the implementation of SLERP and linear Euler interpolation on the actual robot, i.e. RS2, is done using LabVIEW motion control tool kit. The SLERP orientation control is shown to be effective in terms of smooth joint motion and torque when compared to a conventional (linear) Euler interpolation.

Successful 2015-02-12  -  (2015-01-17)  -  A. G. Kosovichev and V. V. Zharkova:  X-ray flare sparks quake inside Sun.  Nature (nr 393, 28 May 1998)  317-318 doi:10.1038/30629  

Successful 2015-02-12  -  (2014-07-31)  -   Ian Garrick-Bethell, Viranga Perera, Francis Nimmo and Maria T. Zuber: The tidal–rotational shape of the Moon and evidence for polar wander.
Nature (2014) doi:10.1038/nature13639 - Received 27 February 2014 - Accepted 01 July 2014 - Published online 30 July 2014  

Successful 2014-06-12  -  (2014-04-29) - J.C. Simo, K.K. Wong: Unconditionally stable algorithms for rigid body dynamics that exactly preserve energy and momentum.
International Journal for Numerical Methods in Engineering, 31:19–52, 1991 - 
ADDENDUM - Correction of this paper: International Journal for Numerical Methods in Engineering, 33, 1321-1323, 1992  -  ReadCube web page  

Successful 2014-06-12
 -   (2014-04-29) - P. Betsch, R. Siebert: Rigid body dynamics in terms of quaternions: Hamiltonian formulation and conserving numerical integration.
International Journal for Numerical Methods in Engineering
, 79:444–473, 2009 - 

Successful 2014-06-12  -   (2014-04-29) - J.C.Simo, N.Tarnow, K.K.Wong: Exact energy-momentum conserving algorithms and symplectic schemes for nonlinear dynamics.
Computer Methods in Applied Mechanics and Engineering
, Volume 100, Issue 1, October 1992, Pages 63–116  -  Web page  

Abstract: It is shown that widely used implicit schemes, in particular the classical Newmark family of algorithms and its variants, generally fail to conserve total angular momentum for nonlinear Hamiltonian systems including classical rigid body dynamics, nonlinear elastodynamics, nonlinear rods and nonlinear shells.
For linear Hamiltonian systems, it is well known that only the Crank-Nicholson scheme exactly preserves the total energy of the system.
This conservation property is typically lost in the nonlinear regime. A general class of implicit time-stepping algorithms is presented which preserves exactly the conservation laws present in a general Hamiltonian system with symmetry, in particular the total angular momentum and the total energy.
Remarkably, the actual implementation of this class of algorithms can be effectively accomplished by means of a simple two-step solution scheme which results in essentially no added computational cost relative to standard implicit methods.
A complete analysis of these algorithms and a related class of schemes referred to as symplectic integrators is given.
The good performance of the proposed methodology is demonstrated by means of three numerical examples which constitute representative model problems of nonlinear elastodynamics, nonlinear rods and nonlinear shells.

Successful 2014-06-12
 -  (2014-04-29) - John Argyris: An excursion into large rotations.
Computer Methods in Applied Mechanics and Engineering, Volume 32, Issues 1–3, September 1982, Pages 85–155  -  Web page  

Abstract: The present discourse develops an enlarged exploration of the matrix formulation of finite rotations in space initiated in [1]. It is shown how a consistent but subtle matrix calculus inevitably leads to a number of elegant expressions for the transformation or rotation matrix T appertaining to a rotation about an arbitrary axis. Also analysed is the case of multiple rotations about fixed or follower axes. Particular attention is paid to an explicit derivation of a single compound rotation vector equivalent to two consecutive arbitrary rotations. This theme is discussed in some detail for a number of cases. Semitangential rotations—for which commutativity holds—first proposed in [2, 3] are also considered. Furthermore, an elementary geometrical analysis of large rotations is also given. Finally, we deduce in an appendix, using a judicious reformulation of quarternions, the compound pseudovector representing the combined effect of n rotations. In the author's opinion the present approach appears preferable to a pure vectorial scheme—and even more so to an indicial formulation— and is computationally more convenient.

Dedicated to Professor Udo Wegner, D.Sc., D.Sc.h.c. on the occasion of his 80th anniversary

Successful 2014-06-12
 -  (2014-02-15) - Ron Goldman: Modeling perspective projections in 3-dimensions by rotations in 4-dimensions.
 [Journal for] Graphical Models, Volume 75 Issue 2, March, 2013, Pages 41-55, Academic Press Professional, Inc. San Diego, CA, USA  -

Abstract: We show how to represent perspective projections in 3-dimensions using rotations in 4-dimensions. This representation permits us to replace classical singular 4x4 matrices for perspective projection with nonsingular 4x4 orthogonal matrices. This approach also allows us to compute perspective projections by sandwiching vectors between two copies of a unit quaternion. In addition to deriving explicit formulas for these 4x4 rotation matrices for perspective projection, we also explain the geometric intuition underlying the observation that perspective projections in 3-dimensions can be represented by rotations in 4-dimensions. We show too that every rotation in 4-dimensions models either a rotation, a reflection, a perspective projection, or one of their composites in 3-dimensions.

Successful 2014-06-12
 -  (2012-07-17)  -  P. W. Anderson: Plasmons, Gauge Invariance, and Mass. Phys. Rev. 130, issue 1, 439–442 (1963),  doi: 10.1103/PhysRev.130.439,  ISSN 0031-899X  
Physical Review Online Archive:  
Entry in TUDElft Library Linking Services  -  Paper copy at Utrecht University Library  

Abstract: Schwinger has pointed out that the Yang-Mills vector boson implied by associating a generalized gauge transformation with a conservation law (of baryonic charge, for instance) does not necessarily have zero mass, if a certain criterion on the vacuum fluctuations of the generalized current is satisfied. We show that the theory of plasma oscillations is a simple nonrelativistic example exhibiting all of the features of Schwinger's idea. It is also shown that Schwinger's criterion that the vector field m≠0 implies that the matter spectrum before including the Yang-Mills interaction contains m=0, but that the example of superconductivity illustrates that the physical spectrum need not. Some comments on the relationship between these ideas and the zero-mass difficulty in theories with broken symmetries are given.

Successful 2014-06-02  -  (2014-06-02) -  W. Pfaff et al.: Unconditional quantum teleportation between distant solid-state quantum bits.
Science Express: May 29th 2014 -  

Successful 2012-08-17
 -  (2012-03-09)  -  Antoine Bérut et al.: Experimental verification of Landauer’s principle linking information and thermodynamics.
Nature 483, 8 March 2012, pp 87-89,  doi:10.1038/nature10872

Successful 2012-08-17
 -  (2012-01-30)  -  Adams C. and J. Shapiro: The Shape of the Universe: Ten Possibilities.
American Scientist 89 (Sep-Oct 2001): 443-453  -  ISSN 0003-0996
No subscriptions at TUDelft Library  -  Subscriptions at UUtrecht Library  

Successful 2012-01-30
 -  (2012-01-30)  -  Broucke R.A. and Cefola P.J.: On the Equinoctial Orbit Elements.  
Celestial Mechanics Vol 5, 1972  -  ISSN 0008-8714
Subscriptions at TUDelft Library: Celestial Mechanics  -  Celestial Mechanics and Dynamical Astronomy  -  Subscription at UUtrecht Library  

Successful 2012-01-30
 -  (2012-01-30)  -  Luminet J.-P. et al.: Dodecahedral Space topology as an Explanation for Weak Wide-Angle- (...).
Nature 425 (2003): 593-595

Successful 2012-01-30  -  (2012-01-24)  -  Herman Batelaan and Akira Tonomura: The Aharonov–Bohm effects: Variations on a subtle theme.
Physics Today, September 2009, page 38  -  Permalink  
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The notion, introduced 50 years ago, that electrons could be affected by electromagnetic potentials without coming in contact with actual force fields was received with a skepticism that has spawned a flourishing of experimental tests and expansions of the original idea.

Successful - 2012-01-24
 -  (2012-10-05)  -  Amir Haji-Akbari et al.: Disordered, quasicrystalline and crystalline phases of densely packed tetrahedra.
Nature 462, 773-777 (10 December 2009) | doi:10.1038/nature08641; Received 5 July 2009; Accepted 3 November 2009
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Successful - 2012-01-24
 -  (2012-01-04)  -  Herb Kunze et al.: Fractal-Based Methods in Analysis. book online at Springer through BibTUD  -  

Editorial Reviews
From the Back Cover

The idea of modeling the behavior of phenomena at multiple scales has become a useful tool in both pure and applied mathematics.
Fractal-based techniques lie at the heart of this area, as fractals are inherently multiscale objects; they very often describe nonlinear phenomena better than traditional mathematical models. In many cases they have been used for solving inverse problems arising in models described by systems of differential equations and dynamical systems.   
"Fractal-Based Methods in Analysis" draws together, for the first time in book form, methods and results from almost twenty years of research in this topic, including new viewpoints and results in many of the chapters.  
For each topic the theoretical framework is carefully explained using examples and applications.   
The second chapter on basic iterated function systems theory is designed to be used as the basis for a course and includes many exercises.  This chapter, along with the three background appendices on topological and metric spaces, measure theory, and basic results from set-valued analysis, make the book suitable for self-study or as a source book for a graduate course.
The other chapters illustrate many extensions and applications of fractal-based methods to different areas.
This book is intended for graduate students and researchers in applied mathematics, engineering and social sciences.   

Herb Kunze is a Professor in the Department of Mathematics and Statistics, University of Guelph.  
Davide La Torre is an Associate Professor in the Department of Economics, Business and Statistics, University of Milan.   
Franklin Mendivil is a Professor in the Department of Mathematics and Statistics, Acadia University.
Edward R. Vrscay is a Professor in the Department of Applied Mathematics, Faculty of Mathematics, University of Waterloo.  
A major focus of their research is fractals and their applications.

About the Authors
Franklin Mendivil is a Professor in the Department of Mathematics and Statistics at Acadia University;
Herb Kunze is a Professor in the Department of Mathematics and Statistics at Guelph University;
Davide La Torre is an Associate Professor in the Department of Economics, Business and Statistics at University of Milan;
Edward R. Vrscay is a Professor at the University of Waterloo.

Successful - 2012-01-24
 -  (2011-12-17)  -  Adrian Cho: First Solid Signs of the Higgs Boson Could Be Announced Next Week.
Science  9 December 2011  -  Vol. 334 no. 6061 p. 1334  -  doi: 10.1126/science.334.6061.1334
URL TUDelft Subscription to "Science"  -  URL UUtrecht subscription to "Science" 

Summary: Next week, physicists working with the world's biggest atom smasher—the Large Hadron Collider (LHC) at the European particle physics laboratory, CERN—will report the latest results of searches for the Higgs, the key to physicists' explanation of how all particles get their mass. Nobody expects a definitive claim of discovery, but given the amount of data the LHC has produced in 2 years of running, some physicists say that—if it's there—the Higgs should begin to emerge from "background" particle collisions like a sapling rising above the grass.

Related full article at 

Successful - 2011-12-14
 -  (2011-12-14)  -  F.. C. Frank: Orientation mapping. Metallurgical and Materials transactions A, Vol 19 Nr 3 March 1988 p 403-408  (URL) 

Successful - 2011-09-06
 -  (2011-09-05)  -  F. Buekenhout, M. Parker: The number of nets of the regular convex polytopes in dimension <= 4.
Discrete Mathematics, Volume 186, Issues 1-3, 15 May 1998, Pages 69-94  
Link into TUDelft library:  

Successful - 2011-08-05
 -  (2011-08-05)  -  Irene Polo Blanco: A classical approach to the study of Archimedean four-dimensional polytopes.  
Mathematische Semesterberichte (at Utrecht University Library), Volume 55, Number 2, 2008, 107-111  -  also at SpringerLink  
Related: Jon González Sánchez   

Successful - 2011-05-26
 -  (2011-05-03)  -  Hajja M. and Walker P.: Equifacial tetrahedra. International Journal of Mathematical Education in Science and Technology, Volume 32, Number 4, 1 July 2001, pp. 501-508(8)

Abstract: In this article, the authors have brought together a number of results on centres of tetrahedra, some ofwhich are new and others scattered through the literature, as explained in Section 6. In several cases, new and more accessible proofs have been given. In particular, a description given of how the various centres coincide for the class of equifacial tetrahedra (also commonly refered to as isosceles tetrahedra), and are distinct otherwise.

Available at BibTUD through THIS LINK  and also as a hardcopy

Available at BibUU through THIS LINK (obsolete; server not found)  -  No hardcopy at BibUU; electronic only

Successful - 2011-05-26
 -  (2011-04-20)  -  Ron Goldman: Understanding quaternions. Graphical Models Vol 73, Issue 2, March 2011  -  ISSN 524-0703

Abstract: Quaternion multiplication can be applied to rotate vectors in 3-dimensions. Therefore in Computer Graphics, quaternions are sometimes used in place of matrices to represent rotations in 3-dimensions. Yet while the formal algebra of quaternions is well-known in the Graphics community, the derivations of the formulas for this algebra and the geometric principles underlying this algebra are not well understood.
The goals of this paper are:

i.To provide a fresh geometric interpretation of quaternions, appropriate for contemporary Computer Graphics;

ii.To derive the formula for quaternion multiplication from first principles;

iii.To present better ways to visualize quaternions,and the effect of quaternion multiplication on points and vectors in 3-dimensions based on insights from the algebra and geometry of multiplication in the complex plane;

iv.To develop simple, intuitive proofs of the sandwiching formulas for rotation and reflection;

v.To show how to apply sandwiching to compute perspective projections.

In Part I of this paper, we investigate the algebra of quaternion multiplication and focus in particular on topics i and ii.
In Part IIwe apply our insights from Part I to analyze the geometry of quaternion multiplication with special emphasis on topics iii, iv and v.

Successful - 2011-05-26
 -  (2010-08-11)  -  Mehmet Koca et al: Group theoretical analysis of 600-cell and 120-cell 4D polytopes with quaternions.
J Phys. A: Math. Theor. (Journal of Physics A: Mathematical and Theoretical): 40 7633  -  -  

Abstract: 600-cell{3, 3, 5} and 120-cell {5, 3, 3} four-dimensional dual polytopesrelevant to quasicrystallography have been studied with thequaternionic representation of the Coxeter group W(H4). The maximal subgroups W(SU(5)):Z2and W(H3) × Z2of W(H4) play important roles in the analysis of cell structures of the dual polytopes. In particular, the Weyl–Coxeter group W(SU(4)) is used to determine the tetrahedral cells of the polytope {3, 3, 5}, and the Coxeter group W(H3)is used for the dodecahedral cells of {5, 3, 3}. Using the Liealgebraic techniques in terms of quaternions, we explicitly constructcell structures forming the vertices of the 4D polytopes.

Successful - 2011-01-24
 -  (2010-07-28) -   -  Lee A. Rubel: Some research problems about algebraic differential equations.
Transactions of the American Mathematical Society Vol 280 Nr 1, November1983, pp 43-52 

Abstract: Twenty-four new research problems are posed, and their background and partial solutions are sketched. Many of these problems are in the (somewhat unexpected) area of interaction between algebraic differential equations, topology, and mathematical logic.

Successful - 2010-11-01
 -  (2010-10-11)  -  James Clerk Maxwell: Matter and Motion.  
Aanvragen bij BibTUD via  en dezelfde dag ophalen
Online op 

Successful - 2010-07-28
 -  (2010-06-30)  -  Schur multipliers of some sporadic simple groups by Robert L. Griess, Jr.
University of Michigan, Ann Arbor, Michigan 48104, U.S.A.
Received 26 September 1972. 
Available online 2 September 2004.

Abstract: We determine the Schur multipliers of several of the sporadic simple groups, and in one case get an upper bound. The groups treated are those of Held, Suzuki, Fischer, and Conway.

At TUDelft Library:  (...)  &md5=b9f4113fb4a2a4941e409c38678722e7  

Refers to conjugacy classes of Co0.

Successful - 2010-06-29
 -  2010-06-13 -  -
An Algorithm to Decompose n-Dimensional Rotations into Planar Rotations
Book Series Lecture Notes in Computer Science 
Publisher Springer Berlin / Heidelberg
ISSN 0302-9743 (Print) 1611-3349 (Online)
Volume Volume 6026/2010
Book Computational Modeling of Objects Represented in Images 
DOI 10.1007/978-3-642-12712-0
Copyright 2010
ISBN 978-3-642-12711-3
DOI 10.1007/978-3-642-12712-0_6
Pages 60-71
Subject Collection Computer Science 
SpringerLink Date Wednesday, April 21, 2010

found in Google as
An Algorithm to Decompose n-Dimensional Rotations into Planar ... 

by A Richard - 2010
It is easy to show that this 4D-rotation can be decomposed into two planar rotations. .... guage for Mathematics and Physics. D.Reidel Pub. Co., Dordrecht (1984) ... 14. Mebius, J.: The Four-dimensional Rotation Group SO(4) (2008), ... 

In Library TUDelft through  (...)  &rft.object_id=954928560451  
Enter Year 2010, Volume 6026 to arrive at  >pages 60-71

Successful - 2010-06-17
 -  Nature (444, 2006, 587-591; 454, 2008, 614-617: about the Antikythera mechanism) - BibTUD - BibUU