an application of the kiefer wolfowitz equivalence theorem to a problem in hadamard transform optics on utilise le theoreme d equivalence de la theorie approchee des plans optimaux pour resoudre des problemes lies a l optique de la transformee de hadamard et les plans de ponderation

complete class results for the moment matrices of designs over permutation invariant sets in 1987 cheng determined p optimal designs for linear regression without intercept over the n dimensional unit cube 0 1 n for p 1 these are uniform distributions on the vertices with a fixed number of entries equal to unity and mixtures of neighboring such designs in 1989 pukelsheim showed that this class of designs is essentially complete and that the corresponding class of moment matrices is minimally complete with respect to what he called kiefer ordering in this paper these results are extended to general permutation invariant design regions

construction of ϕp optimal exact designs with minimum experimental run size for a linear log contrast model in mixture experiments we propose a new method with minimum experimental run size using the properties of hadamard matrices through which some p optimal exact designs including a d and e optimal designs are constructed for a linear log contrast model in mixture experiments copyright 2011 oxford university press

a hierarchy of rational timoshenko dispersion relations abstract this paper shows that the conventional timoshenko dispersion relation for bending waves is the 0 1 member of a two parameter family m n of approximations to the exact dispersion relation obtained from linear elasticity higher members of the family are shown to converge rapidly to the exact dispersion relation in particular any number of branches can be captured accurately over their entire length i e up to arbitrarily high frequencies and wavenumbers the theory admits a rigorous accuracy analysis and demonstrates that the conventional timoshenko dispersion relation is a completely rational approximation thus answering some previous doubts about this matter lower members of the two parameter family include the euler bernoulli dispersion relation and a rayleigh type inertia correction especially useful is the timoshenko 1 2 dispersion relation which extends the conventional timoshenko 0 1 dispersion relation by capturing the first four branches of the exact dispersion relation rather than merely the first two and is accurate over a wide range an inertia corrected timoshenko dispersion relation is also derived and is shown to include many previous approximations as special cases

experimental study of the timoshenko beam theory predictions abstract the theory of flexural vibrations proposed by timoshenko almost 90 years ago has been the subject of several recent papers in the timoshenko beam theory a critical frequency f c is expected and for frequencies f larger than f c some authors argue that a second spectrum exists this is still the matter of much debate in order to settle this question we have performed experimental measurements of flexural normal mode frequencies and amplitudes which are much more precise than what has been obtained up to now for some purposes cylindrical rods are more convenient whereas in other cases rectangular beams are easier to deal with so we analyze rods and beams of different shapes and sizes we show that below f c all observed resonant peaks can be associated with one of the compressional torsional or timoshenko resonances and that no resonant peaks are left undetected the validity of timoshenko beam theory below f c and that only one spectrum appears in this regime is therefore proved the comparison between theory and experiment for rectangular beams also shows that our experimental setup is appropriate so we can use it confidently for f f c the measurements we report here in this regime show the existence of a second spectrum at least for free free boundary conditions

the symmetries of the dirac pauli equation in two and three dimensions we calculate all symmetries of the dirac pauli equation in two dimensional and three dimensional euclidean space further we use our results for an investigation of the issue of zero mode degeneracy we construct explicitly a class of multiple zero modes with their gauge potentials

hopf maps as static solutions of the complex eikonal equation we demonstrate that a class of torus shaped hopf maps with arbitrary linking number obeys the static complex eikonal equation further we explore the geometric structure behind these solutions explaining thereby the reason for their existence as this equation shows up as an integrability condition in certain nonlinear field theories the existence of such solutions is of some interest

variational derivation of governing differential equations for truncated version of bresse timoshenko beams abstract in this paper we provide a variational derivation of modified bresse timoshenko equations this process leads to the additional term to so called truncated set of bresse timoshenko equations this new term is associated with the modified slope inertia the two sets of truncated versions of the bresse timoshenko equations are contrasted with each other as well as with the original bresse timoshenko equations on the example of the a beam that is simply supported at its both ends and b the cantilever beam with end mass it is concluded that application of either truncated sets of equations is advantageous over the original bresse timoshenko equations as far as two truncated sets of equations are concerned the variationally derived set appears to be preferable

locally periodic timoshenko rod experiment and theory the flexural vibrations of a locally periodic rod which consists of n unit cells are discussed both from the experimental and theoretical points of view timoshenko s beam theory and the transfer matrix method are used to calculate the normal mode frequencies and amplitudes the theoretical values are then compared with the experimental ones which are obtained using an electromagnetic acoustic transducer emat good agreement between the numerical results and the experimental measurements is obtained it is shown that as n grows a band spectrum emerges

on the valid frequency range of timoshenko beam theory abstract the frequency equation of timoshenko beam theory factorises for hinged hinged end conditions leading to a first and second spectrum of natural frequencies the latter is largely inaccurate and can be isolated and disregarded for the majority of other end conditions when the frequency equation does not factorise one may think in terms of pseudo second spectrum contributions arising when evanescent waves become propagating above the cut off frequency co ag i and it is conjectured that these may have a corrupting effect on the frequency predictions comparisons with measured and simulated frequencies lead to the conclusion that timoshenko predictions above the cut off frequency should be disregarded for those end conditions for which the frequency equation does not factorise

the second spectrum of timoshenko beam theory further assessment a review of contributions and views on the second spectrum of timoshenko beam theory tbt over the past two decades together with some new results are presented it is shown that the timoshenko frequency equation factorises not solely for hinged hinged end conditions as is often claimed but also for guided guided and guided hinged these new cases may be regarded as portions of a multi span hinged hinged beam a higher derivative lagrangian that leads directly to the well known fourth order timoshenko beam equation is reviewed a simple relationship between the so called ostrogradski energy and the mechanical energy is derived for hinged hinged end conditions it is shown that the ostrogradski energy is positive for the first spectrum but negative for the second within some branches of physics this would be sufficient to conclude that the second spectrum is unphysical a numerical example presented by levinson and cooke is re examined using both tbt and exact plane stress elastodynamic theory agreement is excellent for the first spectrum however the second spectrum predictions are not in consistent agreement with any single mode of vibration for long wavelength it is very close to the second asymmetric mode but as wavelength shortens it becomes closer to the second symmetric then the third asymmetric modes the conclusion remains unchanged the second spectrum predictions of tbt should be disregarded

the local structure of zero mode producing magnetic potentials we consider the class of continuous magnetic potentials on 3 which decay as o x 1 within this class it is shown that the set of potentials whose associated weyl dirac operator produces zero modes with multiplicity m forms a smooth submanifold of co dimension m2 when m 0 1 2 and is contained in a smooth submanifold of co dimension 2m 1 when m 3

log contrast models for experiments with mixtures summary a new form of expected response function involving log contrasts of the proportions is introduced for experiments with mixtures the advantages and disadvantages of log contrast models are discussed and illustrated in applications in particular the parameters of the model are related to certain useful hypotheses about mixtures and some relevant contrasts are identified

the second frequency spectrum of timoshenko beams abstract a second spectrum of frequencies was reported in early analytical work on the vibrations of timoshenko beams however in subsequent finite element modelling this phenomenon was either ignored or not definitively classified and recorded in fact from a recent finite element analysis with a high precision element it was even concluded that there is no separate second spectrum of frequencies except for the special case of hinged hinged beams and it was asserted that previous investigators had misinterpreted some frequencies thus introducing the notion of second frequencies in this paper a simple linear beam element with independent displacement fields and reduced integration to eliminate shear locking is used and enables one to detect the second spectrum accurately guidelines are provided which help to identify and classify the frequencies into two separate spectra

critical contrasting of three versions of vibrating bresse timoshenko beam with a crack abstract this paper deals with natural frequencies of short or thick beams taking into account effects of rotary inetria and shear deformation three versions of the bresse timoshenko beam theory are considered and contrasted in the context of the problem of beam vibration in presence of the single crack namely the a original bresse timoshenko theory b elishakoff s truncated version and c the proposed slope inertia based version the original bresse timoshenko equations contain fourth order derivative with respect to time that is not present in the classical bernoulli euler theory whose correction was the declared goal of s p timoshenko who himself did not overestimate the importance of this term the truncated version of the bresse timoshenko was suggested by elishakoff with no fourth order time derivative incorporated in the theory in this paper variational derivation of the truncated version of the bresse timoshenko beam theory is conducted with attendant additional term containing the fourth derivative with respect to axial coordinate and second derivative with respect to time it appears imperative to conduct thorough comparison of the above three theories in the context of beams containing a crack which is often present in engineering structures the applicability of these three versions with attendant extensive numerical calculations is specifically studied for the titled problem it is demonstrated that the original bresse timoshenko beam theory as an overcomplicated theory is not needed for crack analysis simpler theories namely the truncated version of this theory or the one based on slope inertia are sufficient for crack analysis in all treated cases

largest j simplices in d cubes some relatives of the hadamard maximum determinant problem abstract this paper studies the computationally difficult problem of finding a largest j dimensional simplex in a given d dimensional cube the case in which j d is of special interest for it is equivalent to the hadamard maximum determinant problem it has been solved for infinitely many values of d but not for d 14 the subcase in which j d 3 mod 4 subsumes the famous problem on the existence of hadamard matrices the known results for the case j d are here summarized and used but the main focus is on fixed small values of j when j 1 the problem is trivial and when j 2 or j 3 it is here solved completely i e for all d beyond that the results are fragmentary but numerous and they lead to several attractive conjectures some other problems involving simplices in cubes are mentioned and the relationship of largest simplices to d optimal weighing designs is discussed

elastic waves in timoshenko beams the lost and found of an eigenmode this paper considers propagating waves in elastic bars in the spirit of asymptotic analysis and shows that the inclusion of shear deformation amounts to singular perturbation in the eulerbernoulli

analysis of zero modes for dirac operators with magnetic links abstract in this paper we provide a means to approximate dirac operators with magnetic fields supported on links in s 3 and r 3 by dirac operators with smooth magnetic fields then we proceed to prove that under certain assumptions the spectral flow of paths along these operators is the same in both the smooth and the singular case we recently characterized the spectral flow of such paths in the singular case this allows us to show the existence of new smooth compactly supported magnetic fields in r 3 for which the associated dirac operator has a non trivial kernel using clifford analysis we also obtain criteria on the magnetic link for the non existence of zero modes

new examples of zero modes we construct smooth vector potentials a 1 and a 2 on bbb r3 such that the associated pauli operators scenterdot d a i i 1 2 have zero energy eigenfunctions or zero modes the first example a 1 has compact support and the associated zero mode is contained in l2 the second example can be written in the form a 2 x2 x1 0 t tilde a 2 where tilde a 2 is bounded and supported on x3 1 furthermore the associated zero mode is schwartz class

on the zero modes of pauli operators two results are proved for nul pa the dimension of the kernel of the pauli operator formula in l2 r3 2 i for formula where formula is the magnetic field nul pta 0 except for a finite number of values of t in any compact subset of 0 ii formula contains an open dense subset of l3 2 r3 3

in plane vibrations of a rectangular plate plane wave expansion modelling and experiment abstract theoretical and experimental results for in plane vibrations of a uniform rectangular plate with free boundary conditions are obtained the experimental setup uses electromagnetic acoustic transducers and a vector network analyzer the theoretical calculations were obtained using the plane wave expansion method applied to the in plane thin plate vibration theory the agreement between theory and experiment is excellent for the lower 95 modes covering a very wide frequency range from dc to 20 khz some measured normal mode wave amplitudes were compared with the theoretical predictions very good agreement was observed the excellent agreement of the classical theory of in plane vibrations confirms its reliability up to very high frequencies

on the two frequency spectra of timoshenko beams abstract this paper is concerned with the question of whether there are indeed two distinct spectra of frequencies for the transverse vibrations of timoshenko beams as has been claimed by a number of prior authors for the case of the simply supported beam and more recently for beams supported in an arbitrary manner elementary analysis leads to the conclusion that there is only a single frequency spectrum in the particular case of the simply supported beam the two frequency spectra viewpoint may be expedient as a device to compute frequencies but does not serve otherwise to explain the complex dynamical behavior of timoshenko beams

experimental study of the timoshenko beam theory predictions further results abstract in a previous paper 2012 we presented experimental results proving that the critical frequency f c predicted by timoshenko beam theory indeed exists we also showed that for frequencies f smaller than f c the spectrum is formed by almost equally spaced levels whereas for f f c the spectrum consists of pairs of eigenvalues very close to each other as predicted by numerical solutions of timoshenko s equation we shall refer to them as timoshenko doublets in this work we measure for the first time experimental dispersion relations for this purpose it was necessary to obtain normal mode amplitudes with a high precision which was done with a new experimental setup developed by us we found that experimental dispersion relations coincide very well with theoretical predictions furthermore we provide an explanation of timoshenko doublets