the graph of the generating d tuples of a finite soluble group and the swap conjecture abstract for a d generated group g we consider the graph d g in which the vertices are the ordered generating d tuples and in which two vertices x 1 x d and y 1 y d are adjacent if and only if there exists i 1 d such that i d 2 and x i y i for each i i we prove that if g is a finite soluble then d g is connected we consider also the swap graph d g in which two generating d tuples are adjacent if they differ only by one entry proving the following if g is an arbitrary finite group and d d g 1 then d g is connected

parameter free radial distortion correction with center of distortion estimation we propose a method of simultaneously calibrating the radial distortion function of a camera and the other internal calibration parameters the method relies on the use of a planar or alternatively nonplanar calibration grid which is captured in several images in this way the determination of the radial distortion is an easy add on to the popular calibration method proposed the method is entirely noniterative and hence is extremely rapid and immune to the problem of local minima our method determines the radial distortion in a parameter free way not relying on any particular radial distortion model this makes it applicable to a large range of cameras from narrow angle to fish eye lenses the method also computes the center of radial distortion which we argue is important in obtaining optimal results experiments show that this point may be significantly displaced from the center of the image or the principal point of the camera

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

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

radial multi focal tensors the 1d radial camera maps all points on a plane containing the principal axis onto the radial line which is the intersection of that plane and the image plane it is a sufficiently general model to express both central and non central cameras since the only assumption it makes is of known center of distortion in this paper we study the multi focal tensors arising out of 1d radial cameras there exist no two view constraints like the fundamental matrix for 1d radial cameras however the 3 view and 4 view cases are interesting for the 4 view case we have the radial quadrifocal tensor which has 15 d o f and 2 internal constraints for the 3 view case we have the radial trifocal tensor which has 7 d o f and no internal constraints under the assumption of a purely rotating central camera this can be used to do a non parametric estimation of the radial distortion of a 1d camera even in the case of a non rotating camera it can be used to do parametric estimation assuming a planar scene finally we examine the mixed trifocal tensor which models the case of two 1d radial cameras and one standard pin hole camera of the above radial multifocal tensors only the radial trifocal tensor is useful practically since it doesn t require any knowledge of the scene and is extremely robust we demonstrate results based on real images for this for the quadrifocal tensor too we present a way to do a metric reconstruction of the scene and to undistort the image given a sufficiently dense set of point correspondences we also show results on synthetic images however it must be noted that currently the quadrifocal and mixed trifocal tensors are useful only from a theoretical stand point

finite subgroups of algebraic groups generalizing a classical theorem of jordan to arbitrary characteristic we prove that every finite subgroup of gln over a field of any characteristic p possesses a subgroup of bounded index which is composed of finite simple groups of lie type in characteristic p a commutative group of order prime to p and a p group while this statement can be deduced from the classification of finite simple groups our proof is self contained and uses methods only from algebraic geometry and the theory of linear algebraic groups we believe that our results can serve as a viable substitute for classification in a range of applications in various areas of mathematics

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

generic self calibration of central cameras from two rotational flows we address the self calibration of a smooth generic central camera from only two dense rotational flows produced by rotations of the camera about two unknown linearly independent axes passing through the camera centre we give a closed form theoretical solution to this problem and we prove that it can be solved exactly up to a linear orthogonal transformation ambiguity using the theoretical results we propose an algorithm for the self calibration of a generic central camera from two rotational flows in order to solve the self calibration problem using real images we also study the computation of dense optical flows from image sequences acquired by the rotation of a smooth generic central camera we propose a method for the computation of dense smooth generic flows from rotational camera motions using splines the proposed methods are validated using both simulated and real image sequences

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

the product replacement algorithm and kazhdan s property t a problem of great importance in computational group theory is to generate nearly uniformly distributed random elements in a finite groupg a good example of such an algorithm should start at any given set of generators use no prior knowledge of the structure of g and in a polynomial number of group operations return the desired random group elements see bb2 then these random elements can be used further to determine the structure of g in a pioneer paper bb1 babai found such an algorithm which provably generates nearly uniformly distributed random elements in o log g group multiplications too many for practical applications a different heuristic the product replacement algorithm was designed by leedham green and soicher lg and studied by celler et al in clmno in spite of the fact that very little theoretical justification was known practical experiments showed excellent performance so it quickly became the most popular practical algorithm to generate random group elements and was included in the two most frequently used group algebra packages gap sc and magma bcp a systematic and quantitative approach was carried out by diaconis and saloffcoste ds1 ds2 see also bb2 cg but their results did not reveal the mystery of the truly outstanding performance of the algorithm the aim of this paper is to propose a conceptual explanation based on kazhdan s property t from representation theory of lie groups and to improve some of the previous estimates on the running time the product replacement algorithm works as follows clmno given a finite group g let k g be the set of k tuples g g1 gk of elements of g such that g1 gk g we call elements of k g the generating k tuples given a generating k tuple g1 gk define a move on it in the following way choose uniformly a pair i j such that 1 i 6 j k then apply one of the following four operations with equal probability

connectivity of the product replacement graph of simple groups of bounded lie rank abstract the product replacement algorithm is a practical algorithm for generating random elements of a finite group the algorithm can be described as a random walk on a graph whose vertices are the generating k tuples of the group for a fixed k we show that there is a function c r such that for any finite simple group of lie type with lie rank r the product replacement graph of the generating k tuples is connected for any k c r the proof uses results of larsen and pink m j larsen r pink finite subgroups of algebraic groups preprint 1998 and does not rely on the classification of finite simple groups

self calibration and metric reconstruction inspite of varying and unknown intrinsic camera parameters in this paper the theoretical and practical feasibility of self calibration in the presence of varying intrinsic camera parameters is under investigation the paper s main contribution is to propose a self calibration method which efficiently deals with all kinds of constraints on the intrinsic camera parameters within this framework a practical method is proposed which can retrieve metric reconstruction from image sequences obtained with uncalibrated zooming focusing cameras the feasibility of the approach is illustrated on real and synthetic examples besides this a theoretical proof is given which shows that the absence of skew in the image plane is sufficient to allow for self calibration a counting argument is developed which depending on the set of constraints gives the minimum sequence length for self calibration and a method to detect critical motion sequences is proposed

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

commutator maps measure preservation and t systems let g be a finite simple group we show that the commutator map g g g is almost equidistributed as g 1 this somewhat surprising result has many applications it shows that a for a subset x g we have 1 x g 2 x g o 1 namely is almost measure preserving from this we deduce that almost all elements g 2 g can be expressed as commutators g x y where x y generate g this enables us to solve some open problems regarding t systems and the product replacement algorithm pra graph we show that the number of t systems in g with two generators tends to infinity as g 1 this settles a conjecture of guralnick and pak a similar result follows for the number of connected components of the pra graph of g with two generators some of our results apply for more general finite groups and more general word maps our methods are based on representation theory combining classical character theory with recent results on character degrees and values in finite simple groups in particular the so called witten zeta function g s p 2irr g 1 s plays a key role in the proofs

camera calibration with distortion models and accuracy evaluation a camera model that accounts for major sources of camera distortion namely radial decentering and thin prism distortions is presented the proposed calibration procedure consists of two steps 1 the calibration parameters are estimated using a closed form solution based on a distribution free camera model and 2 the parameters estimated in the first step are improved iteratively through a nonlinear optimization taking into account camera distortions according to minimum variance estimation the objective function to be minimized is the mean square discrepancy between the observed image points and their inferred image projections computed with the estimated calibration parameters the authors introduce a type of measure that can be used to directly evaluate the performance of calibration and compare calibrations among different systems the validity and performance of the calibration procedure are tested with both synthetic data and real images taken by tele and wide angle lenses

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

nonmetric calibration of wide angle lenses and polycameras images taken with wide angle cameras tend to have severe distortions which pull points towards the optical center this paper proposes a simple method for recovering the distortion parameters without the use of any calibration objects since distortions cause straight lines in the scene to appear as curves in the image our algorithm seeks to find the distortion parameters that map the image curves to straight lines the user selects a small set of points along the image curves recovery of the distortion parameters is formulated as the minimization of an objective function which is designed to explicitly account for noise in the selected image points experimental results are presented for synthetic data as well as real images we also present the idea of a polycamera which is defined as a tightly packed camera cluster possible configurations are proposed to capture very large fields of view such camera clusters tend to have a nonsingle viewpoint we therefore provide analysis of what we call the minimum working distance for such clusters finally we present results for a polycamera consisting of four wide angle sensors having a minimum working distance of about 4 m on undistorting the acquired images using our proposed technique we create real time high resolution panoramas