We calculate the coherent radiation in an undulator/wiggler with a vacuum chamber of arbitrary cross section. The backward radiation is a coherent and it has wavelengths about twice the period of the undulator/wiggler. Mostly of coherent radiation is going with the wavelengths approximately the bunch length at small angles however. Classification 3: Linear Colliders, Lepton Accelerators and New...

In this paper, we consider a special kind of overconstrained 6R closed linkages which we call angle-symmetric 6R linkages. These are linkages with the property that the rotation angles are equal for each of the three pairs of opposite joints. We give a classification of these linkages. It turns that there are three types. First, we have the linkages with line symmetry. The second type is new. T...

Almost everyone knows that the inner angles of a triangle sum to 180o. But if you ask the typical mathematician how to sum the solid inner angles over the vertices of a tetrahedron, you are likely to receive a blank stare or a mystified shrug. In some cases you may be directed to the Gram-Euler relations for higher dimensional polytopes [3, 4, 6, 7], a 19th century result unjustly consigned to ...

In contrast to the current rapid evolution in our understanding of the microscopic degrees of freedom of M-theory, the macroscopic picture has changed very little over the past year. The ‘basic’ ingredients remain D=11 supergravity and its 1/2-supersymmetic solutions: the M-wave, the M-2-brane, the M-5-brane and, in the S KaluzaKlein vacuum, the M-monopole (i.e. EuclideanTaub-Nut times 7-dimens...

We interpret a class of 4k-dimensional instanton solutions found by Ward, Corrigan, Goddard and Kent as four-dimensional instantons at angles. The super-position of each pair of four-dimensional instantons is associated with four angles which depend on some of the ADHM parameters. All these solutions are associated with the group Sp(k) and are examples of Hermitian-Einstein connections on E 4k....

We show that configurations of multiple D-branes related by SU(N) rotations will preserve unbroken supersymmetry. This includes cases in which two D-branes are related by a rotation of arbitrarily small angle, and we discuss some of the physics of this. In particular, we discuss a way of obtaining 4D chiral fermions on the intersection of Dbranes. We also rephrase the condition for unbroken sup...

In multi-class support vector machine (MSVM) for classification, one core issue is to regularize the coefficient vectors to reduce overfitting. Various regularizers have been proposed such as `2, `1, and trace norm. In this paper, we introduce a new type of regularization approach – angular regularization, that encourages the coefficient vectors to have larger angles such that class regions can...

A spherical quadrilateral is a bordered surface homeomorphic to a closed disk, with four distinguished boundary points called corners, equipped with a Riemannian metric of constant curvature 1, except at the corners, and such that the boundary arcs between the corners are geodesic. We discuss the problem of classification of these quadrilaterals and perform the classification up to isometry in ...

We introduce the notion of analytically and subanalytically tame measures. These are measures which behave well in the globally subanalytic context; they preserve tameness: integrals of globally subanalytic functions with parameters resp. analytic functions with parameters restricted to globally subanalytic compact sets are definable in an o-minimal structure. We consider the harmonic measure f...