There are no magnetically charged particle-like solutions of the Einstein Yang-Mills equations for Abelian models

We prove that there are no magnetically charged particle-like solutions for Abelian models in Einstein Yang-Mills, but for non-Abelian models the possibility remains open. An analysis of the Lie algebraic structure of the Yang-Mills fields is essential to our results. In one key step of our analysis we use invariant polynomials to determine which orbits of the gauge group contain the possible asymptotic Yang-Mills field configurations. Together with a new horizontal/vertical space decomposition of the Yang-Mills fields this enables us to overcome some obstacles and complete a dynamical system existence theorem for asymptotic solutions with nonzero total magnetic charge. We then prove that these solutions cannot be extended globally for Abelian models and begin an investigation of the details for non-Abelian models.Comment: 48 pages, 1 figur

Infinitely iterated wreath products of metric spaces

The construction of the finitary wreath product of metric spaces and its completion, the infinitely iterated wreath product of metric spaces are introduced. They full isometry groups are described. Some properties and examples of these constructions are considered

The diagonal limits of Hamming spaces

We consider a continuum family of subspaces of the Besicovitch-Hamming space on some alphabet B, naturally parametrized by supernatural numbers. Every subspace is defined as a diagonal limit of finite Hamming spaces on the alphabet B. We present a convenient representation of these subspaces. Using this representation we show that the completion of each of these subspace coincides with the completion of the space of all periodic sequences on the alphabet B. Then we give answers on two questions formulated in [1]

Wreath product of metric spaces

This paper describes a new construction of wreath product of metric spaces. The group of isometries of the wreath product of metric spaces is calculated

A Metric for Gradient RG Flow of the Worldsheet Sigma Model Beyond First Order

Tseytlin has recently proposed that an action functional exists whose gradient generates to all orders in perturbation theory the Renormalization Group (RG) flow of the target space metric in the worldsheet sigma model. The gradient is defined with respect to a metric on the space of coupling constants which is explicitly known only to leading order in perturbation theory, but at that order is positive semi-definite, as follows from Perelman's work on the Ricci flow. This gives rise to a monotonicity formula for the flow which is expected to fail only if the beta function perturbation series fails to converge, which can happen if curvatures or their derivatives grow large. We test the validity of the monotonicity formula at next-to-leading order in perturbation theory by explicitly computing the second-order terms in the metric on the space of coupling constants. At this order, this metric is found not to be positive semi-definite. In situations where this might spoil monotonicity, derivatives of curvature become large enough for higher order perturbative corrections to be significant.Comment: 15 pages; Erroneous sentence in footnote 14 removed; this version therefore supersedes the published version (our thanks to Dezhong Chen for the correction

On all possible static spherically symmetric EYM solitons and black holes

We prove local existence and uniqueness of static spherically symmetric solutions of the Einstein-Yang-Mills equations for any action of the rotation group (or SU(2)) by automorphisms of a principal bundle over space-time whose structure group is a compact semisimple Lie group G. These actions are characterized by a vector in the Cartan subalgebra of g and are called regular if the vector lies in the interior of a Weyl chamber. In the irregular cases (the majority for larger gauge groups) the boundary value problem that results for possible asymptotically flat soliton or black hole solutions is more complicated than in the previously discussed regular cases. In particular, there is no longer a gauge choice possible in general so that the Yang-Mills potential can be given by just real-valued functions. We prove the local existence of regular solutions near the singularities of the system at the center, the black hole horizon, and at infinity, establish the parameters that characterize these local solutions, and discuss the set of possible actions and the numerical methods necessary to search for global solutions. That some special global solutions exist is easily derived from the fact that su(2) is a subalgebra of any compact semisimple Lie algebra. But the set of less trivial global solutions remains to be explored.Comment: 26 pages, 2 figures, LaTeX, misprints corrected, 1 reference adde

Методы фильтрации информации, полученной при гидрографической съемке

Проведено порівняння методів, що застосовуються для постобробки даних глибини, виміряних ехолотом. Визначено, що в порівнянні з вейвлет-фільтрацією, фільтр Калмана є дещо менш ефективним, але фільтрація глибини за допомогою фільтра Калмана дає змогу як очистити дані від шумів, так і відкинути аномальні дані. Предметом подальших досліджень може стати вдосконалення використаних та впровадження нових методів фільтрації та постобробки виміряних даних.Current trends in navigation are characterized by the further increase of demands on the precision of hydrographic information, especially of the nautical maps. Thus, precision of both spatial position and depth bathymetric data is important for ensuring safe navigation, and so problem of data filtering and elimination of outliers arises. In the present work, comparison of methods, used for postprocessing of depth data, measured by echosounder, is done. First of all, review of commonly used data filtering and outlier elimination methods is done, and their advantages and disadvantages are analyzed. As improved outlier elimination algorithm and median filtering has their flaws, Kalman filtering is considered as a measure of outlier elimination and real data estimation. It’s shown that Kalman filter can both effectively filter noise and eliminate outliers; however, quality of the filtered data strongly depends on measurement noise covariation and process noise covariation estimates, R and Q respectively. At that, the lower Q is, the better noise is filtered and the smoother depth profile is; the higher R is, the better outliers are eliminated. However, care must be taken, as depth profile is distorted at high R values, and noise is almost not filtered at low ones. It’s shown that noise covariation estimate has more influence on data filtering; therefore, one should pay attention to correct R estimation. For practical reasons, values of Q = 0,01; R =10 are recommended. In the recent works, wavelet filtering is considered as a promising method of data filtering in postprocessing. Therefore, as a next step, comparison of Kalman filtering and wavelet filtering is done using the real-world data. To that end, white noise is added to filtered and smoothed data, and then those data are filtered by methods, mentioned above. Corellation of source and denoised data is chosen as a criterion of filter effectiveness. It’s shown that Kalman filter is somewhat less effective in data postprocessing than wavelet filter. However, as Kalman filter allows one both to filter noises form the measured data and to eliminate outliers, and can be used for “on-the-fly” data filtering, it’s advisable to use Kalman filtering for real-time measurements during surveys, and wavelets for data postprocessing. Future studies may be devoted to improvement of existing and introduction of new data filtering and postrprocessing methods.Проведено сравнение методов, которые применяются для постобработки данных глубины, измеренных эхолотом. Определено, что в сравнении с вейвлет-фильтрацией, фильтр Калмана несколько менее эффективен, но фильтрация глубины с помощью фильтра Калмана дает возможность как очистить данные от шумов, так и исключить аномальные данные. Предметом последующих исследований может стать усовершенствование примененных и внедрение новых методов фильтрации и постобработки измеренных данных

The 2nd order renormalization group flow for non-linear sigma models in 2 dimensions

We show that for two dimensional manifolds M with negative Euler characteristic there exists subsets of the space of smooth Riemannian metrics which are invariant and either parabolic or backwards-parabolic for the 2nd order RG flow. We also show that solutions exists globally on these sets. Finally, we establish the existence of an eternal solution that has both a UV and IR limit, and passes through regions where the flow is parabolic and backwards-parabolic

On unicyclic graphs of metric dimension 2

A metric basis S of a graph G is the subset of vertices of minimum cardinality such that all other vertices are uniquely determined by their distances to the vertices in S. The metric dimension of a graph G is the cardinality of the subset S. A unicyclic graph is a graph containing exactly one cycle. The construction of a knitting unicyclic graph is introduced. Using this construction all unicyclic graphs with two main vertices and metric dimensions 2 are characterized

On unicyclic graphs of metric dimension 2 with vertices of degree 4

We show that if G is a unicyclic graph with metric dimension 2 and {a, b} is a metric basis of G then the degree of any vertex v of G is at most 4 and degrees of both a and b are at most 2. The constructions of unispider and semiunispider graphs and their knittings are introduced. Using these constructions all unicyclic graphs of metric dimension 2 with vertices of degree 4 are characterized