Numerical model of ultrasonic multi-channel data transfer for servicing subsea production complex

Various researchers focused on different problems, and we can conclude that a single effective communication design with a specific algorithm that could be used in all types of underwater channels was not found. The design of the transmission is highly dependent on the conditions of the canal, as various schemes are used in shallow and deep water, and various algorithms in turbulent and calm waters. The type of channel alignment also depends on parameters such as channel estimation and coding. The ever-growing demand for bandwidth, efficiency, spatial diversity and the performance of underwater acoustic communications has opened the door to using Multiple Input Multiple Output (MIMO) technology. In this paper, we propose a method of ultrasonic data transmission under water based on the MIMO technology (Many emitters, many receivers, or MIMO - Multilpe Input - Multiple Output). This approach will allow for multi-channel data transmission in water and significantly increase the speed of information transfer

Yang-Mills action from minimally coupled bosons on R^4 and on the 4D Moyal plane

We consider bosons on Euclidean R^4 that are minimally coupled to an external Yang-Mills field. We compute the logarithmically divergent part of the cut-off regularized quantum effective action of this system. We confirm the known result that this term is proportional to the Yang-Mills action. We use pseudodifferential operator methods throughout to prepare the ground for a generalization of our calculation to the noncommutative four-dimensional Moyal plane (also known as noncommutative flat space). We also include a detailed comparison of our cut-off regularization to heat kernel techniques. In the case of the noncommutative space, we complement the usual technique of asymptotic expansion in the momentum variable with operator theoretic arguments in order to keep separated quantum from noncommutativity effects. We show that the result from the commutative space R^4 still holds if one replaces all pointwise products by the noncommutative Moyal product.Comment: 37 pages, v2 contains an improved treatment of the theta function in Appendix A.

The Gabor wave front set of compactly supported distributions

We show that the Gabor wave front set of a compactly supported distribution equals zero times the projection on the second variable of the classical wave front set

Detailed balance in Horava-Lifshitz gravity

We study Horava-Lifshitz gravity in the presence of a scalar field. When the detailed balance condition is implemented, a new term in the gravitational sector is added in order to maintain ultraviolet stability. The four-dimensional theory is of a scalar-tensor type with a positive cosmological constant and gravity is nonminimally coupled with the scalar and its gradient terms. The scalar field has a double-well potential and, if required to play the role of the inflation, can produce a scale-invariant spectrum. The total action is rather complicated and there is no analog of the Einstein frame where Lorentz invariance is recovered in the infrared. For these reasons it may be necessary to abandon detailed balance. We comment on open problems and future directions in anisotropic critical models of gravity.Comment: 10 pages. v2: discussion expanded and improved, section on generalizations added, typos corrected, references added, conclusions unchange

Wigner transform and pseudodifferential operators on symmetric spaces of non-compact type

We obtain a general expression for a Wigner transform (Wigner function) on symmetric spaces of non-compact type and study the Weyl calculus of pseudodifferential operators on them

On the first eigenvalue of the Dirichlet-to-Neumann operator on forms

We study a Dirichlet-to-Neumann eigenvalue problem for differential forms on a compact Riemannian manifold with smooth boundary. This problem is a natural generalization of the classical Steklov problem on functions. We derive a number of upper and lower bounds for the first eigenvalue in several contexts: many of these estimates will be sharp, and for some of them we characterize equality. We also relate these new eigenvalues with those of other operators, like the Hodge Laplacian or the biharmonic Steklov operator.Comment: 26 page