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1

A Study of Early/Slow VLF Perturbations Observed at Agra, India

Pandey U., Singh A. K., Singh O. P., Singh B., Saraswat K.

Acta Geophysica

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2016

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Vol. 64, no. 3

755--771

EN

We present here the results of sub-ionospheric VLF perturbations observed on NWC (19.8 kHz) transmitter signal propagating in the Earth-ionosphere waveguide, monitored at our low latitude station Agra. During the period of observation (June-December 2011), we found 89 cases of VLF perturbation, while only 73 cases showing early character associated with strong lightning discharges. Out of 73 events, 64 (~84%) of the early VLF perturbations are found to be early/slow in nature; the remaining 9 events are early/fast. The onset duration of these early/slow VLF perturbations is up to ~ 5 s. A total of 54 observed early events show amplitude change lying between ± 3.0 dB, and phase change ± 12 degree, respectively, and found to occur mainly during nighttime. One of the interesting results we found is that the events with larger recovery time lie far away from the VLF propagation path, while events with smaller duration of recovery are within the ± 50-100 km of signal path. The World Wide Lightning Location Network (WWLLN) data is analysed to find the location of causative lightning and temporal variation. The lightning discharge and associated processes that lead to early VLF events are discussed.

2

An estimate for the resolvent of a non-selfadjoint differential operator on an unbounded domain

Gil` M. I.

Journal of Applied Analysis

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2013

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Vol. 19, nr 2

231--246

EN

We consider the operator T defined by (T f)(x)=(Sf)(x)+q(x)f(x), x ∈ Ω, where Ω ⊂ Rn is an unbounded domain, S is a positive definite selfadjoint operator defined on a domain Dom (S) ⊂ L2(Ω) and q(x) is a bounded complex measurable function with the property Im q(x) ∈ Lν(Ω) for a ν ∈ (1, ∞). We derive an estimate for the norm of the resolvent of T. In addition, we prove that T is invertible, and the inverse operator T-1 is a sum of a normal operator and a quasinilpotent one, having the same invariant subspaces. By the derived estimate, spectrum perturbations are investigated. Moreover, a representation for the resolvent of T by the multiplicative integral is established. As examples, we consider the Schrödinger operators on the positive half-line and orthant.

3

Perturbations of the matrix logarithm

Gil' M.

Journal of Applied Analysis

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2012

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Vol. 18, nr 1

47-68

EN

The paper suggests sharp norm estimates for the matrix logarithm and for the difference of the logarithms of two matrices.

4

Perturbation method in the analysis of manipulator inertial vibrations

Szumiński P.

Mechanics and Mechanical Engineering

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2011

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Vol. 15, nr 2

149-160

EN

An analysis of inertial component of mechanical vibrations induced during a motion of the MAR industrial manipulator is presented. The mathematical analysis of vibrations is based on the perturbation method. The presented considerations include an analytical description of inertial vibrations as well as results of the numerical analysis for the RPP-type manipulator.