The present study reports low velocity impact tests on composite laminate plates reinforced either with Kevlar 29 or Dyneema. The tests are produced using a Rosand Precision Impact tester. The experimental results obtained for Kevlar 29 are simulated numerically. The deflection history and the peak of the impact force are compared with experimental data and used to calibrate the numerical model.

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The paper reports on numerical simulation of impact problems on fiber reinforced plastic composite laminated plates reinforced with Kevlar 29. The ballistic impact caused by STANAG-2920 projectile is analyzed to obtain an estimate for the V50 and the global damage. All estimate have been carried out using the finite difference numerical code AUTODYN-3D, are compared with the experimental data to illustrate the performance of the simulation. Good correlation between resulting simulations and experimental results is demonstrated both in terms of deformation and damage of the laminates and ballistic performance.

The paper is devoted to the compactness of the commutators \(aS_\Gamma - S_\Gamma aI\) and \(W_\alpha S_\Gamma - S_\Gamma W_\alpha\), where \(S_\Gamma\) is the Cauchy singular integral operator, \(a\) is a bounded measurable function, \(W_\alpha\) is the shift operator given by \(W_\alpha f = f\circ\alpha\), and \(\alpha\) is a bi-Lipschitz homeomorphism (shift). The cases of the unit circle and the unit interval are considered. We prove that these commutators are compact on rearrangement-invariant spaces with nontrivial Boyd indices if and only if the function a or, respectively, the derivative of the shift a has vanishing mean oscillation.

We prove criteria for the invertibility of the binomial functional operator
\[
A=aI-bW_\alpha
\]
in the Lebesgue spaces \(L^p(0,1)\), \( 1 < p < \infty\), where \(a\) and \(b\) are continuous functions on \((0,1)\), \(I\) is the identity operator, \(W_\alpha\) is the shift operator, \(W_\alpha f=f\circ\alpha\), generated by a non-Carleman shift \(\alpha:[0,1]\to[0,1]\) which has only two fixed points \(0\) and \(1\). We suppose that \(\log\alpha'\) is bounded and continuous on \((0,1)\) and that \(a,b,\alpha'\) slowly oscillate at \(0\) and \(1\). The main difficulty connected with slow oscillation is overcome by using the method of limit operators.

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The relativistic version of the binary-encounter Bethe (BEB) model is used to calculate cross sections for K-shell ionization of atoms by electron impact. The BEB model requires only two atomic constants, the binding energy and kinetic energy of the K electrons. These constants are listed for carbon to antimony. Comparisons with available experimental data on N, O, Na, Al, Cl, Ca, Cu, Se and Sb show good agreement. The K-shell ionization cross sections for C, Mg, P, S, Cr, As and Cd are tabulated.

Energies of the [( n ,l= n -1),1= n =20] and the [( n ,l= n -2),2= n =20] levels have been calculated for several hydrogenlike kaonic atoms throughout the periodic table, using the current world average kaon mass. Calculations were done in the framework of the Klein–Gordon equation, with finite nuclear size and all-order vacuum polarization corrections.