This paper presents a generalization for systems of partial differential equations of Gronwall's classical integral inequality for ordinary differential equations. The proof is by reducing the vector integral inequality to a vector partial differential inequality and then using a vector generalization of Riemann's method to obtain the final inequality. The final inequality involves a matrix fun...

Aims. A Gaussianity analysis using a goodness-of-fit test has been performed to study the measured Archeops Cosmic Microwave Background (CMB) temperature anisotropy data for a 143 GHz Archeops bolometer. We consider large angular scales, greater than 1.8 degrees, and a large fraction of the North Galactic hemisphere, around 16%, with a galactic latitude b > 15 degrees. Methods. The considered g...

The gyroscopic force acting on a ferromagnetic soliton reflects the tendency of spins to precess. Its components increase linearly with (generalized) velocities soliton. proportionality coefficients form tensor, generalization Thiele's gyrovector. Originally introduced as an auxiliary quantity, tensor turns out be mathematical object fundamental importance long history going back Lagrange. We r...

Magnetic Hopfions are localized magnetic solitons with a non-zero 3D topological charge (Hopf index). Here we present an analytical calculation of the Hopfion gyrovector and show that it does not vanish even in infinite sample. The method is based on concept emergent field. particular case simplest non-trivial toroidal Hopf index |QH|=1 cylindrical dot considered dependencies components sizes c...

A bi-Hamiltonian hierarchy of complex vector soliton equations is derived from geometric flows of non-stretching curves in the Lie groups G = SO(N + 1), SU(N) ⊂ U(N), generalizing previous work on integrable curve flows in Riemannian symmetric spaces G/SO(N). The derivation uses a parallel frame and connection along the curves, involving the Klein geometry of the group G. This is shown to yield...

The Dark Energy Survey (DES) collaboration will study cosmic acceleration with a 5000 deg griZY survey in the southern sky over 525 nights from 2011-2016. The DES data management (DESDM) system will be used to process and archive these data and the resulting science ready data products. The DESDM system consists of an integrated archive, a processing framework, an ensemble of astronomy codes an...

79 L~ST OF ILLUSTRATIONS 1. Elastic Hysteresis 2. Overdamped Vibration 3. Critically Damped Vibration 4. Underdamped Vibration 5. Optimum Damping Factor for Specified Error 6. Free Gyroscope 7. Inclined Plane 8. Sliding Shoe 9. Kingsbury Thrust :Bearing 10. Circular Pad Air :Bearing 11. Cylindrical Pad 12. Oil-Ring-Bearing 13. Lo\-T Friction Ball :Bearing 14. Low Friction Roller Bearing 15. Sec...

The bi-Hamiltonian structure of the two known vector generalizations of the mKdV hierarchy of soliton equations is derived in a geometrical fashion from flows of nonstretching curves in Riemannian symmetric spaces G/SO(N). These spaces are exhausted by the Lie groups G = SO(N + 1), SU(N). The derivation of the bi-Hamiltonian structure uses a parallel frame and connection along the curve, tied t...

A bi-Hamiltonian hierarchy of complex vector soliton equations is derived from geometric flows of non-stretching curves in the Lie groups G = SO(N + 1), SU(N) ⊂ U(N), generalizing previous work on integrable curve flows in Riemannian symmetric spaces G/SO(N). The derivation uses a parallel frame and connection along the curves, involving the Klein geometry of the group G. This is shown to yield...