Tectonic asymmetry of the earth and other planets

The structures of Earth, Mars, Venus, and the Moon are examined and compared. Global tectonic characteristics are presented for each. A comparison of the tectonics reveals the structural asymetry of these planets and the moon. Tectonic asymmetry information for the group is used to interpret certain aspects of the earth's geological past

Using Molecules to Measure Nuclear Spin-Dependent Parity Violation

Nuclear spin-dependent parity violation arises from weak interactions between electrons and nucleons, and from nuclear anapole moments. We outline a method to measure such effects, using a Stark-interference technique to determine the mixing between opposite-parity rotational/hyperfine levels of ground-state molecules. The technique is applicable to nuclei over a wide range of atomic number, in diatomic species that are theoretically tractable for interpretation. This should provide data on anapole moments of many nuclei, and on previously unmeasured neutral weak couplings

Enhanced sensitivity to time-variation of m_p/m_e in the inversion spectrum of ammonia

We calculate the sensitivity of the inversion spectrum of ammonia to possible time-variation of the ratio of the proton mass to the electron mass, mu=m_p/m_e. For the inversion transition (lambda= 1.25 cm^{-1}) the relative frequency shift is significantly enhanced: delta(omega)/omega=-4.46, delta(mu)/mu. This enhancement allows one to increase sensitivity to the time-variation of mu using NH_3 spectra for high redshift objects. We use published data on microwave spectra of the object B0218+357 to place the limit delta(mu)/mu =(0.6 +/- 1.9) 10^{-6} at redshift z=0.6847; this limit is several times better than the limits obtained by different methods and may be significantly improved. Assuming linear time dependence we obtain dot{mu}/mu=(-1 +/- 3) 10^{-16} yr^{-1}

Tectonics and volcanisms of Mars

Televised images of Mars transmitted from interplanetary stations are used to develop a theory of the structure and development of the planet. Crater chronology, the structure of planetary bodies in the Earth group, and a comparison of the Earth planetary bodies are among the factors included

A Necessary Condition for existence of Lie Symmetries in Quasihomogeneous Systems of Ordinary Differential Equations

Lie symmetries for ordinary differential equations are studied. In systems of ordinary differential equations, there do not always exist non-trivial Lie symmetries around equilibrium points. We present a necessary condition for existence of Lie symmetries analytic in the neighbourhood of an equilibrium point. In addition, this result can be applied to a necessary condition for existence of a Lie symmetry in quasihomogeneous systems of ordinary differential equations. With the help of our main theorem, it is proved that several systems do not possess any analytic Lie symmetries.Comment: 15 pages, no figures, AMSLaTe

Radar Range Deception with Time-Modulated Scatterers

Modern radar systems are designed to have high Doppler tolerance to detect fast-moving targets. This means range and Doppler estimations are inevitably coupled, opening pathways to concealing objects by imprinting artificial Doppler signatures on the reflected echoes. Proper temporal control of the backscattered phase can cause the investigating radar to estimate wrong range and velocity, thus cloaking the real position and trajectory of the scatterer. This deception method is exploited here theoretically for arbitrary Doppler tolerant waveforms and then tested experimentally on an example of the linear frequency modulated radar, which is the most common waveform of that class used in practice. The method allows retaining radio silence with a semi passive (battery assisted) approach that can work well with time-dependent metasurfaces. Furthermore, as an insight into new capabilities, we demonstrate that temporally concealed objects could even be made to appear closer than they truly are without violating the laws of relativity

The First Lyapunov Method for Strongly Non-linear Systems of Differential Equations

The article is aimed to give a brief review of works published by authors during at least last 10 years and devoted to the construction of solutions of systems of ordinary differential equations in a neighbourhood of a nonelementary criticai point

Complete integrability versus symmetry

The purpose of this article is to show that on an open and dense set, complete integrability implies the existence of symmetry