Aperiodic/periodic complementary sequence pairs over quaternions

<p style='text-indent:20px;'>Aperodic (or called Golay)/Periodic complementary pairs (GCPs/ PCPs) are pairs of sequences whose aperiodic/periodic autocorrelation sums are zero everywhere, except at the zero shift. In this paper, we introduce GCPs/PCPs over the quaternion group <inline-formula><tex-math id="M1">\begin{document}$ Q_8 $\end{document}</tex-math></inline-formula>, which is a generalization of quaternary GCPs/PCPs. Some basic properties of autocorrelations of <inline-formula><tex-math id="M2">\begin{document}$ Q_8 $\end{document}</tex-math></inline-formula>-sequences are also obtained. We present three types of constructions for GCPs and PCPs over <inline-formula><tex-math id="M3">\begin{document}$ Q_8 $\end{document}</tex-math></inline-formula>. The main ideas of these constructions are to consider pairs of a <inline-formula><tex-math id="M4">\begin{document}$ Q_8 $\end{document}</tex-math></inline-formula>-sequence and its reverse, pairs of interleaving of sequence, or pairs of Kronecker product of sequences. By choosing suitable sequences in these constructions, we obtain new parameters for GCPs and PCPs, which have not been reported before.</p>

Relativistic Fock Space Coupled Cluster Method for Many-Electron Systems: Non-Perturbative Account for Connected Triple Excitations

The Fock space relativistic coupled cluster method (FS-RCC) is one of the most promising tools of electronic structure modeling for atomic and molecular systems containing heavy nuclei. Until recently, capabilities of the FS-RCC method were severely restricted by the fact that only single and double excitations in the exponential parametrization of the wave operator were considered. We report the design and the first computer implementation of FS-RCC schemes with full and simplified non-perturbative account for triple excitations in the cluster operator. Numerical stability of the new computational scheme and thus its applicability to a wide variety of molecular electronic states is ensured using the dynamic shift technique combined with the extrapolation to zero-shift limit. Pilot applications to atomic (Tl, Pb) and molecular (TlH) systems reported in the paper indicate that the breakthrough in accuracy and predictive power of the electronic structure calculations for heavy-element compounds can be achieved. Moreover, the described approach can provide a firm basis for high-precision modeling of heavy molecular systems with several open shells, including actinide compounds.

New coordinates for a simpler canonical derivation of the Hawking effect

In order to achieve a Hamiltonian-based canonical derivation of the Hawking effect, one usually faces multiple hurdles. Firstly, the spacetime foliation using Schwarzschild time does not lead to hyper-surfaces which are always spacelike. Secondly, the null coordinates which are frequently used in covariant approach, do not lead to a true matter Hamiltonian. Recently, an exact canonical derivation was presented using the so-called near-null coordinates. However, there too one faces the difficulty of having to deal with non-vanishing matter diffeomorphism generator as the spatial decomposition involves a non-zero shift vector. Here we introduce a new set of coordinates which allows one to perform an exact canonical derivation of Hawking effect without having to deal with matter diffeomorphism generator.

EXPERIMENTAL IDENTIFICATION OF SENSITIVITY OF TILT SENSOR

Urgency of the research. Robots and vehicles which locomote on high slope ground has tendency to overturning and they lost stability during the locomotion. The problem also occurs in area of automotive industry. Target setting. All vehicles moving on the rough and inclined ground has a problem with stability. Emergency system for warning before dangerous tilt angle can be mounted inside the vehicles and robots as prevention of side overturning. Actual scientific researches and issues analysis. The problem is to find the reliable sensor for detection of dangerous tilt angle. Task is to identify the sensor properties as sensitivity, zero shift and also uncertainty of measurement. Before using it is necessary to identify sensor properties. Uninvestigated parts of general matters defining. The questions of the filtering of data acquisition by tilt angle sensor are uninvestigated, because the next research will be focused to this topic. The research objective. Sine bar is used for verification and testing of tilt sensor. Sine bar angle is adjusted using the parallel length gauge blocks. Sensor reacts to the changed tilt angle proportionally with pulse width on output pulse width signal. Indication of sensed data is made via using the microcontroller and LCD display. Also all calculations are executed inside the microcontroller. The statement of basic materials. The tilt sensor can be mounted inside the problematic vehicles to detect dangerous tilt angle and also automatic system for change the center of gravity position can be designed. The system will compensate the dangerous tilt angle. Conclusions. Evaluated uncertainties are related to overall sensing system and not only for sensor. Only sensor alone cannot be tested, because the sensor has no indication module. Expanded uncertainty of the system for measurement of tilt has been obtained and it is value should be taken into account before the sensor using.