Walsh Spectrum Properties of Rotation Symmetric Boolean Function

Rotation symmetric function was presented by Pieprzyk. The algebraic configuration of rotation symmetric（RotS） function is special. For a Rots n variables function f（x1, x2, …, xn） we have f（ρn^k （x1, x2, …xn））=f（x1, x2, …, xn） for k=0, 1, …, n-1. In this paper, useing probability method we find that when the parameters of RotS function is under circular translation of indices, its walsh spectrum is invariant. And we prove the result is both sufficient and necessary.

Tracking molecular structure deformation of nitrobenzene and its torsion-vibration coupling by intense pumping CARS

The structural deformation induced by intense laser field of liquid nitrobenzene（NB） molecule,a typical molecule with restricting internal rotation,is tracked by time- and frequency-resolved coherent anti-Stokes.Raman spectroscopy（CARS） technique with an intense pump laser.The CARS spectra of liquid NB show that the NO2 torsional mode couples with the NO2 symmetric stretching mode,and the NB molecule undergoes ultrafast structural deformation with a relaxation time of 265 fs.The frequency of NO2 torsional mode in liquid NB（42 cm-1） at room temperature is found from the sum and difference combination bands involving the NO2 symmetric stretching mode and torsional mode in time- and frequency-resolved CARS spectra.

A Class of Rotation Symmetric Boolean Functions with Optimum Algebraic Immunity

For an odd integer n ≥ 7, this paper presented a class of n-variable rotation symmetric Boolean functions （RSBFs） with optimum algebraic immunity. The nonlinearity of the constructed functions is determined.

RESULTS ON PERMUTATION SYMMETRIC BOOLEAN FUNCTIONS

This paper provides a systematic method on the enumeration of various permutation symmetric Boolean functions. The results play a crucial role on the search of permutation symmetric Boolean functions with good cryptographic properties. The proposed method is algebraic in nature. As a by-product, the authors correct and generalize the corresponding results of St^nic~ and Maitra （2008）. Further, the authors give a complete classification of block-symmetric bent functions based on the results of Zhao and Li （2006）, and the result is the only one classification of a certain class of permutation symmetric bent functions after the classification of symmetric bent functions proposed by Savicky （1994）.

Physical processes associated with movement of maximum wind of Typhoon Rammasun(2014)

In this study,the movement of the maximum wind of Typhoon Rammasun(2014)was measured by the radial movement of the maximum symmetric rotational kinetic energy.The weather research and forecasting(WRF)model was used to simulate Typhoon Rammasun,and validated simulation data for the lower troposphere were analyzed to examine the physical processes responsible for the radial movement of the maximum wind.The radii,where maximum symmetric rotational kinetic energy and its maximum tendency were located,were compared to explain radial movement.The tendency in the lower troposphere is controlled by the flux convergence of symmetric rotational kinetic energy and the conversion from symmetric divergent kinetic energy to symmetric rotational kinetic energy,as well as frictional dissipation in the symmetric rotational kinetic energy budget.The inward movement before rapid intensification(RI)resulted from radial flux convergence;cyclonic circulation develops while moving inward.Stationary maximum symmetric rotational kinetic energy and RI were caused by the conversion,which was observed to be proportional to the symmetric rotational kinetic energy.Landfall increased terrain-induced friction dissipation,which led to outward movement and ended the RI.

Some results on the algebraic immunity of Boolean functions

From the motivation of algebraic attacks on stream and block ciphers,the concept of algebraic immunity（AI） of a Boolean function was introduced and studied extensively.High algebraic immunity is a necessary condition for resisting algebraic attacks.In this paper,we give some lower bounds on the algebraic immunity of Boolean functions.The results are applied to give lower bounds on the AI of symmetric Boolean functions and rotation symmetric Boolean functions.Some balanced rotation symmetric Boolean functions with their AI near the maximum possible value「n/2」are constructed.

A type of 2D magnetic equivalent circuit framework of permanent magnet for magnetic system in AEMR

Modeling of permanent magnet（PM） is very important in the process of electromagnetic system calculation of aerospace electromagnetic relay（AEMR）. In traditional analytical calculation, PM is often equivalent to a lumped parameter model of one magnetic resistance and one magnetic potential, but great error is often caused for the inner differences of PM; based on the conception of flux tube, a type of 2D magnetic equivalent circuit framework of permanent magnet model（2D MECF） is established; the element is defined, the relationship between elements is deduced, and solution procedure as well as verification condition of this model is given; by a case study of the electromagnetic system of a certain type of AEMR, the electromagnetic system calculation model is established based on 2D MECF and the attractive force at different rotation angles is calculated; the proposed method is compared with the traditional lumped parameter model and finite element method（FEM）; for some types of electromagnetic systems with symmetrical structure, 2D MECF proves to be of acceptable accuracy and high calculation speed which fit the requirement of robust design for AEMR.