Multi-Value Sequence Generated over Sub Extension Field and Its Properties

Pseudo-random sequences with long period, low correlation, high linear complexity, and uniform distribution of bit patterns are widely used in the field of information security and cryptography. This paper proposes an approach for generating a pseudo-random multi-value sequence (including a binary sequence) by utilizing a primitive polynomial, trace function, and k-th power residue symbol over the sub extension field. All our previous sequences are defined over the prime field, whereas, proposed sequence in this paper is defined over the sub extension field. Thus, it’s a new and innovative perception to consider the sub extension field during the sequence generation procedure. By considering the sub extension field, two notable outcomes are: proposed sequence holds higher linear complexity and more uniform distribution of bit patterns compared to our previous work which defined over the prime field. Additionally, other important properties of the proposed multi-value sequence such as period, autocorrelation, and cross-correlation are theoretically shown along with some experimental results.

An efficient algorithm for factoring polynomials over algebraic extension field

An efficient algorithm is proposed for factoring polynomials over an algebraic extension field defined by a polynomial ring modulo a maximal ideal. If the maximal ideal is given by its CrSbner basis, no extra Grbbner basis computation is needed for factoring a polynomial over this extension field. Nothing more than linear algebraic technique is used to get a characteristic polynomial of a generic linear map. Then this polynomial is factorized over the ground field. From its factors, the factorization of the polynomial over the extension field is obtained. The algorithm has been implemented in Magma and computer experiments indicate that it is very efficient, particularly for complicated examples.

An Introduction to the Theory of Field Extensions

This paper unfolds and reviews the theory of abstract algebra, field extensions and discusses various kinds of field extensions. Field extensions are said to be algebraic or transcendental. We pay much attention to algebraic extensions. Finally, we construct finite extensions of Q and finite extensions of the function field over finite field Fp using the notion of field completion, analogous to field extensions. With the study of field extensions, considering any polynomial with coefficients in the field, we can find the roots of the polynomial, and with the notion of algebraically closed fields, we have one field, F, where we can find the roots of any polynomial with coefficients in F.

CONVERGENCERATESIN THESTRONG LAWSOFASYMPTOTICALLY NEGATIVELY ASSOCIATEDRANDOM FIELDS

In this paper, a notion of negative side ρ \|mixing ( ρ\+- \|mixing) which can be regarded as asymptotic negative association is defined, and some Rosenthal type inequalities for ρ\+- \|mixing random fields are established. The complete convergence and almost sure summability on the convergence rates with respect to the strong law of large numbers are also discussed for ρ\+-\| mixing random fields. The results obtained extend those for negatively associated sequences and ρ\+*\| mixing random fields.

Abnormality Degree Detection Method Using Negative Potential Field Group Detectors

Online monitoring methods have been widely used in many major devices, however the normal and abnormal states of equipment are estimated mainly based on the monitoring results whether monitored parameters exceed the setting thresholds. Using these monitoring methods may cause serious false positive or false negative results. In order to precisely monitor the state of equipment, the problem of abnormality degree detection without fault sample is studied with a new detection method called negative potential field group detectors（NPFG-detectors）. This method achieves the quantitative expression of abnormality degree and provides the better detection results compared with other methods. In the process of Iris data set simulation, the new algorithm obtains the successful results in abnormal detection. The detection rates for 3 types of Iris data set respectively reach 100%, 91.6%, and 95.24% with 50% training samples. The problem of Bearing abnormality degree detection via an abnormality degree curve is successfully solved.

Negative Haloes and Geochemical Field Systems of Hydrothermal Deposits

Primary haloes of hydrothermal deposits were previously considered as positive haloes. Although it has been recently suggested that primary haloes incude positive and negative ones, almost all the research work on primary haloes has still focused on positive haloes for various reasons. In order to understand the source of ore substances a number of large hydrothermal deposits related to magmatism including porphyry, skarn and vein type deposits have been studied. It has been found that negative haloes exist on the peripheries of positive haloes of a mineral deposit. On the basis of the study the authors propose the concept of the geochemical field system of ore-forming elements of hydrotherreal deposits, i. e., with the orebody as the centre outwards there occur the mineralized field, positive halo field, depleted field and background field successively.

On the Composite Fields of Two Cubic Cyclic Extension Fields Over a Number Field

Assume that K is a number field, Li=K(Di1/2)（i=1, 2）, where D1, D2∈K\K2 and L1≠L2. Let L=L1L2. It is well-known that L/K has three intermediate subfields of degree 2, which are L1, L2 and L3=K(D1D21/2).

A COMPLETE DETERMINATION OF THE CUBIC CYCLIC EXTENSION FIELDS OF NUMBER FIELDS

The fundamental topic of algebraic number theory is to determine all Galois extension fields of a number field. The class field theory determines all Abelian extension fields of a number field on theoretical, but it is not concrete. The author has studied the arithmetic properties of cubic cyclic extensions of number fields in [1, 2]. In this report, we determine all cubic cyclic extension fields of any number field K.

Properties study of LiNbO_3 lateral field excited device working on thickness extension mode

This paper investigates the properties of thickness extension mode excited by lateral electric field on LiNbO3 by using the extended Christoffel-Bechmann method. It finds that the lateral field excitation coupling factor for amode （quasi-extensional mode） reaches its maximum value of 28% on Xmcut LiNbO3. The characteristics of a lateral field excitation device made of X-cut LiNbO3 have been investigated and the lateral field excitation device is used for the design of a high frequency ultrasonic transducer. The time and frequency domain pulse/echo response of the LiNbO3 lateral field excitation ultrasonic transducer is analysed with the modified Krimholtz-Leedom-Matthae model and tested using traditional pulse/echo method. A LiNbO3 lateral field excitation ultrasonic transducer with the centre frequency of 33.44 MHz and the -6 dB bandwidth of 33.8% is acquired, which is in good agreement with the results of the Krimholtz-Leedom-Matthae model. Further analysis suggests that the LiNbO3 lateral field excitation device has great potential in the design of broadband high frequency ultrasonic transducers.

Number of primitive elements of field extension GF(p^(nm))/GF(p^n)

Presents the counting of the counts number of primitive elements of finite dimensional field extension GF(p nm )/GF(p n) using (1) the principle of inclusion exclusion, (2) the Mbius inversion, (3) the Euler  function, and the new identity obtained ∑t｜p nm-1 , t p nmq j -1(t)=p nm -∑jp nmq j +∑j 1<j 2p nmqj 1qj 2 -…+(-1) kp nmq 1…q k  where, m>1, p is a prime, (·) is Euler function, and q 1,…,q k are the all distinct prime divisors of m.

Study on the drain bias effect on negative bias temperature instability degradation of an ultra-short p-channel metal-oxide-semiconductor field-effect transistor

This paper studies the effect of drain bias on ultra-short p-channel metal-oxide-semiconductor field-effect transistor （PMOSFET） degradation during negative bias temperature （NBT） stress. When a relatively large gate voltage is applied, the degradation magnitude is much more than the drain voltage which is the same as the gate voltage supplied, and the time exponent gets larger than that of the NBT instability （NBTI）. With decreasing drain voltage, the degradation magnitude and the time exponent all get smaller. At some values of the drain voltage, the degradation magnitude is even smaller than that of NBTI, and when the drain voltage gets small enough, the exhibition of degradation becomes very similar to the NBTI degradation. When a relatively large drain voltage is applied, with decreasing gate voltage, the degradation magnitude gets smaller. However, the time exponent becomes larger. With the help of electric field simulation, this paper concludes that the degradation magnitude is determined by the vertical electric field of the oxide, the amount of hot holes generated by the strong channel lateral electric field at the gate/drain overlap region, and the time exponent is mainly controlled by localized damage caused by the lateral electric field of the oxide in the gate/drain overlap region where hot carriers are produced.

Coherent control of negative refraction based on local-field enhancement and dynamically induced chirality

This paper studies the electromagnetic response of a coherently driven dense atomic ensemble to a weak probe. It finds that negative refraction with little absorption may be achieved in the presence of local-field enhanced interaction and dynamically induced chirality. The complex refractive index governing the probe refraction and absorption depends critically on the atomic density, the steady population distribution, the coherence dephasings, and the frequency de- tunings, and is also sensitive to the phase of the driving field because the photonic transition paths form a close loop. Thus, it can periodically tune the refractive index at a fixed frequency from negative to positive values and vice versa just by modulating the driving phase. Moreover, the optimal negative refraction is found to be near the probe magnetic resonance, which then requires the electric fields of the probe and the drive being on two-photon resonance due to the dipole synchronisation.

High accuracy calculation of the hydrogen negative ion in strong magnetic fields

Using a full configuration-interaction method with Hylleraas-Gaussian basis function, this paper investigates the 1^10^＋, 1^1（-1）^＋ and 1^1（-2）6＋ states of the hydrogen negative ion in strong magnetic fields. The total energies, electron detachment energies and derivatives of the total energy with respect to the magnetic field are presented as functions of magnetic field over a wide range of field strengths. Compared with the available theoretical data, the accuracy for the energies is enhanced significantly. The field regimes 3 〈 γ 〈 4 and 0.02 〈 γ 〈 0.05, in which the 1^1（-1）6＋ and 1^1（-2）^＋ states start to become bound, respectively, are also determined based on the calculated electron detachment energies.

Electric Potential in Surface Produced Negative Ion Source with Magnetic Field Increasing Toward a Wall

Electric potential near a wall for plasma with the surface produced negative ions with magnetic field increasing toward a wall is investigated analytically. The potential profile is derived analytically by using a plasma-sheath equation, where negative ions produced on the plasma grid （PG） surface are considered in addition to positive ions and electrons. The potential profile depends on the amount and the temperature of the surface produced negative ions and the profile of the magnetic field. The negative potential peak is formed in the sheath region near the PG surface for the case of strong surface production of negative ions or low temperature negative ions. As the increase rate of the magnetic field near the wall becomes large, the negative potential peak becomes small.

The Influence of the Negative Radial Electric Field on the Orbit of Banana Particles in Tokamak

This paper explores the patterns of influence of the negative radial electric field on the drift displacement and trajectory of charged particles, for it is essential for further investigation into the transitional mechanism of L-H Mode. In the light of superposition between the poloidal velocity of charged particles and the E × B drift caused by the negative radial electric field, the paper offers a theoretical analysis and value simulations. Under the action of different radial electric fields, results have been obtained in regard to changes in the velocity of charged particles (mainly ions), patterns of changes in drift displacement, regional change of banana particles, and features of transition and change between trajectories of transiting particles and banana particles.

Time evolution of negative binomial optical field in a diffusion channel

We find the time evolution law of a negative binomial optical field in a diffusion channel. We reveal that by adjusting the diffusion parameter, the photon number can be controlled. Therefore, the diffusion process can be considered a quantum controlling scheme through photon addition.

Negative Magnetoresistance Behaviour and Variable Range Hopping Conduction in Insulating NbSi Amorphous Alloys at Very Low Temperature with aagnetic Field

We present results of an experimental study of magnetoresistance (MR) in insulating NbSi amorphous alloys sample showing Variable Range Hopping (VRH) conductivity. The MR is found to be negative in a wide range of low temperature (4.2-20 K) and in the range of moderate magnetic fields (0-4 T). We made tentative analysis using three theoretical models which are the model of quantum interference, the model of Zeeman effect and the model of localized magnetic

Assessment of rice fields by GIS／GPS-supported classification of MODIS data

The new Moderate-Resolution Imaging Spectroradiometer (MODIS) satellite image offers a large choice of opportunities for operational applications. The 1-km Advanced Very High Resolution Radiometer (AVHRR) image is not suitable for retrieval of field level parameter and Landsat data are not frequent enough for monitoring changes in crop parameters during the critical crop growth periods.A methodology to map areas of paddy fields using MODIS,geographic information system (GIS) and global position system (GPS) is introduced in this paper. Training samples are selected and located with the help of GPS to provide maximal accuracy.A concept of assessing areas of potential cultivation of rice is suggested by means of GIS integration. By integration of MODIS with GIS and GPS technologies the actual areas of rice fields in 2002 have been mapped. The classification accuracy was 95.7% percent compared with the statistical data of the Agricultural Bureau of Zhejiang Province.

p-Capitulation over Number Fields with p-Class Rank Two

Theoretical foundations of a new algorithm for determining the p-capitulation type ù(K) of a number field K with p-class rank ?=2 are presented. Since ù(K) alone is insufficient for identifying the second p-class group G=Gal(Fp2K∣K) of K, complementary techniques are deve- loped for finding the nilpotency class and coclass of . An implementation of the complete algorithm in the computational algebra system Magma is employed for calculating the Artin pattern AP(K)=(τ (K),ù(K)) of all 34631 real quadratic fields K=Q(√d) with discriminants 0d<108 and 3-class group of type (3, 3). The results admit extensive statistics of the second 3-class groups G=Gal(F32K∣K) and the 3-class field tower groups G=Gal(F3∞K∣K).

Entanglement properties between two atoms in the binomial optical field interacting with two entangled atoms

The temporal evolution of the degree of entanglement between two atoms in a system of the binomial optical field interacting with two arbitrary entangled atoms is investigated. The influence of the strength of the dipole–dipole interaction between two atoms, probabilities of the Bernoulli trial, and particle number of the binomial optical field on the temporal evolution of the atomic entanglement are discussed. The result shows that the two atoms are always in the entanglement state. Moreover, if and only if the two atoms are initially in the maximally entangled state, the entanglement evolution is not affected by the parameters, and the degree of entanglement is always kept as 1.