A new geometric proof is given for the standard description of subgroups in the Chevalley group G = G(F4, R) of type F4 over a commutative ring R that are normalized by the elementary subgroup E(F4, R). There are two major approaches to the proof of such results. Localization proofs (Quillen, Suslin, Bak) are based on a reduction in the dimension. The first proofs of this type for exceptional g...

OBJECTIVE To explore the laws of traditional Chinese medicine (TCM) syndromes in unstable angina, and to establish the preliminary diagnostic criteria for TCM syndromes. METHODS Multi-center prospective research on TCM syndromes in 815 cases of unstable angina was done with the nonlinear dimension reduction by factor analysis. RESULTS There were five extracted factors in factor analysis: F1...

The formant frequencies of Malaysian Malay children have not been well studied. This article investigates the first four formant frequencies of sustained vowels in 360 Malay children aged between 7 and 12 years using acoustical analysis. Generally, Malay female children had higher formant frequencies than those of their male counterparts. However, no significant differences in all four formant ...

Signature-based algorithms are a popular kind of algorithms for computing Gröbner basis, including the famous F5 algorithm, F5C, extended F5, GV and the GVW algorithm. In this paper, an efficient method is proposed to solve the detachability problem. The new method only uses the outputs of signature-based algorithms, and no extra Gröbner basis computations are needed. When a Gröbner basis is ob...

The perceptual measures are often used to assess distortions in image compression. In this article different images were evaluated using the Picture Quality Scale (PQS) measure with neural network. On the basis of original and compressed images the local distortions in the compressed image are calculated. Then five factors {F1, F2, F3, F4, F5}, which represent these distortions are computed, an...

In this paper, we present an efficient attack on the multivariate Quadratic Quasigroups (MQQ) public key cryptosystem. Our cryptanalysis breaks the MQQ cryptosystem by solving a system of multivariate quadratic polynomial equations using both the MutantXL algorithm and the F4 algorithm. We present the experimental results that show that MQQ systems is broken up to size n equal to 300. Based on ...

In this paper, we present an efficient attack of the multivariate Quadratic Quasigroups (MQQ) cryptosystem. Our cryptanalysis breaks MQQ cryptosystems by solving systems of multivariate quadratic polynomial equations using a modified version of the MutantXL algorithm. We present experimental results comparing the behavior of our implementation of MutantXL to Magma’s implementation of F4 on MQQ ...

A generalized criterion for signature-based algorithms to compute Gröbner bases is proposed in this paper. This criterion is named by “generalized criterion”, because it can be specialized to almost all existing criteria for signature-based algorithms which include the famous F5 algorithm, F5C, extended F5, GV and the GVW algorithm. The main purpose of current paper is to study in theory which ...

In this paper we describe a method for integrating together cryptography and steganography through image processing. In particular, we present a system able to perform steganography and cryptography at the same time using images as cover objects for steganography and as keys for cryptography. We will show such system is an effective steganographic one (making a comparison with the well known F5...