This paper presents an efficient architecture for performing 128 points to 1M points Fast Fourier Transformation (FFT) based on mixed radix-2/4/8 butterfly unit. The proposed FFT architecture reduces the computation cost by taking the advantage of the radix-8 FFT algorithm while remaining compatible with sequences whose data length is an integral power of 2. Further optimizations for reconfigur...

The necessity of extending the graduated plan procedure of 1981 (see Notification mentioned above), which referred exclusively to medicinal products derived from Aristolochia, is resulting from the circumstance that AA I has been detected in three homeopathic mother tinctures of Asarum europaeum, in one mother tincture of Asarum canadense and in samples of the TCM drug Asari radix e rhizoma. Th...

In this study, quantitative and pattern recognition analyses were developed using HPLC/UV for the quality evaluation of Dipsaci Radix. For quantitative analysis, five major bioactive compounds were assessed. The separation conditions employed for HPLC/UV were optimized using ODS C18 column (250 × 4.6 mm, 5 μm) with a gradient of acetonitrile and water as the mobile phase at a flow rate of 1.0 m...

We present a simple algorithm for computing the arithmetic weight of an integer with respect to a given radix r ≥ 2. The arithmetic weight of n is the minimum number of nonzero digits in any signed radix-r representation of n. This algorithm leads to a new family of minimal weight signed radix-r representations which can be constructed using a left-to-right on-line algorithm. These representati...

Although the representation of the real numbers in terms of a base and a set of digits has a long history, new questions arise even in the binary case digits 0 and 1. A binary positional number system (binary radix system) with base equal the golden ratio (1 + √ 5)/2 is fairly well known. The main result of this paper is a construction of infinitely many binary radix systems, each one construct...

The value of using a higher radix for modular multiplication in the context of RSA is investigated. The main conclusion is that for algorithms which perform the multiplication via repeated addition, there is, broadly speaking, a direct trade-off between space and time provided by change of radix. Thus chip area utilised is roughly proportional to speed. However, initially as the radix is increa...

This paper describes an algorithm and architecture based on an extension of a scalable radix-2 architecture proposed in a previous work. The algorithm is proven to be correct and the hardware design is discussed in detail. Experimental results are shown to compare a radix-8 implementation with a radix-2 design. The scalable Montgomery multiplier is adjustable to constrained areas yet being able...

Radix-rational sequences are solutions of systems of recurrence equations based on the radix representation of the index. For each radix-rational sequence with complex values we provide an asymptotic expansion, essentially in the scale N logN . The precision of the asymptotic expansion depends on the joint spectral radius of the linear representation of the sequence of first-order differences. ...

Although the representation of the real numbers in terms of a base and a set of digits has a long history, new questions arise even in the binary case – digits 0 and 1. A binary positional number system (binary radix system) with base equal to the golden ratio (1 + √ 5 )/2 is fairly well known. The main result of this paper is a construction of infinitely many binary radix systems, each one con...

BACKGROUND The Tibetan Plateau is not only the highest and largest plateau on earth; it is also home to numerous freshwater lakes potentially harbouring endemic faunal elements. As it remains largely unknown whether these lakes have continuously existed during the Last Glacial Maximum (LGM), questions arise as to whether taxa have been able to exist on the plateau since before the latest Pleist...