摘要:

AbstractNecessary and sufficient conditions are given for projective plane curves to have cusps isomorphic to the origin of an affine plane curvexa+yb. Based on them, a family of curvesCabhaving only one such cusp as a singular point and a family of curvesrCabhaving only two such cusps as singular points are formulated. Also, the structures of algebraic geometric codes generated on curves contained in these families are shown, whereaandbare relatively prime. Then the genus is (a− 1)/(b− 1)/2 and the basis of linear spaceL(m·P) is given by rational functionsxiyionly. Second, by giving concrete examples, it is shown that families of curvesCabandrCabcontain many curves which attain Hasse‐Weil upper

ISSN:1042-0967    

DOI:10.1002/ecjc.4430761201

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1993

数据来源: WILEY

摘要:

AbstractThis paper presents a method of solving the simultaneous nonlinear equations containing transcendental functions in a specified domain. The features of the method are that the analysis can be executed in the complex domain by using the algebraic analysis and in the infinite range for the variable not contained in the transcendental function. The method is composed of the following procedures.The specified domain of analysis is divided into subdomains, and the transcendental function is approximated by a polynomial in each subdomain. Using the computation algorithm for the Groebner basis, the single‐variable algebraic equation is derived and the number and the value of the approximate solution are determined. The computer algebra is applied to the computation process, and the efficiency of the calculation of the approximate solution is improved by deriving several polynomials called prime basis, together with the single‐variable equation.To calculate the solution for the original equation based on the approximate solution, the techniques for numerical analysis such as Newton's method are employed. The reliability of the solution method is improved by the bifurcation analysis between the real and the complex‐valued solutions whenever nece

ISSN:1042-0967    

DOI:10.1002/ecjc.4430761202

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1993

数据来源: WILEY

摘要:

AbstractThis paper describes various characteristics for a width‐extensional mode quartz crystal resonator. A new cut is proposed for a width‐extensional mode quartz crystal resonator, which is designated the “KT‐cut,” and clarifies its frequency characteristics, frequency temperature behavior, and electrical characteristics.First, a frequency equation is derived under the conditions that widthx0is much larger than thicknessz0but much smaller than lengthy0by solving partial differential equations for a new‐shape GT‐cut quartz crystal resonator already obtained with variational principle. This is because the modified shape for the present resonator is referred to as that of the new‐shape GT resonator.Next, from the obtained equation, relationships of resonant frequency versus widthx0and the first‐ and second‐order temperature coefficients α, β versus a cut angle θ are analyzed theoretically. As a result, a cut angle θ which gives α = 0 approximately is θ = 24.5° at the reference temperature of 20°C and β has a value of β = −0.60 × 10−8/°C2. This value is then compared with the measured values of β = −1.25 × 10−8/°C2and the absolute value in the experiments is found to be about twice the calculated value. In addition, α and β are very dependent on a thickness‐to‐width ratioRzx(thicknessz0/widthx0), and have a parabolic curve versus the ratioRzx. Thus, α and β are also found to vary withRzx.Finally, series resistanceR1, and a quality factorQare primarily examined in the frequency range of approximately 8.7 to 32 MHz. Consequently, e.g., whenf= 16.3 MHz, a width‐extensional mode quartz crystal resonator is found to be obtained successfully

ISSN:1042-0967    

DOI:10.1002/ecjc.4430761203

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1993

数据来源: WILEY

摘要:

AbstractRecently, many applications of integer theory to cryptographic techniques have been observed. The discrete logarithm problem is one such case. Usually, the discrete logarithm problem is the determination of the logarithm for the given arbitrary element with a prime number as the modulus. However, the discrete logarithm problem can also be considered with a composite number as the modulus. It is anticipated that the discrete logarithm problem with a composite number as the modulus is a difficult problem if the prime factors of the composite number, which is used as the modulus, are unknown. Then the problem can be applied to the cryptography.In the general discrete logarithm problem with a composite number as the modulus, it is not always true that an arbitrary element has a logarithm. From such a viewpoint, this paper shows that the exponent of an arbitrary element belonging to the irreducible residue class with a composite number as the modulus has a logarithm. Then the necessary condition in the application to the cryptographic technique is presented.Finally, as an application example of the technique proposed in this paper, a cryptographic technique based on the discrete logarithm problem with the composite number as the modulus is shown.

ISSN:1042-0967    

DOI:10.1002/ecjc.4430761204

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1993

数据来源: WILEY

摘要:

AbstractThe Reed‐Solomon (RS) code is widely applied to various fields including digital memory and communications systems. Since it has desirable properties from various viewpoints, intensive studies are made on its performance such as error correction. The code is not a complete code although it is a maximum‐distance separation (MDS) code, and there is a possibility that the code can correct more errors than the bounded distance decoding. From such a standpoint, this paper presents a method which can fully utilize its potential power for burst error correction when (t+ 1) symbol errors are detected on the binary expanded RS code. The property that each of the sequences obtained by dividing the RS code with a certain parameter according to the basis is a codeword of BCH code, and an algorithm is proposed which estimates the symbol containing the head or tail of the solid burst error by superposing the received sequences. A decoding method is obtained which completely guarantees the error‐correcting power realizable by the bounded distance decoding onGF(2m) and realizes a larger error‐correcting power than the bounded distance decoding for the solid burst error represented onGF(2). The proposed method is also applied to the correction of the high‐density burst error, and the usefulness is dem

ISSN:1042-0967    

DOI:10.1002/ecjc.4430761205

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1993

数据来源: WILEY

摘要:

AbstractThis paper proposes an extension of the real‐coefficient wave digital filter by Fettweis et al. (WDF) to the complex‐coefficient WDF (CWDF) as well as a construction method to realize an arbitrary complex‐coefficient transfer function.The first step of the proposed construction method is to synthesize the lossless reactance circuit containing the imaginary resistors (except for the input terminal) as an analog reference circuit by the continued‐fraction expansion.In this study, theLCladder network containing imaginary resistors is synthesized as the reference network, realizing the denominator polynomial of the transfer function. Then the state‐variable representation is constructed and the numerator polynomial is realized by determining the tap coefficients to the external output, using the transform matrix.In this process, the reference network is transformed into WCDF, and the tap is formed considering the relation between incident/reflected waves and the terminal voltages. By this procedure, the required transfer function can be realized. Finally, the proposed method is compared to other construction methods and the low‐sensitivity property of the proposed method is d

ISSN:1042-0967    

DOI:10.1002/ecjc.4430761206

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1993

数据来源: WILEY

摘要:

AbstractIn this paper, a test generation algorithm STAR for sequential circuits based on Boolean function manipulation is presented. Based on the product machine traversal (PMT) method, which generates test patterns using breadth‐first search of state‐pairs and an implicit state enumeration method of a product machine of fault‐free and faulty machines, STAR algorithm attempts to improve the computational efficiency by introducing a mixture of breadth‐first/depth‐first traversal based on the sequential depth, improvement on the image computation, and the computation of fault‐difference functions by the symbolic single‐fault propagation method. The results of the experiments on ISCAS 89 benchmark circuits show threefold improvement on the computational time over the simp

ISSN:1042-0967    

DOI:10.1002/ecjc.4430761207

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1993

数据来源: WILEY

摘要:

AbstractTo design a reliable system, it is very important to protect data stored or transmitted from intentional forgery in communications network. As a practical means of protecting data or software, it is pointed out by Naor and Yung that a family of one‐way hash functions is useful and can be classified into a universal one‐way hash function family (UOHF) and a collision intractable one‐way hash function family (CIHF). The construction for a UOHF is possible under a weak assumption, i.e., one‐way functions exist. However, the construction for a CIHF is not known to be possible under such a weak assumption.This paper presents a simple construction for a CIHF that is based on the hardness of factoring large composite numbers. The idea on the construction here is completely different from those reported so far and can be expected to provide a theoretical breakthrough to the construction for a CIHF under a general ass

ISSN:1042-0967    

DOI:10.1002/ecjc.4430761208

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1993

数据来源: WILEY

摘要:

AbstractThis paper presents a design method of two‐dimensional (2‐D) perfect reconstruction filter banks for arbitrary sampling lattices. First, a design of 2‐DN‐th‐band digital filters with arbitrary sampling lattices is shown. Next, the relation between the sampling matrix and the number of paths is presented and the band‐limited region and the condition of delays are defined. From these conditions, the approximation problem is shown of the 2‐D allpass filter whose 2‐DN‐th‐band filter is composed and the characteristics of 2‐DN‐th‐band filters are explained. Then 2‐D analysis banks consist of 2‐D discrete Fourier transform (DFT) and 2‐DN‐th‐band filter which consists of some delays and 2‐D interpolated allpass networks. To achieve the perfect reconstruction, by evaluating the aliasing component matrix, it is shown that the synthesis banks can also be cons

ISSN:1042-0967    

DOI:10.1002/ecjc.4430761209

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1993

数据来源: WILEY

摘要:

AbstractIn the area of quantum communication, a situation often arises in which the inner product between the input and output signal quantum states of the channel is not preserved. In this paper, such a quantum channel is treated as a conditional unitary process which is proposed by one of the authors. As a new operator representation to explain this process, the condition unitary operator is derived.Based on the definition of the conditional unitary process, a method is presented for constructing the conditional unitary operator. Next, it is shown that the energy attenuation process of which the analysis is indispensable in the area of quantum communication is a conditional unitary process for the coherent state as a representative input quantum state, photon number state, and squeezed state and that the process can be described by the conditional unitary operation derived by the present method.

ISSN:1042-0967    

DOI:10.1002/ecjc.4430761210

出版商:Wiley Subscription Services, Inc., A Wiley Company    

年代:1993

数据来源: WILEY