The minimum aperiodic crosscorrelation of binary sequences of size M and length n over the alphabet E={1, -1} has been obtained by Levenshtein for M≥4 and n≥2 These bounds improve a long standing bound giv...The minimum aperiodic crosscorrelation of binary sequences of size M and length n over the alphabet E={1, -1} has been obtained by Levenshtein for M≥4 and n≥2 These bounds improve a long standing bound given by Welch. In this paper, the Sarwate bounds for codes over the p th roots of unity with the same parameters M and n are discussed, that is,the lower bounds and trade off are established for the maximum magnitude of the aperiodic crosscorrelation function and the maximum magnitude of the out of phase aperiodic autocorrelation function for the sets of periodic sequences with the same parameters M and n by using the modified Levenshtein method. The results show that new bounds are tighter than Sarwate bounds and Levenshtein bounds.展开更多
Some dominance rules are proposed for the problems of scheduling N jobs on a single machine with due dates, sequence dependent setup times and no preemption. Two algorithms based on Ragatz＇ s branch and bound scheme ...Some dominance rules are proposed for the problems of scheduling N jobs on a single machine with due dates, sequence dependent setup times and no preemption. Two algorithms based on Ragatz＇ s branch and bound scheme are developed including the dominance rules where the objective is to minimize the maximum tardiness or the total tardiness. Computational experiments demonstrate the effectiveness of the dominance rules.展开更多
Using the weight coefficient method, we first discuss semi-discrete Hilbert-type inequalities, and then discuss boundedness of integral and discrete operators and operator norm estimates based on Hilbert-type inequali...Using the weight coefficient method, we first discuss semi-discrete Hilbert-type inequalities, and then discuss boundedness of integral and discrete operators and operator norm estimates based on Hilbert-type inequalities in weighted Lebesgue space and weighted normed sequence space.展开更多
Infinite sequences defined with a finite alphabet are studied and it is shown that the set of sequences with bounded run-length has measure zero with respect to the Borel measure.Such sequences arise in many applicati...Infinite sequences defined with a finite alphabet are studied and it is shown that the set of sequences with bounded run-length has measure zero with respect to the Borel measure.Such sequences arise in many applications including digitization of certain linear systems involving flows on the circle and 2-torus,large scale simulation,and cryptology.They are basic objects of study in ergodic theory.展开更多
In this paper, several periodic Hamming correlation lower bounds for frequency hopping sequences with low hit zone, with respect to the size p of the frequency slot set, the sequence length L, the family size M, low h...In this paper, several periodic Hamming correlation lower bounds for frequency hopping sequences with low hit zone, with respect to the size p of the frequency slot set, the sequence length L, the family size M, low hit zone LH （ or no hit zone NH ）, the maximum periodic Hamming autocorrelation sidelobe Ha and the maximum periodic Hamming crosscorrelation He, are established. It is shown that the new bounds include the known LempeI-Greenberger bounds, T.S. Seay bounds and Peng-Fan bounds for the conventional frequency hopping sequences as special cases.展开更多
In order to reduce or eliminate the multiple access interference in code division multiple access (CDMA) systems, we need to design a set of spreading sequences with good autocorrelation functions (ACF) and crosscorre...In order to reduce or eliminate the multiple access interference in code division multiple access (CDMA) systems, we need to design a set of spreading sequences with good autocorrelation functions (ACF) and crosscorrelation functions (CCF). The importance of the spreading codes to CDMA systems cannot be overemphasized, for the type of the code used, its length, and its chip rate set bounds on the capability of the system that can be changed only by changing the code. Several new lower bounds which are stronger than the well-known Sarwate bounds, Welch bounds and Levenshtein bounds for binary sequence set with respect to the spreading sequence length, family size, maximum aperiodic autocorrelation sidelobe and maximum aperiodic crosscorrelation value are established.展开更多
A sediment-continuous section of Jurassic-Cretaceous (J-K) boundary strata was found in Zhangjiagou of Luanping, northern Hebei Province, China. The boundary strata were systematically divided into 5 sequences, 13 sub...A sediment-continuous section of Jurassic-Cretaceous (J-K) boundary strata was found in Zhangjiagou of Luanping, northern Hebei Province, China. The boundary strata were systematically divided into 5 sequences, 13 subsequences and 139 parasequences by sedimentary cyclicities and facies analysis. According to stable time-ranges of subsequences and parasequences, some boundary ages can be marked as 142.90 Ma of the SQ I (Dabeigou Fm) basal bound, 141.16 Ma of the SQ II basal bound, 140.00 Ma of the SQ III (Dadianzi Fm) basal bound, 138.24 Ma of the SQ VI (Zhangjiagou Fm) basal bound and 135.34 Ma of the SQ V (Zhangjiagou Fm) top-bound. A sequence-stratigraphic framework of the Dabeigou-Zhangjiagou Fms has been constructed by tracing sequence-bounds, marker-beds and fossil zones. The basin-development and tectonic activities are studied based on sequence-stratigraphic evidence. 5 sequences represent 5 tectonic cycles and all the 6 sequence-bounds reflect tectonic activities. Tectonic activities clearly influence the basin-development that can be divided into 3 stages in the J-K transitional period. Each stage consists of a down-faulting-rising process, i.e. from strongly rising of basin-bottom, then violently faulting down (with volcanic eruptions) and to gently rising. The development shows a pattern of bottom down-faulting with basin narrowing and rising with spreading. Keywords sequence - stratigraphy - terrestrial stratotype - Jurassic-Cretaceous bound DOI: 10.1360/03yd0451展开更多
This scientific paper is a comparative analysis of two mathematical conjectures. The newly proposed -3(-n) - 1 Remer conjecture and how it is related to and a proof of the more well known 3n + 1 Collatz conjecture. An...This scientific paper is a comparative analysis of two mathematical conjectures. The newly proposed -3(-n) - 1 Remer conjecture and how it is related to and a proof of the more well known 3n + 1 Collatz conjecture. An overview of both conjectures and their respective iterative processes will be presented. Showcasing their unique properties and behavior to each other. Through a detailed comparison, we highlight the similarities and differences between these two conjectures and discuss their significance in the field of mathematics. And how they prove each other to be true.展开更多
文摘The minimum aperiodic crosscorrelation of binary sequences of size M and length n over the alphabet E={1, -1} has been obtained by Levenshtein for M≥4 and n≥2 These bounds improve a long standing bound given by Welch. In this paper, the Sarwate bounds for codes over the p th roots of unity with the same parameters M and n are discussed, that is,the lower bounds and trade off are established for the maximum magnitude of the aperiodic crosscorrelation function and the maximum magnitude of the out of phase aperiodic autocorrelation function for the sets of periodic sequences with the same parameters M and n by using the modified Levenshtein method. The results show that new bounds are tighter than Sarwate bounds and Levenshtein bounds.
文摘Some dominance rules are proposed for the problems of scheduling N jobs on a single machine with due dates, sequence dependent setup times and no preemption. Two algorithms based on Ragatz＇ s branch and bound scheme are developed including the dominance rules where the objective is to minimize the maximum tardiness or the total tardiness. Computational experiments demonstrate the effectiveness of the dominance rules.
基金Supported by Guangdong Basic and Applied Basic Research Foundation(Grant No.2022A1515012429)Guangzhou Huashang College Research Team Project(Grant No.2021HSKT03)。
文摘Using the weight coefficient method, we first discuss semi-discrete Hilbert-type inequalities, and then discuss boundedness of integral and discrete operators and operator norm estimates based on Hilbert-type inequalities in weighted Lebesgue space and weighted normed sequence space.
文摘Infinite sequences defined with a finite alphabet are studied and it is shown that the set of sequences with bounded run-length has measure zero with respect to the Borel measure.Such sequences arise in many applications including digitization of certain linear systems involving flows on the circle and 2-torus,large scale simulation,and cryptology.They are basic objects of study in ergodic theory.
基金This work was supported by the National Natural Science Foundation of China （Grant No. 60572142） the NSFC/RFBR Joint Research Scheme, the NSFC/K0SEF Joint Research Scheme, and IITA, South Korea.
文摘In this paper, several periodic Hamming correlation lower bounds for frequency hopping sequences with low hit zone, with respect to the size p of the frequency slot set, the sequence length L, the family size M, low hit zone LH （ or no hit zone NH ）, the maximum periodic Hamming autocorrelation sidelobe Ha and the maximum periodic Hamming crosscorrelation He, are established. It is shown that the new bounds include the known LempeI-Greenberger bounds, T.S. Seay bounds and Peng-Fan bounds for the conventional frequency hopping sequences as special cases.
基金supported by the National Natural Science Foundation of China(NSFC)the Research Grants Council of Hong Kong(RGC)joint research scheme(Grant No.60218001)+1 种基金the NSFC project(Grant No.69931050)the National Key Laboratory of Communications(UESTC),and the Royal Society,UK.
文摘In order to reduce or eliminate the multiple access interference in code division multiple access (CDMA) systems, we need to design a set of spreading sequences with good autocorrelation functions (ACF) and crosscorrelation functions (CCF). The importance of the spreading codes to CDMA systems cannot be overemphasized, for the type of the code used, its length, and its chip rate set bounds on the capability of the system that can be changed only by changing the code. Several new lower bounds which are stronger than the well-known Sarwate bounds, Welch bounds and Levenshtein bounds for binary sequence set with respect to the spreading sequence length, family size, maximum aperiodic autocorrelation sidelobe and maximum aperiodic crosscorrelation value are established.
文摘A sediment-continuous section of Jurassic-Cretaceous (J-K) boundary strata was found in Zhangjiagou of Luanping, northern Hebei Province, China. The boundary strata were systematically divided into 5 sequences, 13 subsequences and 139 parasequences by sedimentary cyclicities and facies analysis. According to stable time-ranges of subsequences and parasequences, some boundary ages can be marked as 142.90 Ma of the SQ I (Dabeigou Fm) basal bound, 141.16 Ma of the SQ II basal bound, 140.00 Ma of the SQ III (Dadianzi Fm) basal bound, 138.24 Ma of the SQ VI (Zhangjiagou Fm) basal bound and 135.34 Ma of the SQ V (Zhangjiagou Fm) top-bound. A sequence-stratigraphic framework of the Dabeigou-Zhangjiagou Fms has been constructed by tracing sequence-bounds, marker-beds and fossil zones. The basin-development and tectonic activities are studied based on sequence-stratigraphic evidence. 5 sequences represent 5 tectonic cycles and all the 6 sequence-bounds reflect tectonic activities. Tectonic activities clearly influence the basin-development that can be divided into 3 stages in the J-K transitional period. Each stage consists of a down-faulting-rising process, i.e. from strongly rising of basin-bottom, then violently faulting down (with volcanic eruptions) and to gently rising. The development shows a pattern of bottom down-faulting with basin narrowing and rising with spreading. Keywords sequence - stratigraphy - terrestrial stratotype - Jurassic-Cretaceous bound DOI: 10.1360/03yd0451
文摘This scientific paper is a comparative analysis of two mathematical conjectures. The newly proposed -3(-n) - 1 Remer conjecture and how it is related to and a proof of the more well known 3n + 1 Collatz conjecture. An overview of both conjectures and their respective iterative processes will be presented. Showcasing their unique properties and behavior to each other. Through a detailed comparison, we highlight the similarities and differences between these two conjectures and discuss their significance in the field of mathematics. And how they prove each other to be true.
