In a previous paper published in this journal, it was demonstrated that any bounded, closed interval of the real line can, except for a set of Lebesgue measure 0, be expressed as a union of c pairwise disjoint perfect...In a previous paper published in this journal, it was demonstrated that any bounded, closed interval of the real line can, except for a set of Lebesgue measure 0, be expressed as a union of c pairwise disjoint perfect sets, where c is the cardinality of the continuum. It turns out that the methodology presented there cannot be used to show that such an interval is actually decomposable into c nonoverlapping perfect sets without the exception of a set of Lebesgue measure 0. We shall show, utilizing a Hilbert-type space-filling curve, that such a decomposition is possible. Furthermore, we prove that, in fact, any interval, bounded or not, can be so expressed.展开更多
The perfect sequences are so ideal that all out-of-phase autocorrelation coefficients are zero, and if the sequences are used as the coding modulating signal for the phase-modulated radar, there will be no interferenc...The perfect sequences are so ideal that all out-of-phase autocorrelation coefficients are zero, and if the sequences are used as the coding modulating signal for the phase-modulated radar, there will be no interference of side lobes theoretically. However, it has been proved that there are no binary perfect sequences of period 4 < n≤ 12100. Hence, the almost perfect sequences with all out-of-phase autocorrelation coefficients as zero except one are of great practice in engineering. Currently, the cyclic difference set is one of most effective tools to analyze the binary sequences with perfect periodic autocorrelation function. In this article, two characteristic formulas corresponding to the autocorrelation and symmetric structure of almost perfect sequences are calculated respectively. All almost perfect sequences with period n, which is a multiple of 4, can be figured out by the two formulas. Several almost perfect sequences with different periods have been hunted by the program based on the two formulas and then applied to the simulation program and practical application for ionospheric sounding.展开更多
据说图 G 是 independent-set-deletable 因素批评(简言之， ID-factor-critical ) 因为每个独立人士设定有象 V (G) 的一样的同等值我，我有完美的匹配的 G。图 G 是强烈 IM-extendable 为每跨越 G 的超级图 H，每 H 匹配导致在 H 的...据说图 G 是 independent-set-deletable 因素批评(简言之， ID-factor-critical ) 因为每个独立人士设定有象 V (G) 的一样的同等值我，我有完美的匹配的 G。图 G 是强烈 IM-extendable 为每跨越 G 的超级图 H，每 H 匹配导致在 H 的完美的匹配被包括。G 的 k-th 力量，由 G (k) 表示了，如果并且仅当他们至多有距离，有顶点的图被给二个顶点是邻近的 V 在(G) 在 G 的 k。力量图的 ID-factor-criticality 和 IM-extendability 在这篇文章被讨论。作者证明如果 G 是一张连接的图，那么， G (3 ) 和 T (G)(G 的全部的图) 是 ID-factor-critical，和 G (4 )( 当 V (G) 是平的时) 强烈 IM-extendable；如果 G 是 2-connected，那么， D (2 ) 是 ID-factor-critical。给词调音：独立人士设定；完美的匹配；匹配导致；ID-factor-critical；IM-extendable；展开更多
The concept of the binary sequence pair is generalized from a single binary sequence. Binary sequence pairs are applied in many fields of radar, sonar or communication systems, in which signals with optimal periodic c...The concept of the binary sequence pair is generalized from a single binary sequence. Binary sequence pairs are applied in many fields of radar, sonar or communication systems, in which signals with optimal periodic correlation are required. Several types of almost perfect binary sequence pairs of length T = 2q are constructed, where q is an odd number. These almost perfect binary sequence pairs are based on binary ideal sequence or binary ideal two-level correlation sequence pairs by using Chinese remainder theorem. For these almost perfect binary sequence pairs with good balanced property, their corresponding divisible difference set pairs(DDSPs) are also derived.展开更多
In this study, we consider the problem of triangulated graphs. Precisely we give a necessary and sufficient condition for a graph to be triangulated. This gives an alternative characterization of triangulated graphs. ...In this study, we consider the problem of triangulated graphs. Precisely we give a necessary and sufficient condition for a graph to be triangulated. This gives an alternative characterization of triangulated graphs. Our method is based on the so-called perfectly nested sequences.展开更多
文摘In a previous paper published in this journal, it was demonstrated that any bounded, closed interval of the real line can, except for a set of Lebesgue measure 0, be expressed as a union of c pairwise disjoint perfect sets, where c is the cardinality of the continuum. It turns out that the methodology presented there cannot be used to show that such an interval is actually decomposable into c nonoverlapping perfect sets without the exception of a set of Lebesgue measure 0. We shall show, utilizing a Hilbert-type space-filling curve, that such a decomposition is possible. Furthermore, we prove that, in fact, any interval, bounded or not, can be so expressed.
基金This poject was supported by the National Natural Science Foundation of China (40474066).
文摘The perfect sequences are so ideal that all out-of-phase autocorrelation coefficients are zero, and if the sequences are used as the coding modulating signal for the phase-modulated radar, there will be no interference of side lobes theoretically. However, it has been proved that there are no binary perfect sequences of period 4 < n≤ 12100. Hence, the almost perfect sequences with all out-of-phase autocorrelation coefficients as zero except one are of great practice in engineering. Currently, the cyclic difference set is one of most effective tools to analyze the binary sequences with perfect periodic autocorrelation function. In this article, two characteristic formulas corresponding to the autocorrelation and symmetric structure of almost perfect sequences are calculated respectively. All almost perfect sequences with period n, which is a multiple of 4, can be figured out by the two formulas. Several almost perfect sequences with different periods have been hunted by the program based on the two formulas and then applied to the simulation program and practical application for ionospheric sounding.
基金Project supported by NSFC(10371112)NSFHN (0411011200)SRF for ROCS,SEM
文摘据说图 G 是 independent-set-deletable 因素批评(简言之， ID-factor-critical ) 因为每个独立人士设定有象 V (G) 的一样的同等值我，我有完美的匹配的 G。图 G 是强烈 IM-extendable 为每跨越 G 的超级图 H，每 H 匹配导致在 H 的完美的匹配被包括。G 的 k-th 力量，由 G (k) 表示了，如果并且仅当他们至多有距离，有顶点的图被给二个顶点是邻近的 V 在(G) 在 G 的 k。力量图的 ID-factor-criticality 和 IM-extendability 在这篇文章被讨论。作者证明如果 G 是一张连接的图，那么， G (3 ) 和 T (G)(G 的全部的图) 是 ID-factor-critical，和 G (4 )( 当 V (G) 是平的时) 强烈 IM-extendable；如果 G 是 2-connected，那么， D (2 ) 是 ID-factor-critical。给词调音：独立人士设定；完美的匹配；匹配导致；ID-factor-critical；IM-extendable；
基金supported by the National Natural Science Foundation of China(6160140161501395+6 种基金6160139961671402)Natural Science Foundation of Hebei Province(F2015203150F2016203293F2016203312)Natural Science Research Programs of Hebei Educational Committee(QN2016120)the Independent Research Programs for Young Teachers of Yanshan University(15LGB013)
文摘The concept of the binary sequence pair is generalized from a single binary sequence. Binary sequence pairs are applied in many fields of radar, sonar or communication systems, in which signals with optimal periodic correlation are required. Several types of almost perfect binary sequence pairs of length T = 2q are constructed, where q is an odd number. These almost perfect binary sequence pairs are based on binary ideal sequence or binary ideal two-level correlation sequence pairs by using Chinese remainder theorem. For these almost perfect binary sequence pairs with good balanced property, their corresponding divisible difference set pairs(DDSPs) are also derived.
文摘In this study, we consider the problem of triangulated graphs. Precisely we give a necessary and sufficient condition for a graph to be triangulated. This gives an alternative characterization of triangulated graphs. Our method is based on the so-called perfectly nested sequences.
