Proof of Collatz Conjecture Using Division Sequence

The purpose of this study is to prove the Collatz conjecture using a theorem proving system. First, the division sequence is defined as an alignment of the number of times division by 2 is performed in the Collatz operation. Then, the star conversion is defined, which is a mapping from a specific division sequence to a division sequence. Here it is important to map to some division sequence, not which division sequence. The important point is that the finite length of the division sequence does not change before and after the star conversion. In theorem proving system, we considered two parallel methods: main-proof is a claim to a computer proposition that has the same meaning as the Collatz conjecture. Theorem proving support system “Idris” was used. Moreover, we sub-proved that the 12 “extended star conversion” are closed to the “Collatz operation”. Egison’s computer algebra system is used for proof. The results of the two methods achieved the goal of proving the Collatz conjecture using a theorem proving system.

Division and Correlation of Lacustrine Gravity Flow Reservoirs Based on High-Resolution Sequence Stratigraphic Analysis—Taking Oil Formation I of Lower Es3 in Wuhaozhuang Oilfield as an Example

The phase change of lacustrine gravity flow deposition is fast and complex. In its reservoir division and correlation, the isochronous problem is very important. Taking the oil formation I of Es3 in Wuhaozhuang oilfield as an example, through the analysis of stratigraphic drilling and logging data in the study area, according to the genetic types of different levels of base level cycle interfaces and the characteristics of high-resolution sequence stratigraphy, this paper subdivides the lacustrine gravity flow oil layer of lower Es3 in Wuhaozhuang Oilfield, divides it into four short-term base level cycle sequences, and establishes the high-resolution isochronous stratigraphic framework of this interval. It is found that the mid-term, short-term and ultra short-term base level cycles correspond to the oil formation, sand layer group and single layer in the oil layer correlation unit of the oilfield respectively. Based on this, the oil layer correlation unit of the interval is divided, and the sublayer correlation model is established according to the identification characteristics of the short-term base level cycle.

Time-Hopping Sequence Design for Virtual Full Duplex via Rapid On-Off-Division Duplex

To achieve virtual full-duplex(VFD)communication using half-duplex radios,the rapid on-off-division(RODD)technique has been proposed in recent years.The time-hopping(TH)sequence is critical to controlling self-interference introduced in the paradigm.By constructing the collision model with a symbol level time scale,the periodic collision correlation function properties are introduced as the performance metric for the TH sequence in the RODD system.To achieve the best VFD performance,an optimization-based method for TH sequence design is proposed.In addition,the conventional TH frame structure design for RODD system is improved.Numerical simulations are presented to demonstrate that the proposed approach can significantly increase system performance.Results indicate that the TH sequence design is very effective for the RODD system.

Constructions for almost perfect binary sequence pairs with even length

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.

Low-complexity PTS scheme based on phase factor sequences optimization

In this paper, a new partial transmit sequence（PTS）scheme with low computational complexity is proposed for the problems of high computational complexity in the conventional PTS method. By analyzing the relationship of candidate sequences in the PTS method under the interleaved partition method, it has been discovered that some candidate sequences generated by phase factor sequences have the same peak average power ratio（PAPR）. Hence, phase factor sequences can be optimized to reduce their searching times. Then, the computational process of generating candidate sequences can be simplified by improving the utilization of data and minimizing the calculations of complex multiplication. The performance analysis shows that, compared with the conventional PTS scheme, the proposed approach significantly decreases the computational complexity and has no loss of PAPR performance.

Phase Factor Sequences Algorithm in Partial Transmit Sequence

Partial transmit sequence (PTS) is a promising technique for peak-to-average power ratio (PAPR) re-duction in orthogonal frequency division multiplexing (OFDM). While in optimal PTS, an exhaustive search for all combinations of phase factor sequences is required, this results in huge computation. In this paper, by introducing the orthogonal design, a phase factor sequences algorithm is proposed. The algorithm uses orthogonal table to gen-erate phase factor sequences, and the regular PAPR computation result is then followed by the parameter estima-tion. The simulation result shows that the proposed algorithm reduces the computation notably and obtains a good PAPR performance approaching the optimal PTS.

A LARGE CLASS OF BINARY ZCZ SEQUENCE FAMILIES CONSTRUCTED BY PERIOD DOUBLING

In an Approximately Synchronized Code Division Multiple Access (AS-CDMA) commu-nication system,a family with large number of Zero Correlation Zone (ZCZ) sequences is desired,which can satisfy the rapid increase of users. This paper presents a method to generate a (2L ,2M ,Zc' z )-ZCZsequence family from an original (L ,M ,Z cz)-ZCZsequence family,where Z c' z =Zcz if Z czis even and Z c' z = Zcz 1if Z czis odd. This method can also recursively act on a ZCZ sequence family to construct a series of ZCZ sequence families with large sequence number and zero correlation zone length identical to or one less than that of original ZCZ sequences.

不相关多子集零相关区序列集的构造

在多小区环境下的准同步码分多址(quasi-synchronous code-division multiple-access,QS-CDMA)系统中,不相关多子集零相关区(zero correlation zone,ZCZ)序列集不仅可以消除一定时延内来自相同小区的信号干扰,而且可以完全消除来自相邻小区的信号干扰。针对如何基于仿酉矩阵构造多子集ZCZ序列集的问题,设计了两种构造方法。具体地,通过构造具有一定特性的多个初始矩阵,再结合仿酉矩阵,进而利用不同的初始矩阵产生不同的ZCZ序列集,且序列集间互不相关。所提方法的核心是多个初始矩阵的设计,方法1通过对离散傅里叶变换(discrete Fourier transform,DFT)矩阵进行分块与叠加实现,方法2利用已有的不相关多子集ZCZ序列集实现。由两种方法得到的构造结果,其参数趋近于最优,为解决多小区环境下的干扰抑制问题提供了新的序列设计方法。

元坝地区千佛崖组二段页岩层序与储层特征分析

川东北元坝地区千佛崖组二段半深湖相页岩具有良好的页岩油气勘探前景。通过层序划分,对页岩岩相发育特征进行研究,对不同页岩岩相控制下的储层特征进行分析,明确准层序格架下不同页岩岩相的成因及对储层发育的影响。研究结果表明:千佛崖组二段可划分为7个准层序,根据准层序内的沉积特征,可将准层序划分为湖侵旋回为主型、湖退旋回为主型和均衡型3种不同的沉积模式。千佛崖组二段页岩发育有纹层状页岩相、层状页岩相和块状页岩相三种主要岩相类型,纹层状页岩相整体孔隙更发育,连通性更好,储集物性更好;层状页岩相整体孔隙发育程度和储集物性较纹层状页岩相次之;块状页岩相孔隙发育情况不佳,连通性一般,物性较差。页岩储层受岩相影响呈现出不同的特征,页岩岩相的纵向演化明显受准层序的控制,不同准层序类型的页岩岩相发育特征存在明显差异。整体来看,优质储层在最大洪泛面附近更为发育,优质页岩储层主要发育在湖侵旋回为主型准层序的中上部,有机质富集、孔隙发育且连通性好,是下一步勘探的有利目标;湖退旋回为主型准层序的中下部发育次优储层。

广义频分复用系统峰均功率比抑制算法

为了降低广义频分复用系统存在着多载波系统中固有的高峰均功率比问题,本文提出了一种适用于广义频分复用系统的子载波抑制高峰均功率比算法。该算法以限幅法为基础,降低了系统的高峰均功率比,但与限幅法不同的是,该算法几乎不会对带外性能及误码率性能造成影响。由于子载波抑制高峰均功率比算法的峰均功率比抑制性能略差于限幅法,因此本文进一步提出将部分序列传输与子载波抑制高峰均功率比结合来进一步抑制系统高峰均功率比的算法。仿真表明:本文提出的算法的高峰均功率比抑制性能与限幅法相同,且不会对系统的带外与误码率性能造成影响。

川中地区茅口组碳酸盐岩层序地层及沉积相特征

四川盆地二叠系茅口组碳酸盐岩是油气勘探的重要层位,川中八角场—磨溪—龙女寺地区茅二段目前已获得勘探突破,但因其层序地层结构尚不明确,制约了茅口组沉积演化研究与储集层预测。本研究基于川中广安华蓥山二崖剖面茅口组高精度岩相特征,综合实际钻井资料,开展茅口组沉积相和层序地层格架分析,并解释层序格架对储集层发育特征和分布规律的控制作用。研究结果表明:(1)川中地区茅口组碳酸盐岩可分为8类岩石微相,在茅口组沉积中晚期,构造作用驱动茅口组由缓坡沉积体系向“台地—台内海槽”沉积体系转换。(2)栖霞组上部层序界面SB1和茅二下亚段上部层序界面SB2均为Ⅱ型岩相转换界面,茅二上亚段顶界面SB3为Ⅰ型淹没不整合界面,茅三段顶界面SB4为Ⅰ型剥蚀不整合面。(3)二崖剖面茅口组可划分为3个三级层序、5个四级层序:茅一段构成三级层序SQ1的海侵体系域;茅二下亚段中—下部对应三级层序SQ1的高位体系域,而上部发育三级层序SQ2陆架边缘体系域;茅二上亚段和茅三段分别对应三级层序SQ2和SQ3。(4)磨溪—龙女寺地区茅二下亚段云化储集层分布在三级层序SQ1高位体系域和三级层序SQ2陆架边缘体系域,分别以准同生晚期和准同生早期云化作用为主,受控于Ⅱ型层序界面SB2;广安—八角场地区茅二上亚段台缘滩相白云岩储集层分布在三级层序SQ2高位体系域并且受控于Ⅰ型层序界面SB3,经历了准同生早期基质云化—准同生晚期颗粒溶蚀—埋藏期云化作用阶段。该研究为四川盆地茅口组白云岩储集层分布规律的预测和成因研究提供了层序和沉积约束,对茅口组的油气勘探具有一定的参考意义。

基于变分模态分解的营四段厚层砂砾岩地层细分层序

利用常规测井曲线对厚层砂砾岩储层进行层序细分,存在界面不清难以确定划分标准的问题。变分模态分解(variational mode decomposition, VMD)方法分解精度高并且抗噪性能优越,受模态混叠影响小,可以将测井数据内的各级基准面旋回信息分解出来。本文对松辽盆地徐家围子断陷徐西凹陷营城组四段(简称营四段)厚层砂砾岩地层测井曲线应用VMD方法分解得到各频率域固有模态函数(intrinsic mode function, IMF),优选出相关性高的IMF1和IMF10,根据瞬时频率范围和采样率推算出高频IMF1对应短周期旋回,低频IMF10对应长周期旋回。选取对应周期的IMF可以指导对应级别层序的划分,划分出两个三级层序和五个四级层序。VMD方法在营四段的应用表明,该方法适用于厚层砂砾岩地层的高频层序划分。

辽西凌源地区中元古界洪水庄组沉积相特征及烃源岩评价

基于岩心、野外剖面、薄片和有机地球化学资料,开展辽西淩源地区中元古界洪水庄组沉积相特征研究和烃源岩评价。研究结果表明,中元古界洪水庄组主要为海槽相和碳酸盐岩台地相沉积,自下而上的低位体系域主要为深水海槽相和浅海陆棚相沉积,海侵体系域时期主要为深水海槽相和深水斜坡相沉积,高位体系域主要为深水缓坡和潮缘岸滩相沉积。洪水庄组烃源岩总有机碳w(TOC)平均为4.75%,(S_(1)+S_(2))平均为6.9 mg/g,整体上为好-很好烃源岩,有机质类型通过氢指数与T max交互图和干酪根显微组分综合分析,表明洪水庄组烃源岩主要为Ⅰ-Ⅱ1型干酪根,生油潜力巨大,热演化程度上T max平均为438.3℃,干酪根颜色为棕色,表明正处于成熟生油阶段。整体上看,低位体系域和海侵体系域的海槽相黑色泥岩油气潜力巨大,为下一步勘探研究的重点对象。

改进的可见光通信系统PTS峰均比抑制方法

针对非对称剪切正交频分复用(asymmetric-clipped orthogonal frequency division multiplexing,ACO-OFDM)可见光通信(visible light communication,VLC)系统中信号的高峰均功率比(peak-to-average power ratio,PAPR)问题,采用部分传输序列(partial transmit sequence,PTS)方法,并结合二进制离散粒子群优化(discrete particle swarm optimization,DPSO)算法,提出一种改进的PTS峰均比抑制方法——DPSO-PTS方法。利用DPSO算法对加权的相位因子进行优化处理,选择最佳的相位因子组合来有效控制PAPR的范围,并对乘加权信息的子块进行求和,从而选择出最小PAPR对应的一组信号进行传输。仿真结果表明,在互补累计分布函数(complementary cumulative distribution function,CCDF)为10-4时,DPSO-PTS方法的系统PAPR降低了约4 dB,且相较于传统PTS方法,系统的复杂度和误码率(bit error rate,BER)性能也得到有效的改善。

一种ZC-OFDM雷达干扰一体化波形设计与处理方法

雷达干扰一体化是优化射频资源、实现定向干扰的有效技术路径,雷达干扰一体化波形设计是雷达干扰一体化研究的重点。本文提出一种基于Zadoff-Chu序列和正交频分复用架构的雷达干扰一体化波形,研究了波形的设计与处理方法。波形以正交频分复用为调制方式、以时频分割复用为基本架构、通过Zadoff-Chu和Mersenne-Twister序列对频域子载波进行合理的分配和调制完成探测与干扰功能一体,在信号处理时采用先探干时频分离再脉冲压缩和相参处理的方式实现测距测速。理论分析和仿真试验表明,所提波形同时具备脉冲压缩主副瓣比大、多普勒容限强以及频率对准灵活、干扰随机性强的探干一体性能优点。

考虑交叉口时空相似性的路网动态分区方法

对路网中具备同质性和关联性的交叉口进行分区,是实施路网分区协调控制策略的前提。提出了一种考虑流量时序相似度和交叉口空间邻接关系的路网动态分区方法。首先针对交叉口不同方向进口道的车流量时序数据,提出了时序相似度算法,考虑最长公共子串、豪斯多夫距离计算流量时序相似度矩阵;其次考虑交叉口空间邻接关系,利用谱聚类方法结合相似度矩阵构建了路网动态分区模型;最后以北京国贸周边路网为例,结合模块度为评价准则进行算法性能分析。算例结果表明:提出的两种考虑时空相似性算法的划分方法,其模块度均在0.3至0.7之间,表明空间划分效果好,其中基于最长公共子串的划分方法最优,其模块度为0.49,而基于豪斯多夫距离的划分方法较差为0.33。

基于哈达玛矩阵的改进部分传输序列算法

部分传输序列(Partial Transmit Sequences,PTS)是一种常用的降低正交频分复用(Orthogonal Frequency Division Multiplexing,OFDM)系统峰均功率比(Peak-to-Average Power Ratio,PAPR)的方法,其能确保不给系统带来信号畸变。PTS算法的遍历特点导致计算复杂度大幅提高,文章提出的基于哈达玛矩阵的改进PTS算法将在很大程度上保障信号PAPR的性能,降低计算的复杂度。

Simultaneous biodegradation of nitrogen-containing aromatic compounds in a sequencing batch bioreactor

Many nitrogen-containing aromatic compounds （NACs）, such as nitrobenzene （NB）, 4-nitrophenol （4-NP）, aniline （AN）, and 2,4-dinitrophenol （2,4-DNP）, are environmentally hazardous, and their removal from contaminated water is one of the main challenges facing wastewater treatment plants. In this study, synthetic wastewater containing NB, 4-NP, 2,4-DNP, and AN at concentrations ranging from 50 to 180 mg/L was fed into a sequencing batch reactor （SBR）. Analyses of the SBR system indicated that it simultaneously removed more than 99% of the NACs at loading rates of 0.36 kg NB/（m^3·d）, 0.3 kg 4-NP/（m^3·d）, 0.25 kg AN/（m^3·d）, and 0.1 kg 2,4-DNP/（m^3·d）. Bacterial groups of Bacteriodetes, Candidate division TM7, α-Proteobacteria, and β-Proteobacteria were dominant in the clone libraries of 16S rRNA genes retrieved from the microbial communities in the SBR system. ＂Cycle tests＂ designed to alter feeding and aeration parameters of the SBR system demonstrated that the resident microbial biome of the SBR system responded rapidly to changing conditions. Consumption of O2 was concomitant with the apparent mineralization of NACs. Aromatic ring-cleaving dioxygenase activities suggested that （1） AN and NB were degraded via catechol 2,3-dioxygenase; （2） 4-NP was degraded via 1,2,4-benzentriol 1,2-dioxygenase; and （3） 2,4-DNP was degraded via an unresolved pathway.

Modeling and Optimisation of Precedence-Constrained Production Sequencing and Scheduling for Multiple Production Lines Using Genetic Algorithms

This paper presents an integrated methodology for the modelling and optimisation of precedence-constrained production sequencing and scheduling for multiple production lines based on Genetic Algorithms （GA）. The problems in this class are NP-hard combinatorial problems, requiring a triple optimisation at the same time： allocation of resources to each line, production sequencing and production scheduling within each production line. They are ubiquitous to production and manufacturing environments. Due to nature of constraints, the length of solutions for the problem can be variable. To cope with this variability, new strategies for encoding chromosomes, crossover and mutation operations have been developed. Robustness of the proposed GA is demonstrated by a complex and realistic case study.

基于串行时分CC-CDMA的雷达通信一体化

为了提升目标检测性能,解决多目标和多用户之间的自干扰和互干扰问题,基于串行时分互补码−码分多址(CC-CDMA)技术提出一种雷达通信一体化系统。首先,借用码分复用机理在发射端通过广义普洛黑−修−莫尔斯(GPTM)序列调整互补码中不同子序列对不同时间片上信号的扩频顺序,生成雷达通信一体化信号。其次,雷达接收端通过2次处理,利用逐点最小化方法将处理结果进行融合,提升雷达子系统的目标检测能力。最后,在通信接收端使用对应发射端扩频顺序的子序列对接收到的信号进行解扩,通过交织编码和汉明编码进一步降低误码率。仿真结果表明,与其他雷达通信一体化系统相比,所提系统具有更低的误码率、更高的多普勒分辨率和更好的旁瓣抑制性能。