In this paper, groups of order p^n in which the number of subgroups of possible order is less than or equal to p3 ale classified. It turns out that if p 〉 2, n≥ 5, then the classification of groups of order p^n in w...In this paper, groups of order p^n in which the number of subgroups of possible order is less than or equal to p3 ale classified. It turns out that if p 〉 2, n≥ 5, then the classification of groups of order p^n in which the number of subgroups of possible order is less than or equal to p3 and the classification of groups of order p^n with a cyclic subgroup of index p2 are the same.展开更多
We demonstrate here seven pure cyclic samples, which belongs to two series of oligoesters, cyclic oligo（trimethylene terephthalate）s （COTTs） and cyclic oligo（butylene terephthalate）s （COBTs）, showing odd-even ...We demonstrate here seven pure cyclic samples, which belongs to two series of oligoesters, cyclic oligo（trimethylene terephthalate）s （COTTs） and cyclic oligo（butylene terephthalate）s （COBTs）, showing odd-even effect of degree of oligomerization （repeating units number） on properties. The pentamer of COTT and trimer of COBT show much lower melting temperature, and the trimer of COTT and trimer of COBT show significant lower refractive index, which can be ascribed to the low packing density of cyclic oligoesters with odd number of degree of oligomerization. Our results reveal the discrete property change as a function of cyclic size of oligomers, which can be used to design materials with special properties.展开更多
Periodicity is common in natural processes, however, extraction tools are typically difficult and cumbersome to use. Here we report a computational method developed in MATLAB through a function called Periods with the...Periodicity is common in natural processes, however, extraction tools are typically difficult and cumbersome to use. Here we report a computational method developed in MATLAB through a function called Periods with the aim to find the main harmonic components of time series data. This function is designed to obtain the period, amplitude and lag phase of the main harmonic components in a time series (Periods and lag phase components can be related to climate, social or economic events). It is based on methods of periodic regression with cyclic descent and includes statistical significance testing. The proposed method is very easy to use. Furthermore, it does not require full understanding of time series theory, nor require many inputs from the user. However, it is sufficiently flexible to undertake more complex tasks such as forecasting. Additionally, based on previous knowledge, specific periods can be included or excluded easily. The output results are organized into two groups. One contains the parameters of the adjusted model and their F statistics. The other consists of the harmonic parameters that best fit the original series according to their importance and the summarized statistics of the comparisons between successive models in the cyclic descent process. Periods is tested with both, simulated and actual sunspot and Multivariate ENSO Index data to show its performance and accuracy.展开更多
基金supported by the National Natural Science Foundation of China(No.10671114)the ShanxiProvincial Natural Science Foundation of China(No.2008012001)the Returned Abroad-StudentFund of Shanxi Province(No.[2007]13-56)
文摘In this paper, groups of order p^n in which the number of subgroups of possible order is less than or equal to p3 ale classified. It turns out that if p 〉 2, n≥ 5, then the classification of groups of order p^n in which the number of subgroups of possible order is less than or equal to p3 and the classification of groups of order p^n with a cyclic subgroup of index p2 are the same.
基金financially supported by the National"973"Project(No.2011CB606004)the National Natural Science Foundation of China(Nos.21274099,21234005 and 21474067)a Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions
文摘We demonstrate here seven pure cyclic samples, which belongs to two series of oligoesters, cyclic oligo（trimethylene terephthalate）s （COTTs） and cyclic oligo（butylene terephthalate）s （COBTs）, showing odd-even effect of degree of oligomerization （repeating units number） on properties. The pentamer of COTT and trimer of COBT show much lower melting temperature, and the trimer of COTT and trimer of COBT show significant lower refractive index, which can be ascribed to the low packing density of cyclic oligoesters with odd number of degree of oligomerization. Our results reveal the discrete property change as a function of cyclic size of oligomers, which can be used to design materials with special properties.
文摘Periodicity is common in natural processes, however, extraction tools are typically difficult and cumbersome to use. Here we report a computational method developed in MATLAB through a function called Periods with the aim to find the main harmonic components of time series data. This function is designed to obtain the period, amplitude and lag phase of the main harmonic components in a time series (Periods and lag phase components can be related to climate, social or economic events). It is based on methods of periodic regression with cyclic descent and includes statistical significance testing. The proposed method is very easy to use. Furthermore, it does not require full understanding of time series theory, nor require many inputs from the user. However, it is sufficiently flexible to undertake more complex tasks such as forecasting. Additionally, based on previous knowledge, specific periods can be included or excluded easily. The output results are organized into two groups. One contains the parameters of the adjusted model and their F statistics. The other consists of the harmonic parameters that best fit the original series according to their importance and the summarized statistics of the comparisons between successive models in the cyclic descent process. Periods is tested with both, simulated and actual sunspot and Multivariate ENSO Index data to show its performance and accuracy.
