On pasting -weights

Theorem 3 gives a condition when two -weights can be ``pasted' together to yield another -weight. It is subsequently used in Example 6 to give an example that shows that a necessary condition by Gohberg, Krupnik, and Spitkovsky is not sufficient.

     

Critical behavior of self-avoiding walks on fractals

Using a new graph counting technique suitable for self-similar fractals, exact 18th-order series expansions for SAWs on some Sierpinski carpets are generated. From them, the critical fugacityx _c and critical exponents _SAW and _SAW are obtained. The results show a linear dependence of the critical fugacity with the average number of bonds per site of the lattices studied. We find for some carpets with low lacunarity that _SAW<0.75, thus violating the relation _SAW(fractal) > _SAW (d) for SAWs on the fractals which are embedded in ad-dimensional Euclidean space.     

Evaluation of dead time calculation in liquid chromatography using a linearization procedure for homologous series

A mathematical method for the calculation of the dead time (t_m) in HPLC was evaluated using a computer simulation approach, in which artificial perturbations were introduced to Simulated homolog retention times. The calculation was based on a modified and extended Grobler and Bálisz (GB) method. Investigated wav how the precision of the calculated t_M is affected by: statistical fluctuations in retention times and which, and how many homolog retention times are used. Based on these simulations a two-step procedure for the t_M calculation is proposed: In the first step the linearity of log t_{R, n} vs carbon number n is checked using as many homolog retention times as possible. The slope value b^o of the first linear regression in the GB method is used for the selection of homolog retention times in the final t_M calculation. In the second step the optimal selection of homologs is made and the final t_M calculation is carried out. Guidelines for homolog selection are given.     

Hole doping and superconductivity characteristics of the s=1, 2 and 3 members of the (Cu,Mo)-12s2 homologous series of layered copper oxides

Superconductivity characteristics have been systematically evaluated for a two-CuO₂-plane copper oxide system, (Cu,Mo)-12s2, upon increasing the number of fluorite-structured layers, s, between the two CuO₂ planes. Essentially single-phase samples of (Cu_0.75Mo_0.25)Sr₂YCu₂O_7+δ (s=1), (Cu_0.75Mo_0.25)Sr₂(Ce_0.45Y_0.55)₂Cu₂O_9+δ (s=2) and (Cu_0.75Mo_0.25)Sr₂(Ce_0.67Y_0.33)₃Cu₂O_11+δ (s=3) were synthesized through a conventional solid-state route in air. To make the samples superconductive an additional high-pressure oxygenation (HPO) treatment was required. Such treatment (carried out at 5 GPa and 500 °C in the presence of 75 mol% Ag₂O₂ as an oxygen source to maximize the T_c) compressed the crystal lattice for the three members of the (Cu_0.75Mo_0.25)-12s2 series equally, i.e., by 0.01 Å for the a parameter and by 0.07 Å for the c parameter per formula unit. From both Cu L-edge and O K-edge XANES spectra the s=1 sample was found to possess the highest overall hole-doping level among the HPO samples. Accordingly it exhibited the best superconductivity characteristics. With increasing s, both the T_c (s=1: 88 K, s=2: 61 K, s=3: 53 K) and H_irr values got depressed, being well explained by the trend of decreasing CuO₂-plane hole concentration with increasing s as revealed from O K-edge XANES spectra for the same samples. Hence, the present results do not suggest any significant (negative) impact on the superconductivity characteristics from the gradually thickened fluorite-structured block itself.     

LC and LC-MS Separation of Peptides on Macrocyclic Glycopeptide Stationary Phases: Diastereomeric Series and Large Peptides

Previous work on the LC separation of peptides had shown that macrocyclic glycopeptide stationary phases to be selective for peptides of five to thirteen amino acids in length. In this work, the selectivity of the teicoplanin stationary phase is compared to that of a C18 stationary phase for seven diastereomeric enkephalin peptides. The teicoplanin stationary phase separated all seven diastereomeric enkephalin peptides in a single chromatographic run. The insertion of d-amino acids into the primary enkephalin sequence produced areas of hydrophobicity that influenced retention order on the C18 stationary phase. However, analogous trends are not observed on the teicoplanin stationary phase, which is more polar and structurally diverse. Optimization of the mobile phase and the use of a step-gradient for the enkephalin separation on the teicoplanin stationary phase is discussed. Also, the selectivity of macrocyclic glycopeptide stationary phases for peptides of 14, 28, 30, and 36 amino acids also is investigated and compared to separation on a C18 stationary phase. A method for eluting peptides with multiple basic amino acids, which tend to be strongly retained on the macrocyclic glycopeptide stationary phases, is presented.     

Some exact expressions for the mean and higher moments of functions of sample moments

Examples of exact expressions for the moments (mainly of the mean) of functions of sample moments are given. These provide checks on alternative developments such as asymptotic series for n, and simulation processes. Exact expressions are given for the mean of the square of the sample coefficient of variation, particularly in uniform sampling; Frullani integrals studied by G. H. Hardy arise. It should be kept in mind that exact results for (joint) moment generating functions (mgfs) are of interest as they produce a means of obtaining exact results for (cross) moments—including moments with negative indices. Thus an exact expression for the joint mgf of the 1st two noncentral moments can be used to obtain the mean of the (c.v.)² (but not for the mean of the c..). A general expression is given for the moment generating function of the sample variance. The limitations of Fisher's symbolic formula for the characteristic function of sample moments (or more general statistics) are noted.This research was sponsored by the Applied Mathematical Sciences Research program, Office of Energy Research, U. S. Department of Energy under contract DE-AC0584OR21400 with the Martin Marietta Energy Systems. Inc.     

Proof of some conjectures on the mean-value of Titchmarsh series — III

With some applications in view, the following problem is solved in some special case which is not too special. LetF(s) =Σ _n ^∞ =1a_n λ _n ^−s be a generalized Dirichlet series with 1 =λ ₁ <λ ₂ < …,λ _n≤Dn, andλ _n+1 -λ _n ≥D ^{− 1} λ _n+1 ^{− a} where α>0 andD(≥ 1) are constants. Then subject to analytic continuation and some growth conditions, a lower bound is obtained for . These results will be applied in other papers to appear later.     

On vector-valued random Fourier series

Consider a (complex) Banach spaceX, such thatX C_O, and vectors(X _i ) _i ofX. Consider an independent standard normal sequence(g _i ) _i . Then if anX-valued random Fourier series _{|k| n} e ^ikt g _k x _k satisfies

多柱串联高温HPLC系统的构建及应用

在高效液相色谱(HPLC)中,使用多柱串联能够极大地增加柱效和改善分离效果,提高温度能够明显降低色谱柱反压、加快分析速度.将色谱柱串联与提高柱温相结合构建了多柱串联高温HPLC系统,该系统常温下分析标准样品时(以芴计),绝对柱效达7.6×104塔板数;柱温升高到120℃,色谱柱反压从35.3MPa降低到15.4MPa,分析时间从78.39min缩短为19.26min.采用构建的系统分析中药六味地黄丸,常温下出峰94个,升高温度至100℃出峰80个,分离效果较常规的单柱系统有明显提高;升高温度,使主要组分的出峰时间缩短,可获得更为详尽的组成信息.     

Forecasting COVID-19 Epidemic Trends by Combining a Neural Network with Rt Estimation

On 31 December 2019, a cluster of pneumonia cases of unknown etiology was reported in Wuhan (China). The cases were declared to be Coronavirus Disease 2019 (COVID-19) by the World Health Organization (WHO). COVID-19 has been defined as SARS Coronavirus 2 (SARS-CoV-2). Some countries, e.g., Italy, France, and the United Kingdom (UK), have been subjected to frequent restrictions for preventing the spread of infection, contrary to other ones, e.g., the United States of America (USA) and Sweden. The restrictions afflicted the evolution of trends with several perturbations that destabilized its normal evolution. Globally, Rt has been used to estimate time-varying reproduction numbers during epidemics. Methods: This paper presents a solution based on Deep Learning (DL) for the analysis and forecasting of epidemic trends in new positive cases of SARS-CoV-2 (COVID-19). It combined a neural network (NN) and an Rt estimation by adjusting the data produced by the output layer of the NN on the related Rt estimation. Results: Tests were performed on datasets related to the following countries: Italy, the USA, France, the UK, and Sweden. Positive case registration was retrieved between 24 February 2020 and 11 January 2022. Tests performed on the Italian dataset showed that our solution reduced the Mean Absolute Percentage Error (MAPE) by 28.44%, 39.36%, 22.96%, 17.93%, 28.10%, and 24.50% compared to other ones with the same configuration but that were based on the LSTM, GRU, RNN, ARIMA (1,0,3), and ARIMA (7,2,4) models, or an NN without applying the Rt as a corrective index. It also reduced MAPE by 17.93%, the Mean Absolute Error (MAE) by 34.37%, and the Root Mean Square Error (RMSE) by 43.76% compared to the same model without the adjustment performed by the Rt. Furthermore, it allowed an average MAPE reduction of 5.37%, 63.10%, 17.84%, and 14.91% on the datasets related to the USA, France, the UK, and Sweden, respectively.