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1-1-336/102, Viveknagar, Chikkadpally, Hyderabad-500 020, Telangana, India E-mail : idid_raju@yahoo.com Atoms of chemical elements have three dimensional structures, and it is necessary that periodic table must have 3D shape. "Pams Quan­tum Periodic Table", which is an improvement over the Mendeleev's Pe­riodic Table, without disturbing its basic theme is a three dimensional periodic table. All four quantum numbers can be visualized in this peri­odic table at a time, where as in Mendeleev's Periodic Table only prin­cipal and azimuthal quantum numbers can be displayed at a time. Fold­ing the P, D and F blocks in three dimensional way and wrapping of those three blocks around S block is the effect of the magnetic quantum num­ber. The spin quantum number plays a different role in the case of Pams Quantum periodic table and it divides the total periodic table in to two structures which have mirror image symmetry. This paper shows the per­fect construction of Pams Quantum periodic table according to quantum principles. Pams Quantum periodic table will further help in viewing the data of periodic table trends in new perspective.

The high activity and selectivity of Fe-based heterogeneous catalysts toward a variety of reactions that require the breaking of strong bonds are offset in large part by their considerable instability with respect to oxidative deactivation. While it has been shown that the stability of Fe catalysts is considerably enhanced by alloying them with precious metals (even at the single-atom limit), rational design criteria for choosing such secondary metals are still missing. Since oxidative deactivation occurs due to the strong binding of oxygen to Fe and reduction by adsorbed hydrogen mitigates the deactivation, we propose here to use the binding affinity of oxygen and hydrogen adatoms as the basis for rational design. As it would also be beneficial to use cheaper secondary metals, we have scanned over a large subset of 3d–5d mid-to-late transition metal single atoms and computationally determined their effect on the oxygen and hydrogen adlayer binding as a function of chemical potential and adsorbate coverage. We further determine the underlying chemical origins that are responsible for these effects and connect them to experimentally tunable quantities. Our results reveal a reliable periodic trend wherein oxygen binding is weakened greatest as one moves right and down the periodic table. Hydrogen binding shows the same trend only at high (but relevant) coverages and otherwise tends to have its binding slightly increased in all systems. Trends with secondary metal coverage are also uncovered and connected to experimentally tunable parameters.

Atoms consist of a nucleus that is surrounded by a “cloud” of electrons. Protons, elementary particles carrying positive unit charge (e = 1.602 × 10–19 C), and neutrons, elementary particles carrying no charge, form together the nucleus of diameter of the order 10–14 m. Electrons, elementary particles carrying negative unit charge, have only about 1/1836 the mass of a proton, but are located within a relatively enormously large space of diameter of the order 10–10 m. Hence, with a view to mass distribution, the atom is largely “empty”.

[EN] Understanding and tuning the catalytic properties of metals atomically dispersed on oxides are major stepping-stones toward a rational development of single-atom catalysts (SACs). Beyond individual showcase studies, the design and synthesis of structurally regular series of SACs opens the door to systematic experimental investigations of performance as a function of metal identity. Herein, a series of single-atom catalysts based on various 4d (Ru, Rh, Pd) and Sd (Ir, Pt) transition metals has been synthesized on a common MgO carrier. Complementary experimental (X-ray absorption spectroscopy) and theoretical (Density Functional Theory) studies reveal that, regardless of the metal identity, metal cations occupy preferably octahedral coordination MgO lattice positions under step-edges, hence highly confined by the oxide support. Upon exposure to O-2-lean CO oxidation conditions, FTIR spectroscopy indicates the partial deconfinement of the monatomic metal centers driven by CO at precatalysis temperatures, followed by the development of surface carbonate species under steady-state conditions. These findings are supported by DFT calculations, which show the driving force and final structure for the surface metal protrusion to be metal-dependent, but point to an equivalent octahedral-coordinated M4+ carbonate species as the resting state in all cases. Experimentally, apparent reaction activation energies in the range of 96 +/- 19 kJ/mol are determined, with Pt leading to the lowest energy barrier. The results indicate that, for monatomic sites in SACs, differences in CO oxidation reactivity enforceable via metal selection are of lower magnitude than those evidenced previously through the mechanistic involvement of adjacent redox centers on the oxide carrier, suggesting that tuning of the oxide surface chemistry is as relevant as the selection of the supported metal., XAS experiments were performed at B18 beamline, Diamond Light Source, United Kingdom (proposals Nr. SP17377 and SP19072) and BL22 beamline, ALBA Light Source, Spain (experiment 2019023278). Beamline scientists D. Gianolio (Diamond) and L. Simonelli and C. Marini (ALBA) are acknowledged for their assistance with the beamline setup during XAS experiments. The authors are grateful to M. Garcia, E. Andres, M. E. Martinez, and I. Lopez (ITQ) for assistance during the XAS experiments. J. Ternieden (MPIKOFO) is acknowledged for the performance of XRD experiments. J.M. Salas (ITQ) is acknowledged for his experimental contribution to the CO-FTIR studies, and M.D. Soriano and A. Munoz for the recording of XP spectra. P.N.P. and F.S. acknowledge support by the state of BademWurttemberg through bwHPC (bwUnicluster and JUSTUS, RV bw17D01) and support from the Helmholtz Association is also gratefully acknowledged. This research received funding from the Alexander von Humboldt Foundation (postdoctoral grant to B.B.S.), the Max Planck Society and the Fonds der Chemischen Industry (FCI, Germany). The authors are grateful to Prof. Ferdi Schuth for the provision of lab facilities and support throughout the project. Funding from the Spanish Ministry of Science, Innovation and Universities (projects SEV 2016-0683 and RTI2018-096399-A-100) is also acknowledged.

Short-time traffic speed forecasting is a significant issue for developing Intelligent Transportation Systems applications, and accurate speed forecasting results are necessary inputs for Intelligent Traffic Security Information System (ITSIS) and advanced traffic management systems (ATMS). This paper presents a hybrid model for travel speed based on temporal and spatial characteristics analysis and data fusion. This proposed methodology predicts speed by dividing the data into three parts: a periodic trend estimated by Fourier series, a residual part modeled by the ARIMA model, and the possible events affected by upstream or downstream traffic conditions. The aim of this study is to improve the accuracy of the prediction by modeling time and space variation of speed, and the forecast results could simultaneously reflect the periodic variation of traffic speed and emergencies. This information could provide decision-makers with a basis for developing traffic management measures. To achieve the research objective, one year of speed data was collected in Twin Cities Metro, Minnesota. The experimental results demonstrate that the proposed method can be used to explore the periodic characteristics of speed data and show abilities in increasing the accuracy of travel speed prediction.

Two-dimensional (2D) piezoelectric materials have gained considerable attention since they could play important roles in the nanoelectromechanical systems. Herein, we report a first-principles study on the piezoelectric properties of monolayer group-V binary compounds with theoretically stable honeycomb phases (α-phase and β-phase). Our calculations for the first time reveal that a majority of the monolayers possess extremely high piezoelectric coefficients d11, i.e., 118.29, 142.44, and 243.45 pm/V for α-SbN, α-SbP, and α-SbAs, respectively, comparable to those of recently reported group-IV monochalcogenides (d11 = 75–250 pm/V) with an identical mm2 symmetry. It is found that the giant piezoelectric responses of α-phase monolayers as compared to those of β-phase monolayers are induced by their flexible structures and special symmetry. Meanwhile, the piezoelectric coefficients of α-phase monolayers are found to be surprisingly anisotropic and obey a unique periodic trend which is not exactly identical to ...

Most empirical literature investigates the relation between oil prices and exchange rate through different models. These models measure this relationship on two time scales (long and short terms), and often fail to observe the co-movement of these variables at different time scales. We apply a detrended cross-correlation approach (DCCA) to investigate the co-movements of the oil price and exchange rate in 12 Asian countries. This model determines the co-movements of oil price and exchange rate at different time scale. The exchange rate and oil price time series indicate unit root problem. Their correlation and cross-correlation are very difficult to measure. The result becomes spurious when periodic trend or unit root problem occurs in these time series. This approach measures the possible cross-correlation at different time scale and controlling the unit root problem. Our empirical results support the co-movements of oil prices and exchange rate. Our results support a weak negative cross-correlation between oil price and exchange rate for most Asian countries included in our sample. The results have important monetary, fiscal, inflationary, and trade policy implications for these countries.

A Bayesian testing approach for a periodic unit root in quarterly and monthly data is presented. Further a Bayesian test is introduced to test for unit roots at (non)seasonal spectral frequencies. All procedures admit one structural break in the periodic trend function, where the occurrence of a break and the associated timing are treated as additional model parameters. A Bayesian model averaging (BMA) approach is proposed and power functions of the tests are computed. Overall the results indicate that the BMA periodic unit root test exhibits favourable test properties even in small samples. In an empirical application the presented testing procedures are used to test for (non)seasonal forms of unemployment persistence among OECD countries.

MoS2 nanolayers are versatile systems for new energy technologies such as spintronics and optoelectronic or (electro)catalytic materials, and for current industrial catalytic processes. Using spin-polarized density functional theory (DFT) calculations, we show that the magnetic moment value at edges of 2H MoS2 single nanolayers follows a periodic trend as a function of the 3d metal (Me) dopants (Me = V, Cr, Mn, Fe, Co). The magnetic moment and ordering depend on the Me dopant and also on its location at the M- or S-edge with higher values at M-edge. The maximum values of the magnetic moments are obtained for Me = Mn. In the case of Co–MoS2 single nanolayers, Co atoms located on the M-edge exhibits a weak magnetic moment (0.6–0.7 μB) which may also be considered as a fingerprint of the catalytically active sites located on this given edge. A detailed electronic and structural analysis reveals that a superexchange interaction involves the Me-dopant, S-bridging ligands, and Mo atoms at subedge, particularly ...

Regularities among electronic configurations for common oxidation states in lanthanide complexes and the low involvement of f orbitals in bonding result in the appearance of several periodic trends along the lanthanide series. These trends can be observed on relatively different properties, such as bonding distances or ionization potentials. Well-known concepts like the lanthanide contraction, the double-double (tetrad) effect, and the similar chemistry along the lanthanide series stem from these regularities. Periodic trends on structural and spectroscopic properties are examined through complete active space self-consistent field (CASSCF) followed by second-order N-electron valence perturbation theory (NEVPT2) including both scalar relativistic and spin-orbit coupling effects. Energies and wave functions from electronic structure calculations are further analyzed in terms of ab initio ligand field theory (AILFT), which allows one to rigorously extract angular overlap model ligand field, Racah, and spin-orbit coupling parameters directly from high-level ab initio calculations. We investigated the elpasolite Cs2NaLn(III)Cl6 (Ln(III) = Ce-Nd, Sm-Eu, Tb-Yb) crystals because these compounds have been synthesized for most Ln(III) ions. Cs2NaLn(III)Cl6 elpasolites have been also thoroughly characterized with respect to their spectroscopic properties, providing an exceptionally vast and systematic experimental database allowing one to analyze the periodic trends across the lanthanide series. Particular attention was devoted to the apparent discrepancy in metal-ligand covalency trends between theory and spectroscopy described in the literature. Consistent with earlier studies, natural population analysis indicates an increase in covalency along the series, while a decrease in both the nephelauxetic (Racah) and relativistic nephelauxetic (spin-orbit coupling) reduction with increasing atomic number is calculated. These apparently conflicting results are discussed on the basis of AILFT parameters. The AILFT derived parameters faithfully reproduce the underlying multireference electronic structure calculations. The remaining discrepancies with respect to experimentally derived data are mostly due to underestimation of the ligand field splittings, while the dynamic correlation and nephelauxetic effects appears to be adequately covered by CASSCF/NEVPT2.

Accurate and timely traffic flow forecasting is a critical task of the intelligent transportation system (ITS). The predicted results offer the necessary information to support the decisions of administrators and travelers. To investigate trend and periodic characteristics of traffic flow and develop a more accurate prediction, a novel method combining periodic-trend decomposition (PTD) is proposed in this paper. This hybrid method is based on the principle of &ldquo, decomposition first and forecasting last&rdquo, The well-designed PTD approach can decompose the original traffic flow into three components, including trend, periodicity, and remainder. The periodicity is a strict period function and predicted by cycling, while the trend and remainder are predicted by modelling. To demonstrate the universal applicability of the hybrid method, four prevalent models are separately combined with PTD to establish hybrid models. Traffic volume data are collected from the Minnesota Department of Transportation (Mn/DOT) and used to conduct experiments. Empirical results show that the mean absolute error (MAE), mean absolute percentage error (MAPE), and mean square error (MSE) of hybrid models are averagely reduced by 17%, 17%, and 29% more than individual models, respectively. In addition, the hybrid method is robust for a multi-step prediction. These findings indicate that the proposed method combining PTD is promising for traffic flow forecasting.

Trend and seasonality are the most prominent features of economic time series that are observed at the subannual frequency. Modeling these components serves a variety of analytical purposes, including seasonal adjustment and forecasting. In this paper we introduce unobserved components models for which both the trend and seasonal components arise from systematically sampling a multivariate transition equation, according to which each season evolves as a random walk with a drift. By modeling the disturbance covariance matrix we can encompass traditional models for seasonal time series, like the basic structural model, and can formulate more elaborate ones, dealing with season specific features, such as seasonal heterogeneity and correlation, along with the different role of the nonstationary cycles defined at the fundamental and the harmonic frequencies in determining the shape of the seasonal pattern.

To extract the temperature effect component of the dynamic strain signal through empirical mode decomposition (EMD), which presents the shape of a cycle trend measured from a bridge, the intrinsic mode function (IMF) order number by which temperature strain is constructed should be ascertained. The problem is solved on the basis of the selection of the IMF order threshold. The energy of signal of the IMF is analyzed in the time and frequency domains, and the threshold of the IMF order is acquired through a synthetic analysis of the energy catastrophe order and the correlation coefficient of the Hilbert marginal spectrum. Finally, the temperature effect component of the strain data is extracted by selecting the cycle trend of the IMF according to the IMF order threshold. The result shows that (1) the periodic trend component of a dynamic strain leads to the order catastrophe of the IMF energy from which the value range of the IMF order threshold is preliminarily determined; (2) the correlation coefficient of the IMF marginal spectrum increases rapidly to over 0.8 by analyzing the energy distribution in the frequency domain of the IMF located in a preliminarily determined range. The energy distribution patterns of last-order IMFs are consistent. By applying the method to the in-situ data, the result demonstrates that the IMF order threshold can be precisely obtained by the first correlation coefficient of the IMFs marginal spectrum of over 0.8. After the temperature effect component is extracted based on the threshold, the live load information in the dynamic strain is properly retained.

This chapter proposed a new method: Detrended Moving-average Cross-correlation Analysis (DMCA) to detect the power-law cross-correlation between two correlated non-stationary time series by combining Detrended Cross-Correlation Analysis (DCCA) and Detrended Moving Average (DMA). In order to compare the performance of DMCA and DCCA in the detection of cross-correlation, and to estimate the influence of periodic trend, we generate two cross-correlated time series \( x(i) \) and \( y(i) \) by a periodic two-component fractionally autoregressive integrated moving average (ARFIMA) process. Then we apply both methods to quantify the cross-correlations of the generated series, whose theoretical values are already known to us. By comparing the results we obtained, we find that the performance of this new approach is comparable to DCCA with less calculating amounts; our method can also reduce the impact of trends; furthermore, DMCA (for background and forward moving average case) outperforms DCCA in more accurate estimation when the analyzed times series are short in length. To provide an example, we also apply this new method to the time series of the real-world data from Brent and WTI crude oil spot markets, to investigate the complex cross-market correlation between these commodity markets. In all, our method is another practical choice to detect the cross-correlation between two short period non-stationary time series, and has potential application to real world problems.

Ability to detect potential space-time clusters in spatio-temporal data on disease occurrences is necessary for conducting surveillance and implementing disease prevention policies. Most existing techniques use geometrically shaped (circular, elliptical or square) scanning windows to discover disease clusters. In certain situations, where the disease occurrences tend to cluster in very irregularly shaped areas, these algorithms are not feasible in practise for the detection of space-time clusters. To address this problem, a new algorithm is proposed, which uses a co-clustering strategy to detect prospective and retrospective space-time disease clusters with no restriction on shape and size. The proposed method detects space-time disease clusters by tracking the changes in space–time occurrence structure instead of an in-depth search over space. This method was utilised to detect potential clusters in the annual and monthly malaria data in Khyber Pakhtunkhwa Province, Pakistan from 2012 to 2016 visualising the results on a heat map. The results of the annual data analysis showed that the most likely hotspot emerged in three sub-regions in the years 2013-2014. The most likely hotspots in monthly data appeared in the month of July to October in each year and showed a strong periodic trend.

The network robustness is defined by how well its vertices are connected to each other to keep the network strong and sustainable. The change of network robustness may reveal events as well as periodic trend patterns that affect the interactions among vertices in the network. The evaluation of network robustness may be helpful to many applications, such as event detection, disease transmission, and network security, etc. There are many existing metrics to evaluate the robustness of networks, for example, node connectivity, edge connectivity, algebraic connectivity, graph expansion, R-energy, and so on. It is a natural and urgent problem how to choose a reasonable metric to effectively measure and evaluate the network robustness in the real applications. In this paper, based on some general principles, we design and implement a benchmark, namely BMNR, for the metrics of network robustness. The benchmark consists of graph generator, graph attack and robustness metric evaluation. We find that R-energy can evaluate both connected and disconnected graphs, and can be computed more efficiently.

Microkinetics simulations are presented based on DFT-determined elementary reaction steps of the Fischer-Tropsch (FT) reaction. The formation of long-chain hydrocarbons occurs on stepped Ru surfaces with CH as the inserting monomer, whereas planar Ru only produces methane because of slow CO activation. By varying the metal-carbon and metal-oxygen interaction energy, three reactivity regimes are identified with rates being controlled by CO dissociation, chain-growth termination, or water removal. Predicted surface coverages are dominated by CO, C, or O, respectively. Optimum FT performance occurs at the interphase of the regimes of limited CO dissociation and chain-growth termination. Current FT catalysts are suboptimal, as they are limited by CO activation and/or O removal. State-of-the-art quantum-chemical reaction data were used in a microkinetics simulations study to elucidate the different fundamental kinetic regimes underlying Fischer-Tropsch activity and selectivity. Based on the nature of the rate-controlling steps, three regimes were identified: I) monomer formation, II) chain-growth termination, and III) water formation.

The noble gas binding ability of CN3Be3(+) clusters was assessed both by ab intio and density functional studies. The global minimum structure of the CN3Be3(+) cluster binds with four noble-gas (NG) atoms, in which the Be atoms are acting as active centers. The electron transfer from the noble gas to the Be atom plays a key role in binding. The dissociation energy of the Be-NG bond gradually increases from He to Rn, maintaining the periodic trend. The HOMO-LUMO gap, an indicator for stability, gives additional insight into these NG-bound clusters. The temperature at which the NG-binding process is thermodynamically feasible was identified. In addition, we investigated the stability of two new neutral NG compounds, (NG)BeSe and (NG)BeTe, and found them to be suitable candidates to be detected experimentally such as (NG)BeO and (NG)BeS. The dissociation energies of the Be-NG bond in monocationic analogues of (NG)BeY (Y=O, S, Se, Te) were found to be larger than in the corresponding neutral counter-parts. Finally, the higher the positive charge on the Be atoms, the higher the dissociation energy for the Be-NG bond becomes.

Trends in structure and bonding in a series of metal cubane clusters are examined using broken-symmetry density functional theory. For the metal–sulfur clusters, (C5H5)4Mo4S4 and (C5H5)4Cr4S4, the twelve cluster valence electrons are delocalised in six metal–metal single bonds, giving an approximately tetrahedral metal core. In (C5H5)4Cr4O4, however, no strong Cr–Cr bonds are present, and three cluster valence electrons remain localised on each of the chromium centres. Antiferromagnetic coupling across four of the six edges of the tetrahedron, and ferromagnetic coupling across the remaining two give rise to a spin-singlet ground state and a distinct rhombic distortion. The driving force for the distortion is only 12 kJ mol–1, and consequently inter- and intra-molecular steric effects may play a major role in determining the structure of the cluster in the solid state. Both chromium clusters have low-lying excited states in which the bonding pattern is completely reversed, with six Cr–Cr bonds present in (C5H5)4Cr4O4 but none in (C5H5)4Cr4S4. In each case the excited state lies less than 45 kJ mol–1 above the ground state, despite the fact that a substantial structural rearrangement is involved. Changes in metal–metal bond strength and spin polarisation energy are found to contribute approximately equally to the periodic trend towards electron localisation in the chromium clusters.

Hyperconjugation underlies many chemical phenomena of fundamental and practical importance. Owing to a great deal of interest in the anomeric effect, anomeric-like hyperconjugative effects have been thoroughly investigated in oxygen-containing systems. However, such interactions in the second- and third-row chalcogens are less well-understood and have generated some controversy. Here, we show that the conformational deuterium isotope effect, in combination with Saunders' isotopic perturbation method, permits sensitive and direct experimental probing of the conformational equilibria in dioxane, dithiane, and diselenane analogues by variable-temperature, dynamic NMR spectroscopy. We find that the magnitude of the conformational deuterium isotope effect is 252.1, 28.3, and 7.1 J/mol (±10%) for the oxygen, sulfur, and selenium analogues, respectively. These results reveal the periodic trend for hyperconjugation in the chalcogens, which reflect a decreasing n(x)→σ(C-H(D)) interaction throughout the period, as supported by IR spectroscopy and in agreement with DFT calculations and a natural bond order analysis.

Detrended cross-correlation analysis (DCCA) is a scaling method commonly used to estimate long-range power law cross-correlation in non-stationary signals. However, the susceptibility of DCCA to trends makes the scaling results difficult to analyze due to spurious crossovers. We artificially generate long-range cross-correlated signals and systematically investigate the effect of linear, exponential and periodic trends. Specifically to the crossovers raised by trends, we apply empirical mode decomposition method which decomposes underlying signals into several intrinsic mode functions (IMF) and a residual trend. After the removal of residual term, strong and monotonic trends such as linear and exponential trends are successfully eliminated. But periodic trend cannot be separated out according to the criterion of IMF, which can be eliminated by Fourier transform. As a special case of DCCA, detrended fluctuation analysis presents similar results.

We proposed a new method: Detrended Moving-average Cross-correlation Analysis (DMCA) to detect the power-law cross-correlation between two correlated non-stationary time series by combining Detrended Cross-Correlation Analysis (DCCA) and Detrended Moving Average (DMA). In order to compare the performance of DMCA and DCCA in the detection of cross-correlation, and to estimate the influence of periodic trend, we generate two cross-correlated time series x ( i ) and y ( i ) by a periodic two-component fractionally autoregressive integrated moving average (ARFIMA) process. Then we apply both methods to quantify the cross-correlations of the generated series, whose theoretical values are already known to us. By comparing the results we obtained, we find that the performance of this new approach is comparable to DCCA with less calculating amounts; our method can also reduce the impact of trends; furthermore, DMCA (for background and forward moving average case) outperforms DCCA in more accurate estimation when the analyzed times series are short in length. To provide an example, we also apply this new method to the time series of the real-world data from Brent and WTI crude oil spot markets, to investigate the complex cross-market correlation between these commodity markets. In all, our method is another practical choice to detect the cross-correlation between two short period non-stationary time series, and has potential application to real world problems.

Multifractal detrended cross-correlation analysis (MF-DXA) has been developed to detect the long-range power-law cross-correlation of considered signals in the presence of non-stationarity. However, crossovers arising from extrinsic periodic trends make the scaling behavior difficult to analyze. We introduce a Fourier filtering method to eliminate the trend effects and systematically investigate the multifractal cross-correlation of simulated and real traffic signals. The crossover locations are found approximately corresponding to the periods of underlying trend. Traffic velocity on one road and flows on adjacent roads show strong cross-correlation. They also present weak multifractality after periodic trends are removed. The traffic velocity and flow are cross-correlated in opposite directions which is accordant to their actual evolution.

Rescaled range analysis (R/S analysis), detrended fluctuation analysis (DFA) and detrended moving average (DMA) are widely-used methods for detection of long-range correlations in time series. Detrended cross-correlation analysis (DCCA) is a recently developed method to quantify the cross-correlations of two non-stationary time series. Another method for studying auto-correlations and cross-correlations was presented by Sergio Arianos and Anna Carbone in 2009. Recent studies have reported the susceptibility of this methods to periodic trends, which can result in spurious crossovers. In this paper, we propose the modified methods base on Laplace transform to minimizing the effect of periodic trends. The effectiveness of our techniques are demonstrated on stock data corrupted with periodic trends.

Trends within a hydrologic time series can significantly influence the scaling results of fluctuation analysis, such as rescaled range (RS) analysis and (multifractal) detrended fluctuation analysis (MF-DFA). Therefore, removal of trends is important in the study of scaling properties of the time series. In this study, three detrending methods, including adaptive detrending algorithm (ADA), Fourier-based method, and average removing technique, were evaluated by analyzing numerically generated series and observed streamflow series with obvious relative regular periodic trend. Results indicated that: (1) the Fourier-based detrending method and ADA were similar in detrending practices, and given proper parameters, these two methods can produce similarly satisfactory results; (2) detrended series by Fourier-based detrending method and ADA lose the fluctuation information at larger time scales, and the location of crossover points is heavily impacted by the chosen parameters of these two methods; and (3) the average removing method has an advantage over the other two methods, i.e., the fluctuation information at larger time scales is kept well-an indication of relatively reliable performance in detrending. In addition, the average removing method performed reasonably well in detrending a time series with regular periods or trends. In this sense, the average removing method should be preferred in the study of scaling properties of the hydrometeorolgical series with relative regular periodic trend using MF-DFA.

The structure, stability, and thermochemistry of the H(MF3)+ isomers (M = N–Bi) have been investigated by MP2 and coupled cluster calculations. All the HF–MF2+ revealed weakly bound ion–dipole complexes between MF2+ and HF. For M = N, As, Sb, and Bi they are more stable than the H–MF3+ covalent structures (free energy differences) by 6.3, 14.3, 32.1, and 73.5 kcal mol−1, respectively. H–PF3+ is instead more stable than HF–PF2+ by 21.8 kcal mol−1. The proton affinities (PAs) of MF3 at the M atom range from 91.9 kcal mol−1 (M = Bi) to 156.5 kcal mol−1 (M = P), and follow the irregular periodic trend BiF3