Dispersion Integral Research Articles

Impact of correlations between a_{mu } and alpha _text {QED} on the EW fit

We study the potential impact on the electroweak (EW) fits due to the tensions between the current determinations of the hadronic vacuum polarisation (HVP) contributions to the anomalous magnetic moment of the muon (a_{mu }), based on either phenomenological dispersion integrals using measured hadronic spectra or on Lattice QCD calculations. The impact of the current tension between the experimental measurement of a_{mu } and the total theoretical prediction based on the phenomenological calculations of the HVP is also studied. The correlations between the uncertainties of the theoretical predictions of a_{mu } and of the running of alpha _mathrm{QED} are taken into account in the studies. We conclude that the impact on the EW fit can be large in improbable scenarios involving global shifts of the full HVP contribution, while it is much smaller if the shift is restricted to a lower mass range and/or if the shift in alpha _text {QED} is obtained from that in a_{mu } through appropriate use of the correlations. Indeed, the latter scenarios only imply at most a 2.6/16 increase in the chi ^2/text {n.d.f.} of the EW fits and relatively small changes for the resulting fit parameter values.

Changes in the Electrical Activity of the Brain in the Alpha and Theta Bands during Prayer and Meditation.

Focused attention meditation (FAM) is a category of meditation based on an EEG pattern, which helps the wandering mind to focus on a particular object. It seems that prayer may, in certain respects, be similar to FAM. It is believed that emotional experience correlates mainly with theta, but also with selective alpha, with internalized attention correlating mainly with the synchronous activity of theta and alpha. The vast majority of studies indicate a possible impact of transcendence in meditation on the alpha wave in EEG. No such reports are available for prayer. Seventeen women and nineteen men aged 27–64 years with at least five years of intensive meditation/prayer experience were recruited to participate in the study. We identified the two largest groups which remained in the meditation trend originating from the Buddhist system (14 people) (Buddhist meditators) and in the Christian-based faith (15 people) (Christian meditators). EEG signal was recorded with open eyes, closed eyes, during meditation/prayer, and relaxation. After the EEG recording, an examination was conducted using the Scale of Spiritual Transcendence. Buddhist meditators exhibited a statistically significantly higher theta amplitude at Cz during meditation compared to relaxation. Meanwhile, spiritual openness favored a higher theta amplitude at Pz during relaxation. Our study did not reveal statistically significant differences in frontal areas with regard to alpha and theta, which was often indicated in previous studies. It seems necessary to analyze more closely the midline activity in terms of dispersed neural activity integration.

Tailoring electron transfer with Ce integration in ultrathin Co(OH)2 nanosheets by fast microwave for oxygen evolution reaction

The vertically stacked ultra-thin Co(OH) 2 nanosheets endow the good dispersion of Ce doping. The close integration of Ce into Co(OH) 2 assisted by microwave synthesis promotes electron transfer through “ d – f electronic ladders”, contributing to enhanced OER. • Loose Co(OH) 2 facilitates the diffusion of Ce for large active surface and defects. • Ce incorporation is achieved by high pressure microwave with instantaneous heating. • The intimate CeOx/Co(OH) 2 may tailor electron transfer by “d-f electron ladders”. • The optimized Ce0.21@Co(OH) 2 exhibits excellent activity and stability for OER. The intrinsic activity of Co(OH) 2 for oxygen evolution reaction (OER) may be elaborately improved through the suitable valence adjustment. Ce modification at electronic level is proved to be an efficient strategy owing to the flexible transformation of Ce 3+ /Ce 4+ . Herein, Ce 0.21 @Co(OH) 2 with the optimized Ce doping have been fabricated to tailor the fast electron transfer for the enhanced activity and stability for OER. Firstly, the obtained core–shell structure composed of vertical loose Co(OH) 2 sheets not only exposes a large number of active sites, but also provides channels for Ce doping. Secondly, the high pressure microwave with instantaneous heating can fast introduce Ce into Co(OH) 2 , obtaining Ce x @Co(OH) 2 with well dispersion and close integration. The intimated interaction between Ce and Co species may provide the “ d–f electronic ladders” for accelerating electron transfer of the catalytic surface. Meanwhile, Ce promotes the formation of Co-superoxide intermediate and/or the release of oxygen, which is considered to be the rate-determining step for OER. The electrochemical measurements confirmed the low overpotential of 300 mV at 10 mA cm −2 and great stability of Ce 0.21 @Co(OH) 2 for OER. This work demonstrates a meaningful approach to realize the tuned electronic structure through metal doping.

Photocured conductive PANI/acrylate composites for digital light processing. Influence of HDODA crosslinker in rheological and physicochemical properties

The design of novel photocurable conductive acrylic composites demands thorough research to find appropriate balance between the relative concentrations of monofunctional/ multifunctional monomers, photoinitiators and conductive filler, besides adjusting polymerization conditions. Likewise, when an intrinsically conductive polymer such as polyaniline (PANI) is selected as conductive filler, the homogeneous distribution of its nanometric aggregates is essential to prevent heterogeneous curing due to its strong UV absorption. In this work, the influence of PANI-HCl on the physical properties of acrylic composites based on Ethyleneglycolphenylether acrylate (EGPEA) and Diphenyl(2,4,6-trimethylbenzoyl)phosphine oxide (TPO), photoinitiator, was examined in the frame-work of the percolation model. Rheological testing combined with Scanning Electron Microscopy (SEM) were used for efficient control of the filler dispersion in order to better understand the electrical conductivity-structure behaviour. Infrared Spectroscopy probed the degree of monomer conversion and the filler interaction with the polymer matrix, whereas the thermal properties were evaluated with the aim of establishing the maximum working temperatures. Above the percolation threshold, the formulation with 4.8 wt% PANI was selected as the most suitable composition achieving maximum conductivity (10-3 S cm−1) at the lowest PANI content. The problem of excessive aggregation of PANI clusters was tackled by the addition of a 15 wt% of the reactive diluent 1,6-hexanediol diacrylate (HDODA) to the previous formulation. The outcomes were improved dispersion and better integration of PANI nanorods within the acrylic matrix plus a smoother film surface, while retaining high electrical conductivity. The viscosity of the selected prepolymer formulations and penetration depth of UV photons gave encouraging results for the use of the developed compositions as anticorrosion coatings, digital light processing (DLP) or piezoelectric sensors. The high critical cure dosages obtained will be easily overcome by adjusting the type and/or amount of photoinitiator.

A new evaluation of the hadronic vacuum polarisation contributions to the muon anomalous magnetic moment and to varvec{alpha }({{varvec{m}}}_{{varvec{Z}}}^2)

We reevaluate the hadronic vacuum polarisation contributions to the muon magnetic anomaly and to the running of the electromagnetic coupling constant at the Z-boson mass. We include newest e^+e^- rightarrow mathrm{hadrons} cross-section data together with a phenomenological fit of the threshold region in the evaluation of the dispersion integrals. The precision in the individual datasets cannot be fully exploited due to discrepancies that lead to additional systematic uncertainty in particular between BABAR and KLOE data in the dominant pi ^+pi ^- channel. For the muon (g-2)/2, we find for the lowest-order hadronic contribution (694.0 pm 4.0)cdot 10^{-10}. The full Standard Model prediction differs by 3.3sigma from the experimental value. The five-quark hadronic contribution to alpha (m_Z^2) is evaluated to be (276.0pm 1.0)cdot 10^{-4}.

Impact of Dispersed Wind Farms’ Integration on Transient Stability of Interconnected Grid

In this paper, transient stability of wind farm based on Double-Fed Induction Generators is analyzed and discussed. The uncertainty of wind power production is a challenge to maintain the grid’s power stability. Thus, the contribution of integrating wind farms to the stability of the electrical systems during contingencies depends on several factors, including the location of the wind turbines in the electricity grid, the reliability of transmission lines, the relaying algorithms, the utilized protection devices and the wind turbines’ integration mode. This paper studies the benefits of wind turbines’ dispersed integration in the electrical grid by simulating transient stability voltage, current and rotor angle. Based on a real scenario involving a short circuit fault in the grid, a comparison between different types of wind turbines’ integration in the grid’s power has been established, using an optimal power flow calculation. In addition, this work discusses the reduction of power generation costs, based on the cubic cost model, which has been achieved by integrating the wind farm and comparing the production cost to the conventional power plants’. The aim of this article is to prove that the integration of wind farms in dispersed mode can be used as an alternative solution since it stabilizes grid parameters during strong transients. In fact, the response of active and reactive power to the output of the wind farm is stable during short-circuit faults, it minimizes the tripping events in the grid, it reduces energy losses, and ultimately it decreases energy production costs by optimizing the power flow when injected into high-demand PQ buses.

Nonlinearity- and dispersion- less integrated optical time magnifier based on a high-Q SiN microring resonator

The ability to measure optical signals with fast dynamics is of significant interest in many application fields. Usually, single-shot measurements of non-periodic signals can be enabled by time magnification methods. Like an optical lens in the spatial domain, a time magnifier, or a time lens, stretches a signal in the time domain. This stretched signal can then be further processed with low bandwidth photonics and electronics. For a robust and cost-effective measurement device, integrated solutions would be especially advantageous. Conventional time lenses require dispersion and nonlinear optical effects. Integration of a strong dispersion and nonlinearities is not straightforward on a silicon photonics platform and they might lead to signal distortions. Here we present a time magnifier based on an integrated silicon nitride microring resonator and frequency-time coherence optical sampling, which requires neither a dispersion, nor a nonlinearity. Sampling of signals with up to 100 GHz bandwidth with a stretching factor of more than 100 is achieved using low bandwidth measurement equipment. Nevertheless, with already demonstrated integrated 100 GHz modulators, the method enables the measurement of signals with bandwidths of up to 400 GHz. Since amplitude and phase can be sampled, a combination with the spectrum slicing method might enable integrated, cost-effective, small-footprint analog-to-digital converters, and measurement devices for the characterization of single irregular optical signals with fast dynamics and bandwidths in the THz range.

Risk management of manufacturing multinational corporations: the moderating effects of international asset dispersion and supply chain integration

PurposeThe purpose of this study is to investigate the contingencies of supply chain risk management (SCRM) in manufacturing multinational corporations (MNCs) by exploring the moderating role of international asset dispersion in the performance effect of SCRM, as well as the counteraction effect of supply chain integration (SCI).Design/methodology/approachMulti-country survey data from a sample of 378 responses collected by the sixth round International Manufacturing Strategy Survey were analyzed. Hierarchical regression analysis was conducted to test the proposed hypotheses.FindingsThe results demonstrate that SCRM improves the operational effectiveness of manufacturing MNCs but this performance effect is attenuated by international asset dispersion. Nevertheless, external integration can counteract the negative effect of international asset dispersion and ensure the efficacy of SCRM practices.Practical implicationsThe results of this study provide suggestions for supply chain managers of manufacturing MNCs to better conduct SCRM practices under the condition of dispersed international assets. Besides, supply chain managers can leverage external integration to ensure the efficacy of SCRM practices.Originality/valueAlthough there are plenty of studies on the relationship between SCRM and operational performance, prior findings are inconsistent. This study sheds light on the SCRM-operational performance relationship by considering how a manufacturing MNC’s international asset dispersion can influence the efficacy of SCRM practices and how SCI can attenuate the negative effect of international asset dispersion.

Advancing an interdisciplinary framework to study seed dispersal ecology.

Although dispersal is generally viewed as a crucial determinant for the fitness of any organism, our understanding of its role in the persistence and spread of plant populations remains incomplete. Generalizing and predicting dispersal processes are challenging due to context dependence of seed dispersal, environmental heterogeneity and interdependent processes occurring over multiple spatial and temporal scales. Current population models often use simple phenomenological descriptions of dispersal processes, limiting their ability to examine the role of population persistence and spread, especially under global change. To move seed dispersal ecology forward, we need to evaluate the impact of any single seed dispersal event within the full spatial and temporal context of a plant’s life history and environmental variability that ultimately influences a population’s ability to persist and spread. In this perspective, we provide guidance on integrating empirical and theoretical approaches that account for the context dependency of seed dispersal to improve our ability to generalize and predict the consequences of dispersal, and its anthropogenic alteration, across systems. We synthesize suitable theoretical frameworks for this work and discuss concepts, approaches and available data from diverse subdisciplines to help operationalize concepts, highlight recent breakthroughs across research areas and discuss ongoing challenges and open questions. We address knowledge gaps in the movement ecology of seeds and the integration of dispersal and demography that could benefit from such a synthesis. With an interdisciplinary perspective, we will be able to better understand how global change will impact seed dispersal processes, and potential cascading effects on plant population persistence, spread and biodiversity.

The multi-Regge limit of the eight-particle amplitude beyond leading logarithmic accuracy

We present the computation of the eight-particle three-loop amplitude beyond leading logarithmic accuracy in the multi-Regge limit of planar mathcal{N} = 4 Super Yang-Mills theory. Starting from the all-loop dispersion integral form of the amplitude, we consider the eight-particle case and by analyzing said dispersion integral we associate it to a well-defined Fourier-Mellin transform. By using the properties of the Fourier-Mellin representation and its convolution product structure, we compute the three-loop eight-particle MHV amplitude at next-to-leading logarithmic accuracy. From this MHV result, we obtain the three-loop eight particle amplitude in multi-Regge kinematics for all helicity configurations, including next-to-next-to-MHV. Finally, we find that the result is described by combinations of single-valued multiple polylogarithms of uniform weight, the leading singularity structure of which corresponds to the classification shown at leading logarithmic accuracy.

Optimization modeling method for coal-to-electricity heating load considering differential decisions

Heating by electricity rather than coal is considered one effective way to reduce environmental problems. Thus, the electric heating load is growing rapidly, which may cause undesired problems in distribution grids because of the randomness and dispersed integration of the load. However, the electric heating load may also function as an energy storage system with optimal operational control. Therefore, the optimal modeling of electric heating load characteristics, considering its randomness, is important for grid planning and construction. In this study, the heating loads of distributed residential users in a certain area are modeled based on the Fanger thermal comfort equation and the predicted mean vote thermal comfort index calculation method. Different temperatures are considered while modeling the users’ heating loads. The heat load demand curve is estimated according to the time-varying equation of interior temperature. A multi-objective optimization model for the electric heating load with heat energy storage is then studied considering the demand response (DR), which optimizes economy and the comfort index. A fuzzy decision method is proposed, considering the factors influencing DR behavior. Finally, the validity of the proposed model is verified by simulations. The results show that the proposed model performs better than the traditional method.

Relativistic finite-nuclear-size corrections to the energy levels in light muonic atoms

We consider higher-order finite-nuclear-size (FNS) contributions to the energy levels of light ordinary and muonic hydrogenlike atoms. Relativistic corrections to the leading FNS term have been known in terms of an integration in coordinate space. The related results are model dependent. In the meantime, if the data on the nuclear structure are obtained from electron-nucleus scattering, it is a representation of the electric charge form factor in momentum space rather than the charge density. An example is the case of a proton as a nucleus. Often the electric form factor is presented in terms of a dispersion integral or a Pad\'e approximation. We present explicit results for such representations for leading finite-nuclear-size higher-order (in $Z\ensuremath{\alpha}$ and in $Z\ensuremath{\alpha}m{R}_{N}$) corrections beyond the leading FNS term.

Gas dispersion and deflagration above sea from subsea release and its impact on offshore platform

Flammable gas dispersion and deflagration above sea resulting from subsea release have the possibility to cause an adverse impact on the operation safety of surface vessels. This paper presents a systematic simulation of gas dispersion and deflagration above sea from a subsea release using CFD-based approach, aiming to study the evolution process of accident scenario and assess its impact on surface vessels. A jack-up drilling platform is used as a case to discuss the impact of gas dispersion and deflagration. The uniqueness of this study is the integration of release, dispersion, and deflagration scenarios. The simulation includes the modelling of wind flow, gas dispersion and subsequent deflagration due to accidental ignition. The wind flow above sea surface is given using wind speed profile equation to generate steady wind field around offshore platform. Simulation of gas dispersion is conducted based on the generated wind field. The development of flammable gas cloud is predicted, and the dangerous area on offshore platform is assessed. Considering the appearance of ignition source, a deflagration simulation based on dispersion results is performed to predict the consequences including overpressure, high temperature, and heat radiation. Eventually, the damage criterion is utilized to evaluate their impact on offshore platform.

The seven-gluon amplitude in multi-Regge kinematics beyond leading logarithmic accuracy

We present an all-loop dispersion integral, well-defined to arbitrary logarithmic accuracy, describing the multi-Regge limit of the 2 → 5 amplitude in planar mathcal{N}=4 super Yang-Mills theory. It follows from factorization, dual conformal symmetry and consistency with soft limits, and specifically holds in the region where the energies of all produced particles have been analytically continued. After promoting the known symbol of the 2-loop N -particle MHV amplitude in this region to a function, we specialize to N = 7, and extract from it the next-to-leading order (NLO) correction to the BFKL central emission vertex, namely the building block of the dispersion integral that had not yet appeared in the well-studied six-gluon case. As an application of our results, we explicitly compute the seven-gluon amplitude at next-to-leading logarithmic accuracy through 5 loops for the MHV case, and through 3 and 4 loops for the two independent NMHV helicity configurations, respectively.

A numerical fire simulation approach for effectiveness analysis of fire safety measures in floating liquefied natural gas facilities

Fire remains a serious threat to a floating liquefied natural gas facility. It is of greater concern given the remote locations and limited accessibility of emergency services. This study aims to present a rigorous procedure to study potential accident scenarios in an offshore (floating processing) facility with different ignition source locations and verify the effectiveness of safety measures using computational fluid dynamics code. The uniqueness of the present study is the integration of release, dispersion and fire modeling scenarios, simplifying the fire analysis and increasing its effectiveness from the offshore process system design and analysis perspectives. The first step of the procedure is to identify the range of potential release scenarios and their strength of dispersion in confined and semi-confined spaces. Subsequently, potential fire scenarios are analyzed considering the influence of the location. Computational fluid dynamics models are used to analyze these three steps of the scenarios. Application of the procedure is demonstrated on an offshore facility by analyzing 14 credible scenarios. The ranges of safety measures of these fires are also studied to determine their effectiveness to prevent fires and mitigate their impact. This study provides a simple and efficient way to analyze the impact of key design parameters. In this study, the transition from fire to explosion is not considered and all the environmental factors are assumed to be constants in the simulation.

Environmental mismatch results in emergence of cooperative behavior in a passerine bird

A major problem in the evolution of maternal effects is explaining the origin and persistence of maternally induced phenotypes that lower offspring fitness. Recent work focuses on the relative importance of maternal and offspring selective environments and the mismatch between them. However, an alternative approach is to directly study the origin and performance of offspring phenotypes resulting from mismatch. Here, we capitalize on a detailed understanding of the ecological contexts that provide both the cue and the functional context for expression of maternally induced offspring phenotypes to investigate the consequences of environmental mismatch. In western bluebirds, adaptive integration of offspring dispersal and aggression is induced by maternal competition over nest cavities. When nest cavities are locally abundant, mothers produce nonaggressive offspring that remain in their natal population, and when nest cavities are scarce, mothers produce aggressive dispersers. However, a few offspring neither disperse nor breed locally, instead helping at their parent’s nest, and as a result these offspring have unusually low fitness. Here, we investigate whether females produce helpers to increase their own fitness, or whether helpers result from a mismatch between the cues mothers experience during offspring production and the breeding environment that helpers later encounter. We found that producing helpers does not enhance maternal fitness. Instead, we show that helpers, which were the least aggressive of all returning sons in the population, were most common when population density increased from the time sons were produced to the time of their reproductive maturity, suggesting that the helper phenotype emerges when cues of resource competition during offspring development do not match the actual level of competition that offspring experience. Thus, environmental mismatch might explain the puzzling persistence of maternally induced phenotypes that decrease offspring fitness.

Hadronic Leading Order Contribution to the Muon g-2

We calculate the Standard Model (SM) prediction for the muon anomalous magnetic moment. By using the latest experimental data for e+e- → hadrons as input to dispersive integrals, we obtain the values of the leading order (LO) and the next-to-leading-order (NLO) hadronic vacuum polarisation contributions as ahad, LO VPμ = (693:27 ± 2:46) × 10-10 and ahad, NLO VP μ = (_9.82 ± 0:04) × 1010-10, respectively. When combined with other contributions to the SM prediction, we obtain aμ(SM) = (11659182:05 ± 3.56) × 10-10; which is deviated from the experimental value by Δaμ(exp) _ aμ(SM) = (27.05 ± 7.26) × 10-10. This means that there is a 3.7 σ discrepancy between the experimental value and the SM prediction. We also discuss another closely related quantity, the running QED coupling at the Z-pole, α(M2 Z). By using the same e+e- → hadrons data as input, our result for the 5-flavour quark contribution to the running QED coupling at the Z pole is Δ(5)had(M2 Z) = (276.11 ± 1.11) × 10-4, from which we obtain Δ(M2 Z) = 128.946 ± 0.015.

Kaon transverse charge density from space- and timelike data

We used the world data on the kaon form factor to extract the transverse kaon charge density using a dispersion integral of the imaginary part of the kaon form factor in the timelike region. Our analysis includes recent data from $e^+e^-$ annihiliation measurements extending the kinematic reach of the data into the region of high momentum transfers conjugate to the region of short transverse distances. To calculate the transverse density we created a superset of both timelike and spacelike data and developed an empirical parameterization of the kaon form factor. The spacelike set includes two new data points we extracted from existing cross section data. We estimate the uncertainty on the resulting transverse density to be 5\% at $b$=0.025 fm and significantly better at large distances. New kaon data planned with the 12 GeV Jefferson Lab may have a significant impact on the charge density at distances of $b<$ 0.1fm.

Nucleon form factors in dispersively improved chiral effective field theory: Scalar form factor

We propose a method for calculating the nucleon form factors (FFs) of $G$-parity-even operators by combining Chiral Effective Field Theory ($\chi$EFT) and dispersion analysis. The FFs are expressed as dispersive integrals over the two-pion cut at $t > 4 M_\pi^2$. The spectral functions are obtained from the elastic unitarity condition and expressed as products of the complex $\pi\pi \rightarrow N\bar N$ partial-wave amplitudes and the timelike pion FF. $\chi$EFT is used to calculate the ratio of the partial-wave amplitudes and the pion FF, which is real and free of $\pi\pi$ rescattering in the $t$-channel ($N/D$ method). The rescattering effects are then incorporated by multiplying with the squared modulus of the empirical pion FF. The procedure results in a marked improvement compared to conventional $\chi$EFT calculations of the spectral functions. We apply the method to the nucleon scalar FF and compute the scalar spectral function, the scalar radius, the $t$-dependent FF, and the Cheng-Dashen discrepancy. Higher-order chiral corrections are estimated through the $\pi N$ low-energy constants. Results are in excellent agreement with dispersion-theoretical calculations. We elaborate several other interesting aspects of our method. The results show proper scaling behavior in the large-$N_c$ limit of QCD because the $\chi$EFT calculation includes $N$ and $\Delta$ intermediate states. The squared modulus of the timelike pion FF required by our method can be extracted from Lattice QCD calculations of vacuum correlation functions of the operator at large Euclidean distances. Our method can be applied to the nucleon FFs of other operators of interest, such as the isovector-vector current, the energy-momentum tensor, and twist-2 QCD operators (moments of generalized parton distributions).

AnQCD: A Mathematica package for calculations in general analytic QCD models (new version announcement)

A previously submitted Mathematica package (Ayala and Cvetič, 2015), which evaluates the QCD couplings in several analytic (holomorphic) versions of QCD, has been adjusted (anQCDv2.m) so that it now works in the newest version of Mathematica (version 11) as well. New version program summaryProgram Title: anQCDv2.m; and the supplementary packages s0r.m and Li__nu.mProgram Files doi:http://dx.doi.org/10.17632/vsnjr4bhr9.1Licensing provisions: GPLv3Programming language: Mathematica, versions 9, 10 and 11Supplementary material: file READMEanQCDv2Journal reference of previous version: Comput. Phys. Commun. 190 (2015) 182–199Does the new version supersede the previous version? For the use with Mathematica 11, yes.Reasons for the new version: The previous version (anQCD.m) does not work in Mathematica version 11.Summary of revisions: When calling the previous version (anQCD.m) with Mathematica 11, the message SystemException[“MemoryAllocationFailure”] appears, because version 11 of Mathematica apparently cannot deal efficiently with numerical dispersion integrals where the integration is over semiinfinite interval and is slowly converging. Therefore, in the new version, in the integrals J0[Nf] for the Two-delta analytic QCD model the upper integration bound is changed from ‘Infinity’ to $wmaxJ=108.5. This modification does not change the precision of evaluations in any significant manner.Nature of problem: Evaluation of spacelike physical QCD quantities D(Q2) (Q2≡−q2 nonnegative) in terms of a truncated perturbation series of the perturbative QCD coupling a(Q2)≡αs(Q2)∕π gives us a quantity which has singularities at low positive Q2, because a(Q2) has such singularities. This is incompatible with the holomorphic (analytic) properties of D(Q2) as required by the general principles of Quantum Field Theories. Further, for low |Q2| such evaluations give very unreliable results dominated by the vicinity of the mentioned (unphysical) singularities. However, if using instead a coupling A(Q2) which respects the mentioned analyticity properties in the complex Q2-plane, then such problems do not appear.Solution method: anQCDv2.m package evaluates the coupling A(Q2) and the analogs Aν(Q2) of the powers a(Q2)ν, for three versions of QCD with couplings with aforementioned analytic properties: Analytic Perturbation Theory (APT); Two-delta analytic QCD (2δanQCD); and Massive Perturbation Theory (MPT). The couplings are evaluated by numerical evaluation of the corresponding dispersion integrals.Reference:C. Ayala and G. Cvetič, anQCD: a Mathematica package for calculations in general analytic QCD models, Comput. Phys. Commun. 190 (2015) 182–199 [arXiv:1408.6868 [hep-ph]].