Chemical Processes - Science topic

An oxide that (if it was) is no longer a nanoentity.

you need to have a combination of FTIR, NMR and Mass Spectroscopy. Although any of them can confirm the purity however if possible go for minimum two of them.

According to the information contained in the paper entitled "Hydrogen Production: Thermochemical Water Splitting," prepared by the Office of Energy Efficiency and Renewable Energy, thermochemical water splitting uses high temperatures—from concentrated solar power or the waste heat of nuclear power reactions—and chemical reactions to produce hydrogen and oxygen from water. This long-term technology pathway has potentially low or no greenhouse gas emissions.

How Does It Work?

Thermochemical water-splitting processes use high-temperature heat (500°–2,000°C) to drive a series of chemical reactions that produce hydrogen. The chemicals used in the process are reused within each cycle, creating a closed loop that consumes only water and produces hydrogen and oxygen. The necessary high temperatures can be generated in the following ways:

Numerous solar thermochemical water-splitting cycles have been investigated for hydrogen production, each with different operating conditions, engineering challenges, and hydrogen production opportunities. Typically direct cycles are less complex with fewer steps, but they require higher operating temperatures compared with the more complicated hybrid cycles. More than 300 water-splitting cycles are described in the literature. For more information, see Solar Thermochemical Hydrogen Production Research: Thermochemical Cycle Selection and Investment Priority.

Why Is This Pathway Being Considered?

Because solar- and nuclear-driven high-temperature thermochemical water-splitting cycles produce hydrogen with near-zero greenhouse gas emissions using water and either sunlight or nuclear energy.

Challenges remain, however, in the research, development, and demonstration of commercially viable thermochemical cycles and reactors:

Exciting progress continues in this field, leveraging synergies with concentrated solar power technologies and emerging solar-fuel production technologies.

Dear Dol Lamsal,

The best and simplest choice for the phase-equilibrium calculations and studying such systems (Including Water+Alcohols+Hydrocarbons) is the CPA (Cubic Plus Association) equation of state. I suggest you verify the following references:

Its really serves as a good first estimate

Process Systems Engineering (PSE) cover these aspects. PSE is a new discipline at the interface of chemical/process engineering, computer sciences, and mathematics.

You can recent report published by The National Academic Press.

Please see attached.

Generally for the cement industry it is a stack emission at 10% O2 dry for 500 mg/NM3 of NOx as NO2. The Power Industry at least in Europe is 200

Thank you!

In order to produce a drug by fermentation, there must be an organism that has the necessary metabolic pathway, which would require a set of enzymes, one for each step in the biosynthesis. Synthetic small-molecule drugs that are not natural products are usually produced by chemical synthesis because there is no existing enzymatic pathway for their synthesis in vivo. However, one or more of the starting materials for the chemical synthesis may have a natural origin. Some drugs are chemically modified versions of natural products. In addition, individual steps in the chemical synthesis may be catalyzed by purified enzymes in vitro.

Suhaila Yaman

Heat in an inert atmosphere to 10⁰C below the melting point.

A lot of companies now require software skills along with chemical engineering knowledge. The most prominent one in them is Python. I have a lot of friends working on Python in process modeling & simulation etc.

Highly recommend reading "Molecular Fluorescence - Principles and Applications 2nd Ed. (2012)" written by Bernard Valeur and Mario N. Berberan-Santos. Chapters 1-3 give an excellent overview.

Dear Mohammad Jazirehpour many thanks for posting this interesting technical question. The preparation of Y(NO₃)₃􏰀x6H₂O powder has been reported in the article cited below. It was obtained by dissolving yttrium oxide in 6 M nitric acid:

From our own experinence I would suggest the following procedure: Place the nitric acid in a beaker and heat it to ca. 50-80 °C. With stirring, add a little more than the calculated amount of Y₂O₃ and let the mixture stir until most of the oxide has dissolved. A small excess of oxide is useful to completely consume the acid. Then filter the mixture and evaporate the clear filtrate until crystals begin to form. Pour the hot solution into a crystallization dish and let it stand at room temperature over night so that the remaining water evaporates. Then collect the product.

Good luck and best wishes, Frank Edelmann

Hello Jalali,

Kindly look at this paper

Polystyrene should be quite transparent in the NIR and has strong Raman peaks at ~1004 cm-1 and ~1585 cm-1. Plastic Petri dishes are made of Polystyrene.

https://ramanlife.com/library/polystyrene-raman/

Maybe you can consider the recursive least squares algorithm (RLS). RLS is the recursive application of the well-known least squares (LS) regression algorithm, so that each new data point is taken in account to modify (correct) a previous estimate of the parameters from some linear (or linearized) correlation thought to model the observed system. The method allows for the dynamical application of LS to time series acquired in real-time. As with LS, there may be several correlation equations with the corresponding set of dependent (observed) variables. For the recursive least squares algorithm with forgetting factor (RLS-FF), adquired data is weighted according to its age, with increased weight given to the most recent data.

Years ago, while investigating adaptive control and energetic optimization of aerobic fermenters, I have applied the RLS-FF algorithm to estimate the parameters from the K_La correlation, used to predict the O₂ gas-liquid mass-transfer, hence giving increased weight to most recent data. Estimates were improved by imposing sinusoidal disturbance to air flow and agitation speed (manipulated variables). Simulations assessed the effect of numerically generated white Gaussian noise (2-sigma truncated) and of first order delay. This investigation was reported at (MSc Thesis):

In my recent article on Heat balance in the oxygen steelmaking process, I have mentioned the values. Kindly find the attachment of the link.

Yes, K-Means OR Bayesian Classification framework of Maximum Likelihood Estimation.

following

Dear Dr. Zhong Chuyu ,

I agree with what Dr. Jhonatan Rodriguez-Pereira said.

For simplicity I would act by comparison and focus more on the morphological surface part (Optical Microscopy, Scanning Microscopy, Profilometry, etc.) acting on an unexposed sample and subsequently, trying to evaluate a well-defined area, I would evaluate different attack times in the liquid, compatibly with your needs.

My best regards, Pierluigi Traverso.

For those still interested. In addition to the suggestions given by Nicolas Tardiota some more references with related (background) info:

De Wolf, F. A. (2003). Chapter V Collagen and gelatin. In Progress in biotechnology (Vol. 23, pp. 133-218). Elsevier. (see enclosed file)

De Wolf, F. A., & Keller, R. C. A. (1996). Characterization of helical structures in gelatin networks and model polypeptides by circular dichroism. In Gels (pp. 9-14). Steinkopff.

Keller, R. C. A., & de Wolf, F. A. (1998). Characterization of helical junction zones in gelatin networks-A spectroscopic approach.

Best regards.

Dear Ammar, Chemical activation is much efficient than thermal activation. However, there are some negatives to chemical activation. Depending upon your end application you can select activation methods. Moreover, chemical activated carbon is not suitable for drinking water purification.

This may be unrelated to your problem, but... If by nonlinear and chemical you mean something other than ideal gases, there's a problem. If the fugacity coefficient (indicative of chemical activity) is less than unity, the Gibbs problem (free energy minimization - the driving force and direction of the reaction) is ill-conditioned. The solution is free if you're interested in this aspect of reactions.

Beer fermentation is anaerobic process and the conventional method is submerged free yeast fermentation . You can try immobilized yeast processing in submerged system or on immobilized column.

Dear Branislav Jeremić

You can check journals list and their ranking here https://www.scimagojr.com/journalrank.php?category=2606

Best regards, Amin.

For a somewhat related RG discussion: https://www.researchgate.net/post/Why_flame_synthesized_soot_is_more_stably_adhere_at_quartz_glass_than_amorphous_glass

Thank you Erik Kouba Kouba

Hey all, in order to open the discussion, you'll need to be aware of a few basic principles: a) patentability conditions, b) freedom-to-operate & doctrine of equivalence and c) exceptions of patentability.

a) a patent can be granted when your 'technical' invention is 1° new, 2° inventive and 3° industrial applicable. This third condition is 'here' important here because when talking about algorithms and mathematical formulae, they should be implemented in a particular application, such as a device, an apparatus, a process, etc. More particularly it is not enough to explain only the theoretical background, then you can choose for a scientific publication.

b) be aware of these already patented models, and you'll have to determine their scope of protection. When they claimed broadly and you use these already claimed features (in valid patents, covering your geographical market), you can be attacked for infringement, when entering these markets! So, you'll have to check your freedom-to-operate (FTO) for vending your product, with or without your own patent. Moreover, you can also be accused based on the doctrine of equivalence, when not exactly the same features of the patented technologies of others, but applying the spirit of invention even with your own slight differences. When you solve the same problem in a small different way, applying the fundamentals of the patented technologies, you'll need their authorisation to commercialize, like a license. A profound patent study is required here.

c) some 'non-technical' issues are not patentable, or at least open for discussion. This is i.a. the case with computer implemented inventions (software). This is mentioned in art.52 EPC (European Patent Convention): https://www.epo.org/law-practice/legal-texts/html/epc/2016/e/ar52.html. More specifically, art. 52 (2) (a) en (c) are important here. In the US: https://www.uspto.gov/web/offices/pac/mpep/consolidated_laws.pdf, art. 35 U.S.C. 101 and 103 are important. However, it could give you the impression that patentability is easier, less exclusions, etc... Case law in US states that abstract ideas and just data can be patented. Here again, the condition of a specific applications is required.

To finish my small intervention , a practical approach in a patent database. One of the patent classes that be used to search for models is: https://worldwide.espacenet.com/classification#!/CPC=G05B17/00. An example of a granted patent in this field is https://worldwide.espacenet.com/publicationDetails/originalDocument?FT=D&date=20190925&DB=EPODOC&locale=en_EP&CC=EP&NR=2556414B1&KC=B1&ND=4#. In order to select the granted patents (or thus those that are patentable by the EPO) you'll have to choose EPB in the field of the publication number and combining this with the CPC field: G05B17/low. Another very important Class is https://worldwide.espacenet.com/classification#!/CPC=G16C

Another example: https://worldwide.espacenet.com/publicationDetails/originalDocument?FT=D&date=19990811&DB=EPODOC&locale=&CC=EP&NR=0494110B1&KC=B1&ND=4#. When looking at the claims: claim 1 describes a process for the estimation of the physical parameters....using a computer. The classifications G06F17/50: https://worldwide.espacenet.com/classification#!/CPC=G06F17/50 (which is broader for multiple applications) and G06F19 can also be very useful to search. https://worldwide.espacenet.com/classification#!/CPC=G16B are related to ICT applications (bioinformatics).

So, to conclude: 1° try to find similar granted patents and have a look at the claims what they exactly claim, 2° detect patents that you can infringe and check their legal status (preferably with professional assistance) in the framework of your FTO. If you don't have FTO, your are blocked for your future steps, if FTO think about step 3, 3° ask for a patent professional to analyze your model in order to evaluate the novelty and inventive step, and the techncial application. When you solve the problem with a feature that is not obvious for a skilled person and you don't use the fundamentals of earlier valid patents, unless you can agree a cross-license or an agreement of use, patentability is on the floor. The best.

Thank you Wilson, good addition.

Wave impedance: At a point in an electromagnetic wave, the ratio of the electric field strength to the magnetic field strength. (188) Note 1: If the electric field strength is expressed in volts per meter and the magnetic field strength is expressed in ampere-turns per meter, the wave impedance will have the units of ohms. The wave impedance, Z , of an electromagnetic wave is given by

📷

where is the magnetic permeability and is the electric permitivity. For free space, these values are 4 × 10-7 H/m (henries per meter) and (1/36) F/m (farads per meter), from which 120, i.e., 377, ohms is obtained. In dielectric materials, the wave impedance is 377/n, where n is the refractive index. Note 2: Although the ratio is called the wave impedance, it is also the impedance of the free space or the material medium.

In the following website you find and example and solution to calculate wave impedance.

Thermal remediation is very complex process depending on many factors (pollutants type, matrix quality, water content, chemical characteristics of pollutants to mention some of them), General information you can find in any textbook and on the EPA web site as mentioned @ Rick Manner above.

Regards

Vit

Dear Mouad Hachhach,

Bulk chemical prices database.

I hope the information will help you.

With Best Wishes,

Samir G. Pandya

From chemical reaction engineering kinetics the order of the reaction is dependent on volume of reactor and the reaction is to be considered as constant

volume or constant pressure . There are different types of reactors depending upon the type of reaction used ie liquid / Gas phase and accordingly reactor will

be classified as Batch , CSTR / PFR type of reactors .

dear Antoine and Yuri, we just completed this year an extensive comparative study of the surface energies of as received Si(100) wafers native oxides with different dopants, using 3LCAA and the vOCG theory, and published it in MRS Advances. You may find the results useful to answer your question. We have two more manuscripts in preparation.

I agree with M. Kaveh Zamani

A green product means that it is biodegradable, that in general it does not pollute the environment, a sustainable product means that when we produce it or sell it, the future generations will still have the same possibility of producing it for their benefit, and an organic product means that they not used hormones or pesticides in their production, it is produced in the old way.

You can see the paper DOI:10.1016/j.matchemphys.2007.09.045

I will suggest you search for the information on science direct.

Yes there are. They are called Plackett-Burman Experimental Designs.Please see the attached paper as well as the book in this link:

Best wishes, David Booth

To rinse a powder you need a sieve with the mesh size smaller than the particle size of the powder. For example, such a

laboratory sieve:

For small amounts of powder, it goes without a sieve. You rinse the powder in a large beaker and leave suspension for a while: metal powder sediments on the floor and you can carefully drain off water. Then you dry the powder with the remaining water in a drying oven.

Solid Graphite is not soluble in polar and non-polar solvents, but it may soluble in molten Nickel and warm chlorosulphuric acid.

Hello Djigui, please see the attached paper which may be of assistance.

Good luck in your research.

By saying "nano-silica oxide", do you mean Aerosil from Degussa or its equivalent? Nanoparticulate (or fumed) SiO2 easily forms silica gel, and can be used, for example, for thickening electrolytes in batteries:

DWSIM is an open-source CAPE-OPEN compliant chemical process simulator for Windows, Linux and macOS. DWSIM is built on top of the Microsoft .NET and Mono Platforms and features a Graphical User Interface (GUI), advanced thermodynamics calculations, reactions support and petroleum characterization / hypothetical component generation tools.

HPLC is probably not suitable and first you need to define what kind of component you want to purify.

Looking for the theory of preparative HPLC, just Google and you will find for example

Looking for examples ?

Good luck

Thank you all guys for nice information.

Boiling the mixture of H₂Pc and copper(II) acetate in 1-chloronaphthalene or quinoline should probably work. However, I agree with Tomas Tempesti that making CuPc from scratch would be easier. If you have access to the vacuum sublimation apparatus, then heating bulk mixture of phthalonitrile and copper(II) acetate with with the two subsequent sublimations should yield reasonable amounts of very pure CuPc crystals.

The stretching vibration of imine group in IR

appear around 1630__1590

Also you can check it by HNMR where the signal of azomethaine proton appear at

8.5__9 ppm

Can you tell us more about the application?

In ethylene plant pyrolysis furnaces, a hydrocarbon feed (ethane, propane, etc) is heated to about 1500°F-ish in the tubes of the furnace. The hydrocarbon "cracks" making ethylene, propylene and 50 some other components. In the process, coke is also formed and deposits on the inner walls of the tubes. At some point, the tubes will have to be "decoked". The decoking starts with steam and it followed by allowing air into the tubes at temperatures around 1200°F. The oxygen in the air reacts with the coke converting it to water and carbon dioxide. The decoking could last at to one day, a period after which the tubes are presumed to be clean enough to switch the furnace operation back to cracking.

I hope this helps.

Run 5 or more times and evaluate the averages and standard deviations.

Different strategies including the use of depleting/blocking antibodies (CD25, CTLA-4, CCL2), IL-2/immunotoxin conjugates, cyclophosphamide, or COX2 inhibitors have been tested in mouse models of cancer and pre-clinical trials, but these did not always result in decreased numbers of Tregs or good anti-tumour response (see: Beyer & Schultze. 2006. Blood 108(3)804-11. https://www.ncbi.nlm.nih.gov/pubmed/16861339).

Frederick Arce, in Sergio Quezada’s group (University College London Cancer Institute), has recently published a paper in which they report on the importance of the anti-CD25-depleting antibody isotype in mouse models of transplantable tumour cell lines. They found that using engineered anti-CD25 antibodies with increased binding to Fc receptors results in enhanced depletion of intra-tumoral Tregs. This antibody, used in combination with immune check-point therapy led to complete tumour rejection in mice. Their observation that CD25 expression is restricted to CD4+Foxp3+ in human peripheral and tumour-infiltrating lymphocytes led them to propose that this validates the use of CD25 as a target for therapeutic Treg depletion in humans.

Very interesting paper (https://www.ncbi.nlm.nih.gov/pubmed/28410988) to read and see where the field of combined immunotherapy for cancer is moving. Their results suggest that efficient depletion of Tregs would be possible in clinical trials in order to improve the response to other therapies.

Try DWSIM

Without knowing the details of your process, you should be aware that ethanol and IPA form azeotropes with water. That ultimately means that such mixtures cannot be separated completely via the application of heat alone. For example, in the production of pure ethanol from a mixture of water and ethanol, the distillate (the azeotropic mixture) is further processed - using  temperature swing adsorption, for example - to "break" the azeotrope.

Dear Akin,

The document proposed by messaoud is very interesting, but it is in French. This is one of the few documents that reveal the type of chemicals used in hydraulic fracturing.. Here is an excerpt in English.

At the last meeting of the Congress, the Committee on Energy and Commerce (USA) launched an investigation to examine the practice of hydraulic fracturing in the United States. As part of this investigation, the Committee asked 14 major oil and gas companies to disclose the types and volumes of hydraulic fracturing products used in their fluids between 2005 and 2009 and the chemical content of these products.

Between 2005 and 2009, 14 major oil and gas companies (USA) used more than 2,500 hydraulic fracturing products containing 750 chemicals and other components. Overall, these companies used 780 million gallons of hydraulic fracturing products - not including water added to the well site - between 2005 and 2009. Some of the components used in hydraulic fracturing products were used frequently and generally harmless, such as salt and citric acid. Some were unexpected, such as instant coffee and nut shells. And some are extremely toxic, such as benzene and lead. The most widely used product in hydraulic fracturing during this period, as measured by the number of compounds containing the chemical, was methanol. Methanol, which has been used in 342 hydraulic fracturing products, is a hazardous air pollutant and is on the list of potential "candidates" for regulation under the Safe Drinking Water Act. Some of the most widely used chemicals are isopropyl alcohol (used in 274 products), 2-butoxyethanol (used in 126 products), and ethylene glycol (used in 119 products). BTEX - benzene, toluene, ethylbenzene and xylene - occur in 60 of the hydraulic fracturing products used between 2005 and 2009. Each compound is a BTEX contaminant regulated under the Safe Drinking Water and and a hazardous air pollutant under the Clean Air Act. Benzene is also a carcinogen. Hydraulic fracturing companies injected 11.4 million gallons of products containing at least one BTEX chemical over the five-year period. Between 2005 and 2009, hydraulic fracturing companies used 95 products containing 13 different carcinogens. They include naphthalene (a possible carcinogen for humans), benzene (a carcinogen), and acrylamide (a probable carcinogen for the man). Overall, these companies injected 10.2 million gallons of fracturing products containing at least one carcinogen. Many of the chemical components of hydraulic fracturing fluids used by companies were listed on MSDSs as "proprietary" or "industrial secret". Hydraulic fracking companies used 93.6 million gallons of 279 products containing at least one exclusive element between 2005 and 2009. Here are some of the most widely used toxic chemicals :

Methanol (Methyl alcohol), Isopropanol (Isopropyl alcohol, Propan-2-ol), Ethylene glycol monobutyl ether (2-butoxyethanol), Ethylene glycol (1,2-ethanediol), Hydrotreated light petroleum distillates,

With my best regards

Prof. Bachir ACHOUR

Ozone is best choice. Also permanganate is possible. You may add static electricity if these are not successful. Normally nickel forms a thin durable oxide layer in air, indicated by the loss of reflectivity.

Improved Hummers method should do the trick. Its more controllable and easy to do in the lab.

Chemical Fume hood with good ventilation is best option in a lab

removal of water using Dean-stark is only possible when you heat the solvent to boiling point, and generally the solvent should be imiscible with water.

since your solvent has such a high bp, Dean-stark does not seem to be the way to go. Removal by distillation is possible but depends on the solvent which may trap the water and raise the temperature required to drive off the water. You didn't mention the temperature you run your reaction, so you may not need to heat your reaction for it to proceed.

Another way is to use molecular sieves to remove the water, or chemical drying agents like orthoformates (although this may have other side reactions).

Chloride is an excellent ligand to Cu. Thus, there is only one way to obtain Cl-free CuO samples. Avoid any halide in the precursor! Washing will not help to remove coordinated Cl on the CoO surface.

You can read the book of chemical process industries, process calculations (Himmelblau). It will be useful. Its a vast topic, you need to know and understand the unit operation you are interested in, details of reactant, product and the time and temperature at which the reaction proceed forward or backward or may be irreversible, composition of the feed, composition of the product and reaction pattern that can say some details about the intermediate products (if any). Once you know everything you can make an energy balance and mass balance. Mass balance is super simple and straight forward, to calculate the energy balance, you need to know the chemistry involved and information on the system, like the free energy and how it change and the internal energy, so on. Its very difficult to answer here as you need previous knowledge on this topic and you have to read the above said text book.

Methods used in ASPEN Plus are also available in public. There are many methods. A popular book is Reid and Sherwood,  Properties of Liquids and Gases, where group contribution is the main content.

I very strongly suggest you keep ALL UV out of DSC as it will rapidly degrade most of the organics. Fortunately this is not difficult to do.

Dear Soheila Manshad,

As mentioned above by Dr/Prof Eldenglawey you can use optical techniques. I would not recommend Raman for the dispersion state as it is mainly a surface technique. However, XRD can give you a relative indication whether your GO is exfoliated in your membrane.

Another technique you might consider is microfocus x-ray tomography which I've used in my own studies. It is non-destructive and gives you a decent 3d-image that you can reconstruct to differentiate between the polymer membrane and filler.

Kind regards

Louis van Rooyen

What are you burning alcohol with (or what is the 2nd reactant in the  reaction  with Alcohol)

Alcohol + O₂  >  CO₂, H₂, CO, H₂O, Heat

Alcohol + Air  >  CO₂, H₂, CO, H₂O, NO_x, SO_x, Heat

N and S are  constituents of  Air

N and S may be a contamination in your alcohol.

Ajit:

Thionyl chloride is the most widely used reagent for the preparation of acid chlorides. The procedure normally involves heating the carboxylic acid or dicarboxylic acids with a slight to large excess of SOCl2 in an inert solvent or with SOCl2 itself as the solvent. Performing the conversion at the boiling point of the solvent speeds removal of the byproducts, HCl and SO2. The ease of removal of the byproducts is the chief advantage of SOCl2 over PCl5 and PCl3. This simple procedure gives good yields of the acid chlorides. The reactions are first order in each reactant and electron-withdrawing groups on the acid decrease the rate. This reaction should only be performed in a hood. !! 

The conversion is a pretty standard organic reaction and you could use either thionyl chloride SOCl2 or phosphorus chloride PCl3 or PCl5 avoid contact with zinc.

Good Luck

Steve

Hi Silvia, correct! Actually the protocol is a bit ambiguous. You can find the correct phrasing of the protocol in this paper:

Polish Journal of Microbiology (2009) 58, 205.

Sorry for my late response.

And thank you for your kindness.

Thank you so much Carlos.

You may want to try an agarose or agarose-acrylamide composite gel for such large protein complexes. Here are some references:

Jae Jun Lee:

                         The electrophillic substitution reactions such as nitration on the aromatic hydrocarbons phenanthrene and1,10- phenanthroline are generally difficult/complicated. That is due to the higher reactivity of the functional unit (that may not be real part of aromatic system as shown in attached file) toward addition reactions. Due to its typical reactivity, this structural unit generally behaves like alkene in few reactions and is more prone to give addition reactions rather than substitutions. In your experiment, you have used two oxidizing agents such as nitric acid acid and sulphuric acid. There may be many complicated processes involving in the oxidation. The most reasonable is given in the attachment.

To converge such simulations I initialize the lean solvent stream already with some CO2 content. For MEA, you want to use something from 0.1-0.3 molCO2/molMEA. Then I use the design-spec tool in order to fix the conditions at the stripper's bottom to the same desired CO2 loading by manipulating the reboiler duty. Depending on your operating pressure, you should use a balance block to replace your water and MEA losses by adding a make-up stream. When your recycle stream is similar enough to your lean solvent stream (temperature, pressure, composition), you can use a transfer block to copy the recycle stream into the lean stream on every iteration, virtually closing the recycle. Try changing the tear converging method from Wegstein to Broyden as well. I've found this to be a quite robust approach. If you are interested, a detailed explanation is also given in my linked publication:

I hope that helps,

Best regards,

Alberto