Roof Cleaning Shepton Mallet

Shepton Mallet Moss Removal & Soft Washing

Roof Cleaning Shepton Mallet Somerset (BA4): If you think about it carefully, your home is most likely the largest single investment that you will ever have to make, and if that's not a good enough reason to look after it, I don't know what is! Now, as the saying goes a building is only as sound as its foundation, which I guess is true - but the roof is of equal importance. And this naturally applies to any kind of home in Shepton Mallet, so regardless of whether you live in a mid-terrace, semi or even a picture postcard cottage, it's crucial to keep your roof clean and in good condition.

Quotes for Roof Cleaning Shepton Mallet

If you would like to avoid expensive repairs to your roof it is crucial to have your roof cleaned regularly. It is also advisable to use a roof cleaning service in Shepton Mallet to ensure that the work is done properly. Identifying possible issues like loose or broken roof tiles and other ways that water can gain access to the interior parts of your property, is much easier if you making certain your roof is free of an accumulation of moss or debris. Regular maintenance not only safeguards your roof's longevity but also acts as a steadfast shield against potential water damage intrusions.

Shepton Mallet Roof Cleaning

The most frequent cause for a roof cleaning service being needed in Shepton Mallet is for the removal of the build-up of algae, moss, dirt and lichen. These are naturally occuring over time and there isn't a roof in Shepton Mallet that will not experience this issue at some stage of it's life. Of course, a lot of Shepton Mallet property owners opt to try to do this by themselves using a jet washer, but be very cautious about doing this as it can result in a huge mess over yours and neighbouring properties if you are not careful, and can also cause damage to your roofing tiles.

MOSS CLEANING SHEPTON MALLET

A non-flowering, naturally occuring plant, moss grows across an area creating a dense layer of stems. It does not produce seeds and spreads onto surrounding surfaces through the dispersal of tiny spores into the air. The weatherproofing layer can be compromised and the surfaces of clay, cement and slate tiles, pitted by moss that's left to its own devices. This pitting can develop into holes and fractures which stop your home from being a weatherproof and waterproof building.

SOFT WASHING SHEPTON MALLET

The removal of moss from your roof is typically done by hand, if you use professional roof cleaning services in Shepton Mallet. This approach is mild on the roof and facilitates the easy collection of waste materials during the cleaning process. A special solution is applied to the remaining parts of the roof after the moss has been cleared away. Once dry, a treatment is introduced to tackle any lingering moss spores present on the tiles. The specialist biocide treatment additionally targets lichens and algae, known for thriving in areas that are damp and shaded. While "soft washing" is the trade's common term for this entire process, it can also refer to cleaning the roof without prior scraping of moss or other accumulations.

Roof Moss Removal Shepton Mallet UK (01749)

Moss re-growth may occur within just a few months if you decide not to conduct a biocide treatment like this. The biocide treatment should keep your roof tiles free from growth for three to four years, and a professional roof cleaning company in Shepton Mallet will probably suggest a retreatment every 24-36 months to keep your roof moss, algae and lichen free, and in the best possible condition.

After the roof has been cleared a roof cleaning company in Shepton Mallet should also remove any debris that has fallen into your gutters to prevent any blockages, permitting rainwater to flow freely.

USING PRESSURE WASHING TO CLEAN YOUR ROOF IN SHEPTON MALLET

If your dwelling in Shepton Mallet is older or your roof has been in any way damaged, a roof cleaning service will generally advise against the use of jet washing. You might wonder why this is, however when you consider that a high pressured jet of water can easily damage the water-resistant membrane, infiltrate the tiles and permit water to get into your dwelling, you will understand their fears. It is not advisable to attempt this without the guidance of a professional, despite the fact that this might be the fastest method of finding a leak in your roof!

Quotes for Roof Cleaning in Shepton Mallet

The use of a pressure washing machine, and the highly powerful blast of water that it produces, can inflict significant damage on other elements of your roofing system, such as pointing, soffit boards, guttering, fascias and flashings. At a minimum, you could compromise the waterproof coating on your tiles and reduce their natural lifespan by using a standard pressure washer on your home's roof.

However, there are occasions where this could be possible, and after going through all the negative aspects of this process, we will examine some more favourable circumstances. The best plan of action for tackling your roof will be determined as soon as a roof cleaning company in Shepton Mallet has finished the survey of your roof and tiles. A trustworthy company will attempt to find the cheapest and most viable solution to the cleaning of your roof, and if they come to the conclusion that your tiles can stand up to being jet washed, then that's the method they will suggest.

Shepton Mallet Roof Cleaning Near Me

The power washers used by an established roof cleaning company in Shepton Mallet have got variable pressures for water flow. As a consequence, no damage will be done to your tiles during the power washing procedure. When the jet washing is complete, a separate biocide treatment will be needed, to stop further re-growth of moss and algae, in the same way as is done with hand cleaning.

In relation to roof cleaning you should always steer clear of rogue traders, therefore if anybody raps on your door offering to jet wash your roof in Shepton Mallet, you will need to make certain that they've got suitable insurance coverage, and it's also advisable to ask to see references from people they have worked for previously. It should also be pointed out that thatched roofs shouldn't ever be jet washed. If a roof cleaning "specialist" in Shepton Mallet, recommends cleaning your thatched roof using a pressure washer, you should send them packing!

STEAM CLEANING YOUR ROOF IN SHEPTON MALLET

When looking at the various possibilities for cleaning your roof, the most environmentally friendly alternative of them all is steam cleaning. The procedure doesn't involve the use of harsh cleaning products or unpleasant chemicals, and the heat of the steam quickly eliminates any algae, lichens and moss that are living on your roof tiles. Ground breaking biocides are now being produced which are sustainable and eco-friendly and cause no harm to the wider environment, which is of course extremely important to many homeowners. Green anti-fungal products like Bioxide, which are environmentally safe, non-toxic and suitable for use on any surface after steam cleaning, are attracting considerable interest in the roof cleaning marketplace.

A reduced pressure is required for steam cleaning, than that which is used in pressure washing. Which means it's highly unlikely that your roof will get damaged. There is of course a shortcoming with steam cleaning, and that is that it's the priciest option in relation to roof cleaning.

SAFETY AND PROFESSIONALISM FIRST

Cleaning a roof can be a pretty messy process, and whichever of the aforementioned techniques you decide on, one of the most important things that has to be done is the layout of protective sheeting around your house to catch any moss, leaves or debris that tumbles from your roof. Downspouts should also be covered over to stop any debris falling in and creating a blockage. If needed for the work, scaffolding might also have to be put in position.

Roof Cleaners Shepton Mallet

Fully skilled operatives should be used by any quality Shepton Mallet roof cleaning specialist, and all the Health & Safety standards should be followed in regards to work at height precautions, not harming the environment, the safe use of chemicals and the use of protective clothing. This industry does have some trade organisations which provide certification and training, and also hold details about trustworthy and accredited roof cleaning companies, and these include the "Roof Cleaning Institute UK", the British Window Cleaning Academy (BWCA) and EduPro UK.

To find a roof cleaning specialist you can depend on, it's recommended that you ask for proof of certifications, trade memberships and references when you are getting your price quotes. It should never be too much of a problem for a roof cleaning contractor to provide this type of information, and any decent one will have this readily available on their website, printed flyer or social media.

(Tags: Roof Soft Washing Shepton Mallet, Roof Cleaning Shepton Mallet, Roof Steam Cleaning Shepton Mallet, Moss Removal Shepton Mallet)

Book Roof Cleaning Services in Shepton Mallet UK

You should be able to access roof cleaning providers in Shepton Mallet, and surrounding places like: Oakhill, West Shepton, Ham, Darshill, Stoke St Michael, Downside, Evercreech, Doulting, South Horrington Village, Bowlish, Croscombe, Cranmore, North Wootton, Pilton. Postcode areas like BA4 4TW, BA4 5BS, BA4 5JL, BA4 4AS, BA4 5DQ, BA4 5EG, BA4 5JS, BA4 4EJ, BA4 5HE, BA4 5BN are also covered. If a roof cleaning service has the postcode BA4 and the phone code 01749, you can assume that they work in the Shepton Mallet area. This is just something to confirm if you would like to make sure that you hire local roof cleaning. Shepton Mallet householders can benefit from these roof cleaning services.

Commercial Roof Cleaning

Ensuring the appearance and longevity of a business property involves regular commercial roof cleaning. As time passes, dirt, debris, and moss can build up, making the property look uncared for and unprofessional. Regular cleaning keeps the roof in good condition and improves the impression made on clients or customers.

Commercial Roof Cleaning

In addition to appearance, commercial roof cleaning can prevent long-term damage. Moss and algae can trap moisture against the roof surface, leading to leaks or structural issues over time. Regular cleaning helps to avoid these problems, reducing the risk of costly repairs in the future.

Regular commercial roof cleaning can also improve energy efficiency. Dirt, moss, and debris can affect the reflective properties of certain roofing materials, causing the building to absorb more heat. This can lead to higher cooling costs, particularly in the summer months. By keeping the roof clean, businesses can help maintain optimal energy performance and reduce energy bills.

Due to the larger size and more intricate structures of commercial buildings, hiring professionals for roof cleaning is advisable. They possess the right equipment, including high-pressure washers and safety gear, ensuring the job is done safely and effectively. Regular cleaning by professionals will not only extend the roof's lifespan but also keep the building looking clean and well-maintained. (Tags: Commercial Roof Cleaning)

Roof Cleaning Equipment

Roof cleaning equipment is essential for maintaining the condition of your roof. Simple tools like a broom or leaf blower are perfect for clearing away loose debris such as leaves, dirt, and twigs. These basic tools make the first step of roof cleaning straightforward and efficient.

Roof Cleaning EquipmentIn tougher cleaning scenarios, a pressure washer is often the tool of choice. However, it is important to use a low-pressure setting to avoid causing damage to the roof tiles or shingles. A pressure washer can help remove built-up moss, algae, and grime, making your roof appear fresh and clean again.

A hose with a spray nozzle is a good alternative to a pressure washer. While it won't be as powerful, it can still effectively wash away dirt, algae, and moss when paired with the right cleaning solutions. The adjustable spray settings allow you to control the pressure more easily, making it safer for roof cleaning.

For roof cleaning, specialised solutions or detergents are often used. These products help to break down and remove moss, algae, and stubborn stains without damaging the roof. Applying these with a sprayer and scrubbing with a soft brush ensures a thorough clean without causing any damage to the roofing materials.

Scrapers and water-fed poles are additional tools that can be very helpful for roof cleaning. Scrapers are ideal for manually removing thick layers of algae, moss, or lichen that are difficult to dislodge with a broom or brush. Water-fed poles, on the other hand, are long poles with a brush head attached that spray water while scrubbing, making them perfect for cleaning hard-to-reach areas on the roof without climbing up. These tools offer an effective way to clean stubborn dirt and grime while maintaining a safe distance from the surface of the roof.

When cleaning roofs, safety equipment is paramount. A sturdy ladder, non-slip shoes, and a safety harness are essential, especially when working on a steep or high roof. For larger or more complex tasks, hiring professionals with the necessary tools and experience is often advisable. (Tags: Equipment for Cleaning a Roof)

Roof Inspections

Roof inspections play a crucial role in maintaining a home. Over time, roofs can start to exhibit issues such as cracked slates, loose tiles, or blocked gutters, which, if neglected, may lead to larger problems. By performing regular inspections, homeowners can catch these issues early and avoid the financial burden of expensive repairs.

Roof Inspections

A basic roof inspection entails checking for visible signs of damage, such as moss growth or missing tiles. It's also crucial to inspect the flashing around skylights and chimneys for any gaps that could allow water to enter. If you identify any issues, it's advisable to address them promptly to prevent more severe damage.

Checking your roof twice a year is usually enough to maintain its condition, especially after extreme weather events like heavy rain or strong winds. There's no need to climb onto the roof, as many problems can be observed from the ground with binoculars. If you're unsure, though, it's best to call in a professional.

Professional roof inspectors have the experience and tools to check every part of your roof thoroughly. They can safely get up onto the roof and look for hidden problems that aren't easy to spot. Having a professional inspection done regularly will help keep your roof in great shape and extend its longevity.

Ultimately, regular roof inspections are an easy but vital step in maintaining your home. Whether you inspect it on your own or hire an expert, keeping track of your roof's condition helps to prevent major issues and extends its life. By staying vigilant with inspections, you ensure your roof will protect your home for many more years. (Tags: Roof Inspections)

Bird Deterrent Installation

Installing bird deterrents is a proven technique for maintaining a clean roof and preventing bird mess. Birds often perch and nest on roofs, leading to droppings that can stain roof surfaces and clog gutters. Setting up deterrents like nets, reflective objects or spikes can stop birds from landing and making a mess.

Bird Deterrent Installation

Bird spikes are a popular choice because they are humane and simple to install. By creating an irregular surface, these spikes make it extremely hard for birds to land, leading them to choose a smoother spot. Another solution is netting, which acts as a barrier to prevent birds from getting onto certain areas of the roof, making it particularly effective for bigger areas.

For increased impact, think about the use of reflective objects such as shiny discs or tape. Birds are typically frightened off by the reflection and movement. The installation of these deterrents not only keeps your roof a lot cleaner but also reduces the necessity for regular maintenance and costly repairs caused by bird damage.

Generally speaking, householders should not attempt to carry out this sort of task, so using professional services for installing bird deterrents is vital for effectiveness and safety. To prevent accidents and ensure durability, professionals have the experience needed to install deterrents, and have the right equipment to do the work correctly. By avoiding potential roof damage, this ensures a long-term solution to keep roofs clean and bird-free. (Tags: Bird Deterrents)

Solar Panel Cleaning

Solar panel cleaning by a professional service is vital to maintain the efficiency of the system. Dust, bird mess and debris can accumulate on the panels, blocking sunlight and reducing their effectiveness. Regular cleaning makes certain that your solar panels receive the maximum possible amount of sunlight, helping you get the most out of your investment. This service dramatically improves the performance of your solar system.

Solar Panel Cleaning

Hiring a professional service for solar panel cleaning is both convenient and straightforward. To prevent damage to the panels, technicians use soft sponges or brushes with soapy water to gently scrub the surface, avoiding abrasive materials or high-pressure water. They usually perform cleaning early in the morning or late in the evening to avoid thermal shock, as the solar panels are cool at these times.

Boosting the efficiency of your solar panels, and extending their lifespan requires regular maintenance, such as cleaning. It's advisable to schedule cleaning at least twice annually, or more frequently if you are in an area that is dusty. Ensuring optimal performance, clean solar panels maximise your energy savings and contribute to a greener world. When investing in professional cleaning services, long-term benefits are provided for your solar panel system. (Tags: Solar Panel Cleaning)

Roof Sealing

To safeguard your roof from leaks and damage, roof sealing is a critical service. A specialist sealant applied to the roof surface creates a barrier that prevents water from penetrating the underlying structure, keeping it safe from moisture intrusion.

Roof sealing is a wise choice as it can prevent expensive repairs and increase the lifespan of your roof. In regions with extreme weather conditions, such as snow, heavy rain or extreme heat, roof sealing is crucial.

An expert roof sealing service can examine any existing roof issues and recommend the ideal sealant to ensure your house is fully protected. It proves to be an affordable choice to defend your roof and property from damage. Preventing the growth of algae, moss, and other fungi that can deteriorate your roof's integrity over time is also achievable with a suitably sealed roof.

Brick and Render Cleaning

To ensure your home's exterior remains fresh and well-maintained, it is essential to clean the brick and render. Dirt, grime, algae, and moss can build up over the years, making the property look dull and neglected. Regular cleaning restores its appearance and prevents long-term damage caused by moisture or organic growth.

Brick and Render Cleaning

Using a soft brush and soapy water is suitable for cleaning lightly soiled render and brickwork. For more stubborn moss or dirt, specialised cleaning solutions can be applied to break down the grime. High-pressure washers should be avoided on render, as they can damage the surface and cause it to crack.

In certain situations, a low-pressure steam cleaner is an ideal choice, particularly for delicate surfaces like render. This technique is gentle yet effective at removing algae, dirt, and moss without causing harm. Moreover, steam cleaning sanitises the surface, making it appear fresh and clean.

Hiring professionals is a sensible choice for extensive or difficult cleaning tasks, as they have the right expertise and tools. They can safely remove tough stains and restore your brick or render's appearance without causing damage. Regular cleaning by professionals not only enhances the look of your home but also increases the longevity of your exterior surfaces. (Tags: Brick and Render Cleaning)

Asbestos Roof Cleaning

The fireproof attributes of asbestos, a naturally sourced mineral, led to its extensive use in building projects. Unfortunately, when inhaled it's now known to be extremely hazardous. Exposure to asbestos fibres is a potential cause of a number of serious health problems, including mesothelioma, asbestosis and lung cancer.

The presence of an asbestos roof on your property calls for a focus on safe management. DIY asbestos roof cleaning is both highly hazardous and strongly discouraged. Procedures like pressure washing which can release asbestos fibres into the air, pose a considerable health risk to yourself and those around you.

Asbestos Roof Cleaning

Thank goodness, there are safer options for tackling an asbestos roof:

  1. Leave it Alone: Regular monitoring is paramount for any asbestos roof, but especially for those that are intact and currently causing no issues. In such cases, often the safest strategy is to leave it undisturbed.
  2. Softwashing: This technique uses a low-pressure application of biocide solution to kill moss, algae and other organic growth on the roof. This procedure minimises the risk of disturbing asbestos fibres. The key to safe softwashing of an asbestos roof? Using the services of a qualified specialist. Their equipment and training ensure an effective and safe job.
  3. Encapsulation: A vital aspect of roof management: encapsulation. This approach involves the application of a sealant that binds together the fibres, stopping them from becoming airborne. An excellent long-term option for asbestos roofs, this process requires professional application from the start, with ongoing maintenance to ensure its effectiveness.
  4. Roof Replacement: Serious roof damage or major refurbishments may necessitate the complete replacement of your roof. The expertise of a licensed asbestos removal specialist is essential for the complex task of replacing an asbestos roof.
  5. Vegetation Control: The potential acceleration of an asbestos roof's wear and tear may occur as lichen, moss, algae, and other organic growth trap moisture. Safely removing this growth, a competent professional can use processes that minimise the likelihood of disturbing asbestos fibres.

While asbestos roofs present particular difficulties with regards to cleaning and maintenance, prioritising safety and following established protocols can reduce the risks associated with exposure to asbestos. Don't underestimate the risks! Dealing with an asbestos roof, from routine maintenance to cleaning, requires a high degree of caution and awareness of potential dangers. Observing safety guidelines and seeking specialist assistance when appropriate enables property owners to protect their health and well-being while guaranteeing the safe management of asbestos roofs..... READ MORE. (Tags: Asbestos Roof Cleaning, Asbestos Roof Cleaning Services, Cleaning Asbestos Roofs)

Roof Cleaning Tips

To keep your home looking its best and to prevent long-term damage, it's essential to keep your roof clean. Over time, debris, moss, and algae can gather on the roof, making it look unsightly and causing potential problems. Regular roof cleaning can help you avoid costly repairs and extend the life of your roof.

To clean your roof easily, use a broom or leaf blower to remove loose debris, such as leaves and twigs. It's crucial to avoid using metal tools, as they can damage the tiles. Begin at the top and work down to avoid pushing debris under the roof tiles.

Roof Cleaning Tips

To easily remove algae and moss, use a specialist roof cleaner or a mixture of bleach and water. Apply the solution using a sprayer, leave it for twenty to thirty minutes, and scrub gently with a soft brush. Be certain to rinse the roof thoroughly with clean water to eliminate any residue.

For cleaning your roof, pressure washing can be quite effective, yet caution is essential. High pressure risks damaging roof tiles or forcing water beneath them, which may create leaks. If you're uncertain about doing it yourself, it's best to hire a professional to manage the cleaning safely.

Ensure you always take safety precautions when cleaning your roof. Use a sturdy ladder, wear non-slip shoes, and consider using a harness if the roof is steep. If the job feels too risky, it's advisable to leave it to professionals who have the necessary equipment and experience.

Keeping your roof in good shape relies heavily on conducting regular inspections. Check for any signs of damage, like cracked or missing tiles, and observe the presence of moss or algae. By spotting these issues early, you can avoid more costly repairs later on, and regular cleaning will help prevent additional damage.

Shepton Mallet Roof Cleaning Tasks

Roof Cleaning Tasks Shepton Mallet

There are a range of tasks that can be done by a local roof cleaning service in Shepton Mallet, and we've listed some examples of them here: EPDM roof cleaning, brick cleaning, exterior building cleaning, jet washing, algae & lichen removal, driveway cleaning in Shepton Mallet, moss removal, roof cleaning services, roof sealing, asphalt roof cleaning, soft washing, metal roof cleaning, landlord roof cleaning services Shepton Mallet, steam cleaning in Shepton Mallet, tiled roof cleaning, gutter cleaning, bespoke roof cleaning Shepton Mallet, roof cleaning quotations Shepton Mallet, pressure washing, roof tiles cleaning Shepton Mallet, biocide roof treatments Shepton Mallet, moss removal & roof cleaning Shepton Mallet, soffit cleaning, eco-friendly roof cleaning, asbestos roof cleaning, roof resealing Shepton Mallet, window cleaning, brushed roof cleaning Shepton Mallet. Listed are just a handful of the duties that are undertaken by companies who do roof cleaning. Shepton Mallet professionals will let you know their full range of services. If there are some other Shepton Mallet roof cleaning requirements that you need but can't see here, you can easily mention them on the QUOTE FORM provided. We'll be in touch with specifics just as soon as we are able.

Gutter Cleaning Shepton Mallet

To ensure that there are no blockages to clear or damaged areas to repair, it's advisable to have your guttering inspected while getting your roof cleaned. Every building has them (or should have), and most of us neglect them, yet it's impossible to overemphasise the significance of rain gutters to your property. To reduce the risk of dampness inside your property and to prevent moisture damage to woodwork, window frames, roof timbers and masonry, your gutters channel rain water away from your building in a safe and controlled way.

Gutter Cleaning Shepton Mallet

If they're not cleaned regularly, gutters will quickly get clogged with dead leaves, moss, grass, weeds, and bits of broken roof tile. If grass or weeds have begun to grow in your rain gutters, they're possibly blocked already, and will need to be cleaned pretty promptly. It's high time to bring in the professionals if you're faced with a situation like this.

Some homeowners in Shepton Mallet opt to clean out their own guttering, which is obviously fine if you're comfortable working at height and have access to all the proper equipment. The trouble with guttering, of course, is that it is out of reach, and you're definitely going to be needing a ladder, and a long one one at that. If you are happy working on a ladder that's all well and good, although most homeowners don't like doing this, however there's still the risk of falling and injuring yourself when working up high.

Hiring a specialist tradesperson is by far the best way to get your gutters clean. There's also the additional benefit that while clearing your gutters, an expert will spot any structural problems that you may not otherwise have noticed. If you ask nicely, they will also replace broken gutter clips, do basic repair work and adjust the slope of your gutters. If your gutters need a thorough clean, click HERE to get an estimate.

SHEPTON MALLET ROOF CLEANING QUOTES

Roof Cleaning Near Shepton Mallet

Also find: Oakhill roof cleaning, Stoke St Michael roof cleaning, Ham roof cleaning, Pilton roof cleaning, South Horrington Village roof cleaning, Downside roof cleaning, Cranmore roof cleaning, Bowlish roof cleaning, Evercreech roof cleaning, West Shepton roof cleaning, Doulting roof cleaning, North Wootton roof cleaning, Croscombe roof cleaning, Darshill roof cleaning and more. These towns and settlements are all covered by local specialists in roof cleaning. Shepton Mallet home and property owners can get roof cleaning quotes by clicking here.

Roof Cleaning Services Shepton Mallet

Find Roof Cleaning in Shepton Mallet Here
Shepton Mallet Roof Cleaning Services (01749)
  • Moss Removal
  • Soft Washing
  • Roof Tile Cleaning
  • Gutter & Roof Cleaning
  • Roof Cleaning Price Quotes
  • Residential Roof Cleaning
  • Power Washing
  • Gutter Cleaning
  • Cheap Roof Cleaning
  • Soffit & Fascia Cleaning
  • Solar Panel Cleaning
  • Industrial Roof Cleaning
  • Pressure Washing
  • Roof Cleaning Services

To read local Shepton Mallet info take a look here

Roof cleaning in BA4 area, telephone code 01749.

TOP - Roof Cleaning Shepton Mallet

Pressure Washing Shepton Mallet - Soft Washing Shepton Mallet - Roof Cleaning Services Shepton Mallet - Commercial Roof Cleaning Shepton Mallet - Roof Cleaners Shepton Mallet - Moss Removal Shepton Mallet - Cheap Roof Cleaning Shepton Mallet - Roof Cleaning Estimates Shepton Mallet - Roof Cleaning Near Me

HOME - ROOF CLEANING UK

(This roof cleaning Shepton Mallet information was revised and updated on 16-12-2024)