How to deal with data-sheet and product PDFs which are repeated over the web?

What is the proper way to deal with a situation where a company ( is selling and implementing certain kinds of gadgets?

Each product has its own dedicated HTML product page, with only general information about the product. It also hosts data-sheets and vendor provided PDF documentation about the products linked from the product HTML pages. All together this is a setup that seems to be useful for real users.

Since these PDFs are mostly provided by the manufacturers, they appear in other places over the web, including rival websites. Many of these PDFs are detected as duplicate content by Google and the "Google-selected canonical" is the same PDF on someone else’s website!

Question 1: Does this mean that link-juice is leaked to those other random websites, even though is linking to the PDFs under it’s own domain?

Question 2: If answer to Q1 is yes, is adding rel="nofollow" to those links pointing to the PDFs be recommended?

To make things more complicated when I check the Links section in Google Search Console, I can see that apparently have loads of External links, but when I take a closer look, many of those are pointing to identical copies of these PDFs mostly on another site. In other words Google makes it look like we have incoming external links, whereas in reality other websites has links to these duplicate PDFs on their own domain.

Question 3: Is it a bug in Google Search Console that it shows links to PDFs on other websites as incoming external links to

Also when I look further I can find some of these PDFs, where the Google Selected Canonical seems to be the one on

Question 4: Does that mean that with those PDFs is stealing link juice from other sites, even when they link to their own hosted version of the same PDFs?

Question 5: If Q4 is yes, does that mean should examine the PDFs one-by-one and add rel="nofollow" (or prevent indexing in any other way according to Q2) to those links where the canonical is on another domain, but keep normal links to those PDFs, where has the canonical versions?

PS: I’ve tried to search for this topic for many days without finding even a mention of this kind of a situation. The closest I’ve found is this article, but it is about only a slightly similar topic and it does not offer any solutions to the problem.

5 Reasons to Select Paving Stones Over Concrete

5 Reasons to Select Paving Stones Over Concrete
The walkway or drive that leads to your home should be both a personal statement and a reflection of your good taste. What’s more, the materials should stand up to the weather, look great for years at a time and not be a burden with costly, involved maintenance.
Concrete was the favored material for years because it met some of these criteria. But today paving stones are the clear choice. Here are five reasons why:

1. Stains and other imperfections can be easily hidden with pavers
If you splash a little oil on a concrete drive, the stain usually becomes an ugly, permanent blemish. Not so with pavers. These can be quickly flipped or replaced so you always have a surface that looks pristine.

2. Pavers come in a wide range of attractive colors and designs
Mixing and matching all the possible different combinations will give you a unique drive or patio every time. The different ways you can put paving stones together are limited only by your imagination.

3. A paver walkway is ready to go from the time it’s installed
Unlike concrete, which can take three to five days before it’s ready for traffic, there’s no curing period with pavers — and no waiting.
4. It’s easier to make adjustments with pavers
When a concrete base shifts, cracking can result in costly repairs that are visible even when they’ve been professionally done. It’s much easier to deal with a paver’s base that has moved. Just remove the stones over the affected area, level if needed, then replace the same pavers for a finish that looks as good as new.

5. Better drainage means a secure paver surface
Pavers are solid under your feet. Because of all the joints between paving stones, rain drains away much more easily than it does from flat concrete surfaces. This feature makes pavers much more slip-resistant.
Upgrading to pavers is the right choice for several reasons. This is a durable, worry-free material that will last for years.
Use Paving Stones to Transform Your Outdoor Space
If you find yourself gazing out into your backyard thinking of something you can do to spruce things up, have you considered using paving stones? Installing them is not difficult, and depending on the size of your project, it can be completed in as quickly as one weekend. The concept of using paving stones has been around as long as civilization –and for good reason. It is a simple, tried-and-true choice for builders who want attractive, durable results using simple tools and materials.
Few projects can be accomplished so quickly and last as long. Paving stones are versatile enough to suit jobs of any size or type. Regardless of your project: A simple walkway, a flower garden, a patio with barbeque, or even a driveway –paving stones are ideal. Below are some things to think about before starting your paving stone project:
Find inspiration
Do you already have an idea of what you want? If not, there are plenty of places to find inspiration. View landscaper’s websites and browse their galleries to see what is possible with paving stones. Of course there are always magazines as well. You may find new ideas that you weren’t aware of before you began your search.
Study your yard
Consider your needs and your space limitations. Can you fit your idea into the space you have? Take into consideration proximity to structure and trees. A small tree today may be a big problem in the future as the root system grows.
Types of stones
Are paving stones and stone pavers the same thing? Sort of. Paving stones (also referred to as pavers) are not necessarily made from naturally occurring stone. They are often cast from man-made materials like bricks. Some are cut from natural stone and therefore are called stone pavers. Besides a limitless number of colors, there are different types of pavers, such as brick, concrete, natural stone and even rubber. Most man-made pavers are also available in interlocking shapes.
Draw a picture
A piece of graph paper can be a great help. Draw out your plan, scaling each square as one foot (or other easily converted unit of measure). Color the bricks if you are planning to make a pattern with your stones. Using graph paper makes it easier to count how many stones of each color will be needed.
Unlike a deck, the maintenance for a stone patio is a snap. They are modular in nature, so it is also easy to move them around as your landscaping needs change. Also, have you ever stepped barefoot onto your deck after it’s been in the sun all day? Pavers are cooler on your feet. Finally, pavers won’t crack like concrete can. If planned and installed properly, you’ll be ready for the summer simply by sweeping your patio and bringing out your furniture!

How to design a fireplace with cultured stone
When searching for an easy and cost effective design solution for a fireplace, cultured stone or manufactured stone veneer should definitely be considered. There are a variety of patterns and colors to choose from, and a multitude of ways to enhance any interior space. Culture stones are a cost-effective way to add nature-inspired beauty to any indoor fireplace.
This ledgestone fireplace (left) was built in Parkland, FL. The fireplace was framed with drywall and had a wooden shelf with a large mirror in the center. The floor-to-ceiling fireplace with cultured stones is very interesting, visually.
The manufacturer’s recommendation is to install wire lath on top of the drywall with a scratch-coat of mortar; however, you should simplify this step and use backer boards instead. These provide the proper adhesion and save a considerable amount of labor. After the installation of the backer boards, apply bonding agent on the area getting stoned.
Cultured stones, also called manufactured stones, can be rustic or refined. If you wish to install cultured stones on your own I would advise that you lay out a selection of different stone sizes on the ground. This will make it easier to find the right size and achieve the best blend in color.
Always mix different sizes of stones. Also, alternate or stagger the joints create a pattern that is pleasing to your eyes. A good rule of thumb is to break up the vertical and horizontal joints as often as possible.
Even as Central Delhi begins the kerb stone makeover — paint them saffron and green — the decision, taken by the New Delhi Municipal Council, has come under severe criticism from several quarters, including the traffic police and an NDMC member herself.
Further, the use of regular paints, as opposed to the retro-reflective thermoplastic variety, is considered to violate road rules.
Kerb stones are placed on roads as markers of danger. They are usually painted in ‘black and white’ or ‘black and yellow’. The NDMC had touted the move as an “aesthetic initiative” which would “bring uniformity to the area”.
According to Indian Road Congress, the national body of technical highway engineers, “yellow, white and black are the standard colours used for markings”. The same is stated by the Unified Traffic and Transportation Infrastructure (Planning and Engineering) Centre and International Vienna Convention on Road Signs and Signals, of which India is a ratified member.
Granite Paving Stones Rise in Popularity
Granite paving stones are quickly becoming the “it” hardscape item of the year as more projects seek a product that’s cost effective, unique, and durable. Add those keys to a versatile product for both residential and commercial projects and it’s no wonder they are becoming more popular.
Paving stones (commonly referred to as “pavers”) are typically made from one of three materials: natural stone, brick, or cement. Each one of these provides a different look and feel to a specific project and have their own pros and cons.
4 Reasons Granite Paving Stones Are Trending
Compared to this time last year our sales of natural stone flagging and pavers are up more than 300%. The majority have been granite but a small percentage includes a schist and quartzite and it does not include bluestone. It’s exciting for us to see this growth and when we see a trend like this we look to focus on the “why”.
Sustainability: Natural stone products are natural and durable with minimal carbon footprint. The majority of our stone is from local quarries and our process involves breaking or cutting stone down to size so no chemicals are used in the product. Natural stone is considered to be a “green” building material.
Unique: We hear it on a regular basis, “I want something different”. No two pieces of natural stone are identical so when you lay down your granite pavers it’s going to be different than anything else out there. Even if your neighbor uses the same stone there will be variation.
Quality: We used the word durable in our first point and natural stone, especially from New England, continues to stand the test of time and elements. Granite paving stone is durable which is why you can work with “reclaimed” granite. It’s stone and it’s built to last.
Affordable & Available: Stone is heavy and for a long time was difficult to move or ship. Similar to the introduction of thin stone veneer, advancements in technology have made granite pavers more available, easier to transport, and help reduce the installation time, which saves money on the job.
It’ s exciting to see the growing trend in natural and granite paving stones and we expect to see it continue to increase in demand for the years to come.


Let’s kick off with a question: what is the most valuable clothing brand in the world? That would be sportswear giant Nike , which topped the 2018 league table with a total worth of $28bn, despite a 12 per cent drop due to “challenges” in North America and some executive misconduct. Buoyed by rampant sneaker culture and shifting dress codes, this should be a surprise to no-one, because there has been a fundamental shift in men’s fashion. Comfort got cool. The tastemakers went technical. Tracksuits became high fashion. At what point do we stop compartmentalising it as “sportswear” and just call it fashion, or clothes? Fashion’s brand rankings are a clear indication, if you needed one, that sportswear is no longer restricted to the playing of sport. Trailing behind the mighty swoosh, according to marketing consultants Brand Finance, are high street behemoths H&M and Zara, which finished second and third on $19bn and $17bn respectively, followed by a resurgent Adidas, up 41 per cent year on year to $14bn (one of Nike ’s principle “challenges” in North America). That’s way ahead of the luxurious likes of Hermès, Louis Vuitton and Cartier, which only just reach double figures – of billions of dollars, but still. Being able to wear T-shirts, sweatpants and trainers for more than going to the gym or the corner shop is, after all, the ultimate luxury. What’s changed in recent years is exactly that: sportswear is no longer just casual dress. Even if you work in an office, there’s a good chance you’ll have a pair of sneakers on, perhaps some drawstring trousers. There could be a sweatshirt slung over your chair, a baseball cap on your desk, a track jacket in your bag. Today, it’s completely normal to look smart in clothes that were originally designed to sweat in. This isn’t brand new, of course. Rene Lacoste’s 1927 innovation of a lightweight, breathable “tennis shirt” was subsequently adopted by polo players, Ralph Lauren and the rest of us. Sporting on-court clothing off it is something your grandfather started.
“Sportswear as casualwear is essentially a preppy invention – the carryover from hearty WASP athletic pursuits which gave us the likes of the sweatshirt, sweatpants and letterman jacket,” says Josh Sims, author of books such as Men of Style. “Sportswear was appreciated for being tough and practical.” Like military uniform, that other stalwart of menswear, sportswear has long been valued for the rugged characteristics it both possesses in itself and indicates in its wearer. And in sport, like war, competition results in game-changing technological breakthroughs. What we wear on the fields of battle and play has advanced more dramatically than what we wear elsewhere. If sportswear is at the cutting edge of fashion right now, that’s because – in technical terms – it always has been. The current, unprecedented sportswear boom though can also be seen as a pendulum swing away from the hashtag-menswear sartorialism that followed the economic downturn and increased competition for jobs – coinciding with the 2007 airing of Mad Men. As employment rose again, so did jobs that didn’t impose traditional dress codes and a social media-fuelled emphasis on individual creativity.
Then there’s the swelling fashionability of fitness, which has given us a legitimate excuse to wear sportswear outside the gym beyond comfort and sheer laziness. Instead of spending valuable time fastidiously parting our hair and folding our pocket squares, we’re throwing on hoodies and baseball caps. And if you’re running around town all day, it makes sense to wear shoes designed specifically for marathons. It’s arguably the luxury sector that’s setting the pace. Streetwear designers like Demna Gvasalia at Balenciaga and Virgil Abloh at Louis Vuitton are running the show(s), elevating previously utilitarian sportswear to the very height of fashion. T-shirts, down jackets and sneakers, which grew by 25%, 15% and 10% respectively, were “standout categories” in the 2017 Bain Luxury Study. With its links to skateboarding, surfing and other sports, you could argue that streetwear – whatever that loaded term means – essentially is sportswear. “I’m not sure streetwear is the dominant mode, if you’re talking urban, hip-hop-driven streetwear,” contends Sims. “It’s sportswear with graphics, in effect. “There’s not much original design in streetwear – unlike sportswear, then and now – and what there is tends to be driven by – ta-da – sport.”
Once upon a time, the humble soccer jersey served little purpose other than to tell the difference between two teams.
Occasionally superstition forced a change to the team jersey. For example, up until 1953, Brazil used to play in a white jersey. The mood of a country and the team jersey was forever changed when Sele??o failed to win the 1950 World Cup. A new jersey was debuted 4-years later at the 1954 World Cup and the team has never looked back on their way to winning an unprecedented 5 World Cup titles.
Such a change was rare and certainly never for marketing purposes.
Only when Admiral signed a deal to supply the Leeds United jersey of 1973 did things start to change. The deal meant that Leeds could sell replica jerseys with the Admiral logo on, making them recognizable. A whole new market was born.
Jersey sponsorship wasn’t far behind, although it wasn’t initially something the big clubs caught on to. English side Kettering Town emblazoned ‘Kettering Tyres’ on their kit in 1976, only for the English FA to outlaw the innovation.
Not long after that, Derby County and Bolton Wanderers applied to have advertising on their shirts and in 1977 the FA granted a license. That’s helped pave the way for lots of record-breaking jersey deals over the years, with suppliers and advertisers.
Real Madrid are currently eyeing a $125 million per season deal with Adidas to supply their kit, a long way from the sort of money Kettering Town got.
Not only has the financial aspect of the football shirt developed, but so has the technology used in the shirt itself. Over the years the method by which they’re produced has changed.
An article by sports coach Jimson Lee reveals that it wasn’t just soccer jerseys that saw a technological change. Nike were one of the first companies to introduce a shirt that essentially kept sweat away from sportsman and women, used by golfers and soccer players alike.
The drive to find that sporting edge prompted them to develop lighter jerseys to help with speed and endurance. The dri-fit technology even helps keep sweat away from the players during the game.
Italy’s World Cup 2014 kit took the evolution of soccer jerseys a step further as it “featured a special tape that micro-massaged player’s muscles as they wore it”. The aim was to help a player’s physical recovery by massaging them whilst the jersey was being worn. Labelled a ‘compression kit’, Uruguay also wore a similar jersey at the 2014 tournament.
The technology is only going to progress even further. With sports science becoming an increasingly popular aspect of soccer, jerseys are being developed with heart rate monitors and GPS tracking signals in them. This will help coaches understand their players’ performance and requirements down to the finest detail.
From simply being a way to differentiate between two teams, soccer jerseys have become a huge industry. They’re used as a method to develop revenue and income, with big clubs such as England’s Manchester United making huge sums of money from selling shirts with players’ names on.
They’re also playing a key role in aiding performance and understanding the athletes better, making the soccer jersey an integral part of the modern game in more ways than one.
Early rugby uniform was not unlike those worn above. Matching wool jumpers were paired with white trousers. Although wool was the de facto “tech” fabric of the era (even early swimsuits were made of wool), it quickly became apparent that the itchy, heavy, knit jumpers were less than ideal in a sporting context. Heavy-gauge cotton shirts worked far better on the pitch, and thus the modern rugby shirt was born.
How to Choose Yoga Wear
Refining a downward dog or trying a new balance pose at the yoga studio is challenging enough on its own, but it’s made even harder when you’re fiddling with sagging, too tight or uncomfortable yoga clothes. That’s why it’s important to purchase clothes that are breathable, flexible and comfortable.
Your yoga clothing purchases will depend largely on personal preference, as well as the style of yoga you plan to practice. But at a high level, here’s what to wear to yoga (see below for a more detailed discussion of these yoga basics):

  • Breathable, flexible bottoms like yoga pants or shorts
  • A breathable, narrow- or form-fitting top that won’t hang over your head when you’re upside down.
  • For women, a sports bra or built-in shelf bra that offers enough support for the type of yoga you’re practicing
  • A comfortable, warm top layer for end-of-class savasana (corpse pose) or after class when you’ve cooled down

Yoga wear is made with polyester-nylon-spandex blends, and for good reason—these fabrics offer the right balance of comfort, breathability and flexibility:

  • Comfort: There’s nothing worse than practicing yoga in an uncomfortable piece of clothing. As you tune into your body, you don’t want to focus on itchy seams and tags, saggy or too tight waistbands, or fabric that binds and chafes.
  • Breathability: Depending on the type of yoga you practice, you may sweat a little or a lot. Particularly if you’re sweating a lot, it’s important to wear breathable and moisture-wicking materials to keep you cool and comfortable. Tank tops, shirts with cutouts and yoga pants with mesh pockets will all improve breathability and venting. Avoid cotton, which holds moisture, makes you feel hot and damp, then leaves you prone to chafing or getting chilled when class winds down.
  • Flexibility: Yoga involves bending, stretching, binding, lunging, reaching and rolling. Your clothes need to be able to keep up with these movements, which means they’ll probably be made with at least 15 percent spandex.

Jerseys and shorts
Originally, basketball was played in any type of athletic attire, ranging from track suits to football uniforms. The first official basketball uniforms, as displayed in the Spalding catalog of 1901, featured three types of pants: knee-length padded pants, similar to those worn for playing football, as well as shorter pants and knee-length tights. There were two types of suggested jersey, a quarter-length sleeve and a sleeveless version.The long pants later evolved into medium-length shorts in the 1920s, and by the 1930s, the material used for jerseys changed from heavy wool to the lighter polyester and nylon. In the 1970s and 80s, uniforms became tighter-fitting and shorts were shorter, consistent with the overall fashion trends of these two decades. At this time, women’s basketball uniforms transitioned from longer-sleeved uniforms to tank-top style jerseys similar to men’s basketball uniforms, which more explicitly showed off players’ muscle tone.In 1984, Michael Jordan asked for longer shorts and helped popularize the move away from tight, short shorts toward the longer, baggier shorts worn by basketball players today. Throughout the 1990s, basketball uniforms fell under the influence of hip hop culture, with shorts becoming longer and looser-fitting, team colors brighter, and designs more flashy and suggestive of rappers’ bling. At the turn of the 21st century, basketball uniforms became even more oversized and loose-fitting; the arm holes in women’s basketball jersey remained smaller than men’s, but were wide enough to reveal the players’ sports bras.

MongoDB – Grant permission over one collection that exists on all databases

I have several databases on my MongoDB, all of them have or will have a collection called _schema. Currently, I’m granting permissions like this:

db.grantRolesToUser("userA",[   {"role": "readWrite", "db" : "databaseA", "collection": "_schema"} ]); db.grantRolesToUser("userA",[   {"role": "readWrite", "db" : "databaseB", "collection": "_schema"} ]); . . . db.grantRolesToUser("userA",[   {"role": "readWrite", "db" : "databaseZ", "collection": "_schema"} ]); 

Is there a way to grant readWrite for that particular collection on all databases without granting on each db individually?

(I want the write permission just for that collection, others will be just read)

Mathematica crashes when plotting over region

Mathematica 12.0.0 crashes and kernel quits on my computer (Win 10) when I try the simple exercise of plotting over a region (taken from this Wolfram page):

Plot3D[x y, {x, y} \[Element]  Disk[{0, 0}, 1], ImageSize ->  500,  PlotTheme -> "Web"] 

A similar problem happens when I work with StreamPlot over a Disk region.

Any advice on how to stop this from happening?

Determining the voltage ripple when the transient is over (mistake in result)

Well, I have the following code:

Clear["Global`*"]; u = 5; \[Tau] = (1/2)*10^(-3); c = 10^(-6); r = 1000; y = u*Sum[((1 - E^((-t + \[Tau] + 4 n \[Tau])/(c*r)))  HeavisideTheta[         t - 4 n \[Tau]] HeavisideTheta[         t - \[Tau] - 4 n \[Tau]]) - ((1 - E^((-t + (3 + 4 n) \[Tau])/(          c*r))) HeavisideTheta[t - 4 n \[Tau]] HeavisideTheta[         t - (3 + 4 n) \[Tau]]), {n, 0, Infinity}]; 

And I want to find the ripple in the voltage given by y when the transient part of that function is over. I can do that by finding the period time of that function and I found that I can use:

$ $ \lim_{\text{k}\to\infty}\left|\text{y}\left(\left(2\text{k}+3\right)\tau\right)-\text{y}\left(\left(2\text{k}+1\right)\tau\right)\right|\tag1$ $

Programming that in Mathematica, gives the following code:

FullSimplify[  Limit[Abs[(y /. t -> (2*k + 3)*\[Tau]) - (y /.        t -> (2*k + 1)*\[Tau])], k -> Infinity]] 

And Mathematica returns:

Interval[{0, 20}] 

Which is wrong, because it must return (I know that that is the good answer):

$ $ \frac{5 (e-1)}{1+e}\approx2.31059\tag2$ $

Where is my mistake, is it a coding mistake? Or a mathematical mistake? Thanks for any help.

Solving an equation over the integers

Consider the problem of finding all values of $ n \in \mathbb{N}$ s.t. $ $ \sqrt{n} + \sqrt{n + 2005}$ $

is an integer.

One can easily verify that $ n = 1,004,004$ and $ 39,204$ satisfy this requirement, and in fact are the only such solution values for $ n$ . The simplest approach is to set the right hand side to some variable $ m \in \mathbb{Z}$ , square both sides, manipulate and note the prime factorization of $ 2005$ … that is, $ 2005 = 2005 \cdot 1 = 401 \cdot 5$ and equate factors.

I would like to compute the solution directly, however.

The natural approaches do not work:

Solve[  Sqrt[n] + Sqrt[n + 2005] == m, {n, m}, Integers] 


FindInstance[  Sqrt[n] + Sqrt[n + 2005] == m , {n, m}, Integers] 


Assuming[{n, m} \[Element] Integers,  Solve[Sqrt[n] + Sqrt[n + 2005] == m, {n, m}]] 

I’ve tried a number of minor variations, adding constraints such as $ \{ n, m \} > 0$ , and so forth. None work.

As yarchik shows (below), one can solve this with the result from number theory that each of the component square roots must resolve to an integer (demonstrated here). That leads to two questions:

  • What would we do if we didn’t know that fact from number theory?
  • Supposing we do know that fact from number theory. How would we programmatically impose it as some form of constraint or subsidiary equation rather than "by hand"?


Google Optimize for A/B test: Trying to edit existing HTML but says it’s over the limit even when I test deleting some of it?

I am trying to set up an A/B test of a company’s website for my project. There are certain changes I’d like to make such as changing the ‘favourites’ products on the home page to one with the top selling products which I was trying to do by substituting the existing code simply with the top selling products instead (i.e. their jpg, their links, their names etc).

However I found that when making ANY change (by selecting the element and clicking ‘edit HTML’), even testing it by deleting one character from the original code, that it then pops up with this error notification saying that it’s over the word limit. Even when I put the character back for example, the error message is still there. And it will say weirdly that it is quite a lot of the word limit even though it’s basically the original code! I then have to click cancel every time.

Please see the attached photo for reference (where I deleted one character from the original code to demonstrate how any editing (even deletion of original working code) then comes up with the error that the html is over the limit).

View post on

Thanks in advance!