Latex Product
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Latex Product
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Product notation is represented by the Greek alphabet pi (Π). Many of you think cross notation is product notation but not.
Default \prod command in latex is defined for this pi notation. You will see two uses of the \prod command in latex based on the location of the limit.
The command for displaying a product symbol is \prod and the general syntax for typesetting products with limits in LaTeX is
which types a product with a lower limit min and upper limit max .
Just like the integral and summation signs, the limits of the product appear differently in the inline mode and the display mode. In the inline mode, the limits appear next to the symbol and in the display mode, the limit appear below and above.
There are two commands that are capable of controlling how these limits appear. The first is the \limits command which forcefully pushes the limits below and above of this symbol in all the math modes and the second is the \nolimits command which reverse the effect(forces the limits to stay next to the product symbol in all math modes).
In other ways, you can only use the lower limits, not the upper and lower limits of the symbol. Since you will use a limit, in the lower limit you will have to use conditional symbols like less than, greater than and equal, etc.
In above output, spaces around the limit function can become very large for long indices and the mathematics may not be beautiful or presentable. LaTeX has addressed this problem by providing to commands to regulate and maintain spacing making the mathematics more presentable.
Below is how to use the \smashoperator{operator with limits} and \mathclap{math} commands. Just to emphasize, this commands apply same to summations and integrals.
We apply the two commands respectively to reduce the spacing between the index and f ijk as follows:
The \smashoperator{operator with limits} gives you a possibility to eliminate space either just from the left(l) or right(r) . Below is how to achieve that.
You can clearly see the difference above! However, be sure to use the mathtools package for both commands.
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In LaTeX, \prod (product operator) is rendered as inside math mode . The difference between this and \Pi , which generates the capital letter , is that \prod appears larger, has the correct spacing for operators, and that it supports the limits to be displayed below and above the symbol.
The following example illustrates the difference between \prod and \Pi .
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Most people use cosmetic products containing latex without adverse effects. However, some people may have had allergic reactions to latex-containing products. Because of this the FDA is concerned that consumers might not be aware that some cosmetic products contain natural rubber latex.
Roughly 1-6% [ 1 ] of the general population is allergic to natural rubber latex. Natural rubber latex is a milky fluid that contains extremely small particles of rubber that comes from plants, principally from the H. brasiliensis rubber tree. Natural rubber latex also contains a variety of naturally occurring substances, including the polymer cis-1,4-polyisoprene and various plant proteins, including what are called antigenic proteins that may trigger an immune response. Some of these antigenic proteins may also be allergenic: that is, they can cause a latex-sensitive person to have an allergic reaction. Sensitivity to latex may develop over time, especially for people who are often exposed to it.
From January 2015 to September 2017, the FDA received 30 reports of allergic reactions involving cosmetic products that typically contain natural rubber latex, including hair bonding adhesives, face and body paints, eyeliner, and eyelash adhesives. Allergic reactions can range from skin irritations or rashes to respiratory problems and even to a more severe reaction called anaphylactic shock. Four of these reports appeared to be of anaphylactic reactions. Because reporting is not required, the actual number of cases is likely to be higher than what is reported to the FDA. The only way that the FDA learns about incidents like these is when consumers, physicians or companies voluntarily report them. The current laws regulating cosmetics do not require companies to submit reports about cosmetic-related adverse events to the FDA.
How to Know if a Cosmetic Contains Natural Rubber Latex
Although cosmetic products are not required to include a latex allergy warning, the FDA does require that the labels of cosmetics include a list of ingredients, in order of decreasing amount [ 2 ] . Consumers should review labeling information prior to purchase. Usually the ingredient list is on the package, where the consumer can easily find it. If the product is sold by mail order, including online, the list may be on the package directly or consumers may be directed to a product catalog or a website, or there may be specific information about how to request a copy of the ingredient list. FDA regulations requires that mail-order distributors respond promptly to your request.
Here are some ingredient names to watch for, all of which indicate the presence of latex:
Manufacturers can change their products' ingredients at any time, so it's a good idea to check the ingredient list every time you buy the product - even if you have used it before.
Consumers who are concerned about natural rubber latex allergy may want to take more precautions, such as:
Products marketed only to professionals may not have a list of ingredients. That's because the Fair Packaging and Labeling Act doesn't apply to those cosmetic products sold for professional use. Salon professionals may need to contact the manufacturer to find out what's in these products.
What should I do if I think that I may have a problem with latex?
If you are allergic to natural rubber latex and you have reaction to a cosmetic product, stop using the product and contact your healthcare professional. Please inform the FDA by using our adverse events reporting tools (see below how to report a problem).
If you are a consumer, health professional, attorney, or member of the cosmetics industry who wants to report a complaint or an adverse event (such as an allergic reaction) related to a cosmetic, you have three choices:
When you report a reaction, be sure to include as much information as possible. It is helpful for FDA to know the precise product name, place, and time of purchase, lot number, labeling, and ingredients, especially if you believe you have experienced a reaction to latex. It is also important to let us know if you have a latex allergy or sensitivity.
The law does not require cosmetic companies to report problems to the FDA. Therefore, your report is very important in order to help the FDA monitor the cosmetics market.
Related Resources:
Consumer Update: Don't be Misled by "Latex Free" Claims
2 Under the Fair Packaging and Labeling Act , the FDA requires cosmetics to list their ingredients, in order of decreasing amount, up to greater than 1%, if the cosmetics are marketed to consumers on a retail basis, such as in stores, online, or person to person (see also 21 CFR 701.3 ).
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What is latex made of? The simplest answer: latex is rubber. Typically, it is composed of about fifty-five percent water and around forty percent rubber material.
Latex is the soft white substance found beneath the bark of a mature rubber tree. You may be surprised to think of latex as a natural material, given the strength and man-made feel of so many of its final applications, like tires, rubber gloves, and tennis shoes.
The truth is, natural rubber latex does, in fact, come from nature. Before it is processed, rubber tappers harvest latex from trees using a method that has been passed down for generations.
Most natural rubber latex comes from one species of rubber tree. The composition of latex from different trees varies, but the most common one is native to South America. The tree also thrives in Southeast Asian plantations.
Latex lives just beneath the bark of these rubber trees. When tappers peel back the bark, they disrupt the plant ducts to reveal latex, a milky white substance. From there, they can harvest the latex and send it off to be processed.
The latex harvesting process can only begin once a rubber tree is mature—about five years old. At this point, the tree is ready to start producing rubber.
To tap a rubber tree, tappers remove thin strips of bark. Doing so disrupts the plant ducts, which contain latex. Disrupting these ducts allows the latex to flow down grooves that the tappers cut into the tree. The latex flows down the grooves and into large cups.
Tappers tend to these cups, collecting the latex when they become full and replacing the collection cups to continue harvesting from the tree until it is appropriately tapped.
The rubber creation process begins at the point of harvesting, when they take latex sap from rubber trees.
Next, companies filter the latex so it can be packaged in drums for its next destination.
Once latex is ready to be made into smoked sheets of rubber, companies add acid to the latex. This causes the material to clump. The clumped fluid is then rolled into sheets in a mill. Doing so removes water, so the sheets can be dried and smoked.
Finally, latex is prevulcanized. Prevulcanization involves chemical treatments and gentle heating at low temperatures. Once latex is prevulcanized, it is more convenient to transport. With more heating, the material can now be made into regular rubber.
Of course, not all latex is natural. Some latex is synthetic, composed of petroleum-based chemicals. These chemicals are used to create synthetic rubber polymers, which are clumped and dried, then transported to a manufacturing plant.
The manufacturing plant then mixes the synthetic rubber polymers. Sometimes, they mix in additional ingredients, depending on the end product for the synthetic latex.
The plant rolls the rubber into sheets and cuts them into sheets for further processing. The most common synthetic rubber processing techniques are:
During extrusion, you feed the rubber polymer compound into the extruder, which heats it and compresses the material. This is done by the barrel and screw of the extruder. The polymer compound is then forced through a small opening to be vulcanized or cured.
Injection molding involves mixing rubber strips. Using high pressure, they are forced into a mold. Once in the mold, heat vulcanizes the rubber.
Compression molding starts with preforms of rubber compound. The preforms are shaped to a mold with compression, pressure, and vulcanization.
After processing, latex is an impressive rubber material.
Latex is known for its tensile and elongation abilities, as well as tear resistance and overall resilience. Most common abrasives will not bother latex.
Low temperatures are not a threat, but high temperatures can pose an issue. Above eighty-two degrees, latex can begin to corrode. You can add treatment chemicals to protect latex from corrosion due to heat, sunlight, and oxygen.
It is also best not to use latex alongside petroleum products and solvents. Doing so risks breaking down the latex.
Latex has a wide variety of applications, ranging from everyday items to more specialized uses.
Natural rubber latex is most commonly used to make items like gloves, swim caps, chewing gum, mattresses, catheters, rubber bands, balloons, tennis shoes, and many other sporting goods.
Synthetic latexes are common in coatings, like latex paint. You’ll also find them in glues, thanks to their ability to solidify as water evaporates from the polymer particles in the latex. Synthetic latex can also be added to cement used for resurfacing and patching cracks in cement surfaces.
Ace Products and Consulting is excited to answer your questions and meet your challenges. Contact us to find out what we can do for your latex.
(August 9, 2022, Ravenna, OH) – ACE Laboratories, a longstanding rubber, silicone and latex testing facility, has expanded into servicing the construction materials industry with new dedicated laboratory services. From polymer roofing materials and below grade...
CEO’s prominent role in two international industry events highlights company as a global leader in sustainable silicone and rubber products and processes. It's been a busy summer for ACE Laboratories, including two events where our CEO Erick Sharp connected with other...
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