3.9: Properties of Operations (Part 2)

Properties of Multiplication and Division

Now we’re going to turn our attention to familiar properties of multiplication and division, with the focus still on explaining why these properties are always true.

Here are the four properties you’ll think about:

  • Multiplication of whole numbers is commutative.
  • Multiplication of whole numbers is associative.
  • Multiplication of whole numbers distributes over addition
  • The number 1 is an identity for multiplication of whole numbers

For each of the properties, remember to keep straight:

  • what the property is called and what it means (the definition),
  • some examples that demonstrate the property, and
  • an explanation for why the property holds.

Once again, it’s important to distinguish between examples and explanations. They are not the same! Since there are infinitely many whole numbers, it’s impossible to check every case, so examples will never be enough to explain why these properties hold. You have to figure out reasons for these properties to hold, based on what you know about the operations.


We’ll work out the explanation for the last of these facts, and you will work on the others.

Example: 1 is an Identity for multiplication


The number 1 is an identity for multiplication of whole numbers.

What it Means (words):

When I multiply a number by 1 (in either order), the product is that number.

What it Means (symbols):

For any whole number m, $$m imes 1 = m quad ext{and} quad 1 imes m = m ldotp]


[1 imes 5 = 5, qquad 19 imes 1 = 19, qquad ext{and}; 1 imes 1 = 1 ldotp]

Why does the number 1 act this way with multiplication?

Why It’s True, Explanation 1:

Let’s think first about the definition of multiplication as repeated addition:

  • m × 1 means to add the number one to itself m times: $$egin{split} underbrace{1 + 1 + cdots + 1}& m; ext{times} quad & end{split}$$So we see that m × 1 = m for any whole number m.
  • On the other hand, 1 × m means to add the number m to itself just one time. So 1 × m = m also.
Why It’s True, Explanation 2:

We can also use the number line model to create a justification. If Zed calculates 1×m, he will start at 0 and face the positive direction. He will then take m steps forward, and he will do it just one time. So he lands at m, which means 1 × m = m.

If Zed calculates m × 1, he starts at 0 and faces the positive direction. Then he takes one step forward, and he repeats that mtimes. So he lands at m. We see that m × 1 = m.

Why It’s True, Explanation 3:

In the area model, m × 1 represents m rows with one square in each row. That makes a total of m squares. So m × 1 = m.

Similarly, 1 × m represents one row of m squares. That’s also a total of m squares. So 1 × m = m.

Think / Pair / Share

The example presented several different explanations. Do you think one is more convincing than the others? Or more clear and easier to understand?


Property: Multiplication whole numbers is commutative.

What it Means (words): When I multiply two whole numbers, switching the order in which I multiply them does not affect the product.

What it Means (symbols): For any two whole numbers a and b, $$a cdot b = b cdot a ldotp]

Problem 18

  1. Come up with at least three examples to demonstrate the commutativity of multiplication.
  2. Use our models of multiplication to come up with an explanation. Why does commutativity hold in every case? Note: Your explanation should not use particular numbers. It is not an example!


Property: Multiplication of whole numbers is associative.

What it Means (words): When I multiply three whole numbers in a given order, the way I group them (to multiply two at a time) doesn’t affect the product.

What it Means (symbols): For any three whole numbers a, b, and c, $$(a cdot b) cdot c = a cdot (b cdot c) ldotp]

Problem 19

  1. Come up with at least three examples to demonstrate the associativity of multiplication.
  2. Use our models of multiplication to come up with an explanation. Why does associativity hold in every case?


Property: Multiplication distributes over addition.

What it means: The distributive law for multiplication over addition is a little hard to state in words, so we’ll jump straight to the symbols. For any three whole numbers x, y, and z: $$x cdot (y + z) = x cdot y + x cdot z ldotp]

Examples: We actually did calculations very much like the examples above, when we looked at the area model for multiplication.

[8 cdot (23) = 8 cdot (20 + 3) = 8 cdot 20 + 8 cdot 3 = 160 + 24 = 184]

[5 cdot (108) = 5 cdot (100 + 8) = 5 cdot 100 + 5 cdot 8 = 500 + 40 = 540]

Problem 20

Which of the following pictures best represents the distributive law in the equation

[3 cdot (2 + 4) = 3 cdot 2 + 3 cdot 4 ?]

Explain your choice.

Problem 21

Use the distributive law to easily compute each of these in your head (no calculators!). Explain your solutions.

[45 imes 11 qquad 63 imes 101 qquad 172 imes 1001]

Think / Pair / Share

Use one of our models for multiplication and addition to explain why the distributive rule works every time.


It’s natural to wonder which, if any, of these properties also hold for division (since you know that the operations of multiplication and division are connected).

Example: Is Division Associative?

If division were associative, then for any choice of three whole numbers a, b, and c, we would have

[a : (b : c) = (a : b) : c ldotp]

Remember, the parentheses tell you which two numbers to divide first.

Let’s try the example a = 9, b = 3, and c = 1. Then we have:

[9 : ( 3 : 1 ) = 9 : 3 = 3]


[(9 : 3 ) : 1 = 3 : 1 = 3 ldotp]

So is it true? Is division associative? Well, we can’t be sure. This is just one example. But “division is associative” is a universal statement. If it’s true, it has to work for every possible example. Maybe we just stumbled on a good choice of numbers, but it won’t always work.

Let’s keep looking. Try a = 16, b = 4, and c = 2.

[16 : ( 4 : 2 ) = 16 : 2 = 8]


[(16 : 4) : 2 = 4 : 2 = 2 ldotp]

That’s all we need! A single counterexample lets us conclude:

Division is not associative.

What about the other properties? It’s your turn to decide!

Problem 22

  1. State what it would mean for division to be commutative. You should use words and symbols.
  2. Decide if division is commutative or not. Carefully explain how you made your decision and how you know you’re right.

Problem 23

  1. State what it would mean for division to distribute over addition. You definitely want to use symbols!
  2. Decide if division distributes over addition or not. Carefully explain how you made your decision and how you know you’re right.

Problem 24

  1. State what it would mean for the number 1 to be an identity for division. You should use words and symbols.
  2. Decide if 1 is an identity for division or not. Carefully explain how you made your decision and how you know you’re right.


Problem 25

You probably know another property of multiplication that hasn’t been mentioned yet:

If I multiply any number times 0 (in either order), the product is 0. This is sometimes called the zero property of multiplication. Notice that the zero property is very different from the property of being an identity!

1. Write what the zero property means using both words and symbols:

For every whole number n . .

2. Give at least three examples of the zero property for multiplication.

3. Use one of our models of multiplication to explain why the zero property holds.

Think / Pair / Share

  • For each division problem below, turn it into a multiplication problem. Solve those problems if you can. If you can’t, explain what is wrong. $$5 : 0 qquad 0 : 5 qquad 7 : 0 qquad 0 : 7 qquad 0 : 0$$
  • Use your work to explain why we say that division by 0 is undefined.
  • Use one of our models of division to explain why division by 0 is undefined.

Four Fact Families

In elementary school, students are often encouraged to memorize “four fact families,” for example:

[egin{split} 2 + 3 &= 5 3 + 2 &= 5 end{split} quad egin{split} 5 - 3 &= 2 5 - 2 &= 3 end{split}]

Here’s a different “four fact family”:

[egin{split} 2 cdot 3 &= 6 3 cdot 2 &= 6 end{split} quad egin{split} 6 : 3 &= 2 6 : 2 &= 3 end{split}]

Think / Pair / Share

  • In what sense are these groups of equations “families”?
  • Write down at least two more addition / subtraction four fact families.
  • Use properties of addition and subtraction to explain why these four fact families are each really one fact.
  • Write down at least two more multiplication / division four fact families.
  • Use properties of multiplication and division to explain why these four fact families are each really one fact.

Problem 26

  1. Here’s a true fact in base six: (2_{six} + 3_{six} = 5_{six}). Write the rest of this four fact family.
  2. Here’s a true fact in base six: (11_{six} - 5_{six} = 2_{six}). Write the rest of this four fact family.

Going Deeper with Division

So far we’ve been thinking about division in what’s called the quotative model. In the quotative model, we want to make groups of equal size. We know the size of the group, and we ask how many groups. For example, we think of 20 ÷ 4 as:

How many groups of 4 are there in a group of 20?

Thinking about four fact families, however, we realize we can turn the question around a bit. We could think about the partitive model of division. In the partitive model, we want to make an equal number of groups. We know how many groups, and we ask the size of the group. In the partitive model, we think of 20 ÷ 4 as:

20 is 4 groups of what size?

When we know the original amount and the number of parts, we use partitive division to find the size of each part.

When we know the original amount and the size of each part, we use quotative division to find the number of parts.

Here are some examples in word problems:


number of groups known

find the number in each group

number in each group known

find the number of groups

A movie theater made $6450 in one night of ticket sales.

430 people purchased a ticker.

How much does one ticket cost?

A movie theater made $6450 in one night of ticket sales.

Each ticket cost $12.50.

How many people purchased a ticket?

Think / Pair / Share

For each word problem below:

  • Draw a picture to show what the problem is asking.
  • Use your picture to help you decide if it is a quotative or a partitive division problem.
  • Solve the problem using any method you like.
  1. David made 36 cookies for the bake sale. He packaged the cookies in boxes of 9. How many boxes did he use?
  2. David made 36 cookies to share with his friends at lunch. There were 12 people at his lunch table (including David). How many cookies did each person get?
  3. Liz spent one summer hiking the Appalachin trail. She completed 1,380 miles of the trail and averaged 15 miles per day. How many days was she out hiking that summer?
  4. On April 1, 2012, Chase Norton became the first person to hike the entire Ko‘olau summit in a single trip. (True story!) It took him eight days to hike all 48 miles from start to finish. If he kept a steady pace, how many miles did he hike each day?

Think / Pair / Share

Write your own word problems: Write one partitive division problem and one quotative division problem. Choose your numbers carefully so that the answer works out nicely. Be sure to solve your problems!

Why think about these two models for division? You won’t be teaching the words partitive and quotative to your students. But recognizing the two kinds of division problems (and being able to come up with examples of each) will make you a better teacher.

It’s important that your students are exposed to both ways of thinking about division, and to problems of both types. Otherwise, they may think about division too narrowly and not really understand what’s going on. If you understand the two kinds of problems, you can more easily diagnose and remedy students’ difficulties.

Most of the division problems we’ve looked at so far have come out evenly, with no remainder. But of course, that doesn’t always happen! Sometimes, a whole number answer makes sense, and the context of the problem should tell you which whole number is the right one to choose.

Problem 27

What is 43 : 4?

  1. Write a problem that uses the computation 43 : 4 and gives 10 as the correct answer.
  2. Write a problem that uses the computation 43 : 4 and gives 11 as the correct answer.
  3. Write a problem that uses the computation 43 : 4 and gives 10.75 as the correct answer.

We can think about division with remainder in terms of some of our models for operations. For example, we can calculate that 23 : 4 = 5 R3. We can picture it this way:

[23 = 5 cdot 4 + 3 ldotp]

Think / Pair / Share

  • Explain how the picture above illustrates 23 = 5 · 4 + 3. Where do you see the remainder of 3 in the picture?
  • Explain the connection between these two equations. $$23 : 4 = 5; ext{R} 3 quad ext{and} quad 23 = 5 cdot 4 + 3 ldotp$$
  • How could you use the number line model to show the calculation 23 = 5 · 4 + 3? What does a “remainder” look like in this model?
  • Draw area models for each of these division problems. Find the quotient and remainder. $$40 : 12 qquad 59 : 10 qquad 91 : 16$$

The Python Tutorial¶

Python is an easy to learn, powerful programming language. It has efficient high-level data structures and a simple but effective approach to object-oriented programming. Python’s elegant syntax and dynamic typing, together with its interpreted nature, make it an ideal language for scripting and rapid application development in many areas on most platforms.

The Python interpreter and the extensive standard library are freely available in source or binary form for all major platforms from the Python Web site,, and may be freely distributed. The same site also contains distributions of and pointers to many free third party Python modules, programs and tools, and additional documentation.

The Python interpreter is easily extended with new functions and data types implemented in C or C++ (or other languages callable from C). Python is also suitable as an extension language for customizable applications.

This tutorial introduces the reader informally to the basic concepts and features of the Python language and system. It helps to have a Python interpreter handy for hands-on experience, but all examples are self-contained, so the tutorial can be read off-line as well.

For a description of standard objects and modules, see The Python Standard Library . The Python Language Reference gives a more formal definition of the language. To write extensions in C or C++, read Extending and Embedding the Python Interpreter and Python/C API Reference Manual . There are also several books covering Python in depth.

This tutorial does not attempt to be comprehensive and cover every single feature, or even every commonly used feature. Instead, it introduces many of Python’s most noteworthy features, and will give you a good idea of the language’s flavor and style. After reading it, you will be able to read and write Python modules and programs, and you will be ready to learn more about the various Python library modules described in The Python Standard Library .

Basic Foam Operations - Part 3

Firefighters preparing to engage in a basic foam operation must have a working knowledge of the basics. There is some vocabulary that if used incorrectly, can lead to confusion. Foam concentrate typically comes in 5-gallon pails, or for more major types of operations can be found in 55-gallon drums and even larger storage capacities such as storage containers, called totes, that hold up to 250 gallons of concentrate or more. Foam concentrate must be added into the water stream in the proper ratio.

Firefighters preparing to engage in a basic foam operation must have a working knowledge of the basics. There is some vocabulary that if used incorrectly, can lead to confusion.

Foam concentrate typically comes in 5-gallon pails, or for more major types of operations can be found in 55-gallon drums and even larger storage capacities such as storage containers, called totes, that hold up to 250 gallons of concentrate or more. Foam concentrate must be added into the water stream in the proper ratio.

All of our members, regardless of the facility or community they protect should be thoroughly familiar with the concentrates in use by their department. Consult the web sites for each of the major manufacturers for specific details. See the references at the end of the first part of this series for many high-quality information sources.

For the more typical foam concentrates used on Class B fires, we find manufacturers making concentrates designed to be mixed with water at a 1%, 3%, or 6% ratio. In other words, depending on the type of foam, or the type of fuel, foam concentrate is designed to be mixed with 99 parts water to 1 part concentrate (1 % foam concentrate), 97 parts water to 3 parts (3% foam concentrate), or 94 parts water to 6 parts concentrate (6% foam concentrate).

Foam Solution is the mixing in the correct ratio of water to foam concentrate. After the water and the foam concentrate have been mixed together, the liquid in the hoseline is no longer water alone, nor is it foam concentrate. Rather, we have what is called a foam solution that is only missing one final ingredient.

Finished Foam is the mixing of air (aspiration) to the foam solution in the hoseline. The air being injected into the discharge stream creates the bubbles and “suds” that give foam its finished appearance. This “aeration” gives foam a power to remain in place for a period of time. For example, a thick blanket of foam that may be several inches thick will continue to provide protection and prevent the release of flammable vapors.

Finished foam has great properties in its ability to prevent the release of flammable vapors from mixing with air due to foam’s ability to float on top of a spill and present a barrier between the air and the fuel source. Nevertheless, this foam blanket will not last forever and eventually begins to degrade, especially if affected by fire or residual heat. A foam blanket’s “drain time” is discussed below.

A critical point to be aware of is finished foam’s compatibility with other types of extinguishing agents. As an example, finished foams such as Aqueous Film Forming Foam (AFFF) and Film Forming Fluoroprotein (FFFP) are compatible with dry chemical, and a coordinated attack can be achieved. Always check with the manufacturer regarding the foam concentrate your department uses to see if it is compatible with agents such as dry chemical.

Finished foam can be compatible with various types of extinguishing agents but, ironically, a plain water stream used near a foam stream will only wash away and dilute the finished foam. Therefore, coordination of hoselines is a requirement prior to any application. Even after the finished foam blanket has been applied and is doing its job to prevent the release of vapors, any application of water can destroy this blanket, so use caution near it!

Drain time is how long it takes for a foam blanket to break down. Finished foam can potentially deliver a thick, rich blanket to cover a spill or fire. As time passes, the finished foam blanket begins to degrade. The drainage rate is based on how long 25% of the foam blanket takes to break down. Eventually, a reapplication will be required or the danger of flammable vapors will resurface. If the fuel is hot or the surroundings that contain the fuel are hot, the foam blanket will degrade even more quickly.

The application of foam requires the mixing of the three key ingredients – concentrate, water, and air – in the proper ratio. This finished foam is applied so that it blankets the fuel and excludes the vapors from mixing with the air. This smothering effect prevents the ignition of a spill, or should a fire occur, the finished foam spreads across the fuel and creates a film or barrier.

Water by itself can create additional problems if used on a spill. Fuels that are lighter in weight than water will rise to the top and continue to burn. Even worse, such an application could create a “running” fuel fire where the spill begins to meander downhill creating a river of flame. Polar solvents on the other hand, will mix readily with water.

Finished foam changes the properties of water to an extinguishing agent that is lighter than the flammable or combustible liquids. This change in physical properties gives us the advantage to attack a fire by creating that blanket or barrier on top of the fuel.

In the event a polar solvent fuel was to be attacked, the department would rely on an alcohol-resistant concentrate. This concentrate creates a protective “polymer-based” membrane that also prevents the mixing of fuel vapors with air. To our good fortune, the fire service has access to dual-purpose foams that can be used on both polar solvents and hydrocarbons, such as Alcohol-Resistant AFFF (AR-AFFF). Check with the manufacturer as to the proper ratio to which such foam concentrates should be applied.

For example, past AR-AFFF foams read 3% x 6% foam concentrates. This meant that for a hydrocarbon spill, the ratio of concentrate to water had to be 3%, while a spill involving polar solvents had to be 6%. Newer foams may have different percentages such as 3% x 3% (3% ratio with water for either hydrocarbon or polar solvents), while some foam concentrates rely on a 1% ratio.

In short, know your equipment before it has to be used. Read the directions on the 5-gallon pail of foam that’s on your engine, before it’s needed. The information that’s listed on these containers is of great value. It tells you the uses for and limitations of the concentrate.

We’ll talk later about the proper application of the finished foam blanket, but for our purposes now, let it be understood that foam should be applied in a manner that does not disturb the fuel, such as by banking the foam stream off an object and letting it cascade down on top of the fuel and spread out over top. We want to avoid plunging the stream into the spill as this creates a more dangerous situation.

One of the other advantages of some of today’s foams such as FFFP or AFFF is the ability to shed fuel. This is advantageous because the finished foam will rise to the top and spread out creating that barrier we talked of earlier.

The additional benefits of foam are the ability to create a cooling environment. Foam is mainly water (94% to 99%) and as such it has the advantages of water’s cooling properties. A spill that has ignited and is within a metal barrier such as a tank for example, can reap the benefits of foam’s cooling ability. Lowering the temperature of everything associated with the spill or fire pays large dividends for obvious reasons.

One other important note as we said, foam is mainly water and therefore can create an electrocution hazard. A foam stream should not be used on energized electrical equipment. For fires involving Class C equipment, it is always a safe practice to de-energize the source before applying the stream.

Also, fuels that are too hot can react negatively to the application of foam and break the foam blanket down rapidly. For the typical spills and Class B fires that we respond to, this is not much of an issue, but does require knowledge, just to be safe.

In the next article in this series, we’ll discuss the proportioning of foam concentrate and introduce the typical in-line eductor. The next article in the series is going to build upon all we have covered up to this point. In the meantime, take a look at the foam concentrates you have on your apparatus or in fire station storage. Ask yourself these questions, or as part of a company drill, find out the answers to these:

Resort Operations definition

Kaufman, “Do Lender of Last Resort Operations Require Bank Regulation?” (paper presented at the American Enterprise Institute confer- ence, Is Banking Regulation Necessary?, in Washington, DC, October 27, 1999).

In addition, we earn fees from servicing our own portfolio and the loans provided by third-party developers of our fee-for-service projects to purchasers of their VOIs. Resort Operations and Club Management We enter into a management agreement with the HOA of the VOI owners for timeshare resorts developed by us or a third party.

Schavemaker has served as our Senior Vice President, Customer Experience and Resort Operations since 2007.

Wintergreen Long-term Rental Units shall be subject to the Priority Leasing Process, which shall mean: Wintergreen Long-term Rental Units will be initially offered for 10 days to only Employees, Employers and employees of Adjacent Resort Operations.

Compared to the prior-year period, Resort Operations and Club Management results in the first quarter of 2020 decreased primarily due to a decrease in rental and ancillary services revenue related to the temporary suspension of operations due to COVID- 19.

Support Bundle

Similar to other VMware products there are several easy ways to capture all of the information required to troubleshoot most issues you will experience within your environment.

There are two different types of support bundles you can capture from vROps as outlined below:

The Light Support Bundle option includes 24 hours of logs and basic configuration information for the vROps environment.

The size difference between a Light and Full bundle is significant thus, unless directed by Pure Storage or VMware support, a light support bundle is recommended.

The Full Support Bundle option contains all of the available logs and configuration files.

This option should only be used when directed by Pure Storage or VMware support or when debug logging has been enabled for advanced troubleshooting purposes.

  1. Navigate to the Administrationsection.
  2. Expand Supportin the left hand pane.
  3. Select Logs under the Support section.
  4. Click on the green " + " symbol to begin generating a new support bundle.

  1. When the Generate Support Bundles prompt pops up select the Light Support Bundle (unless otherwise requested by support).
  2. Select the all of the nodes to capture the data on (unless otherwise requested by support).
  3. Click OKto complete the process.

  1. Wait for the Statusto change from "In Progress" to "Succeeded" and download the new log bundle.
  2. Upload the log bundle to the Pure Storage FTPS by following the Uploading Files to Pure Storage KB.
  1. Log into the Master node as root via SSH or Console.
  2. Run the script using this command:

Generating a Light Support Bundle:

Generating a Full Support Bundle:

  1. The support bundle will be placed in the /usr/lib/vmware-vcops/support/timestampdirectory (where timestamp is the milliseconds since epoch time).
  2. Once the support bundle has been successfully generated capture the ".zip" files under the stored directory and upload them to the Pure Storage FTPS by following the Uploading Files to Pure Storage KB.

Below is an example of what the output looks like following the successful creation of a support bundle. Please see below the ".zip" files mentioned in step 4.

]# python /usr/lib/vmware-vcopssuite/utilities/bin/ -a create -f 1,2,3,4 -m
Default Values:
timestamp: -t=1596155572992 (current time in milliseconds)

Option -m=true so only most recent logs will be bundled.
Waiting until support bundle is created

SLF4J: Class path contains multiple SLF4J bindings.
SLF4J: Found binding in [jar:file:/usr/lib/vmware-vcops/tomcat-enterprise/webapps/suite-api/docs/bindings/java/vcops-suiteapi-client-1.11-all.jar!/org/slf4j/impl/StaticLoggerBinder.class]
SLF4J: Found binding in [jar:file:/usr/lib/vmware-vcops/common/lib/slf4j-log4j12-1.7.25.jar!/org/slf4j/impl/StaticLoggerBinder.class]
SLF4J: Found binding in [jar:file:/usr/lib/vmware-vcops/common/lib/vcops-suiteapi-client-1.11-all.jar!/org/slf4j/impl/StaticLoggerBinder.class]
SLF4J: See for an explanation.
SLF4J: Actual binding is of type [org.slf4j.impl.Log4jLoggerFactory]
Tech support bundle is created successfully for timestamp: 1596155572992
------------Generated support bundles----------------
/usr/lib/vmware-vcops/support/1596155572992/1,2, <------ Upload
/usr/lib/vmware-vcops/support/1596155572992/ <------ Upload


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Basic Foam Operations - Part 2

There are a variety of foam concentrates available to the fire service. Some are more specialized than others and some are more common. In order to give company members a working knowledge, we’ll give a brief overview of the different types of foam concentrate and some of the “buzzwords” associated with foam. If you want more information, the major manufacturers have an enormous wealth of information available for free on the web. Take a look at the references at the end of the first part of this series.

There are a variety of foam concentrates available to the fire service. Some are more specialized than others and some are more common. In order to give company members a working knowledge, we’ll give a brief overview of the different types of foam concentrate and some of the “buzzwords” associated with foam. If you want more information, the major manufacturers have an enormous wealth of information available for free on the web. Take a look at the references at the end of the first part of this series.

Chemical Foam was the mixing of powdered chemicals that together created a finished foam product. Sometimes these chemical additives were referred to as Chemical A and Chemical B. It’s important not to confuse this nomenclature with other vocabulary such as Class A and Class B foam concentrates.

With chemical foam there was no single concentrate that was easily added to a hoseline. The two chemical powders were added via a hopper directly into the hoseline. Because of its difficulty in use, and less than perfect quality, it is no longer used in today’s fire service. Chemical foam was replaced by mechanical foam decades ago.

Mechanical Foam is the common product we deal with on a daily basis. Mixing water, foam concentrate, and air in the proper ratios to produce a finished foam blanket creates foam. The three ingredients are mixed via a mechanical process and do not require a chemical reaction to achieve a finished foam blanket. Our studies will primarily be concerned with the correct mixing of these three ingredients and applying the finished product effectively.

There are a variety of foam concentrates on the market today. Depending on the manufacturer, you may find differences in the specific details associated with each concentrate, so make sure you know the specifics of what your department is using. In this series of articles, we’ll offer a very generic look at some of the more common types of concentrates and equipment that can be used, but for specific details, consult the manufacturers.

Protein Foam was an original type of liquid concentrate that was made up of organic materials and other additives. When used to attack a flammable liquid fire, it had a good resistance to heat, but its use was limited to hydrocarbon spills and fires. It is not in use in any great quantity in the municipal fire service any more. Other types of concentrates have replaced protein foam. These more modern concentrates have additional features such as greater fuel shedding properties and the ability to be used on both hydrocarbon and polar solvent spills and fires.

Film Forming Fluoroprotein (FFFP) and Alcohol-Resistant Film Forming Fluoroprotein (AR-FFFP) build upon the benefits of protein foam and protein foam’s successor, Fluoroprotein foam. With synthetic additives as part of the concentrate, these concentrates can be used on fires and spills involving hydrocarbon fuels. With additional additives, these foams can be designed as an alcohol-resistant type of concentrate allowing them to be well-suited to incidents involving polar solvents. FFFP foam has the added benefit of being able to apply a very thin film over top of the spill, thus preventing the release of flammable vapors from mixing with air. With proper application, these types of foam concentrates offer a finished foam that is longer lasting, has good fuel shedding ability, and has good resistance to heat.

It also has similar features to AFFF (see below) in that a film floats ahead of the spill to create a layer that separates the fuel from the air. This concentrate can be used with both fresh and saltwater for even greater versatility. Check with the manufacturer as it relates to freezing and thawing (some sources say the concentrate can be affected by freezing and thawing, while other sources say the opposite). This agent is also compatible with dry chemical extinguishing agent in the event a coordinated attack is required.

Remember that for fires involving polar solvents, the alcohol-resistant concentrate has a polymer additive that allows the finished foam to be of value in controlling such spills and fires. Failure to use an alcohol-resistant concentrate will mean that the foam application will break down quickly and mix with the spilled product. We have to use the correct concentrate for the fuel in question.

Aqueous Film Forming Foam or “A Triple F” (AFFF) and Alcohol-Resistant AFFF (AR-AFFF) are very popular concentrates in today’s fire service. They are synthetic concentrates that do not rely on any protein-based additives like those described. AFFF can be used successfully when attacking a flammable liquid spill or fire that is hydrocarbon based. It can be used with either fresh or saltwater and is compatible with dry chemical extinguishing agents. Like with the fluoroprotein and FFFP concentrates, the physical properties of plain water are altered when mixed with the foam concentrate and the result is an extinguishing agent that has the ability to float on top of a flammable or combustible liquid spill. Recall, for example, that water alone would sink to the bottom of a fuel spill involving gasoline. Gasoline has a specific gravity of less than 1, which means that it is lighter than water and will float on top. The aqueous film that is part of the finished foam forms a seal overtop of the fuel spill. The film prevents the mixture of air with the fuel vapors, thus limiting the chance of ignition. AFFF has a fast drain time, in other words, the finished foam blanket can degrade quickly especially if the fuel is hot, such as immediately after fire knockdown. This requires a re-application to prevent dangerous vapors from igniting. Always make sure that a supply of concentrate is readily available for a minimum application rate. Application rates will be explained in greater depth in a later article.

Not all of the responses we go to are as simple as the typical hydrocarbon spill. Fuels such as alcohols or the newer blends and additives such as ethanol in gasoline make for a potentially difficult situation. AR-AFFF is a close cousin to AFFF and can be of great value to us. Ethanol blended gasoline that has 10% or more ethanol should be handled with an alcohol-resistant foam concentrate. Consult the specific manufacturer for details as it relates to this topic. Some foam concentrates have specific details that differ from other manufacturers.

Due to polymer additives, this type of concentrate (AR-AFFF) has greater capabilities and can be used successfully on both hydrocarbon and polar solvent spills and fires. Like with the example we used a short while ago for polar solvents and the FFFP foam concentrate, it’s important that we also use an alcohol resistant (AR-AFFF) concentrate for fires and spills involving polar solvents. Using AFFF on a polar solvent will cause the foam to break down and mix with the fuel rather quickly.

The destruction of AFFF’s finished foam and its aqueous film on polar solvent spills allows for the release of flammable vapors and the danger of ignition or re-ignition. The answer to this scenario is the use of an alcohol-resistant concentrate. Stronger polar solvents also require a higher application rate just take a look at the specific application rates required for different liquids for the foam concentrates you’re presently using. The additives in alcohol resistant foam (AR-AFFF) gives us a concentrate that when mixed with water and air delivers a finished foam blanket that seals the spill with a protective “polymeric membrane” that prevents the release of ignitable vapors from a polar solvent spill. This type of foam blanket is best applied with an air-aspirating nozzle that we’ll cover later on. The alcohol resistant concentrates are a thicker concentrate compared to the non-alcohol resistant concentrates.

Advantages of Today’s Concentrates

Recall that without oxygen, one side of the fire tetrahedron is missing. The ability of foam to separate the fuel (vapors in this case) from the oxygen allows us to prevent a fire from happening or to extinguish a fire that has begun.

Given today’s incidents that the typical municipal fire department responds to, it is critical that the department has the ability to adapt to a host of situations. The multitude of chemicals that are a part of our everyday lifestyle also means problems for the first responders. As such, a foam concentrate that is good on both hydrocarbon and polar solvent spills and fires would increase any department’s capability. Concentrates such as AR-AFFF are one type of foam that would offer this advantage.

Today’s foam concentrates are designed to be mixed in certain ratios with water. In the past, 3% and 6% were common settings. The directions on a typical 3% x 6% five-gallon pail of AR-AFFF foam concentrate, for example, directed that for hydrocarbon fuels, the mixture of concentrate to water was 3% (in other words 97 gallons of water and 3 gallons of foam concentrate), while for polar solvent spills the ratio was to be set at 6% (6 gallons of concentrate and 94 gallons of water).

Newer concentrates can be as low as 1% mixtures of concentrate to water. Take a look at some of the products available from the different foam manufacturers. Each of their product guides goes in-depth as to the ratio as well as application rates for different types of fuels and spills.

Today’s common foam concentrates can be mixed with both fresh water as well as saltwater. This further increases our advantages. The fire service responds to many different types of incidents and a shore-based community could very well find itself relying on out-of-the-ordinary water supplies for any number of reasons. A response attributed to a manmade disaster or a natural disaster could render the municipal infrastructure and water supply useless. Such a situation calls for out-of-the-box thinking and knowing that saltwater could be a key ingredient in making our strategy work would pay dividends.

During the application of foam, concentrates of the same family, such as AFFF, can be mixed together just prior to eduction, but to batch mix the concentrates of different manufacturers for extended periods of time could become problematic. Also batch mixing for extended periods of times with other types of concentrates can be problematic. Always check with the manufacturer to determine the limitations of your foam concentrate.

Foam is also mildly corrosive and after application it is important that all elements of the foam system (i.e., nozzles, eductors, appliances, etc.) be flushed for at least several minutes.

The shelf life of foam concentrate is another advantage. Most concentrates have lengthy shelf lives of 5 to 25 years, but depending on the manufacturer, type of concentrate, and the storage conditions (such as temperature and exposure to direct sunlight) can all affect the lifespan of the concentrate.

There are many types of concentrates on the market and there are many sources of accurate information readily available. Take a look at some of these additional sources starting with the foam you presently have. Know your equipment before the incident occurs!

The next article in this series will take our studies further into the topic of foam firefighting and how it relates to the typical engine company.

3.9: Properties of Operations (Part 2)

Cross platform library for storage device operations across various interfaces and device types.

Copyright (c) 2014-2021 Seagate Technology LLC and/or its Affiliates, All Rights Reserved

Welcome to opensea-operations, part of the openSeaChest open source project! You can find the openSeaChest project here.

opensea-common - Operating System common operations, not specific to storage standards. Contains functions and defines that are useful to all other libraries.

opensea-transport - Contains standard ATA/SCSI/NVMe functions based on open standards for these command sets. This layer also supports different transporting these commands through operating systems to the storage devices. Code depends on opensea-common.

opensea-operations - Contains common use cases for operations to be performed on a storage device. This layer encapsulates the nuances of each command set (ATA/SCSI) and operating systems (Linux/Windows etc.) Depends on opensea-common and opensea-transport.

Source code for opensea-operations is available in this repo at

See for information on how to build the openSeaChest tools on Windows, Linux, FreeBSD, and Solaris/Illumos.

See for more information on contributions that will be accepted. This document also describes how to create an issue, generate a pull request, and licenses that will be accepted.

See for information on Seagate's security policy for details on how to report security vulnerabilities.

All product names, logos, and brands are property of their respective owners. All company, product and service names mentioned in the source code are for clarification purposes only. Use of these names, logos, and brands does not imply endorsement.

Support and Open Source Statement

Support from Seagate Technology for open source projects is different than traditional Technical Support. If possible, please use the Issues tab in the individual software projects so that others may benefit from the questions and answers. Include the output of --version information in the message. See the user guide section 'General Usage Hints' for information about saving output to a log file.

If you need to contact us through email, please choose one of these two email addresses:

    for general questions and bug reports for specific questions about programming and building the software

Seagate offers technical support for drive installation. If you have any questions related to Seagate products and technologies, feel free to submit your request on our web site. See the web site for a list of world-wide telephone numbers.

This software uses open source packages obtained with permission from the relevant parties. For a complete list of open source components, sources and licenses, please see our Linux USB Boot Maker Utility FAQ for additional information.

The newest online version of the openSeaChest Utilities documentation, open source usage and acknowledgement licenses, and our Linux USB Boot Maker FAQ can be found at:

Copyright (c) 2014-2021 Seagate Technology LLC and/or its Affiliates, All Rights Reserved

BINARIES and SOURCE CODE files of the openSeaChest open source project have been made available to you under the Mozilla Public License 2.0 (MPL). Mozilla is the custodian of the Mozilla Public License ("MPL"), an open source/free software license.

MED Investment Operations – Part 2: “This model is recognized by international institutions such as Standard Conversion environmental assets of Forests in Transaction instruments”

Two weeks ago, REDD-Monitor received an email offering 345 million carbon credits for sale. The carbon credits were from a REDD project in Brazil and a company based in Malta called MED Investment Operations is offering them for sale at US$6.80 each. Last week, I wrote about the companies in Malta behind this incredible offer: MED Investment Operations and The Equivest Alliance.

While I was researching these two companies in Malta, I received an email from Boniface Mburaburirwe. He had first written to REDD-Monitor informing me about this large number of REDD credits for sale. When I asked him for more details, he forwarded an email from Dr. Elena E. Gorshkova of MED Investment Operations and The Equivest Alliance.

In his most recent email, Mburaburirwe forwarded another email from Gorshkova, who in turn forwarded the responses to my questions from Daniel Azzopardi, CEO of MED Investment Operations. Here is the email in full:

From: Boniface Mburaburirwe
Date: 24 July 2016 at 15:33
Subject: Fwd: FW: Redd-M feedback
To: Chris Lang
Cc: Elena, Elena Gorshkova

Please find here below the answers to the questions you asked for in your previous email.

Looking forward to hearing from you soon.

Boniface Mburaburirwe BVM, MRCVS

———- Original Message ———-
From: “Dr. Elena E. Gorshkova”
To: Boniface Mburaburirwe
Date: 24 July 2016 at 11:12
Subject: FW: Redd-M feedback

The answeres to the questions you have sent me from Cris.

Thank you for your email and appologies for the late reply.

We had tremendous back-log following our travels.

Please find the Answers to your questions below.
*Also the latest Bloomberg Screenshot attached.
*The Certificate of Carbon Units by Inbecas.
*Full Methodology Report
*Validation Reports translated.

*Which project are the carbon credits from, and in which country?
All nuclei of economic and sustainable development project MIDIAGEO are located in Brazil in the states of Mato Grosso , Pará and Amazonas.

*Who are the project developers?

*Is it a REDD project?
CAS – Environmental Credit Socioeconomic
The demand for increased agricultural production has led to expansion of production areas through deforestation in various regions of Brazil . In the face of this major environmental problem arises the MIDIAGEO REDD – BRAZIL solution.
This CAS Program – Environmental Credit Socioeconomic MIDIAGEO REDD – BRAZIL aims to generate income through the Preservation of Native Forests and increased production using smaller areas. Through the articulation of people and institutions in the pursuit of a sustainability standard to align the environmental, social and economic links consistently and that had resulted in a sustainable model of operation in their areas of coverage focused on environmental conservation and improvements in quality of life of farmers and regional development.
forest protection project uses a methodology that calculates through REDD , forest carbon stocks in areas with native forests of the region, ie of natural forests each property , not including forests planted for commercial purposes , differing from project REED ( Reducing emissions from Deforestation and Degradation ) not to worry about the emissions curve calculations, since the project is total preservation areas. They will also be included in the work at the stage of monitoring, prevention systems and adjusting for leaks ( leakages ) .
This model is recognized by international institutions such as Standard Conversion environmental assets of Forests in Transaction instruments. We focus viable agricultural activities in rural properties with the use of existing areas in the scope of local, avoiding the spread of deforestation and burning of forest reserves.
The development model proposed by the program provides substantial benefits that justify its existence as one of the enablers and drivers of the new socio-economic and environmental reality that has the main objective of sustainability:

· Zero deforestation of areas of group members,
· Local ecosystem preservation, allowing the preservation of Regularization fauna and environmental suitability of the property,

· Environmental Education – Introduction of environmental education and integration of existing programs such as good environmental practices

· Significant improvement of the economic reality of the group of producers with the mechanism would have an increase in income, employment generation and improvement of living conditions of the families involved,
Consolidation of productive chains in the region,

· Significant collection Expansion in the region,

· Creating a barrier to the expansion of pastures on the Amazon and Cerrado biomes ,

· Economic Viability of productive activities in line with local calling,

· Integration and interaction of the various productive sectors of the region minimizing conflicts of interest .

It is important to note that the benefits provided by this environmental tool will positively affect the bond market as it will provide another application alternative on the market allowing potential investors to acquire credits Environmental Socioeconomic MIDIAGEO REDD BRAZIL safely and transparently.

*What is the vintage of the carbon credits?
The MED Investment Operations ltd credits specifically, refer to
Vintage 2012 ( inventory)

*Who currently owns the carbon credits?
Until full payment of the amounts of credits, ownership of the rights to carbon credits belong to MIDIAGEO GROUP LTD ., The ownership rights transfer Term will be passed by compensation to MED INVESTMENT OPERATIONS LTD acting as Seller and in partnership agreement with MIDIAGEO GROUP LTD.

*Which registry are the credits on?
It was developed between local governments of Brazil SISA – Integrated Environmental Sustainability by InBECAS platform – Brazilian Institute of Carbon and Sustainable Actions stock.

*Are the carbon credits verified and certified?
Yes, validated and certified by INBECAS through technical cooperation terms of validation and licensing with SEMA , IBAMA and MMA

*Could you please send the verification and certification statements (or links to them). And the Project Design Document (PDD)?

All insusceptible document analysis in this step are available in the public link available on the FSIS platform in consultation with the passkey on the “Monitor credit.”
Which is a key that MED INVESTMENT OPERATIONS LTD has in order to gain access and transfer the credits to third parties post contract and payment.

Unfortunately, I couldn’t open the “Methodology Carbon Credit – REDD Brazil.pdf” file. When I clicked on the link I got the following message:

I wrote back to Mburaburirwe and Gorshkova asking them to give my Google account the necessary permission to read the file. So far, they have not done so.

Azzopardi’s response to my question, “Is it a REDD project?” is cut and pasted from MidiaGEO’s website. None of it is reassuring. The fact that REDD is mis-typed as “REED” suggests someone was in a hurry. The fact that following sentence makes no sense whatsoever is alarming:

“This model is recognized by international institutions such as Standard Conversion environmental assets of Forests in Transaction instruments.”

The response to my question about which registry the carbon credits are on is even more alarming. Azzopardi doesn’t say which registry the carbon credits are on. Instead he tells me it was developed by InBECAS. The carbon credits supposedly come from a project called d´Cerrado a´Amazonia REDD Brasil. When we look on the InBECAS website, we find that the project covers an area of 545,430 hectares.

The carbon credits were generated in 2012, so this very large REDD project has been around for several years. I eagerly anticipated reading more. But Google disappointed me:

Azzopardi declined to answer my question about what “carbon credits already invested on Bloomberg” means. He didn’t send me a Project Design Document, instead giving me a “passkey” on the FSIS platform. Whatever that is.

Which leaves us with the validation report that Azzopardi sent. It’s nonsense. Here just some of the more obvious howlers:

  • There is no project description.
  • There is no information about the actions being carried out in the project area to reduce deforestation.
  • The report makes no mention of any corrective action requests, information requests, or opportunities for improvement that the project developers had to carry out before the project could be validated.
  • The report is very short. Verification reports are usually considerably longer. Here’s a more or less randomlyselectedsample, the shortest of which is 49 pages long. The document that Azzopardi sent me is 14 pages long.
  • The validation was carried out by two consultants: Andréia N. Oliveira and Barbara Waldvogel. A search for their names and REDD revealsnothing about their careers as REDD consultants.

In the next instalment, REDD-Monitor will take a look at the D’Cerrado A’Amazonia REDD project in Brazil and the companies supposedly running the project.

How Does a Turbocharger Work?

A turbocharger is made up of two main sections: the turbine and the compressor. The turbine consists of the turbine wheel (1) and the turbine housing (2). It is the job of the turbine housing to guide the exhaust gas (3) into the turbine wheel. The energy from the exhaust gas turns the turbine wheel, and the gas then exits the turbine housing through an exhaust outlet area (4).

The compressor also consists of two parts: the compressor wheel (5) and the compressor housing (6). The compressor’s mode of action is opposite that of the turbine. The compressor wheel is attached to the turbine by a forged steel shaft (7), and as the turbine turns the compressor wheel, the high-velocity spinning draws in air and compresses it. The compressor housing then converts the high-velocity, low-pressure air stream into a high-pressure, low-velocity air stream through a process called diffusion. The compressed air (8) is pushed into the engine, allowing the engine to burn more fuel to produce more power.

Watch the video: Funktionen Teil 1: Eigenschaften, Wichtige Funktionen + Skizze. Vorkurs Mathematik für Studenten (October 2021).