Articles On Testing

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Articles On Testing

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Articles On Testing

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Articles On Testing

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Articles On Testing

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Showing posts with label miscellaneous. Show all posts
Showing posts with label miscellaneous. Show all posts

How to use Outlook Effectively

How to use Outlook Effectively?
Outlook is big, powerful and flexible but it can also be confusing. We always find that people have an idea  of how to compose mails through Outlook they may not know how to use it effectively .
I’d like to share with you some tips about Outlook in this post.
Shall we get started?                                                                                                                                                                                     

1.      How to check your Outlook folders' sizes
2.      How to export your Outlook contacts to a CSV File
3.      How to get reminded to reply to a message in Outlook
4.      How to write a message using a specific message format in Outlook
5.      How to see total (Not Just Unread) inbox message count in Outlook
6.      Restore Outlook mail, contacts and other data from a backup
7.      How to create  a distribution list in Outlook
8.      How to filter one sender's mail to a certain folder automatically
9.      How to forward multiple messages individually in Outlook
10.  How to save multiple attachments at once with Outlook
11.  How to change default language in Microsoft Outlook
12.  How to turn on the Out of Office Assistant
13.  How to use categories to track items in Outlook
14.  Add voting buttons to a message
15.   Outlook shortcuts

How to Check Your Outlook Folders' Sizes


Is your outlook very slow?
Has handling email in Outlook become slow and heavy, or is your hard disk shrinking and you suspect the ten thousand emails with their twenty thousand attachments might be involved?
But which folder is to be blamed, where do the big emails hide? Fortunately, Outlook comes with a small tool that lets you find out exactly how much space each folder occupies.
Check Your Outlook Folders' Sizes

To see the size of your Outlook folders:
Select Tools | Mailbox Cleanup... from the menu. 

Click ‘View Mailbox Size’  

How to Export Your Outlook Contacts to a CSV File


If you move from one email program to the next, you don't want to leave your contacts behind. While Outlook stores everything including mail and contacts in a complicated file, exporting your contacts to a format that most other email programs and services can understand is pretty easy.
1.      Export Your Outlook Contacts to a CSV File
2.      To save your contacts from Outlook to a CSV file:
3.      Select File | Import and Export... from the menu. 




4.Make sure Export to a file is highlighted.  



5.Click ‘Next >’.  


6.Now make sure Comma Separated Values (Windows) is selected.
7.Click Next > again. 

8.Highlight the Contacts folder.
9.Click Next >.
10.Use the ‘Browse...’ button to specify a location and file name for the exported contacts. Something like ‘Outlook.csv’ or ‘ol-contacts.csv’ on your Desktop should work fine. 
Click Next > (once more).
Now click Finish.                    

How to Get Reminded to Reply to a Message in Outlook

 Messages that I do not deal with instantly tend to get forgotten for quite some time. Unfortunately, sometimes I forget to answer a mail until it's too late.
1.      Get Reminded to Reply to a Message in Outlook
2.      To make Outlook reminded you to reply to an email:
3.      Right-clicking on the message you want to set the reminder for.
4.      Select Follow Up | Add Reminder... from the menu.
5.      In Outlook 2000-2003, select Flag for Follow Up from the context menu.
6.      Choose the date when you have to completed the task.
7.      Click OK.  

How to Write a Message Using a Specific Message Format in Outlook


1.      To compose an email using a specific format in Outlook:
2.      Select Actions | New Mail Message Using from the menu in Outlook. 

11.Choose the desired format.  

How to See Total (Not Just Unread) Inbox Message Count in Outlook


To have Outlook show you the total number of messages in any folder, say your Inbox, instead of just counting the unread emails:
1.  Open the desired folder, for example your Inbox, in Outlook.
Select File | Folder | Properties for "folder name" from the menu. 
2.      You can also click on the desired folder with the right mouse button and select Properties from the context menu
3.      Go to the General tab.
4.      Make sure Show total number of items is selected. 

Restore Outlook Mail, Contacts and Other Data from a Backup 


1.      To restore your mail, contacts and other data from a backup copy of an Outlook PST file:
2.      Select File | Import and Export... from the menu in Outlook.
3.      Select Import from another program or file.

9.  Highlight Personal Folder File (PST)
10. Click next again.

10. Now use the Browse button to select the backup copy of the PST file you want to recover from your backup location.
11. Make sure Replace duplicates with items imported is selected.
12. Click Next.
13. Finish the import process with Finish.

How to create a distribution list in Outlook

Ø  Add Members to a Distribution List in Outlook
On the File menu, point to New, and then click Distribution List. 
In the Name box, type a name. 
Click Select Members. 
In the Show names from the list, click the address book that contains the e-mail addresses you want in your distribution list. 
In the Type name or select from list box, type a name you want to include. In the list below, select the name, and then click Members. Do this for each person you want to add to the distribution list, and then click OK. 
If you want to add a longer description of the distribution list, click the Notes tab, and then type the text.
The distribution list is saved in your Contacts folder by the name you give it.  

How to change the language settings in outlook

Ø  Changing the Language
 Go To Outlook->Tools->options
1.) Click Mail Format
2.) Click Editor Options 
3.) Click Popular on the left
4.) Then Click Language Settings
5.) Here you will be able to change the default language      Go to top

How to Forward Multiple Messages Individually in Outlook


Ø  Forward Multiple Messages Individually in Outlook
1.      To have Outlook forward a heap of messages individually for you:
2.      Create a new folder. (Call it "Forward" perhaps.)
3.      Copy all messages you want to forward to the "Forward" folder.
4.      Make sure the "Forward" folder is open.
5.      Select Tools | Rules and Alerts... from the menu.
6.      Click New Rule....
7.      Highlight Check messages when they arrive. 
8.      Click Next >.
9.      Click Next > again, leaving all conditions unchecked.
10.  Click Yes.
11.  Make sure forward it to people or distribution list is checked under Step 1: Select action(s).
12.  You can alternatively check forward it to people or distribution list as an attachment to forward messages not inline but attached.
13.  Click people or distribution list under Step 2: Edit the rule description.
14.  Double-click the desired contact or list from your address book, or type the email address to which you want to forward under To
15.  Click OK.
16.  Click Next >.
17.  Click Next > again.
18.  Make sure Turn on this rule is not checked under Step 2: Setup rule options.
19.  Now make sure Run this rule now on messages already in "Forward" (if you named the folder "Forward").
20.  Click Finish.          

How to Save Multiple Attachments at Once with Outlook


Ø  Save Multiple Attachments at Once with Outlook
1.      To save multiple attachments at once in Microsoft Outlook:
2.      Open the message in Outlook.
3.      Select File | Save Attachments | All Attachments... from the menu.
4.      In Outlook 2002 and Outlook 2003, select File | Save Attachments from the menu.
5.      Click OK.
6.      Select the folder where you want to save the attached files.
7.      Click OK again.   

How to Filter One Sender's Mail to a Certain Folder Automatically


To have Outlook file a particular sender's messages automatically:
1.      Click with the right mouse button on a message from the sender whose messages you want to filter.
2.      Select Create Rule... from the menu that comes up. 
3.      Make sure From {Sender} is checked.
4.      Also check Move the item to folder:.
5.      Click Select Folder....
6.      Highlight the desired target folder.
7.      Click OK.
8.      Click OK again.
9.      To move all existing messages from the sender (albeit only in the current folder) to the filter's target folder right away, check Run this rule now on messages already in the current folder.
10.  Either way, the rule will automatically file the sender's all newly incoming messages in the future, of course.
11.  Click OK once more. 

How to Turn On the Out of Office Assistant


On the Tools menu, click Out of Office Assistant.
1.      In the Out of Office Assistant dialog box, click I am currently Out of the Office. 
2.      In the Auto Reply only once to each sender with the following text box, type the message that you want to send while you are out of the office.

How to Use Categories To Track Items In Outlook


A category is a specific word or phrase that you can use to group your Outlook items so you can easily find them later
Outlook has a predefined set of categories. However, you do have the option of creating your own categories if the existing ones do not meet your requirements. So as an alternative, by performing a few simple steps, you can create your own custom categories.

Ø  Create a new category
Ø  Outlook view

Add voting buttons to a message

1.      In the message, click Options.
2.      Select the Use voting buttons check box, and then click the voting button names you want to use in the box.
3.      To create your own voting button names, delete the default button names, and then type any text you want. Separate the button names with semicolons.

4.      Under Delivery options, select the Save sent message to check box. To select a folder other than the Sent Items folder, click Browse.
5.      Click Close, and then click Send.  

Outlook shortcuts

For basic navigation






For basic navigation
To do this
Click
Switch to Mail
CTRL+1
Switch to Calendar
CTRL+2
Switch to Contacts
CTRL+3
Switch to Tasks
CTRL+4
Switch to Notes
CTRL+5
CTRL+6
Switch to Shortcuts
CTRL+7
Next item (with item open)
CTRL+COMMA
Previous item (with item open)
CTRL+PERIOD
Switch between the Folder List and the main Outlook window
F6 or CTRL+SHIFT+TAB
Move among the Outlook window, the Navigation Pane, and the Reading Pane
TAB
Move around within the Navigation Pane
Arrow keys
Go to a different folder
CTRL+Y
Expand/collapse a group (with a group selected) in the Navigation Pane
PLUS or MINUS SIGN on the numeric keypad
Collapse/expand a group in the e-mail message list
Left and right arrow keys
Switch to Inbox
CTRL+SHIFT+I
Switch to Outbox
CTRL+SHIFT+O
Choose the account from which to send a message
CTRL+TAB (with focus on the To line) and then TAB to the Accounts button
Send
ALT+S
Reply to a message
CTRL+R
Reply all to a message
CTRL+SHIFT+R
Mark a message as not junk
CTRL+ ALT+J
Display blocked external content (in a message)
CTRL+SHIFT+I
Post to a folder
CTRL+ SHIFT+S
Check for new mail
CTRL+M or F9
Go to the next message
UP ARROW
Go to the previous message
DOWN ARROW
Go to the row above (message or group heading)
ALT+ UP ARROW
Go to the row below (message or group heading)
ALT+ DOWN ARROW
Compose a new message
CTRL+N
Open a received message
CTRL+O
Display the Address Book
CTRL+SHIFT+B
Convert an HTML or RTF message to plain text
CTRL+SHIFT+O
Add a Quick Flag to a message
INSERT
Display the Flag for Follow Up dialog box
CTRL+SHIFT+G
Mark as read
CTRL+Q
Show the menu to download pictures, change automatic download settings, or add a sender to the Safe Senders List.
CTRL+SHIFT+W



U can Lock Folders without any S/W (GOOD INFORMSTION & useful also)...

    Folder Lock without any S/W

    Many people have been asking me for an alternative way to lock folders without the use of any alternative software. So, here you go.



Open Notepad and copy the below code and save as locker.bat. Please don't forget to change your password in the code it's shown the place where to type your password.
Now double click on locker .bat
First time start , it will create folder with Locker automatically for u. After creation of the Locker folder, place the contents u want to lock inside the Locker Folder and run locker.bat again .



I hope this comes in handy J

**********************************************************
cls
@ECHO OFF
title Folder Locker
if EXIST "Control Panel.{21EC2020-3AEA-1069-A2DD-08002B30309D}" goto UNLOCK
if NOT EXIST Locker goto MDLOCKER
:CONFIRM
echo Are you sure u want to Lock the folder(Y/N)
set/p "cho=>"
if %cho%==Y goto LOCK
if %cho%==y goto LOCK
if %cho%==n goto END
if %cho%==N goto END
echo Invalid choice.
goto CONFIRM
:LOCK
ren Locker "Control Panel.{21EC2020-3AEA-1069-A2DD-08002B30309D}"
attrib +h +s "Control Panel.{21EC2020-3AEA-1069-A2DD-08002B30309D}"
echo Folder locked
goto End
:UNLOCK
echo Enter password to Unlock folder
set/p "pass=>"
if NOT %pass%== type your password here goto FAIL
attrib -h -s "Control Panel.{21EC2020-3AEA-1069-A2DD-08002B30309D}"
ren "Control Panel.{21EC2020-3AEA-1069-A2DD-08002B30309D}" Locker
echo Folder Unlocked successfully
goto End
:FAIL
echo Invalid password
goto end
:MDLOCKER
md Locker
echo Locker created successfully
goto End
:End


Algorithm Complexity -3

BIG O NOTATION
In mathematics, computer science, and related fields, big O notation  (also known as Big Oh notation, Landau notation, Bachmann–Landau notation, and asymptotic notation) describes the limiting behavior of a function when the argument tends towards a particular value or infinity, usually in terms of simpler functions. Big O notation allows its users to simplify functions in order to concentrate on their growth rates: different functions with the same growth rate may be represented using the same O notation.

Although developed as a part of pure mathematics, this notation is now frequently also used in the analysis of algorithms to describe an algorithm's usage of computational resources: the worst case or average case running time or memory usage of an algorithm is often expressed as a function of the length of its input using big O notation. This allows algorithm designers to predict the behavior of their algorithms and to determine which of multiple algorithms to use, in a way that is independent of computer architecture or clock rate. Because Big O notation discards multiplicative constants on the running time, and ignores efficiency for low input sizes, it does not always reveal the fastest algorithm in practice or for practically-sized data sets. But the approach is still very effective for comparing the scalability of various algorithms as input sizes become large.

A description of a function in terms of big O notation usually only provides an upper bound on the growth rate of the function. Associated with big O notation are several related notations, using the symbols o, Ω, ω, and Θ, to describe other kinds of bounds on asymptotic growth rates. Big O notation is also used in many other fields to provide similar estimates.


Formal definition

Let f(x) and g(x) be two functions defined on some subset of the real numbers. One writes
f(x)=O(g(x))\mbox{ as }x\to\infty\,
if and only if, for sufficiently large values of x, f(x) is at most a constant multiplied by g(x) in absolute value. That is, f(x) = O(g(x)) if and only if there exists a positive real number M and a real number x0 such that
|f(x)| \le \; M |g(x)|\mbox{ for all 
}x>x_0.
In many contexts, the assumption that we are interested in the growth rate as the variable x goes to infinity is left unstated, and one writes more simply that f(x) = O(g(x)).
The notation can also be used to describe the behavior of f near some real number a (often, a = 0): we say
f(x)=O(g(x))\mbox{ as }x\to a\,
if and only if there exist positive numbers δ and M such that
|f(x)| \le \; M |g(x)|\mbox{ for }|x - a| <
 \delta.
If g(x) is non-zero for values of x sufficiently close to a, both of these definitions can be unified using the limit superior:
f(x)=O(g(x))\mbox{ as }x \to a\,
if and only if
\limsup_{x\to a} 
\left|\frac{f(x)}{g(x)}\right| < \infty.

 Example

In typical usage, the formal definition of O notation is not used directly; rather, the O notation for a function f(x) is derived by the following simplification rules:
  • If f(x) is a sum of several terms, the one with the largest growth rate is kept, and all others omitted.
  • If f(x) is a product of several factors, any constants (terms in the product that do not depend on x) are omitted.
For example, let f(x) = 6x4 − 2x3 + 5, and suppose we wish to simplify this function, using O notation, to describe its growth rate as x approaches infinity. This function is the sum of three terms: 6x4, −2x3, and 5. Of these three terms, the one with the highest growth rate is the one with the largest exponent as a function of x, namely 6x4. Now one may apply the second rule: 6x4 is a product of 6 and x4 in which the first factor does not depend on x. Omitting this factor results in the simplified form x4. Thus, we say that f(x) is a big-oh of (x4) or mathematically we can write f(x) = O(x4).
One may confirm this calculation using the formal definition: let f(x) = 6x4 − 2x3 + 5 and g(x) = x4. Applying the formal definition from above, the statement that f(x) = O(x4) is equivalent to its expansion,
|f(x)| \le \; M |g(x)|
for some suitable choice of x0 and M and for all x > x0. To prove this, let x0 = 1 and M = 13. Then, for all x > x0:
\begin{align}|6x^4 - 2x^3 + 5| &\le 6x^4 +
 |2x^3| + 5\\
                                      &\le 6x^4 + 2x^4 + 5x^4\\
                                      &= 13x^4,\\
                                      &= 13|x^4|\end{align}
so
 |6x^4 - 2x^3 + 5| \le 13 \,|x^4 |.

Usage

Big O notation has two main areas of application. In mathematics, it is commonly used to describe how closely a finite series approximates a given function, especially in the case of a truncated Taylor series or asymptotic expansion. In computer science, it is useful in the analysis of algorithms. In both applications, the function g(x) appearing within the O(...) is typically chosen to be as simple as possible, omitting constant factors and lower order terms.
There are two formally close, but noticeably different, usages of this notation: infinite asymptotics and infinitesimal asymptotics. This distinction is only in application and not in principle, however—the formal definition for the "big O" is the same for both cases, only with different limits for the function argument.

Infinite asymptotics

Big O notation is useful when analyzing algorithms for efficiency. For example, the time (or the number of steps) it takes to complete a problem of size n might be found to be T(n) = 4n2 − 2n + 2.
As n grows large, the n2 term will come to dominate, so that all other terms can be neglected — for instance when n = 500, the term 4n2 is 1000 times as large as the 2n term. Ignoring the latter would have negligible effect on the expression's value for most purposes.
Further, the coefficients become irrelevant if we compare to any other order of expression, such as an expression containing a term n3 or n4. Even if T(n) = 1,000,000n2, if U(n) = n3, the latter will always exceed the former once n grows larger than 1,000,000 (T(1,000,000) = 1,000,0003= U(1,000,000)). Additionally, the number of steps depends on the details of the machine model on which the algorithm runs, but different types of machines typically vary by only a constant factor in the number of steps needed to execute an algorithm.
So the big O notation captures what remains: we write either
\ T(n)= O(n^2)
or
T(n)\in O(n^2)
and say that the algorithm has order of n2 time complexity.
Note that "=" is not meant to express "is equal to" in its normal mathematical sense, but rather a more colloquial "is", so the second expression is technically accurate (see the "Equals sign" discussion below) while the first is a common abuse of notation.

 Infinitesimal asymptotics

Big O can also be used to describe the error term in an approximation to a mathematical function. The most significant terms are written explicitly, and then the least-significant terms are summarized in a single big O term. For example,
e^x=1+x+\frac{x^2}{2}+O(x^3)\qquad\hbox{as}\ 
x\to 0
expresses the fact that the error, the difference \ e^x - (1 + x + x^2/2), is smaller in absolute value than some constant times | x3 | when x is close enough to 0.

Properties

If a function f(n) can be written as a finite sum of other functions, then the fastest growing one determines the order of f(n). For example
f(n) = 9 \log n + 5 (\log n)^3 + 3n^2 + 2n^3 
\in O(n^3)\,\!.
In particular, if a function may be bounded by a polynomial in n, then as n tends to infinity, one may disregard lower-order terms of the polynomial.
O(nc) and O(cn) are very different. The latter grows much, much faster, no matter how big the constant c is (as long as it is greater than one). A function that grows faster than any power of n is called superpolynomial. One that grows more slowly than any exponential function of the form cn is called subexponential. An algorithm can require time that is both superpolynomial and subexponential; examples of this include the fastest known algorithms for integer factorization.
O(logn) is exactly the same as O(log(nc)). The logarithms differ only by a constant factor (since log(nc) = clogn) and thus the big O notation ignores that. Similarly, logs with different constant bases are equivalent. Exponentials with different bases, on the other hand, are not of the same order. For example, 2n and 3n are not of the same order.
Changing units may or may not affect the order of the resulting algorithm. Changing units is equivalent to multiplying the appropriate variable by a constant wherever it appears. For example, if an algorithm runs in the order of n2, replacing n by cn means the algorithm runs in the order of c2n2, and the big O notation ignores the constant c2. This can be written as  c^2n^2 \in O(n^2) . If, however, an algorithm runs in the order of 2n, replacing n with cn gives 2cn = (2c)n. This is not equivalent to 2n in general.
Changing of variable may affect the order of the resulting algorithm. For example, if an algorithm's running time is O(n) when measured in terms of the number n of digits of an input number x, then its running time is O(log x) when measured as a function of the input number x itself, because n = Θ(log x).

Product

 f_1 \in O(g_1) \text{ and } f_2\in O(g_2)\, 
\Rightarrow f_1  f_2\in O(g_1  g_2)\,
f\cdot O(g) \in O(f g)

Sum

 f_1 \in O(g_1) \text{ and }
  f_2\in O(g_2)\, \Rightarrow f_1 + f_2\in O(|g_1| + |g_2|)\,
This implies f_1 \in O(g) \text{ and } f_2 \in
 O(g) \Rightarrow f_1+f_2 \in O(g) , which means that O(g) is a convex cone.
If f and g are positive functions, f + O(g) \in O(f + g)

Multiplication by a constant

Let k be a constant. Then:
\ O(k g) = O(g)if k is nonzero.
f\in O(g) \Rightarrow kf\in O(g).

Multiple variables

Big O (and little o, and Ω…) can also be used with multiple variables.
To define Big O formally for multiple variables, suppose f(\vec{x})and g(\vec{x})are two functions defined on some subset of \mathbb{R}^n. We say
f(\vec{x})\mbox{ is }O(g(\vec{x}))\mbox{ as 
}\vec{x}\to\infty
if and only if
\exists C\,\exists M>0\mbox{ such that } 
|f(\vec{x})| \le C |g(\vec{x})|\mbox{ for all }\vec{x} \mbox{ with } 
x_i>M \mbox{ for all }i.
For example, the statement
f(n,m) = n^2 + m^3 + \hbox{O}(n+m) \mbox{ as }
 n,m\to\infty\,
asserts that there exist constants C and M such that
\forall n, m>M\colon |g(n,m)| \le C(n+m),
where g(n,m) is defined by
f(n,m) = n^2 + m^3 + g(n,m).\,
Note that this definition allows all of the coordinates of \vec{x}to increase to infinity. In particular, the statement
f(n,m) = \hbox{O}(n^m) \mbox{ as } 
n,m\to\infty\,
(i.e., \exists C\,\exists M\,\forall n\,\forall
 m\dots) is quite different from
\forall m\colon f(n,m) = \hbox{O}(n^m) \mbox{ 
as } n\to\infty
(i.e., \forall m\,\exists C\,\exists M\,\forall
 n\dots).

Matters of notation

Equals sign

The statement "f(x) is O(g(x))" as defined above is usually written as f(x) = O(g(x)). Some consider this to be an abuse of notation, since the use of the equals sign could be misleading as it suggests a symmetry that this statement does not have. As it is said, O(x) = O(x2) is true but O(x2) = O(x) is not.Knuth describes such statements as "one-way equalities", since if the sides could be reversed, "we could deduce ridiculous things like n = n2 from the identities n = O(n2) and n2 = O(n2)."
For these reasons, it would be more precise to use set notation and write f(x) ∈ O(g(x)), thinking of O(g(x)) as the class of all functions h(x) such that |h(x)| ≤ C|g(n)| for some constant C. However, the use of the equals sign is customary. Knuth pointed out that "mathematicians customarily use the = sign as they use the word 'is' in English: Aristotle is a man, but a man isn’t necessarily Aristotle."

 Other arithmetic operators

Big O notation can also be used in conjunction with other arithmetic operators in more complicated equations. For example, h(x) + O(f(x)) denotes the collection of functions having the growth of h(x) plus a part whose growth is limited to that of f(x). Thus,
g(x) = h(x) + O(f(x))\,
expresses the same as
g(x) - h(x) \in O(f(x))\,.

 Example

Suppose an algorithm is being developed to operate on a set of n elements. Its developers are interested in finding a function T(n) that will express how long the algorithm will take to run (in some arbitrary measurement of time) in terms of the number of elements in the input set. The algorithm works by first calling a subroutine to sort the elements in the set and then perform its own operations. The sort has a known time complexity of O(n2), and after the subroutine runs the algorithm must take an additional 55n3 + 2n + 10 time before it terminates. Thus the overall time complexity of the algorithm can be expressed as
T(n)=O(n^2)+55n^3+2n+10.\
This can perhaps be most easily read by replacing O(n2) with "some function that grows asymptotically slower than n2 ". Again, this usage disregards some of the formal meaning of the "=" and "+" symbols, but it does allow one to use the big O notation as a kind of convenient placeholder.

 Declaration of variables

Another feature of the notation, although less exceptional, is that function arguments may need to be inferred from the context when several variables are involved. The following two right-hand side big O notations have dramatically different meanings:
f(m) = O(m^n)\,,
g(n)\,\, = O(m^n)\,.
The first case states that f(m) exhibits polynomial growth, while the second, assuming m > 1, states that g(n) exhibits exponential growth. To avoid confusion, some authors use the notation
g \in O(f)\,,
rather than the less explicit
g(x) \in O(f(x))\,.

 Complex usages

In more complex usage, O(...) can appear in different places in an equation, even several times on each side. For example, the following are true for n\to\infty
(n+1)^2 = n^2 + O(n)\
(n+O(n^{1/2}))(n + O(\log n))^2 = n^3 + 
O(n^{5/2})\
n^{O(1)} = O(e^n).\
The meaning of such statements is as follows: for any functions which satisfy each O(...) on the left side, there are some functions satisfying each O(...) on the right side, such that substituting all these functions into the equation makes the two sides equal. For example, the third equation above means: "For any function f(n) = O(1), there is some function g(n) = O(en) such that nf(n) = g(n)." In terms of the "set notation" above, the meaning is that the class of functions represented by the left side is a subset of the class of functions represented by the right side.