Computer Network:
Ping: Ping is a computer network administration utility used to test the reachability of a host on an Internet Protocol (IP) network and to measure the round-trip time for messages sent from the originating host to a destination computer. The name comes from active sonar terminology which sends a pulse of sound and listens for the echo to detect objects underwater.
Ping operates by sending Internet Control Message Protocol (ICMP) echo request packets to the target host and waiting for an ICMP response. In the process it measures the time from transmission to reception (round-trip time) and records any packet loss. The results of the test are printed in the form of a statistical summary of the response packets received, including the minimum, maximum, and the mean round-trip times, and sometimes the standard deviation of the mean.
Depending on actual implementation, the ping utility may be executed with various command-line switches to enable special operational modes. For example, options include specifying the packet size of the probe, automatic repeated operation for sending a specified count of probes, and time stamping. Many operating systems provide a companion utility, ping6, for probing Internet Protocol version 6 (IPv6) hosts, but some systems may include this capability within the ping utility.
Ping may be abused as a simple form of denial-of-service attack in the form of a ping flood, in which the attacker overwhelms the victim with ICMP echo request packets.
Database: Clustered and Nonclustered Indexes
An index is an on-disk structure associated with a table or view that speeds retrieval of rows from the table or view. An index contains keys built from one or more columns in the table or view. These keys are stored in a structure (B-tree) that enables SQL Server to find the row or rows associated with the key values quickly and efficiently.
A table or view can contain the following types of indexes:
Clustered: Clustered indexes sort and store the data rows in the table or view based on their key values. These are the columns included in the index definition. There can be only one clustered index per table, because the data rows themselves can be sorted in only one order.
The only time the data rows in a table are stored in sorted order is when the table contains a clustered index. When a table has a clustered index, the table is called a clustered table. If a table has no clustered index, its data rows are stored in an unordered structure called a heap.
Nonclustered: Nonclustered indexes have a structure separate from the data rows. A nonclustered index contains the nonclustered index key values and each key value entry has a pointer to the data row that contains the key value.
The pointer from an index row in a nonclustered index to a data row is called a row locator. The structure of the row locator depends on whether the data pages are stored in a heap or a clustered table. For a heap, a row locator is a pointer to the row. For a clustered table, the row locator is the clustered index key.
You can add nonkey columns to the leaf level of the nonclustered index to by-pass existing index key limits, 900 bytes and 16 key columns, and execute fully covered, indexed, queries. For more information, see Create Indexes with Included Columns.
Both clustered and nonclustered indexes can be unique. This means no two rows can have the same value for the index key. Otherwise, the index is not unique and multiple rows can share the same key value. For more information, see Create Unique Indexes.
Indexes are automatically maintained for a table or view whenever the table data is modified.
Probability
Algebra of events
i) Not A <=> A’
ii) A or B (at least one of A or B) <=> A U B
iii) A and B <=> A ∩ B
iv) A but not B <=> A ∩ B’
v) Neither A nor B <=> A’ ∩ B’
vi) At least one of A, B, or C <=> A U B U C
vii) Exactly one of A and B <=> (A ∩ B’) U (A’ ∩ B)
viii) All three of A, B and C <=> A ∩ B ∩ C
ix) Exactly two of A, B and C <=> (A ∩ B ∩ C’) U (A ∩ B’ ∩ C) U (A’ ∩ B ∩ C)
Set
If A, B, C are finite sets, and U be the finite universal set, then
i) n(A U B)=n(A)+n(B) - n(A ∩ B)
ii) n(A U B)=n(A)+n(B) <=> A,B are disjoint non-void sets.
iii) n(A-B)= n(A)- n(A ∩ B)
iv) n(A ∆ B)= Number of elements which belongs to exactly of A or B
= n(A)+n(B)- 2n(A ∩ B)
v) n(A U B U C)=n(A)+n(B)+n(C)-n(A ∩ B)-n(B ∩ C)-n(C ∩ A)+ n(A ∩ B ∩ C)
vi) Number of elements in exactly two of the sets A, B, C
= n(A ∩ B) + n(B ∩ C) + n(C ∩ A)- 3n(A ∩ B ∩ C)
vii) Number of elements in exactly one of the sets A, B, C
= n(A)+n(B)+n(C)- 2n(A ∩ B) - 2n(B ∩ C) - 2n(C ∩ A) + 3n(A ∩ B ∩ C)
viii) n(A′ U B′)= n((A ∩ B)′)=n(U)-n(A ∩ B)
ix) n(A′ ∩ B′)= n((A U B)′)=n(U)-n(A U B)
i) n(A U B)=n(A)+n(B) - n(A ∩ B)
ii) n(A U B)=n(A)+n(B) <=> A,B are disjoint non-void sets.
iii) n(A-B)= n(A)- n(A ∩ B)
iv) n(A ∆ B)= Number of elements which belongs to exactly of A or B
= n(A)+n(B)- 2n(A ∩ B)
v) n(A U B U C)=n(A)+n(B)+n(C)-n(A ∩ B)-n(B ∩ C)-n(C ∩ A)+ n(A ∩ B ∩ C)
vi) Number of elements in exactly two of the sets A, B, C
= n(A ∩ B) + n(B ∩ C) + n(C ∩ A)- 3n(A ∩ B ∩ C)
vii) Number of elements in exactly one of the sets A, B, C
= n(A)+n(B)+n(C)- 2n(A ∩ B) - 2n(B ∩ C) - 2n(C ∩ A) + 3n(A ∩ B ∩ C)
viii) n(A′ U B′)= n((A ∩ B)′)=n(U)-n(A ∩ B)
ix) n(A′ ∩ B′)= n((A U B)′)=n(U)-n(A U B)
Set
Equal sets: Two sets A and B are said to be equal if every element of A is a member of B, and every element of B is a member of A.
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