B-Trees are tree data structures that allow efficient retrieval of records from disk storage. They work by grouping records into pages that can be read from disk with a single access. This reduces the number of disk accesses needed compared to other tree structures when data exceeds main memory. B-Trees maintain balance by allowing nodes to have a flexible number of children within a minimum and maximum range. Keys are inserted by splitting full nodes and promoting middle keys, and deleted by borrowing from siblings or merging nodes.
VEDIVISION – A FAST BCD DIVISION ALGORITHM FACILITATED BY VEDIC MATHEMATICSijcsit
Of the four elementary operations, division is the most time consuming and expensive operation in modern day processors. This paper uses the tricks based on Ancient Indian Vedic Mathematics System to achieve a generalized algorithm for BCD division in a much time efficient and optimised manner than the conventional algorithms in literature. It has also been observed that the algorithm in concern exhibits remarkable results when executed on traditional mid range processors with numbers having size up to 15 digits (50 bits). The present form of the algorithm can divide numbers having 38 digits (127 bits) which can be further enhanced by simple modifications
VEDIVISION – A FAST BCD DIVISION ALGORITHM FACILITATED BY VEDIC MATHEMATICSijcsit
Of the four elementary operations, division is the most time consuming and expensive operation in modern day processors. This paper uses the tricks based on Ancient Indian Vedic Mathematics System to achieve a generalized algorithm for BCD division in a much time efficient and optimised manner than the conventional algorithms in literature. It has also been observed that the algorithm in concern exhibits remarkable results when executed on traditional mid range processors with numbers having size up to 15 digits (50 bits). The present form of the algorithm can divide numbers having 38 digits (127 bits) which can be further enhanced by simple modifications
This PPT is all about the Tree basic on fundamentals of B and B+ Tree with it's Various (Search,Insert and Delete) Operations performed on it and their Examples...
About
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Technical Specifications
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
Key Features
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface
• Compatible with MAFI CCR system
• Copatiable with IDM8000 CCR
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
Application
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Industrial Training at Shahjalal Fertilizer Company Limited (SFCL)MdTanvirMahtab2
This presentation is about the working procedure of Shahjalal Fertilizer Company Limited (SFCL). A Govt. owned Company of Bangladesh Chemical Industries Corporation under Ministry of Industries.
NUMERICAL SIMULATIONS OF HEAT AND MASS TRANSFER IN CONDENSING HEAT EXCHANGERS...ssuser7dcef0
Power plants release a large amount of water vapor into the
atmosphere through the stack. The flue gas can be a potential
source for obtaining much needed cooling water for a power
plant. If a power plant could recover and reuse a portion of this
moisture, it could reduce its total cooling water intake
requirement. One of the most practical way to recover water
from flue gas is to use a condensing heat exchanger. The power
plant could also recover latent heat due to condensation as well
as sensible heat due to lowering the flue gas exit temperature.
Additionally, harmful acids released from the stack can be
reduced in a condensing heat exchanger by acid condensation. reduced in a condensing heat exchanger by acid condensation.
Condensation of vapors in flue gas is a complicated
phenomenon since heat and mass transfer of water vapor and
various acids simultaneously occur in the presence of noncondensable
gases such as nitrogen and oxygen. Design of a
condenser depends on the knowledge and understanding of the
heat and mass transfer processes. A computer program for
numerical simulations of water (H2O) and sulfuric acid (H2SO4)
condensation in a flue gas condensing heat exchanger was
developed using MATLAB. Governing equations based on
mass and energy balances for the system were derived to
predict variables such as flue gas exit temperature, cooling
water outlet temperature, mole fraction and condensation rates
of water and sulfuric acid vapors. The equations were solved
using an iterative solution technique with calculations of heat
and mass transfer coefficients and physical properties.
Sachpazis:Terzaghi Bearing Capacity Estimation in simple terms with Calculati...Dr.Costas Sachpazis
Terzaghi's soil bearing capacity theory, developed by Karl Terzaghi, is a fundamental principle in geotechnical engineering used to determine the bearing capacity of shallow foundations. This theory provides a method to calculate the ultimate bearing capacity of soil, which is the maximum load per unit area that the soil can support without undergoing shear failure. The Calculation HTML Code included.
Saudi Arabia stands as a titan in the global energy landscape, renowned for its abundant oil and gas resources. It's the largest exporter of petroleum and holds some of the world's most significant reserves. Let's delve into the top 10 oil and gas projects shaping Saudi Arabia's energy future in 2024.
Hierarchical Digital Twin of a Naval Power SystemKerry Sado
A hierarchical digital twin of a Naval DC power system has been developed and experimentally verified. Similar to other state-of-the-art digital twins, this technology creates a digital replica of the physical system executed in real-time or faster, which can modify hardware controls. However, its advantage stems from distributing computational efforts by utilizing a hierarchical structure composed of lower-level digital twin blocks and a higher-level system digital twin. Each digital twin block is associated with a physical subsystem of the hardware and communicates with a singular system digital twin, which creates a system-level response. By extracting information from each level of the hierarchy, power system controls of the hardware were reconfigured autonomously. This hierarchical digital twin development offers several advantages over other digital twins, particularly in the field of naval power systems. The hierarchical structure allows for greater computational efficiency and scalability while the ability to autonomously reconfigure hardware controls offers increased flexibility and responsiveness. The hierarchical decomposition and models utilized were well aligned with the physical twin, as indicated by the maximum deviations between the developed digital twin hierarchy and the hardware.
2. Motivation for B-Trees
• So far we have assumed that we can store an entire data
structure in main memory
• What if we have so much data that it won’t fit?
• We will have to use disk storage but when this happens our
time complexity fails
• The problem is that Big-Oh analysis assumes that all
operations take roughly equal time
• This is not the case when disk access is involved
Dr. AMIT KUMAR @JUET
3. Motivation (cont.)
• Assume that a disk spins at 3600 RPM
• In 1 minute it makes 3600 revolutions, hence one revolution
occurs in 1/60 of a second, or 16.7ms
• On average what we want is half way round this disk – it will
take 8ms
• This sounds good until you realize that we get 120 disk
accesses a second – the same time as 25 million instructions
• In other words, one disk access takes about the same time as
200,000 instructions
• It is worth executing lots of instructions to avoid a disk access
Dr. AMIT KUMAR @JUET
4. Motivation (cont.)
• Assume that we use an Binary tree to store all the details of
people in Canada (about 32 million records)
• We still end up with a very deep tree with lots of different
disk accesses; log2 20,000,000 is about 25, so this takes about
0.21 seconds (if there is only one user of the program)
• We know we can’t improve on the log n for a binary tree
• But, the solution is to use more branches and thus less height!
• As branching increases, depth decreases
Dr. AMIT KUMAR @JUET
5. Definition of a B-tree
• A B-tree of order m is an m-way tree (i.e., a tree where each
node may have up to m children) in which:
1. the number of keys in each non-leaf node is one less than the number
of its children and these keys partition the keys in the children in the
fashion of a search tree
2. all leaves are on the same level
3. all non-leaf nodes except the root have at least m / 2 children
4. the root is either a leaf node, or it has from two to m children
5. a leaf node contains no more than m – 1 keys
• The number m should always be odd
Dr. AMIT KUMAR @JUET
6. An example B-Tree
51 6242
6 12
26
55 60 7064 9045
1 2 4 7 8 13 15 18 25
27 29 46 48 53
A B-tree of order 5
containing 26 items
Note that all the leaves are at the same level
Dr. AMIT KUMAR @JUET
7. • Suppose we start with an empty B-tree and keys arrive in the
following order:1 12 8 2 25 6 14 28 17 7 52 16 48 68
3 26 29 53 55 45
• We want to construct a B-tree of order 5
• The first four items go into the root:
• To put the fifth item in the root would violate condition 5
• Therefore, when 25 arrives, pick the middle key to make a
new root
Constructing a B-tree
1281 2
Dr. AMIT KUMAR @JUET
8. Constructing a B-tree
Add 25 to the tree
1
12
8
2
25
6
14
28
17
7
52
16
48
68
3
26
29
53
55
45
1281 2 25
Exceeds Order.
Promote middle and
split.
Dr. AMIT KUMAR @JUET
9. Constructing a B-tree (contd.)
6, 14, 28 get added to the leaf nodes:
1
12
8
2
25
6
14
28
17
7
52
16
48
68
3
26
29
53
55
45
12
8
1 2 25
12
8
1 2 2561 2 2814
Dr. AMIT KUMAR @JUET
10. Constructing a B-tree (contd.)
Adding 17 to the right leaf node would over-fill it, so we take
the middle key, promote it (to the root) and split the leaf
1
12
8
2
25
6
14
28
17
7
52
16
48
68
3
26
29
53
55
45
1
12
8
2
25
6
14
28
17
7
52
16
48
68
3
26
29
53
55
45
12
8
2 2561 2 2814 2817
Dr. AMIT KUMAR @JUET
11. Constructing a B-tree (contd.)
7, 52, 16, 48 get added to the leaf nodes
1
12
8
2
25
6
14
28
17
7
52
16
48
68
3
26
29
53
55
45
12
8
2561 2 2814
17
7 5216 48
Dr. AMIT KUMAR @JUET
12. Constructing a B-tree (contd.)
Adding 68 causes us to split the right most leaf,
promoting 48 to the root
1
12
8
2
25
6
14
28
17
7
52
16
48
68
3
26
29
53
55
45
8 17
7621 161412 52482825 68
Dr. AMIT KUMAR @JUET
13. Constructing a B-tree (contd.)
Adding 3 causes us to split the left most leaf
1
12
8
2
25
6
14
28
17
7
52
16
48
68
3
26
29
53
55
45
48178
7621 161412 25 28 52 683 7
Dr. AMIT KUMAR @JUET
14. Constructing a B-tree (contd.)
1
12
8
2
25
6
14
28
17
7
52
16
48
68
3
26
29
53
55
45
Add 26, 29, 53, 55 then go into the leaves
481783
1 2 6 7 52 6825 28161412 26 29 53 55
Dr. AMIT KUMAR @JUET
15. Constructing a B-tree (contd.)
Add 45 increases the trees level
1
12
8
2
25
6
14
28
17
7
52
16
48
68
3
26
29
53
55
45
481783
29282625 685553521614126 71 2 45
Exceeds Order.
Promote middle and
split.
Exceeds Order.
Promote middle and
split.
Dr. AMIT KUMAR @JUET
16. Inserting into a B-Tree
• Attempt to insert the new key into a leaf
• If this would result in that leaf becoming too big, split the leaf
into two, promoting the middle key to the leaf’s parent
• If this would result in the parent becoming too big, split the
parent into two, promoting the middle key
• This strategy might have to be repeated all the way to the top
• If necessary, the root is split in two and the middle key is
promoted to a new root, making the tree one level higher
Dr. AMIT KUMAR @JUET
17. Exercise in Inserting a B-Tree
• Insert the following keys to a 5-way B-tree:
• 3, 7, 9, 23, 45, 1, 5, 14, 25, 24, 13, 11, 8, 19, 4, 31, 35, 56
Dr. AMIT KUMAR @JUET
19. Removal from a B-tree
• During insertion, the key always goes into a leaf. For deletion
we wish to remove from a leaf. There are three possible ways
we can do this:
• 1 - If the key is already in a leaf node, and removing it doesn’t
cause that leaf node to have too few keys, then simply remove
the key to be deleted.
• 2 - If the key is not in a leaf then it is guaranteed (by the
nature of a B-tree) that its predecessor or successor will be in
a leaf -- in this case can we delete the key and promote the
predecessor or successor key to the non-leaf deleted key’s
position.
Dr. AMIT KUMAR @JUET
20. Removal from a B-tree (2)
• If (1) or (2) lead to a leaf node containing less than the
minimum number of keys then we have to look at the siblings
immediately adjacent to the leaf in question:
– 3: if one of them has more than the min’ number of keys then we can
promote one of its keys to the parent and take the parent key into our
lacking leaf
– 4: if neither of them has more than the min’ number of keys then the
lacking leaf and one of its neighbours can be combined with their
shared parent (the opposite of promoting a key) and the new leaf will
have the correct number of keys; if this step leave the parent with too
few keys then we repeat the process up to the root itself, if required
Dr. AMIT KUMAR @JUET
21. Type #1: Simple leaf deletion
12 29 52
2 7 9 15 22 56 69 7231 43
Delete 2: Since there are enough
keys in the node, just delete it
Assuming a 5-way
B-Tree, as before...
Note when printed: this slide is animated
Dr. AMIT KUMAR @JUET
22. Type #2: Simple non-leaf deletion
12 29 52
7 9 15 22 56 69 7231 43
Delete 52
Borrow the predecessor
or (in this case) successor
56
Note when printed: this slide is animated
Dr. AMIT KUMAR @JUET
23. Type #4: Too few keys in node and
its siblings
12 29 56
7 9 15 22 69 7231 43
Delete 72
Too few keys!
Join back together
Note when printed: this slide is animated
Dr. AMIT KUMAR @JUET
24. Type #4: Too few keys in node and
its siblings
12 29
7 9 15 22 695631 43
Note when printed: this slide is animated
Dr. AMIT KUMAR @JUET
25. Type #3: Enough siblings
12 29
7 9 15 22 695631 43
Delete 22
Demote root key and
promote leaf key
Note when printed: this slide is animated
Dr. AMIT KUMAR @JUET
26. Type #3: Enough siblings
12
297 9 15
31
695643
Note when printed: this slide is animated
Dr. AMIT KUMAR @JUET
27. Exercise in Removal from a B-Tree
• Given 5-way B-tree created by these data (last exercise):
• 3, 7, 9, 23, 45, 1, 5, 14, 25, 24, 13, 11, 8, 19, 4, 31, 35, 56
• Add these further keys: 2, 6,12
• Delete these keys: 4, 5, 7, 3, 14
Dr. AMIT KUMAR @JUET
29. Analysis of B-Trees
• The maximum number of items in a B-tree of order m and height h:
root m – 1
level 1 m(m – 1)
level 2 m2(m – 1)
. . .
level h mh(m – 1)
• So, the total number of items is
(1 + m + m2 + m3 + … + mh)(m – 1) =
[(mh+1 – 1)/ (m – 1)] (m – 1) = mh+1 – 1
• When m = 5 and h = 2 this gives 53 – 1 = 124
Dr. AMIT KUMAR @JUET
30. Reasons for using B-Trees
• When searching tables held on disc, the cost of each disc
transfer is high but doesn't depend much on the amount of
data transferred, especially if consecutive items are transferred
– If we use a B-tree of order 101, say, we can transfer each node in one
disc read operation
– A B-tree of order 101 and height 3 can hold 1014 – 1 items
(approximately 100 million) and any item can be accessed with 3 disc
reads (assuming we hold the root in memory)
• If we take m = 3, we get a 2-3 tree, in which non-leaf nodes
have two or three children (i.e., one or two keys)
– B-Trees are always balanced (since the leaves are all at the same
level), so 2-3 trees make a good type of balanced tree
Dr. AMIT KUMAR @JUET