Linear Combination, Span And Linearly Independent, Dependent SetDhaval Shukla
In this presentation, the topic of Linear Combination, Span and Linearly Independent and Linearly Dependent Sets have been discussed. The sums for each topic have been given to understand the concept clearly for viewers.
Contains discussion about Parabola based on DepEd MELCS. This also contains examples and solutions with pre-loaded multiple-choice questions for formative assessment.
In this paper, we show that the number of edges for any odd harmonious Eulerian graph is congruent to 0 or 2 (mod 4), and we found a counter example for the inverse of this statement is not true. We also proved that, the graphs which are constructed by two copies of even cycle Cn sharing a common edge are odd harmonious. In addition, we obtained an odd harmonious labeling for the graphs which are constructed by two copies of cycle Cn sharing a common vertex when n is congruent to 0 (mod 4). Moreover, we show that, the Cartesian product of cycle graph Cm and path Pn for each n ≥ 2, m ≡ 0 (mod 4) are odd harmonious graphs. Finally many new families of odd harmonious graphs are introduced.
Linear Combination, Span And Linearly Independent, Dependent SetDhaval Shukla
In this presentation, the topic of Linear Combination, Span and Linearly Independent and Linearly Dependent Sets have been discussed. The sums for each topic have been given to understand the concept clearly for viewers.
Contains discussion about Parabola based on DepEd MELCS. This also contains examples and solutions with pre-loaded multiple-choice questions for formative assessment.
In this paper, we show that the number of edges for any odd harmonious Eulerian graph is congruent to 0 or 2 (mod 4), and we found a counter example for the inverse of this statement is not true. We also proved that, the graphs which are constructed by two copies of even cycle Cn sharing a common edge are odd harmonious. In addition, we obtained an odd harmonious labeling for the graphs which are constructed by two copies of cycle Cn sharing a common vertex when n is congruent to 0 (mod 4). Moreover, we show that, the Cartesian product of cycle graph Cm and path Pn for each n ≥ 2, m ≡ 0 (mod 4) are odd harmonious graphs. Finally many new families of odd harmonious graphs are introduced.
This Presentation will Clear the idea of non linear Data Structure and implementation of Tree by using array and pointer and also Explain the concept of Binary Search Tree (BST) with example
this presentation is made for the students who finds data structures a complex subject
this will help students to grab the various topics of data structures with simple presentation techniques
best regards
BCA group
(pooja,shaifali,richa,trishla,rani,pallavi,shivani)
topologicalsort-using c++ as development language.pptxjanafridi251
topological sort using c++ as programming language to search through a tree structureknljhcffxgchjkjhlkjkfhdffxgchvjbknlkjhgchvjbkjxfghjhiyuighjbyfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffvgvvvvvvvvnbbbbbbbbbfuyfffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggggg
Model Attribute Check Company Auto PropertyCeline George
In Odoo, the multi-company feature allows you to manage multiple companies within a single Odoo database instance. Each company can have its own configurations while still sharing common resources such as products, customers, and suppliers.
Macroeconomics- Movie Location
This will be used as part of your Personal Professional Portfolio once graded.
Objective:
Prepare a presentation or a paper using research, basic comparative analysis, data organization and application of economic information. You will make an informed assessment of an economic climate outside of the United States to accomplish an entertainment industry objective.
Exploiting Artificial Intelligence for Empowering Researchers and Faculty, In...Dr. Vinod Kumar Kanvaria
Exploiting Artificial Intelligence for Empowering Researchers and Faculty,
International FDP on Fundamentals of Research in Social Sciences
at Integral University, Lucknow, 06.06.2024
By Dr. Vinod Kumar Kanvaria
Safalta Digital marketing institute in Noida, provide complete applications that encompass a huge range of virtual advertising and marketing additives, which includes search engine optimization, virtual communication advertising, pay-per-click on marketing, content material advertising, internet analytics, and greater. These university courses are designed for students who possess a comprehensive understanding of virtual marketing strategies and attributes.Safalta Digital Marketing Institute in Noida is a first choice for young individuals or students who are looking to start their careers in the field of digital advertising. The institute gives specialized courses designed and certification.
for beginners, providing thorough training in areas such as SEO, digital communication marketing, and PPC training in Noida. After finishing the program, students receive the certifications recognised by top different universitie, setting a strong foundation for a successful career in digital marketing.
2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
Synthetic Fiber Construction in lab .pptxPavel ( NSTU)
Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.
A review of the growth of the Israel Genealogy Research Association Database Collection for the last 12 months. Our collection is now passed the 3 million mark and still growing. See which archives have contributed the most. See the different types of records we have, and which years have had records added. You can also see what we have for the future.
A Strategic Approach: GenAI in EducationPeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
2. What is A Spanning Tree?
• A spanning tree for an
undirected graph G=(V,E)
is a subgraph of G that is
a tree and contains all the
vertices of G
• Can a graph have more
than one spanning tree?
• Can an unconnected graph
have a spanning tree?
a
b
u
e
c
v
f
d
3. Minimal Spanning Tree.
• The weight of a subgraph
is the sum of the weights
of it edges.
a
4
9
3
b
• A minimum spanning tree
for a weighted graph is a
spanning tree with
minimum weight.
4
u
14
2
10
c
v
3
Mst T: w( T )=
15
f
8
d
• Can a graph have more
then one minimum
spanning tree?
e
(u,v)
T
w(u,v ) is minimized
4. Example of a Problem that
Translates into a MST
The Problem
• Several pins of an electronic circuit must be
connected using the least amount of wire.
Modeling the Problem
• The graph is a complete, undirected graph
G = ( V, E ,W ), where V is the set of pins, E
is the set of all possible interconnections
between the pairs of pins and w(e) is the
length of the wire needed to connect the
pair of vertices.
• Find a minimum spanning tree.
5. Greedy Choice
We will show two ways to build a minimum
spanning tree.
• A MST can be grown from the current
spanning tree by adding the nearest vertex
and the edge connecting the nearest
vertex to the MST. (Prim's algorithm)
• A MST can be grown from a forest of
spanning trees by adding the smallest edge
connecting two spanning trees. (Kruskal's
algorithm)
6. Notation
• Tree-vertices: in the tree constructed so far
• Non-tree vertices: rest of vertices
Prim’s Selection rule
• Select the minimum weight edge between a treenode and a non-tree node and add to the tree
7. The Prim algorithm Main Idea
Select a vertex to be a tree-node
while (there are non-tree vertices) {
if there is no edge connecting a tree node
with a non-tree node
return “no spanning tree”
select an edge of minimum weight between a
tree node and a non-tree node
add the selected edge and its new vertex to
the tree
}
return tree
17. Kruskal„s Algorithm
1. Each vertex is in its own cluster
2. Take the edge e with the smallest weight
- if e connects two vertices in different clusters,
then e is added to the MST and the two clusters,
which are connected by e, are merged into a
single cluster
- if e connects two vertices, which are already
in the same cluster, ignore it
3.
Continue until n-1 edges were selected
Kruskal's Algorithm
27. Graph Traversal
Traversing a graph means visiting all the
vertices in the graph exactly once.
Breadth First Search (BFS)
Depth First Search (DFS)
28. DFS
Similar to in-order traversal of a binary
search tree
Starting from a given node, this traversal
visits all the nodes up to the deepest
level and so on.
31. DFS Traversal
Visit the vertex v
Visit all the vertices along the path which
begins at v
Visit the vertex v, then the vertex
immediate adjacent to v, let it be vx . If vx
has an immediate adjacent vy then visit it
and so on till there is a dead end.
Dead end: A vertex which does not have an
immediate adjacent or its immediate
adjacent has been visited.
32. After coming to an dead end we
backtrack to v to see if it has an
another adjacent vertex other than vx
and then continue the same from it else
from the adjacent of the adjacent
(which is not visited earlier) and so on.
33. Push the starting vertex into the STACK
While STACK not empty do
POP a vertex V
If V is not visited
Visit the vertex V
Store V in VISIT
PUSH all adjacent vertex of V
onto STACK
End of IF
End of While
STOP
35. DFS of G starting at J
[1] Initially push J onto STACK
STACK : J
VISIT: Ø
[2] POP J from the STACK, add it in
VISIT and PUSH onto the STACK all
neighbor of J
STACK: D, K
VISIT: J
36. [3] POP the top element K, add it in
VISIT and PUSH all neighbor of K onto
STACK
STACK: D,E,G
VISIT: J, K
[4] POP the top element G, add it in
VISIT and PUSH all neighbor of G onto
STACK
STACK: D,E, E, C,
VISIT: J, K, G
37. [5] POP the top element C, add it in
VISIT and PUSH all neighbor of C onto
STACK
STACK: D,E,E, F
VISIT: J, K, G, C
[6] POP the top element F, add it in
VISIT and PUSH all neighbor of F onto
STACK
STACK: D,E, E, D
VISIT: J, K, G, C, F
38. [5] POP the top element D, add it in
VISIT and PUSH all neighbor of D onto
STACK
STACK: D,E,E, C
VISIT: J, K, G, C, F,D
[6] POP the top element C, which is
already in VISIT
STACK: D,E, E
VISIT: J, K, G, C, F,D
39. [5] POP the top element E, add it in
VISIT which is already in VISIT and
its neighbor onto STACK
STACK: D,E, D, C, J
VISIT: J, K, G, C, F,D,E
[6] POP the top element J, C, D,E, D
which is already in VISIT
STACK:
VISIT: J, K, G, C, F, D, E
40. A
C
D
J
B
E
F
J, K, G, C, F, D, E
Adjacency List
G
K
A: F,C,B
B: G,C
C: F
D: C
E: D,C,J
F: D
G: C,E
J: D,K
K: E,G
41. BFS Traversal
Any vertex in label i will be visited only
after the visiting of all the vertices in
its preceding level that is at level i – 1
42. BFS Traversal
[1] Enter the starting vertex v in a queue
Q
[2] While Q is not empty do
Delete an item from Q, say u
If u is not in VISIT store u in
VISIT
Enter all adjacent vertices of u
into Q
[3] Stop
44. [1] Insert the starting vertex V1 in Q
Q = V1
VISIT = Ø
[2] Delete an item from Q, let it be u = V1
u is not in VISIT. Store u in VISIT
and its adjacent element in Q
Q = V2 , V 3
VISIT = V1
45. [3] Delete an item from Q, let it be u = V2
u is not in VISIT. Store u in VISIT
and its adjacent element in Q
Q = V2 , V3 , V4 , V5
VISIT = V1 , V2
[4] Delete an item from Q, let it be u = V3
u is not in VISIT. Store u in VISIT
and its adjacent element in Q
Q = V3 , V4 , V5 , V4 , V6
VISIT = V1 , V2 , V3
46. [5] Delete an item from Q, let it be u = V4
u is not in VISIT. Store u in VISIT
and its adjacent element in Q
Q = V4 , V5 , V4 , V6 , V8
VISIT = V1 , V2 , V3 , V4
[6] Delete an item from Q, let it be u =V5
u is not in VISIT. Store u in VISIT
and its adjacent element in Q
Q = V5 , V4 , V6 , V8 , V7
VISIT = V1 , V2 , V3 , V4 , V5
47. [7] Delete an item from Q, let it be u =V4
u is in VISIT.
Q = V4 , V6 , V8 , V7
VISIT = V1 , V2 , V3 , V4 , V5
[8] Delete an item from Q, let it be u =V6
u is not in VISIT. Store u in VISIT
and its adjacent element in Q
Q = V6 , V8 , V7
VISIT = V1 , V2 , V3 , V4 , V5 , V6
48. [9] Delete an item from Q, let it be u =V8
u is not in VISIT. Store u in VISIT and
its adjacent element in Q
Q = V8 , V7 , V1
VISIT = V1 , V2 , V3 , V4 , V5 , V6 ,
V8
[10] Delete an item from Q, let it be u =V7
u is not in VISIT. Store u in VISIT and
its adjacent element in Q
Q = V7 , V1
VISIT = V1 , V2 , V3 , V4 , V5 , V6 ,
V8 , V7
49. [11] Delete an item from Q, let it be u =V1
u is in VISIT.
Q = V1
VISIT = V1 , V2 , V3 , V4 , V5 , V6 ,
V8 , V 7
[12] Q is empty, Stop
Q=
VISIT = V1 , V2 , V3 , V4 , V5 , V6 ,
V8 , V 7