The document uses mathematical induction to prove that 2n is greater than n^2 for all n greater than 4. It shows that the statement holds for n=5. It then assumes the statement is true for some integer k greater than 4, and proves that it must also be true for k+1. Therefore, by the principle of mathematical induction, the statement is true for all integers n greater than 4.
A complete and enhanced presentation on mathematical induction and divisibility rules with out any calculation.
Here are some defined formulas and techniques to find the divisibility of numbers.
A complete and enhanced presentation on mathematical induction and divisibility rules with out any calculation.
Here are some defined formulas and techniques to find the divisibility of numbers.
EXPECTED NUMBER OF LEVEL CROSSINGS OF A RANDOM TRIGONOMETRIC POLYNOMIALJournal For Research
Let EN( T; Φ’ , Φ’’ ) denote the average number of real zeros of the random trigonometric polynomial T=Tn( Φ, É )= . In the interval (Φ’, Φ’’). Assuming that ak(É ) are independent random variables identically distributed according to the normal law and that bk = kp (p ≥ 0) are positive constants, we show that EN( T : 0, 2À ) ~ Outside an exceptional set of measure at most (2/ n ) where β = constant S ~ 1, S’ ~ 1. 1991 Mathematics subject classification (amer. Math. Soc.): 60 B 99.
Yet another prime formula to prove open problemsChris De Corte
In this document, I derive again a new formula to calculate prime numbers and use it to discuss open problems like Goldbach and Polignac or Twin prime conjectures.
The derived formula is an interesting variant of my previous one.
International Journal of Mathematics and Statistics Invention (IJMSI) inventionjournals
International Journal of Mathematics and Statistics Invention (IJMSI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJMSI publishes research articles and reviews within the whole field Mathematics and Statistics, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
EXPECTED NUMBER OF LEVEL CROSSINGS OF A RANDOM TRIGONOMETRIC POLYNOMIALJournal For Research
Let EN( T; Φ’ , Φ’’ ) denote the average number of real zeros of the random trigonometric polynomial T=Tn( Φ, É )= . In the interval (Φ’, Φ’’). Assuming that ak(É ) are independent random variables identically distributed according to the normal law and that bk = kp (p ≥ 0) are positive constants, we show that EN( T : 0, 2À ) ~ Outside an exceptional set of measure at most (2/ n ) where β = constant S ~ 1, S’ ~ 1. 1991 Mathematics subject classification (amer. Math. Soc.): 60 B 99.
Yet another prime formula to prove open problemsChris De Corte
In this document, I derive again a new formula to calculate prime numbers and use it to discuss open problems like Goldbach and Polignac or Twin prime conjectures.
The derived formula is an interesting variant of my previous one.
International Journal of Mathematics and Statistics Invention (IJMSI) inventionjournals
International Journal of Mathematics and Statistics Invention (IJMSI) is an international journal intended for professionals and researchers in all fields of computer science and electronics. IJMSI publishes research articles and reviews within the whole field Mathematics and Statistics, new teaching methods, assessment, validation and the impact of new technologies and it will continue to provide information on the latest trends and developments in this ever-expanding subject. The publications of papers are selected through double peer reviewed to ensure originality, relevance, and readability. The articles published in our journal can be accessed online.
The Art of the Pitch: WordPress Relationships and SalesLaura Byrne
Clients don’t know what they don’t know. What web solutions are right for them? How does WordPress come into the picture? How do you make sure you understand scope and timeline? What do you do if sometime changes?
All these questions and more will be explored as we talk about matching clients’ needs with what your agency offers without pulling teeth or pulling your hair out. Practical tips, and strategies for successful relationship building that leads to closing the deal.
GDG Cloud Southlake #33: Boule & Rebala: Effective AppSec in SDLC using Deplo...James Anderson
Effective Application Security in Software Delivery lifecycle using Deployment Firewall and DBOM
The modern software delivery process (or the CI/CD process) includes many tools, distributed teams, open-source code, and cloud platforms. Constant focus on speed to release software to market, along with the traditional slow and manual security checks has caused gaps in continuous security as an important piece in the software supply chain. Today organizations feel more susceptible to external and internal cyber threats due to the vast attack surface in their applications supply chain and the lack of end-to-end governance and risk management.
The software team must secure its software delivery process to avoid vulnerability and security breaches. This needs to be achieved with existing tool chains and without extensive rework of the delivery processes. This talk will present strategies and techniques for providing visibility into the true risk of the existing vulnerabilities, preventing the introduction of security issues in the software, resolving vulnerabilities in production environments quickly, and capturing the deployment bill of materials (DBOM).
Speakers:
Bob Boule
Robert Boule is a technology enthusiast with PASSION for technology and making things work along with a knack for helping others understand how things work. He comes with around 20 years of solution engineering experience in application security, software continuous delivery, and SaaS platforms. He is known for his dynamic presentations in CI/CD and application security integrated in software delivery lifecycle.
Gopinath Rebala
Gopinath Rebala is the CTO of OpsMx, where he has overall responsibility for the machine learning and data processing architectures for Secure Software Delivery. Gopi also has a strong connection with our customers, leading design and architecture for strategic implementations. Gopi is a frequent speaker and well-known leader in continuous delivery and integrating security into software delivery.
Epistemic Interaction - tuning interfaces to provide information for AI supportAlan Dix
Paper presented at SYNERGY workshop at AVI 2024, Genoa, Italy. 3rd June 2024
https://alandix.com/academic/papers/synergy2024-epistemic/
As machine learning integrates deeper into human-computer interactions, the concept of epistemic interaction emerges, aiming to refine these interactions to enhance system adaptability. This approach encourages minor, intentional adjustments in user behaviour to enrich the data available for system learning. This paper introduces epistemic interaction within the context of human-system communication, illustrating how deliberate interaction design can improve system understanding and adaptation. Through concrete examples, we demonstrate the potential of epistemic interaction to significantly advance human-computer interaction by leveraging intuitive human communication strategies to inform system design and functionality, offering a novel pathway for enriching user-system engagements.
LF Energy Webinar: Electrical Grid Modelling and Simulation Through PowSyBl -...DanBrown980551
Do you want to learn how to model and simulate an electrical network from scratch in under an hour?
Then welcome to this PowSyBl workshop, hosted by Rte, the French Transmission System Operator (TSO)!
During the webinar, you will discover the PowSyBl ecosystem as well as handle and study an electrical network through an interactive Python notebook.
PowSyBl is an open source project hosted by LF Energy, which offers a comprehensive set of features for electrical grid modelling and simulation. Among other advanced features, PowSyBl provides:
- A fully editable and extendable library for grid component modelling;
- Visualization tools to display your network;
- Grid simulation tools, such as power flows, security analyses (with or without remedial actions) and sensitivity analyses;
The framework is mostly written in Java, with a Python binding so that Python developers can access PowSyBl functionalities as well.
What you will learn during the webinar:
- For beginners: discover PowSyBl's functionalities through a quick general presentation and the notebook, without needing any expert coding skills;
- For advanced developers: master the skills to efficiently apply PowSyBl functionalities to your real-world scenarios.
Key Trends Shaping the Future of Infrastructure.pdfCheryl Hung
Keynote at DIGIT West Expo, Glasgow on 29 May 2024.
Cheryl Hung, ochery.com
Sr Director, Infrastructure Ecosystem, Arm.
The key trends across hardware, cloud and open-source; exploring how these areas are likely to mature and develop over the short and long-term, and then considering how organisations can position themselves to adapt and thrive.
Smart TV Buyer Insights Survey 2024 by 91mobiles.pdf91mobiles
91mobiles recently conducted a Smart TV Buyer Insights Survey in which we asked over 3,000 respondents about the TV they own, aspects they look at on a new TV, and their TV buying preferences.
UiPath Test Automation using UiPath Test Suite series, part 4DianaGray10
Welcome to UiPath Test Automation using UiPath Test Suite series part 4. In this session, we will cover Test Manager overview along with SAP heatmap.
The UiPath Test Manager overview with SAP heatmap webinar offers a concise yet comprehensive exploration of the role of a Test Manager within SAP environments, coupled with the utilization of heatmaps for effective testing strategies.
Participants will gain insights into the responsibilities, challenges, and best practices associated with test management in SAP projects. Additionally, the webinar delves into the significance of heatmaps as a visual aid for identifying testing priorities, areas of risk, and resource allocation within SAP landscapes. Through this session, attendees can expect to enhance their understanding of test management principles while learning practical approaches to optimize testing processes in SAP environments using heatmap visualization techniques
What will you get from this session?
1. Insights into SAP testing best practices
2. Heatmap utilization for testing
3. Optimization of testing processes
4. Demo
Topics covered:
Execution from the test manager
Orchestrator execution result
Defect reporting
SAP heatmap example with demo
Speaker:
Deepak Rai, Automation Practice Lead, Boundaryless Group and UiPath MVP
UiPath Test Automation using UiPath Test Suite series, part 3DianaGray10
Welcome to UiPath Test Automation using UiPath Test Suite series part 3. In this session, we will cover desktop automation along with UI automation.
Topics covered:
UI automation Introduction,
UI automation Sample
Desktop automation flow
Pradeep Chinnala, Senior Consultant Automation Developer @WonderBotz and UiPath MVP
Deepak Rai, Automation Practice Lead, Boundaryless Group and UiPath MVP
5. Mathematical Induction
e.g.v Prove 2n n 2 for n 4
Step 1: Prove the result is true for n = 5
LHS 25 RHS 52
32 25
6. Mathematical Induction
e.g.v Prove 2n n 2 for n 4
Step 1: Prove the result is true for n = 5
LHS 25 RHS 52
32 25
LHS RHS
7. Mathematical Induction
e.g.v Prove 2n n 2 for n 4
Step 1: Prove the result is true for n = 5
LHS 25 RHS 52
32 25
LHS RHS
Hence the result is true for n = 5
8. Mathematical Induction
e.g.v Prove 2n n 2 for n 4
Step 1: Prove the result is true for n = 5
LHS 25 RHS 52
32 25
LHS RHS
Hence the result is true for n = 5
Step 2: Assume the result is true for n = k, where k is a positive
integer > 4
i.e. 2k k 2
9. Mathematical Induction
e.g.v Prove 2n n 2 for n 4
Step 1: Prove the result is true for n = 5
LHS 25 RHS 52
32 25
LHS RHS
Hence the result is true for n = 5
Step 2: Assume the result is true for n = k, where k is a positive
integer > 4
i.e. 2k k 2
Step 3: Prove the result is true for n = k + 1
k 1
k 1
2
i.e. Prove : 2
15. Proof:
2 k 1 2 2k
2k 2
k2 k2
k2 k k
16. Proof:
2 k 1 2 2k
2k 2
k2 k2
k2 k k
k 2 4k
17. Proof:
2 k 1 2 2k
2k 2
k2 k2
k2 k k
k 2 4k k 4
18. Proof:
2 k 1 2 2k
2k 2
k2 k2
k2 k k
k 2 4k k 4
k 2 2k 2k
19. Proof:
2 k 1 2 2k
2k 2
k2 k2
k2 k k
k 2 4k k 4
k 2 2k 2k
k 2 2k 8
20. Proof:
2 k 1 2 2k
2k 2
k2 k2
k2 k k
k 2 4k k 4
k 2 2k 2k
k 2 2k 8 k 4
21. Proof:
2 k 1 2 2k
2k 2
k2 k2
k2 k k
k 2 4k k 4
k 2 2k 2k
k 2 2k 8 k 4
k 2 2k 1
22. Proof:
2 k 1 2 2k
2k 2
k2 k2
k2 k k
k 2 4k k 4
k 2 2k 2k
k 2 2k 8 k 4
k 2 2k 1
k 1
2
23. Proof:
2 k 1 2 2k
2k 2
k2 k2
k2 k k
k 2 4k k 4
k 2 2k 2k
k 2 2k 8 k 4
k 2 2k 1
k 1
2
2 k 1
k 1 2
24. Proof:
2 k 1 2 2k
2k 2
k2 k2
k2 k k
k 2 4k k 4
k 2 2k 2k
k 2 2k 8 k 4
k 2 2k 1
k 1
2
2 k 1
k 1 2
Hence the result is true for n = k + 1 if it is also true for n = k
25. Proof:
2 k 1 2 2k
2k 2
k2 k2
k2 k k
k 2 4k k 4
k 2 2k 2k
k 2 2k 8 k 4
k 2 2k 1
k 1
2
2 k 1
k 1 2
Hence the result is true for n = k + 1 if it is also true for n = k
Step 4: Since the result is true for n = 5, then the result is true for
all positive integral values of n > 4 by induction .
26. Proof:
2 k 1 2 2k
2k 2
k2 k2
k2 k k
k 2 4k k 4 Exercise 6N;
k 2 2k 2k 6 abc, 8a, 15
k 2 2k 8 k 4
k 2 2k 1
k 1
2
2 k 1
k 1 2
Hence the result is true for n = k + 1 if it is also true for n = k
Step 4: Since the result is true for n = 5, then the result is true for
all positive integral values of n > 4 by induction .