Combinatorial optimization CO-3
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The document defines a convex set as a set in Euclidean space where the line segment between any two points in the set is also contained in the set. It provides examples of convex and non-convex sets in R1 and R2. Additionally, it defines a convex function as a function where the epigraph (set of points above the graph) forms a convex set, and whose value at any interpolated point between two inputs is less than or equal to the linear interpolation of the function values at the two inputs.
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![Convex Set
• A set S ⊆ Rn is called convex if the line segment joining any two points
is in S. Mathematically for all x, y Rn and λ [0, 1]
z = λx + (1- λ)y S
Convex Set Non Convex Set](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
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2
( )1mod −n
x is principal. It also proves theorems showing that the set of polynomials corresponding to a cyclic code C form an ideal, the generator polynomial g(x) of a cyclic code divides ∈−1n
x , and a polynomial is a codeword if and only if it is divisible by the generator polynomial g(x). The document concludes that principal ideals of cyclic codes can be used for optimal error detection, correction and
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Okay, here are the steps:
1) Given:
2) Transform into spherical unit vectors:
3) Write in terms of spherical components:
So the vector components in spherical coordinates are:
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project report(1)
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Math Analysis I
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Computer Science
Active and Programmable Networks
Active safety systems
Ad Hoc & Sensor Network
Ad hoc networks for pervasive communications
Adaptive, autonomic and context-aware computing
Advance Computing technology and their application
Advanced Computing Architectures and New Programming Models
Advanced control and measurement
Aeronautical Engineering,
Agent-based middleware
Alert applications
Automotive, marine and aero-space control and all other control applications
Autonomic and self-managing middleware
Autonomous vehicle
Biochemistry
Bioinformatics
BioTechnology(Chemistry, Mathematics, Statistics, Geology)
Broadband and intelligent networks
Broadband wireless technologies
CAD/CAM/CAT/CIM
Call admission and flow/congestion control
Capacity planning and dimensioning
Changing Access to Patient Information
Channel capacity modelling and analysis
Civil Engineering,
Cloud Computing and Applications
Collaborative applications
Communication application
Communication architectures for pervasive computing
Communication systems
Computational intelligence
Computer and microprocessor-based control
Computer Architecture and Embedded Systems
Computer Business
Computer Sciences and Applications
Computer Vision
Computer-based information systems in health care
Computing Ethics
Computing Practices & Applications
Congestion and/or Flow Control
Content Distribution
Context-awareness and middleware
Creativity in Internet management and retailing
Cross-layer design and Physical layer based issue
Cryptography
Data Base Management
Data fusion
Data Mining
Data retrieval
Data Storage Management
Decision analysis methods
Decision making
Digital Economy and Digital Divide
Digital signal processing theory
Distributed Sensor Networks
Drives automation
Drug Design,
Drug Development
DSP implementation
E-Business
E-Commerce
E-Government
Electronic transceiver device for Retail Marketing Industries
Electronics Engineering,
Embeded Computer System
Emerging advances in business and its applications
Emerging signal processing areas
Enabling technologies for pervasive systems
Energy-efficient and green pervasive computing
Environmental Engineering,
Estimation and identification techniques
Evaluation techniques for middleware solutions
Event-based, publish/subscribe, and message-oriented middleware
Evolutionary computing and intelligent systems
Expert approaches
Facilities planning and management
Flexible manufacturing systems
Formal methods and tools for designing
Fuzzy algorithms
Fuzzy logics
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Relative superior mandelbrot and julia sets for integer and non integer values
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- 2. Convex Set • A set S ⊆ Rn is called convex if the line segment joining any two points is in S. Mathematically for all x, y Rn and λ [0, 1] z = λx + (1- λ)y S Convex Set Non Convex Set
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