Mathematical optimization | Functions and mappings
A signomial is an algebraic function of one or more independent variables. It is perhaps most easily thought of as an algebraic extension of multivariable polynomials—an extension that permits exponents to be arbitrary real numbers (rather than just non-negative integers) while requiring the independent variables to be strictly positive (so that division by zero and other inappropriate algebraic operations are not encountered). Formally, a signomial is a function with domain which takes values where the coefficients and the exponents are real numbers. Signomials are closed under addition, subtraction, multiplication, and scaling. If we restrict all to be positive, then the function f is a posynomial. Consequently, each signomial is either a posynomial, the negative of a posynomial, or the difference of two posynomials. If, in addition, all exponents are non-negative integers, then the signomial becomes a polynomial whose domain is the positive orthant. For example, is a signomial. The term "signomial" was introduced by Richard J. Duffin and Elmor L. Peterson in their seminal joint work on general algebraic optimization—published in the late 1960s and early 1970s. A recent introductory exposition involves optimization problems. Nonlinear optimization problems with constraints and/or objectives defined by signomials are harder to solve than those defined by only posynomials, because (unlike posynomials) signomials cannot necessarily be made convex by applying a logarithmic change of variables. Nevertheless, signomial optimization problems often provide a much more accurate mathematical representation of real-world nonlinear optimization problems. (Wikipedia).
What is the definition of scientific notation
👉 Learn about scientific notations. Scientific notation is a convenient way of writing very large or very small numbers. A number written in scientific notation is of the form a * 10^n where a is the first non-zero number between 1 and 10, (1 included) and n is the number of digits up to t
From playlist Scientific Notation | Learn About
What is an Injective Function? Definition and Explanation
An explanation to help understand what it means for a function to be injective, also known as one-to-one. The definition of an injection leads us to some important properties of injective functions! Subscribe to see more new math videos! Music: OcularNebula - The Lopez
From playlist Functions
301.5C Definition and "Stack Notation" for Permutations
What are permutations? They're *bijective functions* from a finite set to itself. They form a group under function composition, and we use "stack notation" to denote them in this video.
From playlist Modern Algebra - Chapter 16 (permutations)
Injective, Surjective and Bijective Functions (continued)
This video is the second part of an introduction to the basic concepts of functions. It looks at the different ways of representing injective, surjective and bijective functions. Along the way I describe a neat way to arrive at the graphical representation of a function.
From playlist Foundational Math
How to simplify an expression by following order of operations and distributive property
👉 Learn how to simplify mathematics expressions. A mathematis expression is a finite combination of numbers and symbols formed following a set of operations or rules. To simplify a mathematics expression means to reduce the expression into simpler form. For expressions having parenthesis
From playlist Simplify Expressions Using Order of Operations
What is the alternate in sign sequence
👉 Learn about sequences. A sequence is a list of numbers/values exhibiting a defined pattern. A number/value in a sequence is called a term of the sequence. There are many types of sequence, among which are: arithmetic and geometric sequence. An arithmetic sequence is a sequence in which
From playlist Sequences
Simplifying an expression with a parenthesis ex 4, 10 - (2^3 + 4)/3 - 1
👉 Learn how to simplify mathematics expressions. A mathematis expression is a finite combination of numbers and symbols formed following a set of operations or rules. To simplify a mathematics expression means to reduce the expression into simpler form. For expressions having parenthesis
From playlist Simplify Expressions Using Order of Operations
Number Theory | Congruence Modulo n -- Definition and Examples
We define the notion of congruence modulo n among the integers. http://www.michael-penn.net
From playlist Modular Arithmetic and Linear Congruences
Using the order of operations for an expression with two parentheses
👉 Learn how to simplify mathematics expressions. A mathematis expression is a finite combination of numbers and symbols formed following a set of operations or rules. To simplify a mathematics expression means to reduce the expression into simpler form. For expressions having parenthesis
From playlist Simplify Expressions Using Order of Operations
Definition of an Injective Function and Sample Proof
We define what it means for a function to be injective and do a simple proof where we show a specific function is injective. Injective functions are also called one-to-one functions. Useful Math Supplies https://amzn.to/3Y5TGcv My Recording Gear https://amzn.to/3BFvcxp (these are my affil
From playlist Injective, Surjective, and Bijective Functions