In statistical mechanics, the translational partition function, is that part of the partition function resulting from the movement (translation) of the center of mass. For a single atom or molecule in a low pressure gas, neglecting the interactions of molecules, the canonical ensemble can be approximated by: where Here, V is the volume of the container holding the molecule (volume per single molecule so, e.g., for 1 mole of gas the container volume should be divided by the Avogadro number), Λ is the Thermal de Broglie wavelength, h is the Planck constant, m is the mass of a molecule, kB is the Boltzmann constant and T is the absolute temperature.This approximation is valid as long as Λ is much less than any dimension of the volume the atom or molecule is in. Since typical values of Λ are on the order of 10-100 pm, this is almost always an excellent approximation. When considering a set of N non-interacting but identical atoms or molecules, when QT ≫ N , or equivalently when ρ Λ ≪ 1 where ρ is the density of particles, the total translational partition function can be written The factor of N! arises from the restriction of allowed N particle states due to Quantum exchange symmetry.Most substances form liquids or solids at temperatures much higher than when this approximation breaks down significantly. (Wikipedia).
Sigmoid functions for population growth and A.I.
Some elaborations on sigmoid functions. https://en.wikipedia.org/wiki/Sigmoid_function https://www.learnopencv.com/understanding-activation-functions-in-deep-learning/ If you have any questions of want to contribute to code or videos, feel free to write me a message on youtube or get my co
From playlist Analysis
How to find the horizontal and vertical compressions, stretches of multiple functions
👉 Learn how to identify transformations of functions. Transformation of a function involves alterations to the graph of the parent function. The transformations can be dilations, translations (shifts), reflection, stretches, shrinks, etc. To sketch the graph of a transformed function, we s
From playlist I don't know where to put it
Transform Part 1 - Transforming Functions
From playlist CAS Programs
Overview transformations horizontal shifts - Online Tutor - Free Math Videos
👉 Learn how to determine the transformation of a function. Transformations can be horizontal or vertical, cause stretching or shrinking or be a reflection about an axis. You will see how to look at an equation or graph and determine the transformation. You will also learn how to graph a t
From playlist Characteristics of Functions
Thermodynamics and Chemical Dynamics 131C. Lecture 06. The Rotational Partition Function.
UCI Chem 131C Thermodynamics and Chemical Dynamics (Spring 2012) Lec 06. Thermodynamics and Chemical Dynamics -- The Rotational Partition Function -- View the complete course: http://ocw.uci.edu/courses/chem_131c_thermodynamics_and_chemical_dynamics.html Instructor: Reginald Penner, Ph.D.
From playlist Chemistry 131C: Thermodynamics and Chemical Dynamics
Thermodynamics and Chemical Dynamics 131C. Lecture 11. Midterm I Review.
UCI Chem 131C Thermodynamics and Chemical Dynamics (Spring 2012) Lec 11. Thermodynamics and Chemical Dynamics -- Midterm I Review -- View the complete course: http://ocw.uci.edu/courses/chem_131c_thermodynamics_and_chemical_dynamics.html Instructor: Reginald Penner, Ph.D. License: Creati
From playlist Chemistry 131C: Thermodynamics and Chemical Dynamics
Learn how to describe a horizontal translation
👉 Learn how to identify transformations of functions. Transformation of a function involves alterations to the graph of the parent function. The transformations can be dilations, translations (shifts), reflection, stretches, shrinks, etc. To sketch the graph of a transformed function, we s
From playlist Characteristics of Functions
Lec 26 | MIT 5.60 Thermodynamics & Kinetics, Spring 2008
Lecture 26: Partition function (Q) - many particles. View the complete course at: http://ocw.mit.edu/5-60S08 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
From playlist MIT 5.60 Thermodynamics & Kinetics, Spring 2008
Chem 131B. Molecular Structure & Statistical Mechanics. Lecture 23. Partition Functions Pt. 1
UCI Chem 131B Molecular Structure & Statistical Mechanics (Winter 2013) Lec 23. Molecular Structure & Statistical Mechanics -- Partition Functions -- Part 1. View the complete course: http://ocw.uci.edu/courses/chem_131b_molecular_structure_and_elementary_statistical_mechanics.html Instruc
From playlist Chem 131B: Molecular Structure & Statistical Mechanics
Entropy Equipartition along almost Geodesics in Negatively Curved Groups by Amos Nevo
PROGRAM : ERGODIC THEORY AND DYNAMICAL SYSTEMS (HYBRID) ORGANIZERS : C. S. Aravinda (TIFR-CAM, Bengaluru), Anish Ghosh (TIFR, Mumbai) and Riddhi Shah (JNU, New Delhi) DATE : 05 December 2022 to 16 December 2022 VENUE : Ramanujan Lecture Hall and Online The programme will have an emphasis
From playlist Ergodic Theory and Dynamical Systems 2022
Ex: Function Notation for Horizontal and Vertical Stretches and Compressions
This video explains how to recognize a horizontal and vertical compression or stretch using function notation. Site: http://mathispower4u.com
From playlist Determining Transformations of Functions
Thermodynamics and Chemical Dynamics 131C. Lecture 05. The Equipartition Theorum.
UCI Chem 131C Thermodynamics and Chemical Dynamics (Spring 2012) Lec 05. Thermodynamics and Chemical Dynamics -- The Equipartition Theorum -- View the complete course: http://ocw.uci.edu/courses/chem_131c_thermodynamics_and_chemical_dynamics.html Instructor: Reginald Penner, Ph.D. Licens
From playlist Chemistry 131C: Thermodynamics and Chemical Dynamics
Thermodynamics and Chemical Dynamics 131C. Lecture 07. Vibrational Partition Functions.
UCI Chem 131C Thermodynamics and Chemical Dynamics (Spring 2012) Lec 07. Thermodynamics and Chemical Dynamics -- Vibrational Partition Functions -- View the complete course: http://ocw.uci.edu/courses/chem_131c_thermodynamics_and_chemical_dynamics.html Instructor: Reginald Penner, Ph.D.
From playlist Chemistry 131C: Thermodynamics and Chemical Dynamics
Proofs, Circuits, Communication, and Lower Bounds in Complexity Theory - Robert Robere
Computer Science/Discrete Mathematics Seminar II Topic: Proofs, Circuits, Communication, and Lower Bounds in Complexity Theory Speaker: Robert Robere Affiliation: Member, School of Mathematics Date: February 11, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics
Why do we care about characters of tilting modules? - Shotaro Makisumi
SL2 Seminar Topic: Why do we care about characters of tilting modules? Speaker: Shotaro Makisumi Affiliation: Columbia University; Member, School of Mathematics Date: January 26, 2021 For more video please visit http://video.ias.edu
From playlist Mathematics
What do a and b do to the transformations of a function
👉 Learn how to determine the transformation of a function. Transformations can be horizontal or vertical, cause stretching or shrinking or be a reflection about an axis. You will see how to look at an equation or graph and determine the transformation. You will also learn how to graph a t
From playlist Characteristics of Functions
V. Franceschi - Sub-riemannian soap bubbles
The aim of this seminar is to present some results about minimal bubble clusters in some sub-Riemannian spaces. This amounts to finding the best configuration of m ∈ N regions in a manifold enclosing given volumes, in order to minimize their total perimeter. In a n-dimensional sub-Riemanni
From playlist Journées Sous-Riemanniennes 2018