Isosceles and Equilateral Triangles
... Draw a large isosceles triangle ABC, with exactly two congruent sides, AB and AC. What is symmetry? How many lines of symmetry does it have? Label the point of intersection D. ...
... Draw a large isosceles triangle ABC, with exactly two congruent sides, AB and AC. What is symmetry? How many lines of symmetry does it have? Label the point of intersection D. ...
Symplectic Geometry and Geometric Quantization
... 2. Cotangent bundle : M = T ? N, where N is a manifold. M is the phase space of a system whose configuration space is N. M can be endowed with coordinates (qa , pb ), where at each point x = (q1 , ..., qn ) in N the components of a form α ∈ T x? N are (p1 , ..., pn ) (i.e. α = pi dqi ). The symplect ...
... 2. Cotangent bundle : M = T ? N, where N is a manifold. M is the phase space of a system whose configuration space is N. M can be endowed with coordinates (qa , pb ), where at each point x = (q1 , ..., qn ) in N the components of a form α ∈ T x? N are (p1 , ..., pn ) (i.e. α = pi dqi ). The symplect ...
Locality of Gravitational Systems from Entanglement of
... near-AdS region, there are totally geodesic surfaces that pass through this point and go deep into the bulk, where the geometry can depart significantly from AdS. However, contributions from these surfaces are negligible when Ez ≪ 1, where E is the typical energy scale of the CFT state. In this case ...
... near-AdS region, there are totally geodesic surfaces that pass through this point and go deep into the bulk, where the geometry can depart significantly from AdS. However, contributions from these surfaces are negligible when Ez ≪ 1, where E is the typical energy scale of the CFT state. In this case ...
Further Aspects of Weak Interaction Dynamics
... a system of weak dipoles does not emit radiation. The foregoing discussion holds for a motionless weak dipole. Hence, in order to prove this claim one has to examine the general case of fields of an arbitrarily moving weak dipole. The fact that the weak fields satisfy the four homogeneous Maxwell eq ...
... a system of weak dipoles does not emit radiation. The foregoing discussion holds for a motionless weak dipole. Hence, in order to prove this claim one has to examine the general case of fields of an arbitrarily moving weak dipole. The fact that the weak fields satisfy the four homogeneous Maxwell eq ...
Unit 2: Lorentz Invariance
... means we should be able to replace x with Λx at any time without changing anything. ...
... means we should be able to replace x with Λx at any time without changing anything. ...
BALANCE PRINCIPLES
... functional form to the second Piola-Kirchhoff stress tensor-a fundamental ingredient in the dynamical equations. The study of this functional form is the main goal of Chapter 3 on constitutive theory. We shall set up the basic equations (or inequalities) as integral balance conditions. Therefore, th ...
... functional form to the second Piola-Kirchhoff stress tensor-a fundamental ingredient in the dynamical equations. The study of this functional form is the main goal of Chapter 3 on constitutive theory. We shall set up the basic equations (or inequalities) as integral balance conditions. Therefore, th ...
Interactive Chalkboard
... because all of the vertices lie on the circle and the circle is a circumscribed circle because it contains all of the vertices of the polygon. ...
... because all of the vertices lie on the circle and the circle is a circumscribed circle because it contains all of the vertices of the polygon. ...
Geometry Vertical Angles and Transversal powerpoint
... Prove the Alternate Interior Angles Theorem. SOLUTION ...
... Prove the Alternate Interior Angles Theorem. SOLUTION ...
Vertical Angles and Transversal Powerpoint
... Prove the Alternate Interior Angles Theorem. SOLUTION ...
... Prove the Alternate Interior Angles Theorem. SOLUTION ...
Noether's theorem
Noether's (first) theorem states that every differentiable symmetry of the action of a physical system has a corresponding conservation law. The theorem was proven by German mathematician Emmy Noether in 1915 and published in 1918. The action of a physical system is the integral over time of a Lagrangian function (which may or may not be an integral over space of a Lagrangian density function), from which the system's behavior can be determined by the principle of least action.Noether's theorem has become a fundamental tool of modern theoretical physics and the calculus of variations. A generalization of the seminal formulations on constants of motion in Lagrangian and Hamiltonian mechanics (developed in 1788 and 1833, respectively), it does not apply to systems that cannot be modeled with a Lagrangian alone (e.g. systems with a Rayleigh dissipation function). In particular, dissipative systems with continuous symmetries need not have a corresponding conservation law.