Find the sum of the measures of the interior angles of each convex
... angles are congruent. Thus, the alternate interior angles at top and bottom must both have a measure of 4y as shown . Since the opposite sides of the parallelogram are parallel, the consecutive interior angles must be supplementary. So, set the sum of 42, 23, 4y, and 83 equal to 180 and solve for y. ...
... angles are congruent. Thus, the alternate interior angles at top and bottom must both have a measure of 4y as shown . Since the opposite sides of the parallelogram are parallel, the consecutive interior angles must be supplementary. So, set the sum of 42, 23, 4y, and 83 equal to 180 and solve for y. ...
4, 2710 (2013)
... concept for understanding exotic phenomena in many different systems18–23. A natural question to ask is whether MFs can also exist in an FF or LO superconductor or superfluid? In this article, we propose that FF superconductors/superfluids may support MFs if they possess two crucial elements: gapped b ...
... concept for understanding exotic phenomena in many different systems18–23. A natural question to ask is whether MFs can also exist in an FF or LO superconductor or superfluid? In this article, we propose that FF superconductors/superfluids may support MFs if they possess two crucial elements: gapped b ...
Quantum Gravity : Motivations and Alternatives 1
... The well-established, empirically well-confirmed precursor theories – General Relativity and Quantum Mechanics –, together with the already existing empirical data that confirmed these theories, are still the only concrete elements that constitute a reasonable starting point for the different attemp ...
... The well-established, empirically well-confirmed precursor theories – General Relativity and Quantum Mechanics –, together with the already existing empirical data that confirmed these theories, are still the only concrete elements that constitute a reasonable starting point for the different attemp ...
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Linear and non-linear response phenomena of molecular systems
... that we look at. For example, in an optical absorption experiment, we apply light (the external perturbation) and we look at the light that comes back from the system (the response). In this particular case both correspond to the same type of perturbation, but this does not have to be the case, we m ...
... that we look at. For example, in an optical absorption experiment, we apply light (the external perturbation) and we look at the light that comes back from the system (the response). In this particular case both correspond to the same type of perturbation, but this does not have to be the case, we m ...
A unification of photons, electrons, and gravitons under qbit
... A unification of photons, electrons, and gravitons under qbit models ...
... A unification of photons, electrons, and gravitons under qbit models ...
Lectures on Quantum Mechanics (nonlinear PDE point of view)
... These lectures correspond to a three-semester course given by the author at the Faculty of Mathematics of the Vienna University in the academic years 2002/2003 and 2003/2004. We expose well known Schrödinger quantum mechanics with traditional applications to Hydrogen atom, but the form of the expos ...
... These lectures correspond to a three-semester course given by the author at the Faculty of Mathematics of the Vienna University in the academic years 2002/2003 and 2003/2004. We expose well known Schrödinger quantum mechanics with traditional applications to Hydrogen atom, but the form of the expos ...
72 063623 (2005) .
... However, after averaging over the whole phase space, we find that the fidelity decay can be well fitted by an inverse power law 1 / t, as shown in Fig. 4. In this case, for the quantum evolution of initial coherent state BEC, high fidelity can be expected, because the fidelity has a slow power-law d ...
... However, after averaging over the whole phase space, we find that the fidelity decay can be well fitted by an inverse power law 1 / t, as shown in Fig. 4. In this case, for the quantum evolution of initial coherent state BEC, high fidelity can be expected, because the fidelity has a slow power-law d ...
How long does it take until a quantum system
... the initial state were precisely known, it would be impossible to predict with certainty what the final quantum state will be. Moreover, the pure initial state has zero entropy, M2 but at the end, according to Hawking, its entropy is of the order of m 2 , where M is the Pl total mass of the system a ...
... the initial state were precisely known, it would be impossible to predict with certainty what the final quantum state will be. Moreover, the pure initial state has zero entropy, M2 but at the end, according to Hawking, its entropy is of the order of m 2 , where M is the Pl total mass of the system a ...
The stuff the world is made of: physics and reality
... exercises an action, or inversely, within which it can be acted upon, is restricted to a cube of side one millionth of a centimeter. This is a very small volume indeed, and one of the problems that we are confronted with is that we lose all intuitive feeling on such small scales. To understand fully ...
... exercises an action, or inversely, within which it can be acted upon, is restricted to a cube of side one millionth of a centimeter. This is a very small volume indeed, and one of the problems that we are confronted with is that we lose all intuitive feeling on such small scales. To understand fully ...
From Principles to Diagrams
... geometric sense. For this space the metric matters and the radius of CP1 turns out to allow identification in terms of Planck length. Gravitational interaction would bring in Planck length as a basic scale in this manner. P T in turn would define the twistor space in which the twistorial lifts of im ...
... geometric sense. For this space the metric matters and the radius of CP1 turns out to allow identification in terms of Planck length. Gravitational interaction would bring in Planck length as a basic scale in this manner. P T in turn would define the twistor space in which the twistorial lifts of im ...
National 5 Mathematics Revision Notes
... To refresh your memory of the method you were taught in class when you are stuck on a homework question or a practice test question. To memorise key facts when revising for the exam. The key to revising for a maths exam is to do questions, not to read notes. As well as using this booklet, you sh ...
... To refresh your memory of the method you were taught in class when you are stuck on a homework question or a practice test question. To memorise key facts when revising for the exam. The key to revising for a maths exam is to do questions, not to read notes. As well as using this booklet, you sh ...
M00.pdf
... stability, and small zones of chaoticity separated by irrational KAM tori exist for slightly larger values of kick strength, global chaos begins to set in at the critical kick strength, where the last surviving KAM torus breaks into a cantorus, and for very large kick strength strong chaos reigns th ...
... stability, and small zones of chaoticity separated by irrational KAM tori exist for slightly larger values of kick strength, global chaos begins to set in at the critical kick strength, where the last surviving KAM torus breaks into a cantorus, and for very large kick strength strong chaos reigns th ...
Constructive Geometry - Proof theory and straightedge
... A theorem in the algebraic setting Suppose that we do require B 6= C for the definedness of Circle3(A, B, C). Then: Theorem (with Freek Wiedijk) Circle3 is not definable from the other operations. Proof. Let t be a term definable without Circle3, with one free point variable x. Then t becomes undefi ...
... A theorem in the algebraic setting Suppose that we do require B 6= C for the definedness of Circle3(A, B, C). Then: Theorem (with Freek Wiedijk) Circle3 is not definable from the other operations. Proof. Let t be a term definable without Circle3, with one free point variable x. Then t becomes undefi ...
Singularity of the time-energy uncertainty in adiabatic perturbation
... sphere is a cycloid traced by a circle rolling along an adiabatic path. As the magnetic field rotates more and more slowly, the time-energy uncertainty, proportional to the length of the quantum trajectory, calculated by the exact solution is entirely different from the one obtained by the adiabatic ...
... sphere is a cycloid traced by a circle rolling along an adiabatic path. As the magnetic field rotates more and more slowly, the time-energy uncertainty, proportional to the length of the quantum trajectory, calculated by the exact solution is entirely different from the one obtained by the adiabatic ...
Functorial Field Theories and Factorization Algebras
... According to the main result of the Lagrangian formulation of classical mechanics, solutions of Newton’s differential equation (2.2) correspond essentially to critical points of the action functional S. However, we need boundary conditions to obtain the correct statement (without them, the functiona ...
... According to the main result of the Lagrangian formulation of classical mechanics, solutions of Newton’s differential equation (2.2) correspond essentially to critical points of the action functional S. However, we need boundary conditions to obtain the correct statement (without them, the functiona ...
Document
... 2. Motivation: a critical view • The big picture – In QC the circuits are prone to frequent failures – Safe recovery is a problem – A successful FTAM (for our error model – single random fault) means that, for a x fault rate, the overall circuit error rate is x 2 – Besides coding, structural redunda ...
... 2. Motivation: a critical view • The big picture – In QC the circuits are prone to frequent failures – Safe recovery is a problem – A successful FTAM (for our error model – single random fault) means that, for a x fault rate, the overall circuit error rate is x 2 – Besides coding, structural redunda ...
89, 053618 (2014)
... Hereafter in our numerical simulation we set t = 1 throughout this work as the basic energy scale. All other energies are scaled by t. The total length of the 1D optical lattice is chosen as N = 100, which is long enough to ensure that the coupling between two ends is vanishingly small (10−7 t). An ...
... Hereafter in our numerical simulation we set t = 1 throughout this work as the basic energy scale. All other energies are scaled by t. The total length of the 1D optical lattice is chosen as N = 100, which is long enough to ensure that the coupling between two ends is vanishingly small (10−7 t). An ...
Regular/irregular phase space structure of HCN/HNC
... means that regular/irregular or mode localized/delocalized states are found in both mechanics but the onset of quantum chaos occurs at higher energies than in classical dynamics. (ii) There is a specificity in the appearance of chaos in overtone excitations. The excitation of the bending mode leads ...
... means that regular/irregular or mode localized/delocalized states are found in both mechanics but the onset of quantum chaos occurs at higher energies than in classical dynamics. (ii) There is a specificity in the appearance of chaos in overtone excitations. The excitation of the bending mode leads ...
