Frames of reference

Move toward pleasure You should love me because.. I m kind, gentle, and good in bed.  

Move away from pain You will miss out on one of the most amazing and interesting men you ever could have dated if you don t give me your phone number right now - Brett Baggett 

Applies to ALL DECISIONS. For example say you are considering attending my 2-Day Seminar so you can use these techniques. 

If you respond by moving toward pleasure I would say Imagine the confident feelings you will have when you leave my seminar after investing two days of your time to be able to walk up to any stranger and develop instant rapport, turn just friends into lovers, and use language to create states of wanton lust with anyone you choose  

On the other hand, if you are motivated by avoiding pain STOP... and listen to how you would be persuaded to buy.  

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This representation is slightly inconvenient since Ey and 2 in equation (Al.6.56) are explicitly time-dependent. For a monocln-omatic light field of frequency oi, we can transfonn to a frame of reference rotating at the frequency of the light field so that the vector j s a constant. To completely remove the time dependence... 

Examples of even processes include heat conduction, electrical conduction, diflfiision and chemical reactions [4], Examples of odd processes include the Hall effect [12] and rotating frames of reference [4], Examples of the general setting that lacks even or odd synnnetry include hydrodynamics [14] and the Boltzmaim equation [15]. 

The Bloch equation is simplified, and the experiment more readily understood, by transfonnation into a frame of reference rotating at the frequency ciDq=X Bq about die z-axis whereupon ... 

Suppose that a gradient, G=G u is applied in the /-direction. In a local frame of reference rotating about the... 

Figure Bl.24.2. A schematic representation of an elastic collision between a particle of massM and energy Eq and a target atom of mass M2. After the collision the projectile and target atoms have energies of and 2 respectively. The angles 0 and ( ) are positive as shown. All quantities refer to tire laboratory frame of reference.

A unifonn monoenergetic beam of test or projectile particles A with nnmber density and velocity is incident on a single field or target particle B of velocity Vg. The direction of the relative velocity m = v -Vg is along the Z-axis of a Cartesian TTZ frame of reference. The incident current (or intensity) is then = A v, which is tire number of test particles crossing unit area nonnal to the beam in unit time. The differential cross section for scattering of the test particles into unit solid angle dO = d(cos vji) d( ) abont the direction ( )) of the final relative motion is... 

Theorists calculate cross sections in the CM frame while experimentalists usually measure cross sections in the laboratory frame of reference. The laboratory (Lab) system is the coordinate frame in which the target particle B is at rest before the collision i.e. Vg = 0. The centre of mass (CM) system (or barycentric system) is the coordinate frame in which the CM is at rest, i.e. v = 0. Since each scattering of projectile A into (v[i, (ji) is accompanied by a recoil of target B into (it - i[/, ([) + n) in the CM frame, the cross sections for scattering of A and B are related by... 

Kramers and Kistemaker evaluated the momentum transfer Co the wall by molecular impacts in a frame of reference moving with the mole mean velocity This has some algebraic advantage over working in the rest frame of the tube... 

Components of a second-order tensor T in a three-dimensional frame of reference are written as the following 3x3 matrix... 

In maldug electrochemical impedance measurements, one vec tor is examined, using the others as the frame of reference. The voltage vector is divided by the current vec tor, as in Ohm s law. Electrochemical impedance measures the impedance of an electrochemical system and then mathematically models the response using simple circuit elements such as resistors, capacitors, and inductors. In some cases, the circuit elements are used to yield information about the kinetics of the corrosion process. 

To permit a more general discussion, we can replace the snowplow with a piston, and replace the snow with any fluid (Fig. 2,3), We consider the example shown in a reference frame in which the undisturbed fluid has zero velocity. When the piston moves, it applies a planar stress, a, to the fluid. For a non-viscous, hydrodynamic fluid, the stress is numerically equal to the pressure, P, The pressure induces a shock discontinuity, denoted by which propagates through the fluid with velocity U. The velocity u of the piston, and the shocked material carried with it (with respect to the stationary frame of reference), is called the particle velocity, since that would be the velocity of a particle caught up in the flow, or of a particle of the fluid. 

This statement refers to a frame of reference in which the initial state of the material is stationary. It is not true for all frames of reference, e.g., one which moves with the shock velocity. 

In practice, particle tracking is usually performed in a Lagrangian frame of reference, and the motion of a particle is governed by... 

The quantitative formulation of chemical exchange involves modification of the Bloch equations making use of Eq. (4-67). We will merely develop a qualitative view of the result." We adopt a coordinate system that is rotating about the applied field Hq in the same direction as the precessing magnetization vector. Let and Vb be the Larmor precessional frequencies of the nucleus in sites A and B. Eor simplicity we set ta = tb- As the frequency Vq of the rotating frame of reference we choose the average of Va and Vb, thus. 

Suppose we adopt a rotating frame of reference with coordinates x, y, z such that the fixed field Hq lies along the z axis and the x, y coordinate system rotates about the z axis with the frequency of the field ff,. Let Hi be stationary along the x axis. 

The models derived for continuous oxide layers remain valuable when porous oxides are formed they provide a frame of reference against which deviations may be examined and give a basis for understanding the factors governing the location of new oxide. In many cases, however, the experimentally derived rate laws no longer have a unique interpretation. For example, the linear rate law relating the thickness of oxide, x, to the time, t... 

P should also minimize distinction.s between conventionally distinct but atomic. primitives (such as space, mass, time, etc.). The vision is to take one more step along the metaphoric road remove jnan from the center of the universe —> remove all privileged frames of reference —> remove all absolutes —> remove all distinction between space and matter—r remove all distinction ( ) Start by eliminating the tacit assumption that whatever physics is self-organizing itself out of the soup of the current crop of physicists is the physics of this universe in short, go from a solipsistic phys-ics to a fundamentally relativistic physics, wherein even physics itself becomes a set (an infinite hierarchical set ) of self-consistent world-views rather than a prescribed set of exactly/uniquely prescribed laws operating independently of all observers. 

I Worked Examples are now titled to give students a frame of reference. Each Worked Example includes a Strategy and a worked-out Solution, and then is followed by problems for students to try on their own. This book has more than 1800 in-text and end-of-chapter problems. 

New Insights into the data. Mapping our data into an appropriate factor space can provide a new frame of reference wherein patterns that were not apparent in the native coordinate space become evident. Factor spaces can help us understand how many components are actually present, or which samples are similar or different to which other samples. 

So we have found a pair of axes that we can use as the basis of a new coordinate system. And since each axis spans the maximum possible amount of variance in the data, we can be assured that there are no axes that can serve as a more efficient frame of reference than these two. Each axis is a factor or principal component of the data. Together, they comprise the basis space of this data set. 

Notice also, that PRESS, as defined, is not standardized to any absolute frame of reference. The more samples we have in our data set, the more errors there are to be squared and summed, and the larger PRESS is likely to be. Thus, PRESS is only useful for comparisons within a given data set. 

In a quantum mechanical framework, Postulate 1 remains as stated. It implies that there exists a well-defined connection and correspondence between the labels attributed to the space-time points by each observer, between the state vectors each observer attributes to a given physical system, and between observables of the system. Postulate 2 is usually formulated in terms of transition probabilities, and requires that the transition probability be independent of the frame of reference. It should be stated explicitly at this point that we shall formulate the notion of invariance in terms of the concept of bodily identity, wherein a single physical system is viewed by two observers who, in general, will have different relations to the system. 

Now in quantum theory the description of a physical system in the Heisenberg picture for a given observer O is by means of operators Q, which satisfy certain equations of motion and commutation rules with respect to O s frame of reference (coordinate system x). The above notion of an invariance principle can be stated alternatively as follows If, when we change this coordinate frame of reference (i.e., for observer O ) we are able to find a new set of operators that obeys the same equations of motion and the same commutation rules with respect to the new frame of reference (coordinate system x ) we then say that these observers are equivalent and the theory invariant under the transformation x - x. The observable consequences of theory in the new frame (for observer O ) will then clearly be the same as those in the old frame. 

Consider for example the theory under discussion, namely, quantum electrodynamics under the circumstance that the frame of reference with respect to which phenomena are described is changed from a right-handed to a left-handed coordinate system, i.e., from one in which the space-time coordinates are labeled by to one in which they are labeled by sc, with... 

The above description refers to a Lagrangian frame of reference in which the movement of the particle is followed along its trajectory. Instead of having a steady flow, it is possible to modulate the flow, for example sinusoidally as a function of time. At sufficiently high frequency, the molecular coil deformation will be dephased from the strain rate and the flow becomes transient even with a stagnant flow geometry. Oscillatory flow birefringence has been measured in simple shear and corresponds to some kind of frequency analysis of the flow... 

Evaporative two-phase flow in a heated micro-channel resembles a two-phase slug flow with distinct domains of liquid and vapor. These domains are divided by the infinitely thin evaporating front, which propagates relatively to the fluid with a velocity u f equal (numerically) to the linear rate of liquid evaporation. In the frame of reference associated with micro-channel walls, the velocity of the evaporation front is... 

The conditions on the interface express the continuity of the mass and heat fluxes and the equilibrium of all acting forces (Landau and Lifshitz 1959). In the frame of reference associated with the interface they are ... 

After the establishment of a cylindrical flame, continuous reduction of the flame speed relative to an external frame of reference was observed. This reduction was linear in time and quenching occurred in the system when the flame speed was close to zero. The declining flame speed was attributed to heat losses to the walls (reducing the effective expansion ratio in the flame) and quenching was interpreted in terms of the following criterion ... 

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