DOF, Degree of Freedom

Variable definitions AX (xylan conversion, %) AG (glucan conversion, %) l (inoculum amount, mg of P. ostreatus/g of stems) M (moisture content, g of H20/g of stems) t (time, d). 6 DOF, degrees of freedom for the regression analysis. 

In this section, we present a two DOF (degree-of-freedom) planar robot finger employing the multi-stacked DE actuator that has been discussed in Chapter 7. Since the proposed actuator is embedded in the link, the finger becomes compact, simple in mechanism, and lightweight. The design and control issues of the finger are briefly addressed in this Section. 

Xgm = grand mean = 6.284 dof = degrees of freedom within data sets = 30 dn/g = degrees of freedom between data sets = 4 dofj = total degrees of freedom - 34 ... 

DOF degrees-of-freedom MP-RAGE magnetization prepared rapid gradient echo... 

It is also remarkable that no comparison between the various devices proposed and the mouse has been included in the above papers. One would have hoped that if any of the devices was to become as widely used as the mouse for an application or an interface, there should be some comparison made. In table 1 (next) we list the cube-based interfaces and compare their DoF (Degree of Freedom), we also include the mouse. 

CPK = Corey, Pauling, and Koltun CRT = cathode ray tube CSM = color shadow mask DOF = degrees-of-freedom. 

We can state these ideas precisely as follows. Consider any optimization problem with n variables, let x be any feasible point, and let act(x) be the number of active constraints at x. Recall that a constraint is active at x if it holds as an equality there. Hence equality constraints are active at any feasible point, but an inequality constraint may be active or inactive. Remember to include simple upper or lower bounds on the variables when counting active constraints. We define the number of degrees of freedom (dof) at x as... 

As explained in the Introduction, most mixed quantum-classical (MQC) methods are based on the classical-path approximation, which describes the reaction of the quantum degrees of freedom (DoF) to the dynamics of the classical DoF [9-22]. To discuss the classical-path approximation, let us first consider a diabatic... 

In the MQC mean-field trajectory scheme introduced above, all nuclear DoF are treated classically while a quantum mechanical description is retained only for the electronic DoF. This separation is used in most implementations of the mean-field trajectory method for electronically nonadiabatic dynamics. Another possibility to separate classical and quantum DoF is to include (in addition to the electronic DoF) some of the nuclear degrees of freedom (e.g., high frequency modes) into the quantum part of the calculation. This way, typically, an improved approximation of the overall dynamics can be obtained—albeit at a higher numerical cost. This idea is the basis of the recently proposed self-consistent hybrid method [201, 202], where the separation between classical and quantum DoF is systematically varied to improve the result for the overall quantum dynamics. For systems in the condensed phase with many nuclear DoF and a relatively smooth distribution of the electronic-vibrational coupling strength (e.g.. Model V), the separation between classical and quanmm can, in fact, be optimized to obtain numerically converged results for the overall quantum dynamics [202, 203]. 

By definition, a mixed quantum-classical method treats the various degrees of freedom (DoF) of a system on a different dynamical footing—for example, quantum mechanics for the electronic DoF and classical mechanics for the... 

There are a variety of formalisms that allow for a mapping of a discrete quantum system onto a continuous analog (for reviews see Refs. 218 and 219). The most prominent examples are Schwinger s theory of angular momentum [98] and the Holstein-Primakoff transformation [97], both of which allow a continuous representation of spin degrees of freedom. To discuss these two theories, we consider a spin DoF that is described by the spin operators Si,S2,Si with commutation relations... 

Because the mapping approach treats electronic and nuclear dynamics on the same dynamical footing, its classical limit can be employed to study the phase-space properties of a nonadiabatic system. With this end in mind, we adopt a onemode two-state spin-boson system (Model IVa), which is mapped on a classical system with two degrees of freedom (DoF). Studying various Poincare surfaces of section, a detailed phase-space analysis of the problem is given, showing that the model exhibits mixed classical dynamics [123]. Furthermore, a number of periodic orbits (i.e., solutions of the classical equation of motion that return to their initial conditions) of the nonadiabatic system are identified and discussed [125]. It is shown that these vibronic periodic orbits can be used to analyze the nonadiabatic quantum dynamics [126]. Finally, a three-mode model of nonadiabatic photoisomerization (Model III) is employed to demonstrate the applicability of the concept of vibronic periodic orbits to multidimensional dynamics [127]. 

For designing single-component formulations, we have two degrees of freedom (DOF) choice of component and the chemical potential or concentration of the component in formulation. Let us assume that the candidate pool of possible components is made of n" different chemicals. 

Fig. 2.1 Shape recognition by the binding site increases with the geometrical complexity of the site. The number DOF represents the degrees of freedom that must be satisfied for a perfect fit...

Degrees of Freedom (DOF) Site Group c3h Factor Group dh Modes... 

Why has this elegant reaction theory not been applied to general reactive systems with many DOFs It was because their algorithm depends crucially on finding pure unstable periodic orbits in the nonreactive degrees of freedom. As pointed out previously [44], it is always possible to find this regulatory object in... 

It is designed for multidimensional systems. This is a qualitative difference from the existing formulations which attempt to extrapolate to three or more degrees of freedom (DOF) geometrical methods that work for systems with two DOFs. 

TABLE 4.4 Analysis of the degree of freedom (DOF) of the process streams across a barrel set consisting of five of casks, see Fig. 4.9... 

A degree of freedom (DOF) analysis around the CSTR (total moles not speeified) gives... 

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