Dependency problems

The most reliable results are obtained using ah initio methods with moderate-to large-sized polarized basis sets. The use of gauge-independent atomic orbitals (GIAO) removes gauge dependency problems. 

In time-dependent problems, all the above conditions can be time-dependent functions, such as a machine heating cycle or another time-dependent process under study. 

In time-dependent problems, of course, a good guess (or knowledge) of the initial conditions is much more important. 

Self-similarity applies to one-dimensional, time-dependent problems in which dependence on one of two independent variables can be eliminated by nondimen-... 

The method of false transients converts a steady-state problem into a time-dependent problem. Equations (4.1) govern the steady-state performance of a CSTR. How does a reactor reach the steady state There must be a startup transient that eventually evolves into the steady state, and a simulation of... 

The program can solve both steady-state problems as well as time-dependent problems, and has provisions for both linear and nonlinear problems. The boundary conditions and material properties can vary with time, temperature, and position. The property variation with position can be a straight line function or or a series of connected straight line functions. User-written Fortran subroutines can be used to implement more exotic changes of boundary conditions, material properties, or to model control systems. The program has been implemented on MS DOS microcomputers, VAX computers, and CRAY supercomputers. The present work used the MS DOS microcomputer implementation. 

In this section we consider the one-dimensional heat conduction equation with constant coefficients and difference schemes in order to develop various methods for designing the appropriate difference schemes in the case of time-dependent problems. 

The time-dependent problems are generally simpler than the time-independent ones and the corresponding version of the ZN formulas is presented in Section C. This corresponds to the LZ type, since the NT type does not occur in the time-dependent case. 

The formulas derived in the time-independent framework can be easily transferred into the corresponding time-dependent solutions. The formulas in the time-independent linear potential model, for example, provide the formulas in the time-dependent quadratic potential model in which the two time-dependent diabatic quadratic potentials are coupled by a constant diabatic coupling [1, 13, 147]. The classically forbidden transitions in the time-independent framework correspond to the diabatically avoided crossing case in the time-dependent framework. One more thing to note is that the nonadiabatic tunneling (NT) type of transition does not show up and only the LZ type appears in the time-dependent problems, since time is unidirectional. 

Heinzen, C., Microencapsulation solve time-dependent problems of foodmakers. Fur. Food Drink Rev., 3, 27, 2002. 

Most SECM experiments at liquid-liquid interfaces have principally involved the determination of the steady-state tip current response as a function of the separation between the tip and the interface (approach curve measurements). However, in some situations complementary information can be gleaned from the transient behavior (as illustrated below for SECMIT). We therefore describe models for the time-dependent problem from which the steady-state characteristics can be developed from the longtime limit. 

She also had experimented with LSD and cocaine freebasing numerous times within the past 2 years. Throughout her history of substance abuse she experienced an increasing frequency of periods of dazed consciousness and blackouts multiple times yearly, while under the influence of alcohol. Further, she reported that other family members had chemical dependency problems, though her parents never abused drugs/a1cohol. 

The spectral method is used for direct numerical simulation (DNS) of turbulence. The Fourier transform is taken of the differential equation, and the resulting equation is solved. Then the inverse transformation gives the solution. When there are nonlinear terms, they are calculated at each node in physical space, and the Fourier transform is taken of the result. This technique is especially suited to time-dependent problems, and the major computational effort is in the fast Fourier transform. 

Program DGC04 solves the time-dependent problem. Subroutine EQUATIONS evaluates the coefficients of the unknown delys in the manner just outlined, and then subroutine GAUSS solves for the values of dely. Subroutine STEPPER steps forward in time by incrementing x and y. Subroutine SPECS sets the values of the parameters of the problem, converting units where necessary, and PRINTER writes the results to a file for plotting. 

For description of a time-dependent problem, the Kohn-Sham equations ... 

A pitch is made for a renewed, rigorous and systematic implementation of the GW method of Hedin and Lundquist for extended, periodic systems. Building on previous accurate Hartree-Fock calculations with Slater orbital basis set expansions, in which extensive use was made of Fourier transform methods, it is advocated to use a mixed Slater-orbital/plane-wave basis. Earher studies showed the amehoration of approximate linear dependence problems, while such a basis set also holds various physical and anal3ftical advantages. The basic formahsm and its realization with Fourier transform expressions is explained. Modem needs of materials by precise design, assisted by the enormous advances in computational capabilities, should make such a program viable, attractive and necessary. 

The maxEnt approach suffers from the scale dependence problem. Nevertheless, perhaps a distribution may be judged to be better than not assigning a distribution. Consequences of using uniform or maxEnt distributions for different scales can be explored in a sensitivity analysis. An additional difficulty is that in order to apply the maxEnt approach, particular features of a distribution may need to be assumed known when those features may actually be substantially uncertain. 

The adverse reactions include slowing of gastrointestinal propulsion with the ensuing risk of constipation, which can be prevented with lactulose or lactitol. Opioid treatment can also cause nausea and sometimes vomiting. There is also a dependence problem and a risk of respiratory depression. The latter may be a practical problem in anaesthetic practice or in overdose, but rarely in the case of treatment with slowly increased oral doses. The nausea is... 

Drawing on the interviews with parents I will first outline their views on the force of their dependency problems and then move to depict some of the routines associated with drug use as a means of showing how these necessarily impinge upon the care and wellbeing of children, even despite the efforts of the parent to protect them from exposure to drugs and the associated lifestyle. 

In the middle of drug dependency problems, this narrow focus on drugs is probably what sustains the determination to find and use drugs, often against quite remarkable odds. It is also what makes their children most vulnerable because it armours parents against seeing the damage they can do to their children ... 

Drugs so fettered her relationship with her daughter that it was the exception not the norm to hold and play with her or to take much pleasure in the process. This sense of emotional disconnectedness was characterized similarly by many other parents and was part and parcel of the overwhelming experience of parenting whilst also in the midst of a drug dependency problem. 

An alternative approach is to solve the time-dependent problem in which the development of the flow is calculated from some arbitrary initial state. Eq. (5-1) is unchanged, but 5(ZR sin 0)/3t must be added to the left side of Eq. (5-2), where... 

Since the stream function depends upon Reynolds number, the rate of transfer will depend upon both Re and Sc except in the limit Re 0 treated in Chapter 3. Solutions to Eq. (5-19) have been obtained using the techniques discussed earlier, i.e., finite-difference schemes (A6, D5, II, M6, W9), solution to the time-dependent problem (Hll), and series expansions (D5). 

The first is a variational approach that maps the position-dependent problem to an effective parabolic barrier transfer problem, with an effective friction that is position-independent. This approach leads to a result for the rate that can be interpreted as a Grote-Hynes coefficient with a position-dependent friction. 

Comparison of the Kohn-Sham and Skyrme functionals leads to a natural question why these two functionals exploit, for the time-dependent problem, so different sets of basic densities and currents If the Kohn-Sham functional is content with one density, the Skyrme forces operate with a diverse set of densities and currents, both T-even and T-odd. Then, should we consider T-odd densities as genuine for the description of dynamics of finite many-body systems or they are a pequliarity of nuclear forces This question is very nontrivial and still poorly studied. We present below some comments which, at least partly, clarify this point. 

Available evidence suggests that due to this better tolerability, SSRIs are the best choice for patients with PD ( 113). SSRIs also offer benefits of ease of dosing and no safety or dependence problems. This contrasts with the poor tolerance associated with TCAs and with dependence problems associated with BZDs ( 114). In addition, because of the longer half-life, fluoxetine at doses ranging from 10 to 60 mg administered once weekly appears to be an effective maintenance treatment for patients with PD whose successful initial treatment was with daily fluoxetine (115). 

The quantum theory of molecular collisions in external fields described in this chapter is based on the solutions of the time-independent Schrodinger equation. The scattering formalism considered here can be used to calculate the collision properties of molecules in the presence of static electric or magnetic fields as well as in nonresonant AC fields. In the latter case, the time-dependent problem can be reduced to the time-independent one by means of the Floquet theory, discussed in the previous section. We will consider elastic or inelastic but chemically nonreac-tive collisions of molecules in an external field. The extension of the formalism to reactive scattering problems for molecules in external fields has been described in Ref. [12]. 

However, for axially segregated (left/right) loading, the scale-up factors depended on cohesion, indicating that scale-up is a mixture-dependent problem. As shown in Figure 9A, the most cohesive system mixed much more slowly in the smaller (IQ) blender. However, all three systems mixed at nearly the same rate in the larger (28Q) vessel (Fig. 9B). 

With the use of major tranquillisers, for example, thioridazine, chlorpromazine, or perphenazine, it is possible to withdraw opiate dependents who are highly motivated. The dosages can be titrated to the degree of clinical symptoms and this can be monitored with key carers through an out-patient clinic. The use of hypnotics should be restricted to short-term use due to their own dependency problems, but they can be a useful addition, particularly in the early phases of the treatment programme. 

The general solution of the time-dependent problem (2.5) is a superposition of the normal modes... 

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