Problem characterizing

In vapor-liquid equilibria, if one phase composition is given, there are basically four types of problems, characterized by those variables which are specified and those which are to be calculated. Let T stand for temperature, P for total pressure, for the mole fraction of component i in the liquid phase, and y for the mole fraction of component i in the vapor phase. For a mixture containing m components, the four types can be organized in this way ... 

The model describing interaction between two bodies, one of which is a deformed solid and the other is a rigid one, we call a contact problem. After the deformation, the rigid body (called also punch or obstacle) remains invariable, and the solid must not penetrate into the punch. Meanwhile, it is assumed that the contact area (i.e. the set where the boundary of the deformed solid coincides with the obstacle surface) is unknown a priori. This condition is physically acceptable and is called a nonpenetration condition. We intend to give a mathematical description of nonpenetration conditions to diversified models of solids for contact and crack problems. Indeed, as one will see, the nonpenetration of crack surfaces is similar to contact problems. In this subsection, the contact problems for two-dimensional problems characterizing constraints imposed inside a domain are considered. 

Chemical Sensitization Evidence suggests that some people may develop health problems characterized by effects such as dizziness, eye and throat irritation, chest tightness, and nasal congestion that appear whenever they are exposed to certain chemicals. People may react to even trace amounts of chemicals to which they have become "sensitized."... 

Coiiimon-pool problems characterize many resources where it is difficult to define property rights to restrain access and use. In North America, common-pool conditions in oil and natural gas production are created when firms compete for hydrocarbons in the same formation under the common-law rule of capture (which also governs fisheries and many other natural resources). 

There are several possible ways of introducing the Born-Oppenheimer model " and here the most descriptive way has been chosen. It is worth mentioning, however, that the justification for the validity of the Bom-Oppenheimer approximation, based on the smallness of the ratio of the electronic and nuclear masses used in its original formulation, has been found irrelevant. Actually, Essen started his analysis of the approximate separation of electronic and nuclear motions with the virial theorem for the Coulombic forces among all particles of molecules (nuclei and electrons) treated in the same quantum mechanical way. In general, quantum chemistry is dominated by the Bom-Oppenheimer model of the theoretical description of molecules. However, there is a vivid discussion in the literature which is devoted to problems characterized by, for example, Monkhorst s article of 1987, Chemical Physics without the Bom-Oppenheimer Approximation... ... 

Other terms used to describe this phase of the risk assessment process include problem dehnition, problem characterization, risk profiling (EC 2000), and scoping phase. ... 

This simply means that one must be willing to identify one of the unperturbed states as the best approximation to the state being sought. This, of course, implies that one must therefore strive to find an unperturbed model problem, characterized by H that represents the true system as accurately as possible, so that one of the d>k will be as close as possible to /k. 

In a given problem, characterized by a force-function and boundary condition, we look for sets /, of functions for which the surface integral in Eq. (7) vanishes and for which, if f is a member of such a set, V2/, and K f can be written as linear combinations of members of the set. Then Eq. (7) may become a recursion relation which in principle (and sometimes in practice) can be solved for the time-dependent behavior of the quantities in terms of their values at 1 = 0. Let ( denote the expectation of/at time t, and 0 its expectation at t = 0. In the absence of a subscript, the angular brackets will denote the usual ensemble average over equilibrium states. 

In this chapter we address the following problem characterize all weakly face-regular ( a, b], 3)-maps on sphere or torus (see Chapter 9 for strictly face-regular ones). 

Equations (2), (4), and (5) can be combined with the deviatoric elasticity equation and the equilibrium equations to form a set of field equations consisting of a Navier-type equation and two coupled diffusion equations. For the class of problems characterized by an irrotational displacement field with chemical and hydraulic loadings only, the two coupled diffusion equations simplify to... 

An example from our own laboratory is the methylphenidate bioanalyti-cal chiral LC-MS/MS assay in support of toxicokinetics (TK) and PK studies (vide infra). Attention-deflcit hyperactivity disorder (ADHD) is a recognized medical problem characterized by symptoms of inattention, hyperactivity, and impulsivity. Methylphenidate (MPH Ritalin methyl-alpha-phenyl-2-piperid-inacetate hydrochloride) is prescribed for the treatment of ADHD. MPH has two chiral centers yielding enantiomers with distinct pharmacokinetic and pharmacodynamic properties in humans. It is known that the t/-threo [2R,2 R]-MPH (i.e., (-i-)-threo) exhibits greater pharmacological activity than the... 

Here, what said in Section 4.2 about time-dependent perturbations is worth recalling, trying to give a more detailed analysis. The best approach to treat problems characterized by the presence of a P(t) function is provided by the quantum electrodynamics theories, where P is described in terms of an expansion over normal modes of the dielectric polarization. This model can be simplified by considering only two terms, often called the fast and the slow contribution to P (the Pekar separation introduced in eq.(18) of Section 4.2) ... 

An eigenvalue problem characterizing the EOMXCC theory, Eq. (86), is similar to an eigenvalue problem characterizing the EOMCC formalism [cf. Eq. (33)]. The only essential difference is the type of the similarity transformed Hamiltonian used in both theories (H in EOMCC and H in EOMXCC). Similarity between the EOMCC and EOMXCC theories becomes even more transparent when we realize that we can replace the operator product Hu,open Ck,open in Eq. (86), by the explicitly connected expression Hu,open Ck, open)c>... 

The scope of work in a first phase of the project included the adaptation of this peat pyrolysis system for conversion of agricultural residues, preliminary testing to identify operating problems, characterization of two feedstocks (oat straw and corn stover) and finally, experiments to determine product yield and composition at various operating conditions. 

The case-control method does have its problems. Characterization of past exposure experiences by both cases and controls is sometimes based on memory. Individuals will be able to recall their occupations, but may not be able to pinpoint specific chemicals. They almost certainly can not specify the quantity of exposure (chemical concentrations), although they may perhaps recall the total time they were exposed. Study interpretation is sometimes complicated by the possibility that cases and controls may differ in their recollections of past exposures if this is the case (and it s not easy to tell if it is), the study may not meet the criteria expected for a truly controlled situation. In some cases recollection can be checked by turning to documentary records of those exposures, but past record keeping on most occupational exposures was typically irregular and incomplete. Other problems exist in selecting appropriate controls, and there are sometimes serious technical difficulties associated with statistical analysis of study results. 

Methylphenidate is a mild stimulant prescribed to individuals (usually for children, and sometimes controversially) who have behavioral problems characterized by hyperactivity and short attention span. The National Institute of Mental Health estimates that approximately 3-5 percent of the general population has attention-deficit disorder (ADD) or attention-deficit hyperactivity disorder (ADHD). The administration of methylphenidate to children diagnosed with hyperactivity and/or attention-deficit disorder can have a calming effect on the children and can enable them to focus on schoolwork. Methylphenidate is also used to treat narcolepsy, a sleep disorder characterized by a permanent and overwhelming feeling of sleepiness and fatigue. 

Toxicological studies have linked some phthalate esters to liver and kidney damage, and to possible testicular or reproductive birth defect problems, characterizing them as endocrine disruptors. In this way, up to 12 phthalate esters, such as DBF, BBP, DEHP, DIDP, and DINP are within the list of the proposed substances suspected to produce endocrine alterations published by the EU. The endocrine disruption potential of pthalate esters was recently reviewed by Harris and Sumpter. The U.S. Agency for Toxic Substances and Disease Registry (ASTDR), the World... 

Perturbation theory for detector response in inhomogeneous systems provides the foundation for efficient and interesting methods for the solution of deep-penetration problems characterized by a large source-detector distance and a localized geometrical irregularity. 

A numerical method used to approximate the solution of boundary- and initial-value problems characterized by partial differential equations. 

The problem characterization, which will be presented in this section, mainly draws from Droguett et al. (2007) and Droguett et al. (2008). For validation purposes, the solution provided by the 2A-mathematical and munerical approaches is compared to the A -method given in Janssen Manca (2001) and the MC simulation. 

For the problem characterized above, an isoperibol calorimeter is needed. The sensitivity should be as large as possible to detect even low bacterial... 

Bieniasz LK (1996) A method-oriented approach to the formulation of algorithms for electrochemical kinetic simulations. Part 2. Extension to kinetic problems characterized by the simultaneous presence of bulk and interfacial species. J Electroanal Chem 404 195-208... 

In addition, on-lees aging lowers white wine sensitivity to oxidative pinking. This problem, characterized by a color evolution towards a grayish-pink (Simpson, 1977), occurs when wine is slightly oxidized during stabilization or bottling. 

---