Branch differentiation, control

It turns out that there is another branch of mathematics, closely related to tire calculus of variations, although historically the two fields grew up somewhat separately, known as optimal control theory (OCT). Although the boundary between these two fields is somewhat blurred, in practice one may view optimal control theory as the application of the calculus of variations to problems with differential equation constraints. OCT is used in chemical, electrical, and aeronautical engineering where the differential equation constraints may be chemical kinetic equations, electrical circuit equations, the Navier-Stokes equations for air flow, or Newton s equations. In our case, the differential equation constraint is the TDSE in the presence of the control, which is the electric field interacting with the dipole (pemianent or transition dipole moment) of the molecule [53, 54, 55 and 56]. From the point of view of control theory, this application presents many new features relative to conventional applications perhaps most interesting mathematically is the admission of a complex state variable and a complex control conceptually, the application of control teclmiques to steer the microscopic equations of motion is both a novel and potentially very important new direction. 

In summary, a number of parameters of outgrowth initiation, elongation, branching and cessation combine to generate axonal or dendritic geometry. These components can be modulated in vitro by a variety of soluble and substrate-bound factors, suggesting that, in vivo, control over morphological differentiation is multifactorial. 

Three years later. List and coworkers extended their phosphoric acid-catalyzed dynamic kinetic resolution of enoUzable aldehydes (Schemes 18 and 19) to the Kabachnik-Fields reaction (Scheme 33) [56]. This transformation combines the differentiation of the enantiomers of a racemate (50) (control of the absolute configuration at the P-position of 88) with an enantiotopic face differentiation (creation of the stereogenic center at the a-position of 88). The introduction of a new steri-cally congested phosphoric acid led to success. BINOL phosphate (R)-3p (10 mol%, R = 2,6- Prj-4-(9-anthryl)-C H3) with anthryl-substituted diisopropylphenyl groups promoted the three-component reaction of a-branched aldehydes 50 with p-anisidine (89) and di-(3-pentyl) phosphite (85b). P-Branched a-amino phosphonates 88 were obtained in high yields (61-89%) and diastereoselectivities (7 1-28 1) along with good enantioselectivities (76-94% ee) and could be converted into... 

Fig. 3.2.5 Profiles of acylcarnitines as their butyl esters in plasma (precursor of m/z 85 scan) of a normal control (a) and patients with various organic acidemias. Propionylcarnitine (C> m/z 274 peak 3) is the primary marker for both propionic acidemia (b) and methylmalonic acidemias (c). Note that an elevation of methylmalonylcarnitine (C4-UC m/z 374) is not typically found in patients with methylmalonic acidemias. In the three cases of ethylmalonic encephalopathy (d) analyzed in our laboratory, elevations of ,- (m/z 288 peak 4) and C5-acylcarnitine (m/z 302 peak 5) species were noted. Isolated C5-acylcarnitine elevations are encountered in patients with isovaleric acidemia (e), where it represents isovalerylcarnitine. Cs-Acylcarnitine is also elevated in patients with short/branched chain acyl-CoA dehydrogenase deficiency, where it represents 2-methylbutyrylcarnitine (see Fig. 3.2.4), and in patients treated with antibiotics that contain pivalic acid, where it represents pivaloylcarnitine [20, 59, 60]. Patients with /3-ketothio-lase deficiency (f) present with elevations of tiglylcarnitine (C5 i m/z 300 peak 6) and C5-OH acylcarnitine (m/z 318 peak 7). In most cases of 3-methylcrotonyl-CoA carboxylase deficiency (g) Cs-OH acylcarnitine is the only abnormal acylcarnitine species present. The differential diagnosis of C5-OH acylcarnitine elevations includes eight different conditions (Table 3.2.1). Also note that C5-OH acylcarnitine represents 3-hydroxy isovalerylcarnitine in 3-methylcrotonyl-CoA carboxylase deficiency (g), and 2-methyl 3-hydroxy butyrylcarnitine in / -ketothiolase deficiency...

Two important cases of negative differential conductivity (NDC) are described by an iV-shaped or an -shaped j (F) characteristic, and denoted by NNDC and SNDC, respectively. However, more complicated forms like Z-shaped, loop-shaped, or disconnected characteristics are also possible [15]. NNDC and SNDC are associated with voltage- or current-controlled instabilities, respectively. In the NNDC case the current density is a singlevalued function of the field, but the field is multivalued the F j) relation has three branches in a certain range of j. The SNDC case is complementary in the sense that F and j are interchanged. In case of NNDC, the NDC branch is often but not always - depending upon external circuit and boundary conditions - unstable against the formation of nonuniform field... 

Figure 6-11. Schematic of plasma-chemical microwave system with magnetic field (1) plasma-chemical reactor (2) converter of type of electromagnetic wave (3, 4) solenoids (5) vacuum pump (6) liquid nitrogen trap (7) refrigerator, (8) gas tanks (9) control volumes (10) vacuum-meter (11, 12) differential manometers (13) waveguide branching system (14) spectrograph (15, 16) microwave detectors (17) semi-transparent mirror (18) photo-electronic amplifier (M) magnetron microwave source (K) klystron microwave source (S) window for diagnostics.

In order to differentiate a control flow from a data flow error, we check the PC evolution and compare it with a golden module. In case of a mismatch, the fault is classified as a control flow effect. If not, it is classified as a data flow effect. In some cases, a fault with a data flow effect may cause a control flow effect. An example could be an error in a register used to decide whether a branch should be taken or not. In such cases, we consider it as a control flow effect. 

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