Preferred gauge

in general terms, let be a normalized Hilbert space 

A gauge invariant reference section 10(5 )) is a nonlinear functional of l0(j)) defined as [25,26] 

suppose there is a single isolated point G /iCjv aeross whieh (n(0o)lw(0jfc)) goes through zero and changes sign. For such a point, it follows that 

Extending this to the whole closed path we may assume it contains K angles 01. 0K, all across which (n(0o)ln(0)) goes through zero and changes sign. Then, the gauge invariant reference section reads 

Notice that J (0 0q) is a local quantity as it only depends upon the angles 01. 0if, whose location is gauge invariant once the initial electronic eigenstate (0o) has been chosen. 

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The nonlocal and topological nature of the molecular Aharonov-Bohm (MAB) effect is examined for real electronic Hamiltonians. A notion of preferred gauge for MAB is suggested. The MAB effect in the linear + quadratic 08 Jahn-Teller system is shown to be essentially analogues to an anisotropic Aharonov-Casher effect for an electrically neutral spin — particle encircling a certain conhguration of lines of charge. 

In Section 2, we extend the argumentation of Sjoqvist [24] to the case of arbitrary molecular systems with real electronic Hamiltonians. A notion of preferred gauge for MAB in this case is suggested in Section 3 and applied in detail to the E e Jahn-Teller system. The analogue between the MAB effect in the E< e Jahn-Teller system and the Aharonov-Casher (AC) effect [34], as pointed out in Ref. [24], is further developed in Section 4, so as to treat hnear and quadratic coupling simultaneously. The paper ends with the conclusions. 

It is important to notice that this criterion for a nontrivial MAB is only fulfilled if the effective nuclear motion has physical access to the whole closed path C y. To see this, let n 0Q) n d)) change sign at the angles 0i,...,0if along C f. In the preferred gauge the effective Hamiltonian operator for the nuclear motion in the 0 direction reads... 

Figure 7 shows nozzle locations and support arrangements for a typical horizontal vessel (7). The saddles used for support are sustained by concrete pedestals or steel stmctures. Sufficient clearance between the bottom nozzles and the support saddles needs to be provided for access to the nozzle flange bolts. The manway can be located on the end head of the vessel, the topside of the vessel, or the side of the vessel. The preference is for an end manway wherever possible for accessibiHty, except when it is limited by the level gauges and controls that are commonly mounted off the heads. 

Eveiy effort should be made to eliminate direct (Bourdon-type) pressure gauges. Diaphragm pressure gauges constructed of appropriate corrosion-resistant materials are preferred. Flow limiters should be used to limit flow in case of loss of integrity... 

Blowdown is generally provided only for a few seconds, or sufficient to drop the water level in the gauge glass by perhaps 1/2 inch (1.25 cm). Where 10 seconds ofBD is required, it is much preferable to stagger this over a period of time rather than all at once. 

TB skin testing with the 5-TU strength of brand purified protein derivative (PPD), also known as the Mantoux test, is the preferred method for skin testing.2,16,20 The product is injected into the skin (not subcutaneously) with a fine (27-gauge) needle and produces a small, raised, blanched wheal to be read by an experienced professional in 48 to 72 hours. Criteria for interpretation are listed in Table 72-1.1,2,6,16,20 The Centers for Disease Control and Prevention (CDC) does not recommend the routine use of... 

The hole sizes used vary from 2.5 to 12 mm 5 mm is the preferred size. Larger holes are occasionally used for fouling systems. The holes are drilled or punched. Punching is cheaper, but the minimum size of hole that can be punched will depend on the plate thickness. For carbon steel, hole sizes approximately equal to the plate thickness can be punched, but for stainless steel the minimum hole size that can be punched is about twice the plate thickness. Typical plate thicknesses used are 5 mm (3/16 in.) for carbon steel, and 3 mm (12 gauge) for stainless steel. 

When highly accurate Pq measurements are necessary, a platinum resistance thermometer can be placed in the bath adjacent to the sample cell. Equation (13.1) can then be used to calculate the nitrogen vapor pressure. Alternatively and perhaps preferably, the vapor pressure can be measured directly by condensing nitrogen in a cell contained in the coolant and connected directly to a manometer or sensitive pressure gauge. 

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