Reciprocal operation

For each element in a group, there is an inverse or reciprocal operation which is also an element of the group and satisfies the following condition ... 

Differentiation and integration are reciprocal operations in the same sense that multiplication is the inverse of division, addition of subtraction. Thus,... 

By symbolizing the spatial operators by an operator of distance r (with a hatfor the reciprocal of the contra-gradient and by a reciprocal operator of area A for the integration on a surface, the relation between global property and reduced property is written as... 

This algebraic expression in the Formal Graph is read as an equivalence of paths between the elementary path of the global property and the composed path of the spatial derivation (contragradi-ent), of the conductivity and of collect on the considered surface. In reasoning on the reciprocal operator of resistance, it can be observed that this equivalence corresponds to a loop making use of... 

The subduction of the subgroup irreps by the group irrep can be considered as the reciprocal operation to the induction of the group reps by the irreps of the subgroup... 

Fig. 13 shows the dynamic friction coefficient during the reciprocating operation for each PFPE. The amplitude of the saw tooth pattern in the friction curve is significantly high for the Z-DOL tapes these fluctuations in sliding resulted from the stick-slip process and are associated with squeal and chatter. However, the dynamic friction coefficient was relatively constant and the stick-slip phenomenon is only slightly observed for the ammonium salt tapes (Lubricant 11). 

Fig. 13. Change in dynamic friction coefficient during the reciprocating operation for the different PFPE.

For air compressors Operating safety Thermal stability, Volatility Resistance to oxidation Extreme pressure and anti-wear (compressors) properties Low coking tendency (hot reciprocating compressors)... 

The principle of operation of the hydraulic reciprocating pump is similar to the beam pump, with a piston-like sub-surface pump action. The energy to drive the pump, however, is delivered through a hydraulic medium, the power fluid, commonly oil or water. The power fluid drives a downhole hydraulic motor which in turn drives the pump. A separate surface pump delivers the hydraulic power. The power fluid system can be of the closed loop or of the open type. In the latter case, the power fluids are mixed with the produced fluid stream. The performance of the hydraulic pump is primarily monitored by measuring the discharge pressures of both surface and sub-surface pumps. 

Gas turbine driven centrifugal compressors are very efficient under the right operating conditions but require careful selection and demand higher levels of maintenance than reciprocating compressors. Compression facilities are generally the most expensive item in an upstream gas process facility. 

When the curvature of the reaction vessel is too great for the efficient operation of the bar type magnetic stirrer, a miniature solenoid-operated reciprocating stirrer may be employed (Fig. XII, 2, 19). This stirrer may be easilj constructed from a telephone relay or electric bell. It is advisable to have a control for adjusting the stroke while running. 

A particular concentration measure of acidity of aqueous solutions is pH which usually is regarded as the common logarithm of the reciprocal of the hydrogen-ion concentration (see Hydrogen-ION activity). More precisely, the potential difference of the hydrogen electrode in normal acid and in normal alkah solution (—0.828 V at 25°C) is divided into 14 equal parts or pH units each pH unit is 0.0591 V. Operationally, pH is defined by pH = pH(soln) + E/K, where E is the emf of the cell ... 

Positive Pumps. Positive pumps employed by the food industry have a rotating cavity between two lobes, two gears that rotate in opposite directions, or a crescent or stationary cavity and a rotor. Rotary positive pumps operate at relatively low speed. Fluid enters the cavity by gravity flow or from a centrifugal pump. The positive pump also may use a reciprocating cavity, and may be a plunger or piston pump. These pumps are not truly positive with respect to displacement, but are used for metering product flow. 

Ideal Performance and Cooling Requirements. Eree carriers can be excited by the thermal motion of the crystal lattice (phonons) as well as by photon absorption. These thermally excited carriers determine the magnitude of the dark current,/ and constitute a source of noise that defines the limit of the minimum radiation flux that can be detected. The dark carrier concentration is temperature dependent and decreases exponentially with reciprocal temperature at a rate that is determined by the magnitude of or E for intrinsic or extrinsic material, respectively. Therefore, usually it is necessary to operate infrared photon detectors at reduced temperatures to achieve high sensitivity. The smaller the value of E or E, the lower the temperature must be. 

From the definition of specific speed (eqs. 9 and 10), it follows that reciprocating pumps operate at high pressures and low flow rates. Conversely, centrifugal pumps are appHed at lower pressures and higher flow rates. Many rotary pumps are selected for viscous Hquids having pressures equal to or less than, and capacities lower than, centrifugal pumps. However, these limits are relative and a gray area exists as some pump types cross boundaries into the domain of other types. 

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