Algebra maxima/minima

Values of thermal-expansion coefficients to be used in determining total displacement strains for computing the stress range are determined from Table 10-52 as the algebraic difference between the value at design maximum temperature and that at the design minimum temperature for the thermal cycle under analysis. 

Load amplitude One-half of the algebraic difference between the maximum and minimum loads in the load cycle. 

We think there is a need to investigate the algebraic properties underlying the various graph and matrix representations in order to discover the properties which are common to every stereoisomerization, to every ligand partition and perhaps, to every coordination number. This attempt is necessary if we want to understand the maximum number of phenomena with a minimum number of concepts. 

The object of the present paper is to expound a theory which accounts in an algebraically precise manner for all known forms of DP curves. Four general types of such curves are known (A) The DP goes through a maximum. (B) The DP rises to a maximum constant value. (C) The DP falls to a minimum constant value. (D) The DP goes through a minimum. These types are illustrated in Figures 1,5-7. In a few systems the DP varies in a manner which can be considered as a combination of two of these types. 

One of the most important applications of the differential calculus is the determination of maximum and minimum values of a function. Many of the following examples can be solved by special algebraic or geometric devices. The calculus, however, offers a sure and easy method for the solution of these problems. 

Both AS ME Code, Section 1I1, Division 2 and AS ME Code, Section III, utilize the maximum shear stress criterion. This theor) closely approximates experimental results and is also easy to use. This theory also applies to triaxial states of stress. In a triaxial stress state, this theory predicts that yielding will occur whenever one-half the algebraic difference betu een the maximum and minimum stress is equal to one-half the yield stress. Where 0 > a i> 0.3. the maximum shear stress is (oi —03)72. 

For simple analysis upon which the thickness formulas for ASME Code, Section I or Section VIII, Division I, are based, it makes little difference whether the maximum stress theory or maximum shear stress theory is used. For example, according to the maximum stress theory, the controlling stress governing the thickness of a cylinder is circumferential stress, since it is the largest of the three principal stresses. According to the maximum shear stress theory, the controlling stress would be one-half the algebraic difference between the maximum and minimum stress ... 

In the above equation, Kf and Gnijw) are the cutting force coefficient and the real part of the transfer function in the chip thickness direction, respectively. When the maximum (algebraic minimum) value of Gr is substituted, the minimum or absolute stability limit is obtained. Absolute stabihty is the minimum stable depth of cut which can be removed without chatter regardless of the cutting speed. However, since the chatter frequency, and thus the transfer function, varies... 

Tolerance - the difference between the maximum limit of size and the minimum limit of size (or, in other words, the algebraic difference between the upper deviation and lower deviation). 

A peculiarity of an elastic solid in comparison with other systans that are containers of capacitive energy (see case study A6 Chemical Species or A5 Electric Charges ) is to have a lower limit for the basic quantity This limit is the minimum displacement corresponding to the maximum possible compression without destroying the solid. The model is based on a generalization of the notion of activity (see case study A6 Chemical Species ) whose dependency on the effort has an exponential form and the algebraic expression of its relationship with the displacement is as follows ... 

---