characteristic equationn.

1828 Philos. Mag. 3 334 From this is immediately derived the characteristic equation of the surfaces capable of being evolved in a plane, namely..^ddz/ _dx²·^ddz/ _dy² − (^ddz/ _dx·dy)² = 0.

1871 S. Earnshaw Partial Differential Equations x. 101 This is the characteristic equation of developable surfaces. Its terms are not linear, but from its peculiar form it can be integrated by means of the above formulae.

1912 A. R. Forsyth Lect. Differential Geom. Curves & Surfaces v. 126 When the primitive of the characteristic equation is not known, it may happen that some special integral is known.

1959 T. J. Willmore Introd. Differential Geom. 305 Prove that..G is of the form Au² + 2Bu + C... The Gauss characteristic equation..may be assumed.

2008 S. P. Radzevich Kinematic Geom. Surface Machining ii. 45 The property of surfaces that allows for sliding over can be interpreted in terms of fundamental forms if Gauss' characteristic equation and the Codazzi-Mainardi's relationships of compatibility are satisfied.

1841 Cambr. Math. Jrnl. 2 68 It has only been necessary to differentiate the even powers,..an operation which is immediately effected by the aid of the characteristic equation.

1865 B. Price Treat. Infinitesimal Calculus (ed. 2) II. 636 Each term of the series comprehended within the symbol of aggregation vanishes, because a₁, a₂,…a_n are the n roots of the characteristic equation.

1936 W. B. Ford Asymptotic Devel. Functions viii. 118 The characteristic equation (78) now comes to have its roots equal, both being 0, with which the asymptotic solutions become exceptional in character.

2013 A. M. Haghighi & D. P. Mishev Difference & Differential Equations with Applic. in Queueing Theory iii. 178 Solve the associated homogeneous equation y′′ − y′ − 2y = 0. The characteristic equation..is a quadratic equation r² − r − 2 = 0 that has two distinct real roots r₁ = −1 and r₂ = 2.

1849 Amer. Jrnl. Sci. 57 16 The geometrical aspect which the formula affects, is that of the hypothenuse of a triangle or the arc of a curve, having a general characteristic equation of the form yⁿ = ax.

1881 Philos. Trans. (Royal Soc.) 172 321 The equations of electromotive force are now reduced to the single characteristic equation ^σ/ _4π∇²P = ^d/ _dt(P + P₀).

1962 H. Konno in J. Lewins et al. Adv. in Nucl. Sci. & Technol. 35 The characteristic equation of the linearized equation for the model (83) is given by..p + ατ exp(−p) = 0.

2012 J. L. Semmlow Signals & Syst. Bioengineers (ed. 2) vi. 236 The denominator of the transfer function is sometimes called the characteristic equation: The characteristic equation defines the general type of system described by the transfer function.

1857 C. H. Davis tr. C. F. Gauss Theory Motion Heavenly Bodies 3 A single general equation..on which all others can be based, will answer our purpose. And it appears to be particularly advantageous to select that one to which, while investigating the curve described according to the law of attraction, we are conducted as a characteristic equation.

1881 Analyst 8 83 In article 3 Gauss uses a linear form for the equation of conic sections r + αx + βy = γ, in which γ is always positive; and he calls this the characteristic equation of these curves.

1899 Proc. Physical Soc. 16 454 He desires to indicate the relation which must exist between the formula assigned to the Joule–Thomson effect, considered as a function of the temperature, and the particular form adopted for the characteristic equation of a gas.

1938 J.-B. O. Sneeden Introd. Internal Combustion Engin. (new ed.) ii. 9 R is known as the gas constant and the equation PV = RT is called the characteristic equation for 1 lb. of gas.

2013 M. Shukuya Exergy v. 262 It is convenient to express the moist-air exergy as a volumetric intensive quantity..making use of the characteristic equation of ideal gas.

1900 Proc. Amer. Acad. Arts & Sci. 35 585 It will be found that one or more of the roots of the characteristic equation of the matrix..is equal to unity, irrespective of the value of t.

1949 Econ. Jrnl. 59 554 The nature of the solutions is determined by the roots of the characteristic equation of the matrix.

2006 P. J. Nahin Dr. Euler's Fabulous Formula i. 20 The Cayley–Hamilton theorem..any square matrix A satisfies its own characteristic equation.