He marveled at Westlake's lack of concern, but as a first time visitor to the heart of nature's fury it was still a white-knuckle trip as lightning flashes and near-simultaneous thunderclaps erupted in every direction.
A simultaneous insurrection at Massa - Carrara was crushed with similar vigour.
A pilgrimage feast must be fixed in date to ensure the simultaneous presence of the pilgrims. There are, besides, seeming references to the feast in the early prophets, as Hosea xii.
In general it will be simultaneous covariant of the different forms n 1 rz 2 n3 a, b x, ?
- We have seen that (ab) is a simultaneous invariant of the two different linear forms a x, bx, and we observe that (ab) is equivalent to where f =a x, 4)=b.
(a m b n) k (ab) kamkbn-k x, x - x it is clear that the k th transvectant is a simultaneous covariant of the two forms.
In general we may have any two forms 01/1X1+ 'II ï¿½ Yy + 02x2) p Y'x =, / / being the umbrae, as usual, and for the kth transvectant we have (4)1,,, 4)Q) k = (4)) k 4)2 -krk, a simultaneous covariant of the two forms. We may suppose of, 4, 2 to be any two covariants appertaining to a system, and the process of transvection supplies a means of proceeding from them to other covariants.
If the invariants and covariants of this composite quantic be formed we obtain functions of X such that the coefficients of the various powers of X are simultaneous invariants of f and 4).
The simultaneous system of two quadratic forms ai, ay, say f and 0, consists of six forms, viz.
If ai, bx, cx be different forms we obtain, after development of the squared determinant and conversion to the real form (employing single and double dashes to distinguish the real coefficients of bx and cz), a(b'c"+b"c'-2 f'f") +b(c'a"+c"a'-2g'g") +c(a' +a"b'-2h'h")+2f(g'h"+g"h'-a' + 2g (h ' f"+h"f'-b'g"-b"g')+2h(f'g"+f"g'-c'h"-c"h'); a simultaneous invariant of the three forms, and now suppressing the dashes we obtain 6 (abc+2fgh -af t - bg 2 -ch2), the expression in brackets being the S well-known invariant of az, the vanishing of which expresses the condition that the form may break up into two linear factors, or, geometrically, that the conic may represent two right lines.
He successfully considers the systems of two and three simultaneous ternary quadratics.
+bx 2, every leading coefficient of a simultaneous covariant vanishes by the operation of a+Sib=aoda +alda.2+...+a7,-1d a P+bod b Observe that we may employ the principle of suffix diminution to obtain from any seminvariant one appertaining to a (p-I)i c and a q - I ie, and that suffix augmentation produces a portion of a higher seminvariant, the degree in each case remaining unaltered.
In general the Boolian system, of the general n i °, is coincident with the simultaneous system of the n i °' and the quadratic x 2 +2 cos w xy+y2.
It may denote a simultaneous orthogonal invariant of forms of orders n i, n2, n3,...; degree 0 of the covariant in the coefficients.
Heating or exposure to sunlight reduces it to the red oxide; it fires when ground with sulphur, and oxidizes ammonia to nitric acid, with the simultaneous formation of ammonium nitrate.
Various currents are then passed through the magnetizing coil, the galvanometer readings and the simultaneous magnetometer deflections being noted.
His fleet, too, lingered uselessly in the harbour, till after a defeat in which Eurymedon perished, though the simultaneous land attack was unsuccessful.
About Mikhelson's army I understand--Tolstoy's too... a simultaneous expedition....
This simultaneous discussion of many topics did not prevent a clear understanding but on the contrary was the surest sign that they fully understood one another.
When, for instance, we say that Napoleon ordered armies to go to war, we combine in one simultaneous expression a whole series of consecutive commands dependent one on another.