If a, a be the linear forms, above defined, he raises the identity ax(0) =ax(aJ3) - (3x(aa) to the fifth power (and in general to the power n) obtaining (aa) 5 f = (a13) 5 az - 5 (a0) 4 (aa) ax?3 -F...
May be a simultaneous invariant of a number of different forms az', bx 2, cx 3, ..., where n1, n 2, n3, ...
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.
1 - az 2.
1 -az 74 - 2.1 -azn-4....1 - azn+4.1 - az n+2.1 - az-n in which we have to take the coefficient of aezne-2', the expansion.
Denominator factors, that the complete system of the quadratic is composed of the form itself of degree order I, 2 shown by az 2, and of the Hessian of degree order 2, o shown by a2.
Again, for the cubic, we can find A3(z) - -a6z6 1 -az 3.1 -a 2 z 2.1 -a 3 z 3.1 -a4 where the ground forms are indicated by the denominator factors, viz.: these are the cubic itself of degree order I, 3; the Hessian of degree order 2, 2; the cubi-covariant G of degree order 3, 3, and the quartic invariant of degree order 4, o.
1 Az P. 1 B.
Taking The First Generating Function, And Writing Az P, Bz4, 2 For A, B And Z Respectively, We Obtain The Coefficient Of Aobe'Zpo 0' 2W That Is Of A E B E 'Z ï¿½, In 1 Z 2 1 Azp. 1 Azp 2....1 A2 P 2.1 Az P .
1 Az I.
Foremost among these stood the so-called " French " school, founded by George Bessenyei, the author of several dramatic pieces, and of an imitation of Pope's " Essay on Man," under the title of Az embernek probdja (Vienna, 1772).
His national romances, however, and especially Etelka (Pozsony, 1787) and Az arany pereczek (Pest and Pozsony, 1790), attracted public attention, and were soon adapted for the stage.
The lyrics of Anthony Varady (1875, 1877) are somewhat dull and unequal in tone; both he and Baron Ivor Kaas, author of Az itelet napja (Day of Judgment, 1876), have shown skill rather in the art of dramatic verse.
Az ember tragoedidja (The Tragedy of Man), by Emeric Madach (1861), is a dramatic poem of a philosophical and contemplative character, and is not intended for the stage.
Especially is this the case with Nicholas Josika's Abafi (1836), A csehek Magyarorszagon (The Bohemians in Hungary), and Az utolso Bdtori (The Last of the Bathoris), published in 1847.
The Az utolso Bebek (The Last of the Bebeks), by the late Charles Petery, is a work rich in poetic invention, but meagre in historical matter.
Magyar history is indebted to Paul Jaszay for his careful working out of certain special periods, as, for instance, in his A Magyar nemzet napjai a legregibb idOtOl az arany bullaig (Days of the Hungarian nation from the earliest times to the date of the Golden Bull).
As important original monographs we note-Az drapoly a Fiumei obolben (Ebb and Flow in the Gulf of Fiume), by Emil Stahlberger (1874); Magyarorszdg pokfaundja (The Arachnida of Hungary), by Otto Hermann (1876-1878); Magyarorszdg vaskovei es vastermenyei (The Iron Ores and 1 The translator of Macaulay.
Other novelists belonging to this school are: Desiderius Malonyai (Az utolso, " The Last "; Judith konyve, " The Book of Judith "; Tanulmdnyfejek, "Typical Heads "); Julius Pekar (Dodo fohadnagy problemai, " Lieutenant Dodo's Problems "; Az aranykesztyus kisasszony, " The Maid with the Golden Gloves "; A szoborszep asszony, " The Lady as Beautiful as a Statue "; Az esztendo legenddja, " The Legend of the Year "); Thomas Kobor (Aszfalt, " Asphalt "; 0 akarta, " He Wanted It "; A csillagok fele, " Towards the Stars "); Stephen Szomahazy (Huszonnegy Ora, " Twenty-four Hours "; A Clairette Keringd, " The Clairette Valse "; Pdratlan szerddk, " Incomparable Wednesdays "; Nydri felhok, " Clouds of Summer "); Zoltan Thury (Ullrich fdhadnagy es egyeb tortenetek, " Lieutenant Ullrich and other Tales "; Urak es parasztok, " Gentlemen and Peasants "); also Desiderius Szomory, Odon Gero, Arpad Abonyi, Koloman Szanto, Edward Sas, Julius Vertesi, Tibor Denes, Akos Pinter, the Misses Janka and Stephanie Wohl, Mrs Sigismund Gyarmathy and others.
Besides Stephen Petelei (Jetti, a name - "Henrietta " - Felhok, " Clouds ") and Zoltan Ambrus (Pokhdlo Kisasszony, " Miss Cobweb "; Gyanu, " Suspicion") must be mentioned especially Francis Herczeg, who has published a number of very interesting studies of Hungarian social life (Simon Zsuzsa, " Susanna Simon "; Fenn es lenn, " Above and Below "; Egy ledny tortenete, " The History of a Girl "; Idegenete kozott, " Amongst Strangers "); Alexander Brody, who brings a delicate yet resolute analysis to unfold the mysterious and fascinating inner life of persons suffering from overwrought nerves or overstrung mind (A kitlelkil asszony, " The Double-Souled Lady "; Don Quixote kisasszony, " Miss Don Quixote "; Faust orvos, " Faust the Physician "; Tiinder Ilona, Rejtelmek, "Mysteries"; Az eziest kecske, " The Silver Goat "); and Edward Kabos, whose sombre and powerful genius has already produced works, not popular by any means, but full of great promise.
Arpad Berczik's Nezd meg az anyjdt (" Look at her Mother "), A protekczio (" Patronizing "), also followed on the lines of Csiky.
After the school of Comte, yet to a large extent original, is the Az ember es vildga (" Man and his World ") of Charles Bohm, who in 1881 started a philosophical review (Magyar Filozofiai Szemle), subsequently edited by Joseph Bokor, a vigorous thinker.
Realism, more particularly of the Wundt type, is represented by Emericus Pauer, Az ethikai determinismus (" Ethical Determinism "), and Eugen Posch (Az idorb'l, " On Time ").
The Hungarian scholar Samuel Brassai published, in 1896, Az igazi pozitiv filozofia (" The True Positive Philosophy ").
Uniplanar motion alone is so far amenable to analysis; the velocity function 4 and stream function 1G are given as conjugate functions of the coordinates x, y by w=f(z), where z= x +yi, w=4-Plg, and then dw dod,y az = dx + i ax - -u+vi; so that, with u = q cos B, v = q sin B, the function - Q dw u_vi=g22(u-}-vi) = Q(cos 8+i sin 8), gives f' as a vector representing the reciprocal of the velocity in direction and magnitude, in terms of some standard velocity Q.
He overran a part of Elam and took the city of Az on the Persian Gulf.
I g h oo hsuvii where T is the area of a trapezette whose ordinates at successive distances h are o, Ali' (x i), (Al +A4), g 5' (x2), (Az +A 2 + ...
,k /fi Az' s, i_t K4,.iei.N 10.at) t I C2 Nrrft I.,11/4.11< 11 t E t h d _.i _ ?
472, taken from the Shapurakan, as part of a description of the sun-god in his ship or reservoir the sun, we have a mention of Az and Ahriman and the devas (demons), the Pairikas.
470, descriptive of the conflagration of the world, we read of how, after Az and the demons have been struck down, the pious man is purified and led up to sun and moon and to the being of Ahura Mazda, the Divine.
The I, Oogonium (og) with the an5, Fertilized oogonium sur theridial branch (az) applied rounded by two layers of to its surface.
Bi 1.- Then, by 36, the angular - ~ - ---- -E velocity-ratio is Az - P-~ ai/aiCiPi/C2Pi.
The relative velocity pet-pendicular to P~Pi of the teeth at their point of contactthat is, their velocity of sliding on each otheris found by supposing one of the wheels, such as I, to be fixed; the line of centres CXCi to rotate backwards round C~ with the angular velocity aj, and the wheel 2 to rotate round C2 as before, with the angular velocity az relatively to the line of centres CiC2, so as to, have the same motion as if its pitch-circle rolled,on the pitch-circle of the first wheel.
First observe that with f x =a: = b z = ï¿½ï¿½ï¿½,f1 = a l a z ', f 2 = a 2 az-', f x =f,x i +f 2 x i, we find (ab) - (a f) bx - (b f) ax.
Such a symbolic product, if its does not vanish identically, denotes an invariant or a covariant, according as factors az, bz, cz,...