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Since the determinant having two identical rows, and an3 an3 ï¿½ï¿½ï¿½ ann vanishes identically; we have by development according to the elements of the first row a21Au+a22Al2 +a23A13+ï¿½ï¿½ï¿½ +a2nAin =0; and, in general, since a11A11+a12A12 +ai 3A13+ï¿½ï¿½ ï¿½ +ainAin = A, if we suppose the P h and k th rows identical a A +ak2 A 12 +ak3A13+ï¿½ï¿½ï¿½ +aknAin =0 (k > i) .and proceeding by columns instead of rows, a li A lk +a21A2k + a 31A3k+ï¿½ï¿½ï¿½+aniAnk = 0 (k .>

64The two forms ax, bx, or of, 0, may be identical; we then have the kth transvectant of a form over itself which may, or may not, vanish identically; and, in the latter case, is a covariant of the single form.

56This system of equations must involve the three conditions of equilibrium of the extraneous forces which are already identically satisfied, by hypothesis; there remain therefore 2n ~ independent relations to determine the 2n3 unknown stresses.

32+(m -3) D 5(213) (214) (15) - (13) (14) (14), as= and and we see further that (alai +a2a2+...+amam) k vanishes identically unless (mod m).

23Such a symbolic product, if its does not vanish identically, denotes an invariant or a covariant, according as factors az, bz, cz,...

23+XL vanishes identically, and X is indeterminate.

11The nomenclature of the numerous ranges in this part of the Kuen-lun is extremely confusing, owing to different travellers having applied the same name to different ranges and to different travellers have applied different names to what is probably often identically the same range.

11On the ist of August Palmerston wrote to Ponsonby impressing upon him that the representatives of the powers, in their communications with the Porte, "should act not only simultaneously in point of time, but identically in point of manner" - a principle important in view of later developments.

11On the other hand, this corporeal thing is veritably and identically reason, mind, and ruling principle (X6-yos, vas, iiyE,uovtKOv); in virtue of its divine origin Cleanthes can say to Zeus, " We too are thy offspring," and a Seneca can calmly insist that, if man and God are not on perfect equality, the superiority rests rather on our side.

11" The mutual independence of the two (codes) is rather to be argued from the absence of laws identically formulated, the lack of agreement in order either in the whole or in smaller portions, and the fact that of the peculiar motives and phrases of R D there is no trace in H (Lev.

11Max Muller asked (when speaking of the mental condition of men when myths were developed), " was there a period of temporary madness through which the human mind had to pass, and was it a madness identically the same in the south of India and the north of Iceland?

11On the other hand, this corporeal thing is veritably and identically reason, mind, and ruling principle (X6-yos, vas, iiyE,uovtKOv); in virtue of its divine origin Cleanthes can say to Zeus, " We too are thy offspring," and a Seneca can calmly insist that, if man and God are not on perfect equality, the superiority rests rather on our side.

11For in this case the n equations are not independent since identically Alï¿½ft+ A2ï¿½ f2+...+Anï¿½fn = 0, and assuming that the minors do not all vanish the satisfaction of ni of the equations implies the satisfaction of the nth.

12If, moreover, 0 vanishes identically f is a perfect cube.

12The quartic has four equal roots, that is to say, is a perfect fourth power, when the Hessian vanishes identically; and conversely.

12The .sextic covariant t is seen to be factorizable into three quadratic factors 4 = x 1 x 2, =x 2 1 - 1 - 2 2, 4) - x, which are such that the three mutual second transvectants vanish identically; they are for this reason termed conjugate quadratic factors.

12We can see that (abc)a x b x c x is not a covariant, because it vanishes identically, the interchange of a and b changing its sign instead of leaving it unchanged; but (abc) 2 is an invariant.

12When a z and the invariants B and C all vanish, either A or j must vanish; in the former case j is a perfect cube, its Hessian vanishing, and further f contains j as a factor; in the latter case, if p x, ax be the linear factors of i, f can be expressed as (pa) 5 f =cip2+c2ay; if both A and j vanish i also vanishes identically, and so also does f.

12There are at least two possibilities: (1) that in Latium g and k were pronounced almost identically, as, e.g., in the German of Wurttemberg or in the Celtic dialects, the difference consisting only in the greater energy with which the k-sound is produced; (2) that the confusion is graphic, K being sometimes written I C, which was then regarded as two separate symbols.

12" To this we may answer that the human mind had to pass through the savage stage of thought, that this stage was for all practical purposes " identically the same " everywhere, and that to civilized observers it does resemble " a temporary madness."

12There are at least two possibilities: (1) that in Latium g and k were pronounced almost identically, as, e.g., in the German of Wurttemberg or in the Celtic dialects, the difference consisting only in the greater energy with which the k-sound is produced; (2) that the confusion is graphic, K being sometimes written I C, which was then regarded as two separate symbols.

12At that meeting he was struck for the first time by the endless variety of men's minds, which prevents a truth from ever presenting itself identically to two persons.

12For a single quantic of the first order (ab) is the symbol of a function of the coefficients which vanishes identically; thus (ab) =a1b2-a2bl= aw l -a1ao=0 and, indeed, from a remark made above we see that (ab) remains unchanged by interchange of a and b; but (ab), = -(ba), and these two facts necessitate (ab) = o.

13To obtain the corresponding theorem concerning the general form of even order we multiply throughout by (ab)2' 2c272 and obtain (ab)2m-1(ac)bxc2:^1=(ab)2mc2 Paying attention merely to the determinant factors there is no form with one factor since (ab) vanishes identically.

00The first transvectant, (f,f') 1 = (ab) a x b x, vanishes identically.

00Equation (I) and the first pair of equations {2) are thus satisfied identically.

00But by Green's transformation f flpdS = f f PPdxdydz, (2) thus leading to the differential relation at every point = dy dp The three equations of equilibrium obtained by taking moments round the axes are then found to be satisfied identically.

00pronounced identically with the much less common word rite.

00The work region and ScrollBars in the MainWindow behave identically to the work region and ScrollBars in the ScrolledWindow widget.

00Since the determinant having two identical rows, and an3 an3 Ã¯¿½Ã¯¿½Ã¯¿½ ann vanishes identically; we have by development according to the elements of the first row a21Au+a22Al2 +a23A13+Ã¯¿½Ã¯¿½Ã¯¿½ +a2nAin =0; and, in general, since a11A11+a12A12 +ai 3A13+Ã¯¿½Ã¯¿½ Ã¯¿½ +ainAin = A, if we suppose the P h and k th rows identical a A +ak2 A 12 +ak3A13+Ã¯¿½Ã¯¿½Ã¯¿½ +aknAin =0 (k > i) .and proceeding by columns instead of rows, a li A lk +a21A2k + a 31A3k+Ã¯¿½Ã¯¿½Ã¯¿½+aniAnk = 0 (k .>

00If the jth column be identical with the i ll ' the determinant A vanishes identically; hence if j be not equal to i, k, or r, a 11 a 21 a31 0 =I alk a2k a3k A11.

00Denote by A the determinant (a11a22Ã¯¿½Ã¯¿½Ã¯¿½ann)Ã¯¿½ Multiplying the equations by the minors A l, .., A2,,,,Ã¯¿½Ã¯¿½Ã¯¿½Ani., respectively, and adding, we obtain x 1 (ai, Aig+a2p.A2lc+Ã¯¿½Ã¯¿½Ã¯¿½+anÃ¯¿½AnÃ¯¿½) =xÃ¯¿½A=o, since from results already given the remaining coefficients of x 11' x 2, ...x Ã¯¿½ 'i xÃ¯¿½+I,...x, vanish identically.

00For in this case the n equations are not independent since identically AlÃ¯¿½ft+ A2Ã¯¿½ f2+...+AnÃ¯¿½fn = 0, and assuming that the minors do not all vanish the satisfaction of ni of the equations implies the satisfaction of the nth.

00+(m -3) D 5(213) (214) (15) - (13) (14) (14), as= and and we see further that (alai +a2a2+...+amam) k vanishes identically unless (mod m).

00For a single quantic of the first order (ab) is the symbol of a function of the coefficients which vanishes identically; thus (ab) =a1b2-a2bl= aw l -a1ao=0 and, indeed, from a remark made above we see that (ab) remains unchanged by interchange of a and b; but (ab), = -(ba), and these two facts necessitate (ab) = o.

00To obtain the corresponding theorem concerning the general form of even order we multiply throughout by (ab)2' 2c272 and obtain (ab)2m-1(ac)bxc2:^1=(ab)2mc2 Paying attention merely to the determinant factors there is no form with one factor since (ab) vanishes identically.

00The two forms ax, bx, or of, 0, may be identical; we then have the kth transvectant of a form over itself which may, or may not, vanish identically; and, in the latter case, is a covariant of the single form.

00The first transvectant, (f,f') 1 = (ab) a x b x, vanishes identically.

00If, moreover, 0 vanishes identically f is a perfect cube.

00The quartic has four equal roots, that is to say, is a perfect fourth power, when the Hessian vanishes identically; and conversely.

00The .sextic covariant t is seen to be factorizable into three quadratic factors 4 = x 1 x 2, =x 2 1 - 1 - 2 2, 4) - x, which are such that the three mutual second transvectants vanish identically; they are for this reason termed conjugate quadratic factors.

00Such a symbolic product, if its does not vanish identically, denotes an invariant or a covariant, according as factors az, bz, cz,...

00We can see that (abc)a x b x c x is not a covariant, because it vanishes identically, the interchange of a and b changing its sign instead of leaving it unchanged; but (abc) 2 is an invariant.

00When a z and the invariants B and C all vanish, either A or j must vanish; in the former case j is a perfect cube, its Hessian vanishing, and further f contains j as a factor; in the latter case, if p x, ax be the linear factors of i, f can be expressed as (pa) 5 f =cip2+c2ay; if both A and j vanish i also vanishes identically, and so also does f.

00+XL vanishes identically, and X is indeterminate.

00Equation (I) and the first pair of equations {2) are thus satisfied identically.

00But by Green's transformation f flpdS = f f PPdxdydz, (2) thus leading to the differential relation at every point = dy dp The three equations of equilibrium obtained by taking moments round the axes are then found to be satisfied identically.

00The nomenclature of the numerous ranges in this part of the Kuen-lun is extremely confusing, owing to different travellers having applied the same name to different ranges and to different travellers have applied different names to what is probably often identically the same range.

00On the ist of August Palmerston wrote to Ponsonby impressing upon him that the representatives of the powers, in their communications with the Porte, "should act not only simultaneously in point of time, but identically in point of manner" - a principle important in view of later developments.

00This system of equations must involve the three conditions of equilibrium of the extraneous forces which are already identically satisfied, by hypothesis; there remain therefore 2n ~ independent relations to determine the 2n3 unknown stresses.

00" The mutual independence of the two (codes) is rather to be argued from the absence of laws identically formulated, the lack of agreement in order either in the whole or in smaller portions, and the fact that of the peculiar motives and phrases of R D there is no trace in H (Lev.

00Max Muller asked (when speaking of the mental condition of men when myths were developed), " was there a period of temporary madness through which the human mind had to pass, and was it a madness identically the same in the south of India and the north of Iceland?

00" To this we may answer that the human mind had to pass through the savage stage of thought, that this stage was for all practical purposes " identically the same " everywhere, and that to civilized observers it does resemble " a temporary madness."

00The work region and ScrollBars in the MainWindow behave identically to the work region and ScrollBars in the ScrolledWindow widget.

00Creative hackers will fashion websites that replicate other websites nearly identically in the hopes of someone utilizing the website and providing personal information.

00Sheet Cakes: A smaller wedding cake can be augmented with identically flavored sheet cakes for a fraction of the cost of adding more tiers to the large cake.

00Measure your backsplash in sections and mark off an identically sized area on the floor nearby.

00Mikimoto is legendary for identically matching every pearl on any given strand, a feat not easily achieved when, by their very nature, every pearl is unique.

00Tea bag folding is a paper craft that involves connecting several identically folded sheets of paper together in order to make one larger design.

00As fun as it may be to name them similarly and dress them identically, researchers feel that this is bad for their mental and emotional development.

00Not all solitaires are styled identically.

00Whether the rings match identically or just share similarities is not as important as the promise the individuals share together, and as long as they both keep that promise, the feelings behind it will be identical.

00Even a quick trek to a local college campus would likely reveal an army of similar carryalls, swinging identically from the arms of coeds, perhaps in varying colors.

00The most common dishes, though identically named, express the local flavor of the region.

00

The word usage examples above have been gathered from various sources to reflect current and historial usage. They do not represent the opinions of YourDictionary.com.