By Chen Y., Chen G.-P.

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Gos. 91, No. 4290-B91 (1991). 6. V. I. Glizburg, "The reduction of a bundle of p-frames invariantly defined by an ordinary differential system of order/~ > 3," Mosk. Ped. Gos. 91, No. 4291-B91 (1991). 7. V. I. Glizburg, "An invariant description of ordinary higher-order differential systems," Izv. Vuzov. , No. 1, 51-57 (1992). 8. L. E. Evtushik, "Nonlinear higher-order connections," Izv. Vuzov. , No. 2, 32-44 (1969). 9. L. E. Evtushik, "Reductive Cartan connections and Norden's generalized affine-normalized structures," Izv.

Banaru, "Connections adjoined to the equation y(5) = f(x, y, y', y", y(a), y(4)),,, Smolensk. Gos. Ped. 90, No. 3948-B90 (1990). 2. G. A. Banaru, "Projective connection adjoined to an ordinary differential equation of fifth order," Smolensk. Gos. Ped. 92, No. 847-B92 (1992). 3. A. M. Vasil'ev, "Invariant analytical methods in differential geometry," Dokl. Akad. Nauk SSSR, 79, No. 1, 5-7 (1951). 4. A. M. Vasil'ev, The Theory of Differential-Geometric Structures [In Russian], Mosk. Gos. , Moscow (1987).

But this problem is apparently especially complicated. In this case, a quite concrete class of equations is selected by some set of invariant conditions and it demands to be characterized. Two basic questions must be answered: what is the set of equations forming the selected class and what is the special geometry induced on the plane (z, y) by the equations belonging to the class considered. T h e answer is contained in the theorems which we suggest for the conclusion of this review. 283 T h e o r e m 4.

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A Bit Progress on Word-Based Language Model by Chen Y., Chen G.-P.


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