By Dolgii Y. F., Nidchenko S. N.

We examine balance of antisymmetric periodic options to hold up differential equations. Weintroduce a one-parameter relations of periodic recommendations to a different procedure of normal differential equations with a variable interval. stipulations for balance of an antisymmetric periodic method to a hold up differential equation are said when it comes to this era functionality.

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**Sample text**

D / may go to infinity but slower than exponentially in " 1 C d . If weak tractability does not hold then we say that INT is intractable. "; d / is an exponential function of d for some " then we say that INT suffers from the curse of dimensionality. "; d / may grow no faster than polynomially in " 1 and d . 0; 1/; d 2 N; then we say that INT is strongly polynomially tractable, and the infimum of p satisfying the last bound is called the exponent of strong polynomial tractability. "; d / can occur in many ways.

Dd /: It seems interesting to check what kinds of reproducing kernels we obtain for various kinds of L2 discrepancy. t / D Œ0; t /. xj ; yj / for all x; y 2 Dd j D1 which corresponds to the Sobolev space anchored at 1. This agrees with our previous results. Consider now the L2 discrepancy anchored at ˛. 3. t / D Œ˛; t / for t > ˛. Therefore D1 D Œ0; 1 and Dd D Œ0; 1d . x; y/ for all x; y 2 Œ0; 1/: This corresponds to the Sobolev space anchored at 0. 0; 1/. K1 / is the space of functions f defined over Œ0; 1 such that f vanishes at 0 and 1.

Assume first that ˛ D 0, which corresponds to the L2 discrepancy anchored at the origin. b 1 j i C j /1Œ0;b/ . j / bj C j j bj C. 2 j jj j b/1Œb;1 . j /; : Note that this indeed holds if we take j D tj and b D 1, or j D 1 tj and b D 0. 2. Assume now that ˛ D 1. By symmetry, we again have two solutions. The first one is for j D tj and b D 0, and the second for j D 1 tj and b D 1. a tj / mod 1 and b D a: Indeed, let tj 2 Œ0; a/. Then j D a tj . 2a tj /; so they agree. 1 C tj 2a/, whereas for integration it is .