Some estimates in theL p metric in the central limit theorem for additive functions

The convergence of the value distributions of a normalized sequence of strongly additive arithmetic functions to the standard normal law in theL _p metric is considered. An asymptotic formula for the variance is obtained. In both cases, the remainders are expressed in terms of the third absolute moment of the additive function. Vilnius University, Naugarduko 24, 2006 Vilnius, Lithuania. Translated from Lietuvos Matematikos Rinkinys, Vol. 39, No. 1, pp. 74–80, January–March, 1999. Translated by A. Mačiulis     

Intrinsic normalizations of a hyperplane distribution on the Grassmann manifold. I

We consider intrinsic normalizations of a hyperplane distribution on the Grassmann manifold of ann-dimensional projective space. Vilnius University, Naugarduko 24, 2600 Vilnius, Lithuania. Translated from Lietuvos Matematikos Rinkinys, Vol. 39, No. 2, pp. 257–273, April–June, 1999. Translated by V. Mackevičius     

On the intrinsic normalizations of the seminonholonomic complexesSN Gr(m, n, (m+1)(n−m)−ϱ). I

Some intrinsic normalizations of seminonholonomic complexes of then-dimensional projective space are considered. Vilnius University, Naugarduko 24, 2006 Vilnius, Lithuania. Translated from Lietuvos Matematikos Rinkinys, Vol. 39, No. 4, pp. 517–538, October–December, 1999. Translated by R. Lapinskas     

Stochastic processes with independent increments for random mappings

Using additive functions defined on the combinatorial structure of all mappings of anN set into itself, we define paths in the space endowed with the Skorokhod topology. Taking a mapping with equal probability, we get a sequence of random processes. Necessary and sufficient conditions for the weak convergence of this sequence to a stochastic process with independent increments are established. It is shown that the class of such processes contains all possible limits, provided that, on the components of a mapping, the additive functions have values small in average. Partially supported by the Lithuanian State Science and Studies Foundation. Vilnius University, Naugarduko 24, 2006 Vilnius, Lithuania. Translated from Lietuvos Matematikos Rinkinys, Vol. 39, No. 4, pp. 498–516, October–December, 1999. Translated by E. Manstavičius     

The von mises theorem for farey fractions

We consider systems of strongly additive functions defined on the set of rational numbers and taking the values 0 and 1 on prime elements of ℚ. For these systems, we obtain necessary and sufficient conditions for the weak convergence to the Poisson law. Research supported by the Lithuanian State Science and Studies Foundation. Vilnius University, Naugarduko 24, 2600 Vilnius, Lithuania. Translated from Lietuvos Matematikos Rinkinys, Vol. 39, No. 3, pp. 425–439, July–September, 1999. Translated by J. <Siaulys     

On the rate of normal approximation inD[0, 1]

The paper gives estimates of the rate of convergence in the central limit theorems for stochastically continuous cadlag processes proved recently by Bézandry and Fernique (Ann. Inst H. Poincare,28) and Bloznelis and Paulauskas (to appear inStoch. Proc. Appl.). Research supported by the SFB 343 at Bielefeld, by a Grant from the Lithuanian Government, and by V.P. Grant 94. Vilnius University, Naugarduko 24; Institute of Mathematics and Informatics, Akademijos 4, 2600 Vilnius, Lithuania. Published in Lietuvos Matematikos Rinkinys, Vol. 37, No. 3, pp. 280–294, July–September, 1997.     

On the asymptotic independence of Dirichlet series

The joint limit distribution of functions given by Dirichlet series is studied. The necessary and sufficient condition when this distribution is a product of marginal distributions is found. An example of such Dirichlet series with linear independent systems of exponents is presented. Partially supported by the Lithuanian State Science and Studies Foundation. Vilnius University, Naugarduko 24, 2006 Vilnius; Šiauliai University, P. Višinskio 25, 5419 Šiauliai, Lithuania. Translated from Lietuvos Matematikos Rinkinys, Vol. 39, No. 1, pp. 65–73, January–March, 1999. Translated by A. Laurinčikas     

Some remarks on subfields of algebraic number fields

Vilnius University, Naugarduko 24, 2006 Vilnius, Lithuania. Translated from Lietuvos Matematikos Rinkinys, Vol. 35, No. 2 pp. 231–232, April–June, 1995     

On a problem of A. M. Vasil'ev

Vilnius Pedagogical University, Studentu 39, 2034 Vilnius, Lithuania. Translated from Lietuvos Matematikos Rinkinys, Vol. 34, No. 3, pp. 388–407, July–September, 1994.     

On the blow-up of solutions of a system of nonlinear Schrödinger equations

Vilnius University, Naugarduko 24, 2006 Vilnius, Lithuania. Translated from Lietuvos Matematikos Rinkinys, Vol. 35, No. 2, pp. 181–189, April–June, 1995.     

Difference scheme for the nonlinear problem of magnetization

Vilnius University, Naugarduko 24, 2006 Vilnius, Lithuania. Translated from Lietuvos Matematikos Rinkinys, Vol. 32, No. 2, pp. 237–248, April–June, 1992.     

Limit distributions of sums of random variables defined on a finite homogeneous Markov chain. II

Vilnius University, Naugarduko 24, 2600 Vilnius, Lithuania. Translated from Lietuvos Matematikos Rinkinys, Vol. 34, No. 1, pp. 94–106, January–March, 1994.     

Large deviations for integer centered poisson approximation

Large deviations in a centered Poisson approximation are examined. For lattice distributions, the centered Poisson approximation is more universal than the normal and standard Poisson laws. Vilnius University, Naugarduko 24, 2600 Vilnius, Lithuania. Translated from Lietuvos Matematikos Rinkinys, Vol. 39, No. 1, pp. 9–23, January–March, 1999. Translated by V. Čekanavičius     

On convergence to the poisson law for distributions of the sum of random variables connected into a chain

This paper deals with the triangular array of random variables where every sequence is connected into a stationary Markov chain. For the uniformly strongly mixing chain we find conditions under which the distributions of the sum converge to the Poisson law. A more general case of theL ^p-regular Markov chain is also considered. Institute of Mathematics and Informatics, Akademijos 4, 2600 Vilnius, Lithuania. Translated from Lietuvos Matematikos Rinkinys, Vol. 35, No. 3, pp. 297–307, July–September, 1995. Translated by R. Lapinskas     

Some estimates of thenth difference quotient of a function analytic in a convex region

Vilnius Technical University, Saulètekio 11, 2600 Vilnius, Lithuania. Translated from Lietuvos Matematikos Rinkinys, Vol. 35, No. 4, pp. 489–501, October–December, 1995.     

Approximation to the Sobolev classesW q r of functions of several variables by bilinear forms inL p for 2≤q≤p≤∞

We study the approximation of functions of several variables by bilinear forms that are the pairwise products of functions of fewer variables. The order of approximation of Sobolev classesW _q ^r by bilinear forms inL _p for 2≤q≤p≤∞ is found. Translated by N. K. Kulman Translated fromMatematicheskie Zametki, Vol. 62, No. 1, pp. 18–34, July, 1997.     

Extended Euler-Maclaurin summation formulas

Vilnius Technical University, Saulétekio 11, 2600 Vilnius, Lithuania. Translated from Lietuvos Matematikos Rinkinys, Vol. 32, No. 2, pp. 249–260, April–June, 1992.     

Behavior of the homogeneous symmetric polynomial in an angular region

Vilnius Technical University, Saulétekio al. 11, 2600 Vilnius, Lithuania. Translated from Lietuvos Matematikos Rinkinys Vol. 35, No. 4, pp. 469–488, October–December, 1995.     

Infinitary calculus for a restricted first-order linear temporal logic without contraction on quantified formulas

An infinitary calculus for a restricted fragment of the first-order linear temporal logic is considered. We prove that for this fragment one can construct the infinitary calculusG _Lω ^* without contraction on predicate formulas. The calculusG _Lω ^* possesses the following properties: (1) the succedent rule for the existential quantifier is included into the corresponding axiom; (2) the premise of the antecedent rule for the universal quantifier does not contain a duplicate of the main formula. The soundness and completness ofG _Lω ^* are also proved. Institute of Mathematics and Informatics, Akademijos 4, 2600 Vilnius, Lithuania. Translated from Lietuvos Matematikos Rinkinys, Vol. 39, No. 3, pp. 378–397, July–September, 1999. Translated by R. Lapinskas     

Entire functions of bernstein's class that are not fourier-stieltjes transforms

We consider certain subclasses of the class of entire functions of exponential type bounded on the real axis. We construct functions that belong to these subclasses but are not Fourier-Stieltjes transforms. Particular attention is given to the distribution of zeros of such functions. The results obtained allow us to study the stability of completeness of systems of exponentials inC andL ^p under small perturbations of the exponents. Translated fromMatematicheskie Zametki, Vol. 61, No. 3, pp. 367–380, March, 1997. Translated by M. A. Shishkova