Multiplicative processes on the set of shifted primes

The asymptotical behavior of the distributions of stochastic processes defined by multiplicative functions in the set of shifted primes is considered. The first author was supported by Konferenz der deutschen Akademien der Wissenschaften. Vilnius University, Naugarduko 24, 2006 Vilnius, Lithuania. Paderborn University, Warburger 100, 33098 Paderborn, Germany. Published in Lietuvos Matematikos Rinkinys, Vol. 39, No. 4, pp. 441–460, October–December, 1999.     

The provability of certain sequents in additive arithmetic

Vilnius Pedagogical University, Studentų 39, 2034 Vilnius, Lithuania. Published in Lietuvos Matematikos Rinkinys, Vol. 35, No. 4, pp. 518–526, October–December, 1995.     

On approximation of stochastic differential equations with coefficients depending on the past

Vilnius University, Naugarduko 24, 2006 Vilnius, Lithuania. Published in Lietuvos Matematikos Rinkinys, Vol. 32, No. 2, pp. 285–298, April–June, 1992.     

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.     

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.     

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.     

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     

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     

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     

Some limit theorems for a Dirichlet series related to the Euler function

Using some conjectures on the mean-value of generalized numbers, limit theorems in the sense of the weak convergence of probability measures for the Dirichlet series related to the Euler function are proved. Also, the limit measure is studied. Partially supported by the Lithuanian State Science and Studies Foundation. Vilnius University, Naugarduko 24, 2006 Vilnius, Lithuania: Šiauliai University, P. Višinskio 25, 5400 Šiauliai, Lithuania. Translated from Lietuvos Matematikos Rinkinys, Vol. 39, No. 3, pp. 331–342, July–September, 1999. Translated by A. Laurinčikas     

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     

Multiplicative dependence of quadratic polynomials

We investigate the multiplicative dependence relations with the values of quadratic integer polynomials at integer points. In particular, we use some elementary identities and the Pell equation in showing that such a relation exists between four values of the polynomial. Partially supported by the Lithuanian State Science and Studies Foundation. Vilnius University, Naugarduko 24, 2006 Vilnius, Lithuania. Published in Lietuvos Matematikos Rinkinys, Vol. 38, No. 3, pp. 295–303, July–September, 1998.     

Processes of Meixner type

Canonical form, self-decomposability, and the Esscher transforms of Meixner processes are discussed. Mixed Meixner processes are defined and characterized as Markov processes or semimartingales. Ornstein-Uhlenbeck and selfsimilar processes of Meixner type are also described. Partially supported by the Lithuanian State Science and Studies Foundation. Institute of Mathematics and Informatics, Akademijos 4; Vilnius University, Naugarduko 24, 2600 Vilnius, Lithuania. Published in Lietuvos Matematikos Rinkinys, Vol. 39, No. 1, pp. 40–51, January–March, 1999.     

Fast Fourier wavelet packet transformation

The wavelet basis generated by Shannon's sampling theorem is presented. Periodical finite dimensional wavelet and Fourier wavelet packets are suggested. A link of constructed bases with complex trigonometric series and discrete Fourier transformation is considered. The Fourier wavelet packet may be used as widely as discrete Fourier transformation. Vilnius University, Naugarduko 24, 2006 Vilnius, Lithuania. Published in Lietuvos Matematikos Rinkinys, Vol. 34, No. 4, pp. 411–433, October–December, 1994.     

On the average difference between two conjugates of an algebraic number

We give a lower bound for |α−1|, where α is an algebraic number, and also an upper bound for the number of real zeros of a polynomial. A lower bound for the maximal modulus of conjugates of a totally real algebraic integer is also obtained. Vilnius University, Naugarduko 24, 2006 Vilnius, Lithuania. Published in Lietuvos Matematikos Rinkinys, Vol. 35, No. 4, pp. 421–431, October–December, 1995.