Lithuanian Mathematical Journal

Items from 1 to 20 out of 39 results

article

A Population Dynamics Model with Parental Care

V. Skakauskas

Lithuanian Mathematical Journal > 2002 > 42 > 1 > 71-80

A model for an age‐structured unlimited population dynamics with parental care of offspring is presented (migration of individuals is not taken into account). The model consists of six partial integro‐differential equations for single males, single females, pairs with offspring under parental care, pairs without offspring under parental care, and offspring of the male and female sex. A class of separable...

article

The Convergence Rate to the Normal Law of a Certain Variable Defined on Random Polynomials

V. Zacharovas

Lithuanian Mathematical Journal > 2002 > 42 > 1 > 88-107

In this paper, we investigate the convergence rate to the normal law of the distribution of the logarithm of the degree of the splitting field of a random polynomial over a finite field F _q. The exact convergence rate is obtained. A similar result is proved for the distribution of the order of a random permutation.

article

On Small Values of the Riemann Zeta‐Function on the Critical Line and Gaps Between Zeros

A. Ivić

Lithuanian Mathematical Journal > 2002 > 42 > 1 > 25-36

Small values of $${\text{|}}\zeta (\frac{1}{2} + it){\text{|}}$$ are investigated, using the value distribution results of A. Selberg. This gives an asymptotic formula for $$\mu (\{ 0 < t \leqslant T:|\zeta (\frac{1}{2} + it)| \leqslant c\} )$$ Some related problems involving values of $${\text{|}}\zeta (\frac{1}{2} + it){\text{|}}$$ and gaps between ordinates of consecutive zeros...

article

A Discrete Limit Theorem for the Matsumoto Zeta‐Function in the Space of Meromorphic Functions

R. Kačinskaitė

Lithuanian Mathematical Journal > 2002 > 42 > 1 > 37-53

In the paper, a discrete limit theorem for the Matsumoto zeta‐function in the space of meromorphic functions is proved.

article

Aggregation in ARCH Models

R. Leipus, M.'C. Viano

Lithuanian Mathematical Journal > 2002 > 42 > 1 > 54-70

The paper studies a new class of nonnegative random coefficient ARCH(∞) models. Conditions for the stationarity of the underlying random parameter process as well as of the aggregated processes, which are given by Volterra'type series, are established. We prove that, under weak assumptions, which link the distributional properties of the random coefficients and of the noise, the covariance function...

article

Large‐Deviation Local Theorem for Additive Functionals of a Markov Gaussian Field. IV

S. Čepulėnas

Lithuanian Mathematical Journal > 2002 > 42 > 1 > 15-24

This paper is a continuation of [1]-[3].

article

Differentiable Connections with Poincaré Groups of Local Transformations. II

R. Vosylius

Lithuanian Mathematical Journal > 2002 > 42 > 1 > 81-87

In the canonical smooth fiber bundles Π:∝ⁿ⁺¹↑∝ⁿ, we study generalized differentiable connections constructed by the author in his previous works. Special emphasis is laid on the investigation of the behavior of these connections under local transformations of the classical Poicaré ℙ(1,n) and extended Poincaré groups $$\tilde {\mathbb{P}}(1,n)$$ canonically acting in the given connections. We...

article

The Rate of Convergence for Subexponential Distributions and Densities

A. Baltrūnas, E. Omey

Lithuanian Mathematical Journal > 2002 > 42 > 1 > 1-14

A distribution function F on the nonnegative real line is called subexponential if lim_x↑∞(1-F ^*n(x)/(1 - F(x)) = n for all n ≥ 2, where F ^*n denotes the n‐fold Stieltjes convolution of F with itself. In this paper, we consider the rate of convergence in the above definition and in its density analogue. Among others we discuss the asymptotic behavior of the remainder term R _n (x) defined by R...

article

The Effect of Spatial Autocorrelation on the Error Rates of the Linear Discriminant Functions

K. Dučinskas, J. Šaltytė

Lithuanian Mathematical Journal > 2002 > 42 > 2 > 133-139

The problem of classification of the realization of the intrinsically stationary multivariate Gaussian random field into one of two populations with different means and factorized covariance matrices is considered. Unknown means and the common covariance matrix of the feature vector components are estimated from the spatially correlated training samples assuming spatial correlations to be known. Two...

article

The Logarithmic Frequency of Values of Additive Functions

J. Šiaulys

Lithuanian Mathematical Journal > 2002 > 42 > 2 > 204-210

We consider the weak convergence of distribution functions (∑_m≤x 1/ m)^-1 ∑ _{m ≤ x},f_x(m)<u 1/ m to the Poisson law. Here f_x is a set (x ≥2) of strongly additive functions such that f_x(p)∈{0,1} for each prime number p.

article

Differentiable Connections with Poincar{e} Groups of Local Transformations. {III}

R. Vosylius

Lithuanian Mathematical Journal > 2002 > 42 > 2 > 211-218

In the canonical smooth fiber bundles Π:∝ⁿ⁺¹↑∝ⁿ, we study generalized differentiable connections constructed by the author in papers [4] and [5]. Special emphasis is laid on the investigation of the behavior of these connections under local transformations of the classical Poincar{e} groups ℙ(1,n) and extended Poincar{e} groups $$\tilde {\mathbb {P}}(1,n)$$ canonically acting in the given connections...

article

Interaction of Flows on Quadrics

M. Rahula, D. Tseluiko

Lithuanian Mathematical Journal > 2002 > 42 > 2 > 182-190

We interpret the Rodrigues formula describing a torsion of a rigid body in terms of Lie derivatives. We consider a more general situation where vector fields on quadrics (ellipsoids and hyperboloids) are dragged by other vector fields. The question is about the adjoint representation of a Lie group which is more general than the usual torsion group of the three‐dimensional Euclidean space.

article

A Joint Limit Theorem for General Dirichlet Series

A. Laurinčikas, J. Steuding

Lithuanian Mathematical Journal > 2002 > 42 > 2 > 163-173

In this paper, a joint limit theorem in the sense of the weak convergence of probability measures in the space of meromorphic functions for general Dirichlet series is proved. The explicit form of the limit measure is given.

article

(φ,ξ,η,λ)‐Structures of Parabolic Type

A. Baškienė

Lithuanian Mathematical Journal > 2002 > 42 > 2 > 109-119

We consider (φ,ξ,η,λ)‐structures of parabolic type on hypersurfaces of dual spaces and study the rank of the affinor φ. We consider almost contact metric structures of parabolic type of the first kind on hypersurfaces of 4‐dimensional dual metric space. We study the properties of these structures and give examples of normal, integrable, and Sasakian parabolic structures.

article

Tableaus with Invertible Rules for Many‐Valued Modal Propositional Logics

J. Sakalauskaitė

Lithuanian Mathematical Journal > 2002 > 42 > 2 > 191-203

We investigate tableau‐based theorem proving for some families of many‐valued modal propositional logics. We consider many‐valued counterparts of well‐known two‐valued modal logics obtained from various combinations of four basic properties of the accessibility relation, i.e., reflexivity, transitivity, seriality, and Euclideaness. For each of these logics we introduce tableau systems with certain...

article

Some Remarks on Additive Arithmetical Semigroups

K.‐H. Indlekofer

Lithuanian Mathematical Journal > 2002 > 42 > 2 > 146-162

Under weak conditions called axioms $${\mathcal{A}}_1 $$ and $${\mathcal{A}}_2 $$ , we prove Chebyshev‐type estimates and asymptotic formulas, respectively, for the prime elements in general additive arithmetical semigroups. As applications, we derive asymptotic laws for the mean behavior of prime divisor functions and of distinct degrees of prime factors.

article

Decidability of Some Classes of Modal Logic

S. Norgėla

Lithuanian Mathematical Journal > 2002 > 42 > 2 > 174-181

We describe a modal sequential calculus some modal rules of which do not contain duplications of the main formula. We also prove its equivalence to the modal calculus S4 and the decidability of some classes of formulas containing only one‐place predicate variables.

article

On a Positivity Property of the Riemann ξ‐Function

R. Garunkštis

Lithuanian Mathematical Journal > 2002 > 42 > 2 > 140-145

We consider a quantitative version of the positivity condition of the Riemann ξ‐function. J. C. Lagarias obtained that $$\{ \Re (\frac{{\xi '}}{\xi }(\sigma + it)): - \infty < t < \infty \} = \frac{{\xi '}}{\xi }(\sigma )$$ for σ>10. The main aim of this paper is to prove the equality for σ ∞ 1.

article

Stability Tests for Two Common Classes of Linear Time‐Delay and Hybrid Systems

M. de la Sen

Lithuanian Mathematical Journal > 2002 > 42 > 2 > 120-132

The stability of linear time‐delay systems with point internal delays is difficult to deal with in practice because of the fact that their characteristic equation is usually of transcendent type rather than of polynomial type. This feature usually causes the system to possess an infinite number of poles. In this paper, stability tests for this class of systems are obtained based either on extensions...

article

A Joint Limit Theorem for the Riemann Zeta-Function in the Space of Analytic Functions

R. Šleževičienė

Lithuanian Mathematical Journal > 2002 > 42 > 3 > 308-314

In this paper, we prove a joint limit theorem for the Riemann zeta-function in the space of analytic functions in the sense of weak convergence of probability measures.

Volume:
42
Year:
2002

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4 (11)
3 (9)
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Keywords

WEAK CONVERGENCE (7)
PROBABILITY MEASURE (5)
SUBEXPONENTIAL DISTRIBUTIONS (3)
BOUNDS FOR TAIL PROBABILITIES (2)
DIFFERENTIABLE CONNECTIONS (2)
DIRICHLET SERIES (2)
INVARIANT PROPERTY (2)
LARGE DEVIATIONS (2)
MARTINGALE (2)
MODAL LOGIC (2)
PROBABILITIES OF LARGE DEVIATIONS (2)
RIEMANN ZETA-FUNCTION (2)
L P NORM (1)
O‐REGULAR VARIANTION (1)
(Φ,Ξ,Η,Λ)‐STRUCTURE OF PARABOLIC TYPE (1)
ABELIAN GROUP (1)
ADDITIVE ARITHMETICAL SEMIGROUP (1)
ADDITIVE FUNCTION (1)
AGE‐SEX‐STRUCTURED POPULATION (1)
AGGREGATION (1)
ALLELIC PARTITION (1)
ARCH (∞) MODEL (1)
ARITHMETIC FUNCTION (1)
ASYMPTOTIC EVALUATION (1)
ASYMPTOTIC EXPANSION (1)
AZUMA'SINEQUALITY (1)
BAYES CLASSIFICATION RULE (1)
BENNETT INEQUALITY (1)
BERNSTEIN INEQUALITY (1)
BLOW-UP (1)
BOUNDED DIFFERENCES AND RANDOM VARIABLES (1)
BOUNDED RANDOM VARIABLES (1)
BUSY PERIODS (1)
CENTRAL LIMIT THEOREM (1)
CHEBYSHEV ESTIMATE (1)
CHILD CARE (1)
COMPENSATOR (1)
COMPLETENESS (1)
CONVERGENCE RATE (1)
CONVOLUTIONS (1)
CRAMÉR CONDITION (C) (1)
CUMULANTS (1)
DECIDABLE CLASSES (1)
DEVIATION INEQUALITIES (1)
DIRICHLET POLYNOMIAL (1)
DISTRIBUTION FUNCTION (1)
DOMINATED VARIATION (1)
ELLIPTIC EQUATION (1)
ENTIRE FUNCTION OF EXPONENTIAL TYPE (1)
ESTIMATORS (1)
EXTREME VALUES (1)
FACTORIAL MOMENTS (1)
FOURIER INTEGRAL (1)
FOURIER TRANSFORM OF A DISTRIBUTION (1)
FUNCTIONAL LIMIT THEOREM (1)
FUNDAMENTAL THEOREM OF ALGEBRA (1)
GARCH (1,1) MODEL (1)
GENERALIZED DIFFERENTIATION OPERATOR (1)
GI/G/1 QUEUE (1)
GLIVENKO CLASSES (1)
GROUPS OF TRANSFORMATION (1)
GROUPS OF TRANSFORMATIONS (1)
HEAVY TRAFFIC (1)
HELLINGER TRANSFORM (1)
HILBERT SPACE (1)
HOEFFDING INEQUALITY (1)
HOEFFDING'SINEQUALITIES (1)
HYBRID SYSTEMS (1)
HÖLDER SPACE (1)
INDEPENDENT RANDOM VARIABLES (1)
INEQUALITIES (1)
INFINITELY DIVISIBLE RANDOM VECTORS (1)
INTEGRABILITY (1)
INVARIANCE PRINCIPLE (1)
LAW OF ITERATED LOGARITHM (1)
LERCH ZETA-FUNCTION (1)
LIE DERIVATIVES (1)
LIE GROUPS (1)
LIMIT DISTRIBUTION (1)
LIMIT THEOREM (1)
LINEAR DISCRIMINANT FUNCTION (1)
LINEAR OPERATOR (1)
LIPSCHITZ FUNCTIONS (1)
LOCAL LIMIT THEOREM (1)
LOWER BOUND (1)
MANY‐VALUED LOGIC (1)
MARKOV GAUSSIAN RANDOM FIELD (1)
MEAN VALUE (1)
MEASURE CONCENTRATION (1)
MEASURE CONCENTRATION PHENOMENA (1)
METHOD OF MAJORANTS (1)
MISCLASSIFICATION PROBABILITY (1)
MULTIPHASE QUEUEING SYSTEMS (1)
MULTIPLICATIVE OPERATOR (1)
MULTIVARIATE (MARKED) POINT PROCESSES (1)
NONLINEAR PROBLEM (1)
NORMAL LAW (1)
NORMALITY (1)
O-REGULAR VARIATION (1)
ORDER OF PERMUTATION (1)
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INFONA - science communication portal

Lithuanian Mathematical Journal

A Population Dynamics Model with Parental Care

The Convergence Rate to the Normal Law of a Certain Variable Defined on Random Polynomials

On Small Values of the Riemann Zeta‐Function on the Critical Line and Gaps Between Zeros

A Discrete Limit Theorem for the Matsumoto Zeta‐Function in the Space of Meromorphic Functions

Aggregation in ARCH Models

Large‐Deviation Local Theorem for Additive Functionals of a Markov Gaussian Field. IV

Differentiable Connections with Poincaré Groups of Local Transformations. II

The Rate of Convergence for Subexponential Distributions and Densities

The Effect of Spatial Autocorrelation on the Error Rates of the Linear Discriminant Functions

The Logarithmic Frequency of Values of Additive Functions

Differentiable Connections with Poincar{e} Groups of Local Transformations. {III}

Interaction of Flows on Quadrics

A Joint Limit Theorem for General Dirichlet Series

(φ,ξ,η,λ)‐Structures of Parabolic Type

Tableaus with Invertible Rules for Many‐Valued Modal Propositional Logics

Some Remarks on Additive Arithmetical Semigroups

Decidability of Some Classes of Modal Logic

On a Positivity Property of the Riemann ξ‐Function

Stability Tests for Two Common Classes of Linear Time‐Delay and Hybrid Systems

A Joint Limit Theorem for the Riemann Zeta-Function in the Space of Analytic Functions

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