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Nodal solutions for some semipositone problemsvia bifurcation theory Lith. Math. J. (IF 0.4) Pub Date : 2024-03-14 Yali Zhang, Ruyun Ma
We show the existence of nodal solutions of the second-order nonlinear boundary value problem $$\begin{array}{l}-{u}^{^{\prime\prime} }\left(x\right)=\lambda \left(g\left(u\left(x\right)\right)+p\left(x,u\left(x\right),{u}^{\mathrm{^{\prime}}}\left(x\right)\right)\right),x\in \left(\mathrm{0,1}\right),\\ u\left(0\right)=u\left(1\right)=0,\end{array} ({\text{P}})$$ where λ > 0 is a parameter, p : [0
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Closure under infinitely divisible distribution roots and the Embrechts–Goldie conjecture Lith. Math. J. (IF 0.4) Pub Date : 2024-02-17 Hui Xu, Changjun Yu, Yuebao Wang, Dongya Cheng
We show that the distribution class ℒ(γ) \ 𝒪𝒮 is not closed under infinitely divisible distribution roots for γ > 0, that is, we provide some infinitely divisible distributions belonging to the class, whereas the corresponding Lévy distributions do not. In fact, one part of these Lévy distributions belonging to the class 𝒪ℒ\ℒ(γ) have different properties, and the other parts even do not belong to
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Second Hankel determinant of logarithmic coefficients of inverse functions in certain classes of univalent functions Lith. Math. J. (IF 0.4) Pub Date : 2024-02-16 Sanju Mandal, Molla Basir Ahamed
The Hankel determinant \({H}_{\mathrm{2,1}}\left({F}_{f-1}/2\right)\) of logarithmic coefficients is defined as \({H}_{\mathrm{2,1}}\left({F}_{f-1}/2\right):=\left|\begin{array}{cc}{\Gamma }_{1}& {\Gamma }_{2}\\ {\Gamma }_{2}& {\Gamma }_{3}\end{array}\right|={\Gamma }_{1}{\Gamma }_{3}-{\Gamma }_{2}^{2},\) where \({\Gamma }_{1},{\Gamma }_{2},\) and \({\Gamma }_{3}\) are the first, second, and third
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Limit theorems for linear processes with tapered innovations and filters Lith. Math. J. (IF 0.4) Pub Date : 2024-02-16
Abstract We consider the partial-sum process \({\sum }_{k=1}^{\left[nt\right]}{X}_{k}^{\left(n\right)},\) where \(\left\{{X}_{k}^{\left(n\right)}={\sum }_{j=0}^{\infty }{\alpha }_{j}^{\left(n\right)}{\xi }_{k-j}\left(b\left(n\right)\right), k\in {\mathbb{Z}}\right\},\) n ≥ 1, is a series of linear processes with tapered filter \({\alpha }_{j}^{\left(n\right)}={\alpha }_{j} {1}_{\left\{0\le j\le\la
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Rates of convergence in the strong law of large numbers for weighted averages of nonidentically distributed random variables Lith. Math. J. (IF 0.4) Pub Date : 2024-02-16
Abstract Integral tests are found for the convergence of two Spitzer-type series associated with a class of weighted averages introduced by Jajte [On the strong law of large numbers, Ann. Probab., 31(1):409–412, 2003]. Our main theorems are valid for a large family of dependent random variables that are not necessarily identically distributed. As a byproduct, we improve the Marcinkiewicz–Zygmund strong
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The existence of solutions to higher-order differential equations with nonhomogeneous conditions Lith. Math. J. (IF 0.4) Pub Date : 2024-02-16 Boddeti Madhubabu, Namburi Sreedhar, Kapula Rajendra Prasad
We prove the existence and uniqueness of solutions to the differential equations of higher order \({x}^{\left(l\right)}\left(s\right)+g\left(s,x\left(s\right)\right)=0,s\in \left[c,d\right],\) satisfying three-point boundary conditions that contain a nonhomogeneous term \(x\left(c\right)=0,{x}{\prime}\left(c\right)=0,{x}^{^{\prime\prime} }\left(c\right)=0,\dots {x}^{\left(l-2\right)}\left(c\right)=0
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Complete convergence for weighted sums of random variables satisfying generalized Rosenthal-type inequalities* Lith. Math. J. (IF 0.4) Pub Date : 2024-02-16 Chang Liu, Yu Miao
In the paper, we establish the complete convergence for weighted sums of random variables satisfying generalized Rosenthal-type inequalities. Our results partially extend some known results and weaken their conditions. As statistical applications, we study the nonparametric regression model and obtain the complete consistency of the weighted regression estimator for the unknown regression functions
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Spectral collocation methods for fractional multipantograph delay differential equations* Lith. Math. J. (IF 0.4) Pub Date : 2024-01-15 Xiulian Shi, Keyan Wang, Hui Sun
In this paper, we propose and analyze a spectral collocation method for the numerical solutions of fractional multipantograph delay differential equations. The fractional derivatives are described in the Caputo sense. We present that some suitable variable transformations can convert the equations to a Volterra integral equation defined on the standard interval [−1, 1]. Then the Jacobi–Gauss points
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Existence results for a class of two-fold saddle point parabolic differential equations Lith. Math. J. (IF 0.4) Pub Date : 2024-01-09
Abstract We propose and analyze an abstract framework to study the well-posedness for a family of linear degenerate parabolic augmentedmixed equations.We combine the theory for linear degenerate parabolic problems with results about stationary two-fold saddle point equations to deduce sufficient conditions for the existence and uniqueness of a solution for the problem. Finally, we show some applications
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Ground state solution for a weighted fourth-order Schrödinger equation with exponential growth nonlinearity Lith. Math. J. (IF 0.4) Pub Date : 2024-01-06 Rima Chetouane, Brahim Dridi, Rached Jaidane
In this paper, we establish the existence of a ground state solution for a weighted fourth-order equation of Shrödinger type under boundary Dirichlet condition in the unit ball B of ℝ4. The potential V is a continuous positive function bounded away from zero in B. The nonlinearity of the equation is assumed to have exponential growth due to Adams-type inequalities combined with polynomial term. We
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An interview with Donatas Surgailis Lith. Math. J. (IF 0.4) Pub Date : 2023-12-23 Viktor Skorniakov
The International Conference on Number Theory and Probability Theory took place in Palanga from September 11 to 15, 2023, in commemoration of the anniversaries of Lithuanian mathematicians Jonas Kubilius, Donatas Surgailis, Antanas Laurinˇcikas, Eugenijus Manstaviˇcius, K˛estutis Kubilius, and Alfredas Raˇckauskas. This is an interview article with one the jubilarians, D. Surgailis, known for his work
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Multiseasonal discrete-time risk model revisited Lith. Math. J. (IF 0.4) Pub Date : 2023-12-23 Andrius Grigutis, Jonas Jankauskas, Jonas Šiaulys
In this work, we set up the distribution function of \(\mathcal{M}:={\mathrm{sup}}_{n\ge 1}{\sum }_{i=1}^{n}\left({X}_{i}-1\right),\) where the random walk \({\sum }_{i=1}^{n}{X}_{i},n\in {\mathbb{N}},\) is generated by N periodically occurring distributions, and the integer-valued and nonnegative random variablesX1,X2, . . . are independent. The considered random walk generates a so-called multiseasonal
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On normal approximation for φ-mixing and m-dependent random variables Lith. Math. J. (IF 0.4) Pub Date : 2023-12-05 Jonas Kazys Sunklodas
In this paper, we estimate the difference |Eh(Zn) − Eh(Y)| between the expectations of real finite Lipschitz function h of the sum Zn = (X1 + ⋯ + Xn)/Bn, where \({B}_{n}^{2}\) = E(X1 + ⋯ + Xn)2 > 0, and a standard normal random variable Y, where real centered random variables X1,X2,… satisfy the φ-mixing condition, defined between the “past” and “ future”, or are m-dependent. In particular cases, under
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Solvability of a nonlinear parabolic problem arising in modeling surface reactions Lith. Math. J. (IF 0.4) Pub Date : 2023-11-28 Algirdas Ambrazevičius, Vladas Skakauskas
We investigate the existence, uniqueness, and long-time behavior of classical solutions to a coupled system of seven nonlinear parabolic equations. Four of them are determined in the interior of a region, and the other three are solved on a part of the boundary. In particular, such systems arise in modeling of surface reactions that involve the bulk diffusion of reactants toward and reaction products
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Sharp bounds on the third Hankel determinant for the Ozaki close-to-convex and convex functions Lith. Math. J. (IF 0.4) Pub Date : 2023-11-08 Lei Shi, Muhammad Arif
Our main purpose in this paper is to obtain certain sharp estimates of the third Hankel determinant for the class ℱ of Ozaki close-to-convex functions. This class was introduced by Ozaki in 1941. Functions in ℱ are not necessarily starlike but are convex in one direction and so are close-to-convex. We prove that the sharp bounds of ℋ3,1(f) and ℋ3,1(f−1) for f ∈ ℱ are all equal to 1/16. We also calculate
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On general sums involving the floor function with applications to k-free numbers Lith. Math. J. (IF 0.4) Pub Date : 2023-11-08 Wei Zhang
In this paper, we consider sums related to the floor function. We improve previous results for some special arithmetic functions considered by O. Bordellès [On certain sums of number theory, Int. J. Number Theory, 18(9):2053– 2074, 2022], J. Stucky [The fractional sum of small arithmetic functions, J. Number Theory, 238:731–739, 2022], and J. Wu [Note on a paper by Bordellès, Dai, Heyman, Pan and Shparlinski
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Evaluation of functional relation formula for the Clausen and Glaisher functions and multiple L-values Lith. Math. J. (IF 0.4) Pub Date : 2023-09-22 Yayoi Nakamura, Yoshitaka Sasaki
We provide evaluation formulas for the multiple Clausen and Glaisher functions, the multiple L-values with Dirichlet characters, and Mordell–Tornheim L-values.
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Some definite integrals arising from selfdecomposable characteristic functions Lith. Math. J. (IF 0.4) Pub Date : 2023-09-13 Zbigniew J. Jurek
In the probability theory, selfdecomposable or class L0 distributions play an important role as they are limit distributions of normalized partial sums of sequences of independent, not necessarily identically distributed, random variables. The class L0 is quite large and includes many known classical distributions. For this note, the most important feature of the selfdecomposable variables are their
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Cramér–Lundberg model for some classes of extremal Markov sequences Lith. Math. J. (IF 0.4) Pub Date : 2023-08-23 Barbara Helena Jasiulis-Gołdyn, Alicja Lechańska, Jolanta KrystynaMisiewicz
The classical Cramér–Lundberg model was the first attempt to describe the financial condition of the insurance company. The incomes were approximated by a steady stream of money, and insurance payments were not limited and could take any value from zero to infinity. The society did not invest any part of its money and does not have any employees, shareholders, or enterprise maintenance costs. There
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Generalized moments of sums with heavy-tailed random summands Lith. Math. J. (IF 0.4) Pub Date : 2023-08-23 Mantas Dirma, Neda Nakliuda, Jonas Šiaulys
In this paper, we investigate the asymptotic behavior of randomly weighted sums of the form of \({S}_{n}^{\theta \xi }={\theta }_{1}{\xi }_{1}+\cdots +{\theta }_{n}{\xi }_{n}\) under the transformation φ: ℝ → ℝ satisfying several asymptotic properties. The collection {ξ1,…,ξn} consists of dominatedly varying, not necessarily identically distributed, random variables following a specific dependence
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On the arguments of the roots of the generalized Fibonacci polynomial Lith. Math. J. (IF 0.4) Pub Date : 2023-08-07 Adel Alahmadi, Oleksiy Klurman, Florian Luca, Hatoon Shoaib
We revisit the classical subject of equidistribution of the roots of Littlewood-type polynomials. More precisely, we show that the roots of the family of polynomials Ψk(z) = zk−zk−1−⋯−1, k ⩾ 1, are uniformly distributed around the unit circle in the strong quantitative form, confirming a conjecture from [C.-A. Gómez and F. Luca, Commentat. Math. Univ. Carol., On the distribution of roots of zk − zk−1
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Inequalities for the generalized point pair function Lith. Math. J. (IF 0.4) Pub Date : 2023-08-03 Oona Rainio
We study a new generalized version of the point pair function defined with a constant α > 0. We prove that this function is a quasi-metric for all values of α > 0 and compare it to several hyperbolic-type metrics, such as the j∗-metric, the triangular ratio metric, and the hyperbolic metric. Most of the inequalities presented here have the best possible constants in terms of α. Furthermore, we research
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Joint occupation times in an infinite interval for spectrally negative Lévy processes on the last exit time Lith. Math. J. (IF 0.4) Pub Date : 2023-08-03 Yingqiu Li, Yushao Wei, Yangli Hu
For spectrally negative Lévy processes (often abbreviated as SNLP), using the Poisson approach and perturbation approach, we find some joint Laplace transforms of the last exit time by their joint occupation times over semiinfinite intervals (−∞, 0) and (0,∞). These expressions are in terms of the associated scale functions.
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Richter’s local limit theorem, its refinement, and related results* Lith. Math. J. (IF 0.4) Pub Date : 2023-07-25 Sergey G. Bobkov, Gennadiy P. Chistyakov, Friedrich Götze
We give a detailed exposition of the proof of Richter’s local limit theorem in a refined form and establish the stability of the remainder term in this theorem under small perturbations of the underlying distribution (including smoothing).We also discuss related quantitative bounds for characteristic functions and Laplace transforms.
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Structural stability for temperature-dependent bidispersive flow in a semi-infinite pipe Lith. Math. J. (IF 0.4) Pub Date : 2023-07-25 Yuanfei Li, Xuejiao Chen
We study the bidispersive flow describing real phenomena such as reservoir exploitation or landslides with their catastrophic effect on human life. By using the differential inequality technique we derive the L4 norm for temperature and a priori estimates of the solution under Newton’s cooling boundary conditions. Using a prior estimates of the solutions and setting an appropriate “energy” function
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A functional limit theorem for self-normalized linear processes with random coefficients and i.i.d. heavy-tailed innovations Lith. Math. J. (IF 0.4) Pub Date : 2023-07-07 Danijel Krizmanić
In this paper, we derive a self-normalized functional limit theorem for strictly stationary linear processes with i.i.d. heavy-tailed innovations and random coefficients under the condition that all partial sums of the series of coefficients are a.s. bounded between zero and the sum of the series. The convergence takes place in the space of càdlàg functions on [0, 1] with the Skorokhod M2 topology
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Estimates of the convergence rate in a limit theorem for geometric sums and some of their applications Lith. Math. J. (IF 0.4) Pub Date : 2023-06-19 Kateryna Akbash, Natalia Doronina, Ivan Matsak
We establish new nonuniform estimates of the convergence rate to the exponential distribution in the boundary theorem for geometric sums. We give examples of their application to extrema of regenerative random birth and death processes.
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On some approximations for sums of m-dependent random variables Lith. Math. J. (IF 0.4) Pub Date : 2023-06-19 Jonas Kazys Sunklodas
In this paper, we obtain estimates of the difference |Eh(Sn) − Eh(Zn)| of the expectations of smooth real functions h of the sums Sn = ξ1+⋯+ξn and Zn = Y1+⋯+Yn, where ξ1,…, ξn are m-dependent random variables, Y1,…, Yn are m0-dependent random variables, and m ≥ m0 ≥ 0 are integers. We use the smart path interpolation method.
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On some sums involving the counting function of nonisomorphic Abelian groups* Lith. Math. J. (IF 0.4) Pub Date : 2023-06-08 Haihong Fan, Wenguang Zhai
Let a(n) denote the number of nonisomorphic Abelian groups with n elements. In 1991, Ivić proved an asymptotic formula for the sum Σn≤x a(n + a(n)). In this paper, we prove a sharper asymptotic formula for this sum. Also, we extend this process to the divisor function and construct a similar result.
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Sumset of three arithmetic progressions in the complex plane Lith. Math. J. (IF 0.4) Pub Date : 2023-05-20 Artūras Dubickas
In this note, we give a necessary and sufficient condition on α, β, γ ∈ ℂ under which the sumset of three infinite arithmetic progressions ℤα+ℤβ+ℤγ is everywhere dense in ℂ. This is the case if and only if the imaginary parts \(\mathfrak{I}\left(\alpha \overline{\beta }\right),\mathfrak{I}\left(\beta \overline{\gamma }\right),\mathfrak{I}\left(\gamma \overline{\alpha }\right)\) are linearly independent
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Sums of multiplicative coefficients twisted by Frobenius traces Lith. Math. J. (IF 0.4) Pub Date : 2023-05-17 Yuxuan Zhou
Let \({a}_{\mathbb{E}}\)(n) be the normalized Frobenius traces. For any multiplicative function f satisfying some mild conditions, we investigate the sum \({\sum }_{n=1}^{N}f(n){a}_{\mathbb{E}}(n)\) and obtain a nontrivial bound. We also prove cancelation in the sum of Frobenius traces twisted by the coefficients of automorphic L-function on GLm.
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On some properties of Lévy vectors and their variations Lith. Math. J. (IF 0.4) Pub Date : 2023-05-10 Paweł Klinga, Andrzej Nowik
We investigate some properties of Lévy vectors of vector series Σn∈ω vn. We consider a generalization of an example from [P. Klinga, Rearranging series of vectors on a small set, J. Math. Anal. Appl., 424(2):966–974, 2015] proving that for a special class of vector series, there exists a subseries that has no convergent subseries with the sum range equal to the plane. To prove this result, we introduce
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Almost sure central limit theorems for the maxima of randomly chosen random variables Lith. Math. J. (IF 0.4) Pub Date : 2023-04-27 Tomasz Krajka
In this paper, we give an almost sure central limit theorem (ASCLT) version of a maximum limit theorem (MLT) with an arbitrary sequence {dn, n ≥ 1} of weighted means of max{Xk, k ∈ An}, where {Xn, n ≥ 1} is a sequence of independent random variables, and {An, n ≥ 1} is a sequence of almost surely finite random subsets of positive integers independent of {Xn, n ≥ 1}. Thus we generalize the cases considered
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Wright function in the solution to the Kolmogorov equation of the Markov branching process with geometric reproduction of particles* Lith. Math. J. (IF 0.4) Pub Date : 2023-04-13 Assen Tchorbadjieff, Penka Mayster
The topic of this work is the supercritical geometric reproduction of particles in the model of a Markov branching process. The solution to the Kolmogorov equation is expressed by the Wright function. The series expansion of this representation is obtained by the Lagrange inversion method. The asymptotic behavior is described by using two different equivalent forms for the Laplace transform. They include
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A Kesten-type inequality for randomly weighted sums of dependent subexponential random variables with applications to risk theory* Lith. Math. J. (IF 0.4) Pub Date : 2023-04-12 Bingzhen Geng, Zaiming Liu, Shijie Wang
In this paper, we first establish a Kesten-type inequality for randomly weighted sums, in which the primary random variables are assumed to be real-valued and subexponential following a general dependence structure proposed by J. Geluk and Q. Tang [Asymptotic tail probabilities of sums of dependent subexponential random variables, J. Theor. Probab., 22(4):871–882, 2009], and the random weights are
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Variance asymptotics for the area of planar cylinder processes generated by Brillinger-mixing point processes Lith. Math. J. (IF 0.4) Pub Date : 2023-03-22 Daniela Flimmel, Lothar Heinrich
We introduce cylinder processes in the plane defined as union sets of dilated straight lines (appearing as mutually overlapping infinitely long strips) generated by a stationary independently marked point process on the real line, where the marks describe the width and orientation of the individual cylinders. We study the behavior of the total area of the union of strips contained in a space-filling
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On the notions of stochastic domination and uniform integrability in the Cesàro sense with applications to weak laws of large numbers for random fields* Lith. Math. J. (IF 0.4) Pub Date : 2023-03-03 Thai Van Dat, Nguyen Chi Dzung, Vo Thi Hong Van
In this paper, we simplify the notion of stochastic domination in the Cesàro sense for arrays of random variables and provide some sharp sufficient conditions for a multidimensional array of random variables stochastically dominated in the Cesàro sense. We establish relationships between stochastic domination in the Cesàro sense and uniform integrability in the Cesàro sense for a random field. We give
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On estimation and prediction in spatial functional linear regression model Lith. Math. J. (IF 0.4) Pub Date : 2023-02-10 Stéphane Bouka, Sophie Dabo-Niang, Guy Martial Nkiet
We consider a spatial functional linear regression, where a scalar response is related to a square-integrable spatial functional process. We use a smoothing spline estimator for the functional slope parameter and establish a finite sample bound for variance of this estimator. Then we give the optimal bound of the prediction error under mixing spatial dependence. Finally, we illustrate our results by
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Statistical causality, optional and predictable projections* Lith. Math. J. (IF 0.4) Pub Date : 2023-02-10 Dragana Valjarević, Slađana Dimitrijević, Ljiljana Petrović
We consider the statistical concept of causality in continuous time within filtered probability spaces based on Granger’s definition of causality. The given causality concept is connected to the optional and predictable processes important in stochastic integration. More precisely, we establish that the preservation of predictability with respect to larger filtrations is implied by the considered notion
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Asymptotic behaviors of convolution powers of the Riemann zeta distribution Lith. Math. J. (IF 0.4) Pub Date : 2023-01-18 Takahiro Aoyama, Ryuya Namba, Koki Ota
In probability theory, there are discrete and continuous distributions. Generally speaking, we do not have sufficient kinds and properties of discrete ones compared to the continuous ones. In this paper, we treat the Riemann zeta distribution as a representative of few known discrete distributions with infinite supports. We discuss some asymptotic behaviors of convolution powers of the Riemann zeta
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On some formulae related to Euler sums Lith. Math. J. (IF 0.4) Pub Date : 2022-12-07 Marc-Antoine Coppo, Bernard Candelpergher
Using the Ramanujan summation method, we derive some unusual formulas for a class of Euler sums (including divergent Euler sums) similar to the classical relations due to Euler.
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Limit behaviors for a heavy-tailed β-mixing random sequence∗ Lith. Math. J. (IF 0.4) Pub Date : 2022-12-07 Yu Miao, Qing Yin
Let {X,Xn, n ≥ 1} be a stationary sequence of nonnegative β-mixing random variables with heavy-tailed distributions, and let Sn = X1 + X2 + · · · + Xn be the partial sums. In the present paper, we establish the logarithmic asymptotic behavior for the tail probability P(Sn > bn) for some b > 1 and the weak law of large numbers for Sn.
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Solving word problems with reasoned judgement* Lith. Math. J. (IF 0.4) Pub Date : 2022-11-11 Ieva Kilienė, Rimas Norvaiša
What assures that a mathematical representation of a word problem is correct? The response of problem solvers to a request like “Explain your answer” does not necessarily provide assurance. Instead, we complement the traditional algebraic word problem with a request to establish a mathematical representation generalizing the problem situation and then to justify the derivation of this mathematical
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A Bombieri–Vinogradov-type result for exponential sums over Piatetski-Shapiro primes Lith. Math. J. (IF 0.4) Pub Date : 2022-11-02 Stoyan Ivanov Dimitrov
In this paper, we establish a theorem of Bombieri–Vinogradov type for exponential sums over Piatetski-Shapiro primes p = [n1/γ] with 865/886 < γ < 1.
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Precise large deviations for aggregate claims of a compound renewal risk model with arbitrary dependence between claim sizes and waiting times* Lith. Math. J. (IF 0.4) Pub Date : 2022-11-02 Shijie Wang, Yu Gao
We consider a compound renewal risk model with individual claim sizes and interarrival times forming a sequence of independent identically distributed nonnegative random pairs with a generic pair (X, θ) and the numbers of claims caused by individual events constituting another sequence of independent identically distributed positive integer-valued random variables, independent of the random pairs.
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Asymptotic analysis of Sturm–Liouville problem with Neumann and nonlocal two-point boundary conditions Lith. Math. J. (IF 0.4) Pub Date : 2022-10-27 Artūras Štikonas, Erdoğan Şen
In this study, we obtain asymptotic expansions for eigenvalues and eigenfunctions of the one-dimensional Sturm–Liouville equation with one classical Neumann-type boundary condition and a two-point nonlocal boundary condition. We investigate solutions of special initial value problem and find their asymptotic expansions of any order. We analyze the characteristic equation of the boundary value problem
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Asymptotic behavior of some cone-valued infinitely divisible stochastic process through projection Lith. Math. J. (IF 0.4) Pub Date : 2022-10-20 Hajer Rejeb, Afif Masmoudi
Let (Yt)t>0 be a stochastic process on a proper cone K associated with a family of distributions (ℱt)t>0. We investigate the asymptotic behavior of the distribution of 〈Yt, u〉−t for u ∈ K as the parameter t approaches zero. Next, we consider the case that ℱt belongs to an exponential family. Under some conditions, we prove that the limiting distribution of 〈Yt, u〉−t as t → 0+ is a Pareto type law,
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Green’s function and existence of solutions for a third-order boundary value problem involving integral condition Lith. Math. J. (IF 0.4) Pub Date : 2022-09-05 Sergey Smirnov
We prove the existence of at least one nontrivial solution for a third-order boundary value problem with an integral condition under different growth assumptions on the nonlinearity in the equation. The main tool in the proofs is Schauder’s fixed point theorem. To compare the applicability of the obtained results, we consider some examples.
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Uniform estimates for sums of coefficients of symmetric power L-functions Lith. Math. J. (IF 0.4) Pub Date : 2022-09-05 Guohua Chen, Xiaoguang He
Let f(z) be a holomorphic Hecke eigenform of even weight k for SL(2, ℤ), and denote by L(s, symmf) the corresponding symmetric power L-function associated with f. Denote by ⋋symmf (n) the nth normalized coefficient of L(s, symmf). In this paper, we investigate the sum Σn≤x ⋋symmf (n) for m ≥ 2 and get the uniform upper bound extending the previous results.
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Stable fluctuations of iterated perturbed random walks in intermediate generations of a general branching process tree* Lith. Math. J. (IF 0.4) Pub Date : 2022-08-17 Alexander Iksanov, Alexander Marynych, Bohdan Rashytov
Consider a general branching process, a.k.a. Crump–Mode–Jagers process, generated by a perturbed random walk η1, ξ1 + η2, ξ1 + ξ2 + η3, …, where (ξ1, η1), (ξ2, η2), … are independent identically distributed random vectors with arbitrarily dependent positive components. Denote by Nj(t) the number of the jth generation individuals with birth times ⩽ t. Assume that j = j(t) → ∞ and j(t) = o(ta) as t →
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The local regularity conditions for the Navier–Stokes equations via one directional derivative of the velocity Lith. Math. J. (IF 0.4) Pub Date : 2022-08-17 Zhengguang Guo, Petr Kucera, Zdenek Skalak
We study the local regularity of solutions to the Navier–Stokes equations. We show for a suitable weak solution (u, p) on an open space-time domain D that if \( {\partial}_3u\in {L}_t^p{L}_x^q(D) \), where 2/p + 3/q = 2 and q ∈ (27/16, 5/2), then the solution is regular in D.
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A k-Sample Test for Functional Data Based on Generalized Maximum Mean Discrepancy Lith. Math. J. (IF 0.4) Pub Date : 2022-08-13 Armando Sosthène Kali Balogoun, Guy Martial Nkiet, Carlos Ogouyandjou
In this paper, we deal with the problem of testing the equality of k probability distributions. We introduce a generalization of the maximum mean discrepancy that permits to characterize the null hypothesis. Then we propose its estimator as a test statistic and derive its asymptotic distribution under the null hypothesis. Simulations show that the introduced procedure outperforms a classical one.
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Compound Poisson Approximations to Sums of Extrema of Bernoulli Variables Lith. Math. J. (IF 0.4) Pub Date : 2022-07-22 Gabija Liaudanskaite, Vydas Čekanavičius
Let Sn = X1 + X2 + · · · + Xn, where Xj = max(ξj, ξj+1), and ξ1, ξ2, . . . , ξn+1 are independent Bernoulli random variables. If all P(ξj = 1) are small, then we approximate Sn by a compound Poisson random variable with two matching moments. If all P(ξj = 1) are large, then we apply compound Poisson and negative binomial approximations to n − Sn. We estimate the accuracy of approximation in the total-variation
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Some Limit Theorems for the Cell Load in the Generalized Allocation Scheme Lith. Math. J. (IF 0.4) Pub Date : 2022-07-22 Yu Miao, Qian Du, Zhen Wang
In the paper, we consider the generalized allocation scheme and study the asymptotic behaviors of the extreme η(N−s), where η(N−s) denotes the (n − s)th-order statistics from the allocation scheme. We establish asymptotic representations and large and moderate deviations for η(N−s).
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Universality Theorem for the Iterated Integrals of the Logarithm of the Riemann Zeta-Function Lith. Math. J. (IF 0.4) Pub Date : 2022-07-22 Kenta Endo
In this paper, we prove the universality theorem for the iterated integrals of the logarithm of the Riemann zeta-function on a line parallel to the real axis.
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On ℤ-Dependency of Algebraic Integers Satisfying Cubic and Quartic Polynomials Lith. Math. J. (IF 0.4) Pub Date : 2022-07-22 Mitashree Behera, Prasanta Kumar Ray
Drungilas and Klimavičius [Multiplicative dependence of cubic algebraic numbers, Liet. Mat. Rink., Proc. Lith. Math. Soc., Ser. A, 58:7–9, 2017] proposed an infinite family of cubic algebraic integers that are ℤ-dependent. In this note, we provide a new family of cubic algebraic integers and show its ℤ-dependency. We also investigate the ℤ-dependency of algebraic integers satisfying some cubic and
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The Estimation of Parameters for the Tapered Pareto Distribution from Incomplete Data Lith. Math. J. (IF 0.4) Pub Date : 2022-06-01 Igor Rodionov, Marijus Vaičiulis
In this paper, we consider estimation of unknown parameters of the tapered Pareto distribution, which belongs to the class of semiheavy distributions, by a sample with excluded ℓn largest and kn smallest observations. We establish necessary and sufficient conditions in terms of proportions kn/n and ℓn/n for weak consistency and joint asymptotic normality of parameterizedmoment-type estimators for the
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On the solvability of one boundary value problem for one class of higher-order semilinear hyperbolic systems Lith. Math. J. (IF 0.4) Pub Date : 2022-05-06 Sergo Kharibegashvili, Bidzina Midodashvili
In this paper, we consider the boundary value problem for one class of higher-order semilinear hyperbolic systems. We prove the theorems on the existence, uniqueness, and nonexistence of solutions of this problem.
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The law of large numbers for weakly correlated random elements in the spaces lp, 1 ⩽ p < ∞ Lith. Math. J. (IF 0.4) Pub Date : 2022-05-05 Valeri Berikashvili, George Giorgobiani, Vakhtang Kvaratskhelia
We prove an analogue of Khinchin’s theorem for weakly correlated random elements with values in the spaces lp, 1 ⩽ p < ∞.
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Additive arithmetic functions meet the inclusion–exclusion principle: Asymptotic formulas concerning the GCD and LCM of several integers Lith. Math. J. (IF 0.4) Pub Date : 2022-05-06 Olivier Bordellès, László Tóth
We obtain asymptotic formulas for the sums \( {\sum}_{n_1,\dots, {n}_k\leqslant x} \) f((n1, . . . , nk)) and \( {\sum}_{n_1,\dots, {n}_k\leqslant x} \) f([n1, . . . , nk]), involving the GCD and LCM of the integers n1, . . . , nk, where f belongs to certain classes of additive arithmetic functions. In particular, we consider the generalized omega function Ωℓ(n) = \( {\sum}_{p^{\nu}\Big\Vert {n}^{v^{\ell