Special Multiplicative Operators for the Solution of ODE – Invariants and Representations

The generalized multiplicative operator of differentiation is introduced in this paper. It is shown that the generalized multiplicative operator can be expressed as a product of two noncommutative but multiplicative exponential operators, though the generalized multiplicative operator is not an exponential operator itself. The generalized multiplicative operator is effectively exploited for the construction of solutions to nonlinear ordinary differential equations through formal transformations of invariants and representations of initial conditions. The concept of the generalized multiplicative operator provides the insight into the algebraic structure of solutions to nonlinear ordinary differential equations which cannot be identified using conventional exponential operators

Generalized solitary waves in nonintegrable KdV equations

The generalization of the classical Korteweg-de-Vries (KdV) solitary wave solution is presented in this paper. The amplitude and the propagation speed of generalized KdV solitary waves vary in time. Generating partial differential equations and conditions of existence of the generalized KdV solitary waves are derived using the inverse balancing method. Computational experiments illustrate the variety of new solitary solutions and their generating equations

Generalized solitary waves in nonintegrable KdV equations

The generalization of the classical Korteweg-de-Vries (KdV) solitary wave solution is presented in this paper. The amplitude and the propagation speed of generalized KdV solitary waves vary in time. Generating partial differential equations and conditions of existence of the generalized KdV solitary waves are derived using the inverse balancing method. Computational experiments illustrate the variety of new solitary solutions and their generating equations

An operator-based approach for the construction of closed-form solutions to fractional differential equations

An operator-based approach for the construction of closed-form solutions to fractional differential equations is presented in this paper. The technique is based on the analysis of Caputo and Riemann-Liouville algebras of fractional power series. Explicit solutions to a class of linear fractional differential equations are obtained in terms of Mittag-Leffler and fractionally-integrated exponential functions in order to demonstrate the viability of the proposed technique

Alcohol-attributable mortality and alcohol control policy in the Baltic Countries and Poland in 2001–2020 : an interrupted time-series analysis

Publisher Copyright: © 2023, The Author(s).Background: The Baltic countries–Lithuania, Latvia and Estonia–are characterized by a high rate of fully alcohol-attributable mortality, compared with Poland. Alcohol control policy measures implemented since 2001 in the Baltic countries included a restriction on availability and an increase in excise taxation, among others. The aim of the current study was to evaluate the relationship between alcohol control policy implementation and alcohol-attributable mortality in the Baltic countries and Poland. Methods: Alcohol-attributable mortality data for 2001–2020 was defined by codes 100% alcohol-attributable for persons aged 15 years and older in the Baltic countries and Poland. Alcohol control policies implemented between 2001 and 2020 were identified, and their impact on alcohol-attributable mortality was evaluated using an interrupted time-series methodology by employing a generalized additive model. Results: Alcohol-attributable mortality was significantly higher in the Baltic countries, compared with Poland, for both males and females. In the final reduced model, alcohol control policy significantly reduced male alcohol-attributable mortality by 7.60% in the 12 months post-policy implementation. For females, the alcohol control policy mean-shift effect was higher, resulting in a significant reduction of alcohol-attributable mortality by 10.77% in the 12 months post-policy implementation. The interaction effects of countries and policy tested in the full model were not statistically significant, which indicated that the impact of alcohol control policy on alcohol-attributable mortality did not differ across countries for both males and females. Conclusions: Based on the findings of the current study, alcohol control policy in the form of reduced availability and increased taxation was associated with a reduction in alcohol-attributable mortality among both males and females.Peer reviewe

Alcohol control policies reduce all-cause mortality in Baltic Countries and Poland between 2001 and 2020

Funding Information: Research reported in this publication was supported by the National Institute on Alcohol Abuse and Alcoholism of the National Institutes of Health (NIAAA) (Award Number 1R01AA028224). Publisher Copyright: © 2023, The Author(s).Alcohol consumption in the Baltic countries and Poland is among the highest globally, causing high all-cause mortality rates. Contrary to Poland, the Baltic countries have adopted many alcohol control policies, including the World Health Organization (WHO) "best buys". The aim of this study was to evaluate the impact of these policies, which were implemented between 2001 and 2020, on all-cause mortality. Monthly mortality data for men and women aged 20+ years of age in Estonia, Latvia, Lithuania, and Poland were analysed for 2001 to 2020. A total of 19 alcohol control policies, fulfilling an a-priori defined definition, were implemented between 2001 and 2020 in the countries of interest, and 18 of them could be tested. Interrupted time-series analyses were conducted by employing a generalized additive mixed model (GAMM) for men and women separately. The age-standardized all-cause mortality rate was lowest in Poland and highest in Latvia and had decreased in all countries over the time period. Taxation increases and availability restrictions had short-term effects in all countries, on average reducing the age-standardized all-cause mortality rate among men significantly (a reduction of 2.31% (95% CI 0.71%, 3.93%; p = 0.0045)). All-cause mortality rates among women were not significantly reduced (a reduction of 1.09% (95% CI - 0.02%, 2.20%; p = 0.0554)). In conclusion, the alcohol control policies implemented between 2001 and 2020 reduced all-cause mortality among men 20+ years of age in Baltic countries and Poland, and thus, the practice should be continued.publishersversionPeer reviewe

Special Multiplicative Operators for the Solution of ODE – Invariants and Representations

The generalized multiplicative operator of differentiation is introduced in this paper. It is shown that the generalized multiplicative operator can be expressed as a product of two noncommutative but multiplicative exponential operators, though the generalized multiplicative operator is not an exponential operator itself. The generalized multiplicative operator is effectively exploited for the construction of solutions to nonlinear ordinary differential equations through formal transformations of invariants and representations of initial conditions. The concept of the generalized multiplicative operator provides the insight into the algebraic structure of solutions to nonlinear ordinary differential equations which cannot be identified using conventional exponential operators

Direct and inverse relationships between Riccati systems coupled with multiplicative terms

An analytical and computational framework for the derivation of solitary solutions to biological systems describing the cooperation and competition of species and expressed by the system of Riccati equations coupled with multiplicative terms is presented in this paper. It is demonstrated that relationships between these solitary solutions can be either direct or inverse. Thus, an infinitesimal perturbation of one population would lead to an infinitesimal change in the other population – if only both solitary solutions are coupled with the direct relationship. But, in general, that is not true if solitary solutions are coupled with the inverse relationship – an infinitesimal perturbation of one population may result into a non-infinitesimal change in the other population. Necessary and sufficient conditions for the existence of solitary solutions are derived in the space of the system's parameters and initial conditionsKauno technologijos universitetasVytauto Didžiojo universitetasŠvietimo akademij

F-Operators for the Construction of Closed Form Solutions to Linear Homogenous PDEs with Variable Coefficients

A computational framework for the construction of solutions to linear homogenous partial differential equations (PDEs) with variable coefficients is developed in this paper. The considered class of PDEs reads: ∂p∂t−∑j=0m∑r=0njajrtxr∂jp∂xj=0 F-operators are introduced and used to transform the original PDE into the image PDE. Factorization of the solution into rational and exponential parts enables us to construct analytic solutions without direct integrations. A number of computational examples are used to demonstrate the efficiency of the proposed scheme

An Operator-Based Scheme for the Numerical Integration of FDEs

An operator-based scheme for the numerical integration of fractional differential equations is presented in this paper. The generalized differential operator is used to construct the analytic solution to the corresponding characteristic ordinary differential equation in the form of an infinite power series. The approximate numerical solution is constructed by truncating the power series, and by changing the point of the expansion. The developed adaptive integration step selection strategy is based on the controlled error of approximation induced by the truncation. Computational experiments are used to demonstrate the efficacy of the proposed scheme