10 research outputs found
Piecewise Polynomial Aggregation as Preprocessing for Data Numerical Modeling
Abstract. Data aggregation issues for numerical modeling are reviewed in the present study.
The authors discuss data aggregation procedures as preprocessing for subsequent numerical
modeling. To calculate the data aggregation, the authors propose using numerical probabilistic
analysis (NPA). An important feature of this study is how the authors represent the aggregated
data. The study shows that the offered approach to data aggregation can be interpreted as the
frequency distribution of a variable. To study its properties, the density function is used. For
this purpose, the authors propose using the piecewise polynomial models. A suitable example
of such approach is the spline. The authors show that their approach to data aggregation allows
reducing the level of data uncertainty and significantly increasing the efficiency of numerical
calculations. To demonstrate the degree of the correspondence of the proposed methods to
reality, the authors developed a theoretical framework and considered numerical examples
devoted to time series aggregation
Piecewise Polynomial Aggregation as Preprocessing for Data Numerical Modeling
Data aggregation issues for numerical modeling are reviewed in the present study.
The authors discuss data aggregation procedures as preprocessing for subsequent numerical
modeling. To calculate the data aggregation, the authors propose using numerical probabilistic
analysis (NPA). An important feature of this study is how the authors represent the aggregated
data. The study shows that the offered approach to data aggregation can be interpreted as the
frequency distribution of a variable. To study its properties, the density function is used. For
this purpose, the authors propose using the piecewise polynomial models. A suitable example
of such approach is the spline. The authors show that their approach to data aggregation allows
reducing the level of data uncertainty and significantly increasing the efficiency of numerical
calculations. To demonstrate the degree of the correspondence of the proposed methods to
reality, the authors developed a theoretical framework and considered numerical examples
devoted to time series aggregatio
Ground state of a periodic elastic atomic chain in an arbitrary periodic potential
Π’Π΅ΠΊΡΡ ΡΡΠ°ΡΡΠΈ Π½Π΅ ΠΏΡΠ±Π»ΠΈΠΊΡΠ΅ΡΡΡ Π² ΠΎΡΠΊΡΡΡΠΎΠΌ Π΄ΠΎΡΡΡΠΏΠ΅ Π² ΡΠΎΠΎΡΠ²Π΅ΡΡΡΠ²ΠΈΠΈ Ρ ΠΏΠΎΠ»ΠΈΡΠΈΠΊΠΎΠΉ ΠΆΡΡΠ½Π°Π»Π°
The ground state of the FrenkelβKontorova model
Π’Π΅ΠΊΡΡ ΡΡΠ°ΡΡΠΈ Π½Π΅ ΠΏΡΠ±Π»ΠΈΠΊΡΠ΅ΡΡΡ Π² ΠΎΡΠΊΡΡΡΠΎΠΌ Π΄ΠΎΡΡΡΠΏΠ΅ Π² ΡΠΎΠΎΡΠ²Π΅ΡΡΡΠ²ΠΈΠΈ Ρ ΠΏΠΎΠ»ΠΈΡΠΈΠΊΠΎΠΉ ΠΆΡΡΠ½Π°Π»Π°
The ground state of the FrenkelβKontorova model
Π’Π΅ΠΊΡΡ ΡΡΠ°ΡΡΠΈ Π½Π΅ ΠΏΡΠ±Π»ΠΈΠΊΡΠ΅ΡΡΡ Π² ΠΎΡΠΊΡΡΡΠΎΠΌ Π΄ΠΎΡΡΡΠΏΠ΅ Π² ΡΠΎΠΎΡΠ²Π΅ΡΡΡΠ²ΠΈΠΈ Ρ ΠΏΠΎΠ»ΠΈΡΠΈΠΊΠΎΠΉ ΠΆΡΡΠ½Π°Π»Π°
Ground state of a periodic elastic atomic chain in an arbitrary periodic potential
Π’Π΅ΠΊΡΡ ΡΡΠ°ΡΡΠΈ Π½Π΅ ΠΏΡΠ±Π»ΠΈΠΊΡΠ΅ΡΡΡ Π² ΠΎΡΠΊΡΡΡΠΎΠΌ Π΄ΠΎΡΡΡΠΏΠ΅ Π² ΡΠΎΠΎΡΠ²Π΅ΡΡΡΠ²ΠΈΠΈ Ρ ΠΏΠΎΠ»ΠΈΡΠΈΠΊΠΎΠΉ ΠΆΡΡΠ½Π°Π»Π°
Hermitian finite element complementing the BognerβFoxβSchmit rectangle near curvilinear boundary
Π’Π΅ΠΊΡΡ ΡΡΠ°ΡΡΠΈ Π½Π΅ ΠΏΡΠ±Π»ΠΈΠΊΡΠ΅ΡΡΡ Π² ΠΎΡΠΊΡΡΡΠΎΠΌ Π΄ΠΎΡΡΡΠΏΠ΅ Π² ΡΠΎΠΎΡΠ²Π΅ΡΡΡΠ²ΠΈΠΈ Ρ ΠΏΠΎΠ»ΠΈΡΠΈΠΊΠΎΠΉ ΠΆΡΡΠ½Π°Π»Π°