66 research outputs found
Some New Observations for F-Contractions in Vector-Valued Metric Spaces of Perov's Type
The main purpose of this article is to improve, generalize and complement some recently established results for Perov's type F-contractions. In our approach, we use only the property (F1) of Wardowski while other authors employed all three conditions. Working only with the fact that the function F is strictly increasing on (0, +infinity)(m), we obtain as a consequence new families of contractive conditions in the realm of vector-valued metric spaces of Perov's type. At the end of the article, we present an example that supports obtained theoretical results and genuinely generalizes several known results in existing literature
Variations in the Tensorial Trapezoid Type Inequalities for Convex Functions of Self-Adjoint Operators in Hilbert Spaces
In this paper, various tensorial inequalities of trapezoid type were obtained. Identity from classical analysis is utilized to obtain the tensorial version of the said identity which in turn allowed us to obtain tensorial inequalities in Hilbert space. The continuous functions of self-adjoint operators in Hilbert spaces have several tensorial norm inequalities discovered in this study. The convexity features of the mapping f lead to the variation in several inequalities of the trapezoid type
Some New Observations for F-Contractions in Vector-Valued Metric Spaces of Perov's Type
The main purpose of this article is to improve, generalize and complement some recently established results for Perov's type F-contractions. In our approach, we use only the property (F1) of Wardowski while other authors employed all three conditions. Working only with the fact that the function F is strictly increasing on (0, +infinity)(m), we obtain as a consequence new families of contractive conditions in the realm of vector-valued metric spaces of Perov's type. At the end of the article, we present an example that supports obtained theoretical results and genuinely generalizes several known results in existing literature
Numerical simulation of turbulent flows over real complex terrains
Π£ Π΄ΠΈΡΠ΅ΡΡΠ°ΡΠΈΡΠΈ ΡΠ΅ ΠΏΡΠ΅Π΄ΡΡΠ°Π²ΡΠ΅Π½Π° Π½ΠΎΠ²Π° ΠΈ ΡΠ½Π°ΠΏΡΠ΅ΡΠ΅Π½Π° ΠΏΡΠΎΡΠ°ΡΡΠ½ΡΠΊΠ° ΠΏΡΠΎΡΠ΅-
Π΄ΡΡΠ° Π±Π°Π·ΠΈΡΠ°Π½Π° Π½Π° ΠΌΠ΅ΡΠΎΠ΄ΠΈ ΠΊΠΎΠ½Π°ΡΠ½ΠΈΡ
Π·Π°ΠΏΡΠ΅ΠΌΠΈΠ½Π°, ΠΊΠΎΡΠ° ΡΠ΅ ΡΠ°Π·Π²ΠΈΡΠ΅Π½Π° Π·Π° ΠΏΠΎΡΡΠ΅Π±Π΅
ΡΠΈΠΌΡΠ»Π°ΡΠΈΡΠ΅ ΡΡΡΠ±ΡΠ»Π΅Π½ΡΠ½ΠΈΡ
Π²Π°Π·Π΄ΡΡΠ½ΠΈΡ
ΡΡΡΡΡΠ°ΡΠ° Π½Π°Π΄ ΡΠ΅Π°Π»Π½ΠΈΠΌ ΠΊΠΎΠΌΠΏΠ»Π΅ΠΊΡΠ½ΠΈΠΌ
ΡΠ΅ΡΠ΅Π½ΠΈΠΌΠ°. Π£ Π΄ΠΈΡΠ΅ΡΡΠ°ΡΠΈΡΠΈ ΡΡ ΡΠ°Π·ΠΌΠ°ΡΡΠ°Π½Π΅ Π΅ΡΠΈΠΊΠ°ΡΠ½Π° Π°ΠΏΡΠΎΠΊΡΠΈΠΌΠ°ΡΠΈΡΠ° ΠΊΠΎΠ²Π΅ΠΊΡΠΈΡΠ΅,
Π΄ΠΈΡΡΠ·Π½ΠΈΡ
ΡΠ»Π°Π½ΠΎΠ²Π°, ΡΠ΅ΠΊΠΎΠ½ΡΡΡΡΠΊΡΠΈΡΠ° ΡΠ΅Π»ΠΈΡΡΠΊΠΈ-ΡΠ΅Π½ΡΡΠΈΡΠ°Π½ΠΈΡ
Π³ΡΠ°Π΄ΠΈΡΠ΅Π½Π°ΡΠ°, ΡΠΏΡΠ΅-
Π·Π°ΡΠ΅ ΠΏΠΎΡΠ° ΠΏΡΠΈΡΠΈΡΠΊΠ° ΠΈ Π±ΡΠ·ΠΈΠ½Π΅ ΠΏΡΠ΅ΠΊΠΎ SIMPLE Π°Π»Π³ΠΎΡΠΈΡΠΌΠ° ΡΠ° Π²ΠΈΡΠ΅ΡΡΡΡΠΊΠΎΠΌ ΡΠ΅-
ΡΠ°Π²Π°ΡΠ΅ΠΌ ΡΠ΅Π΄Π½Π°ΡΠΈΠ½Π΅ Π·Π° ΠΊΠΎΡΠ΅ΠΊΡΠΈΡΡ ΠΏΡΠΈΡΠΈΡΠΊΠ° Ρ ΡΠ΅ΠΊΠ²Π΅Π½ΡΠΈ ΠΊΠΎΡΠ°ΠΊΠ° Π½Π΅ΠΎΡΡΠΎΠ³ΠΎΠ½Π°Π»-
Π½ΠΈΡ
ΠΊΠΎΡΠ΅ΠΊΡΠΈΡΠ°. ΠΠ΄ ΠΏΠΎΡΡΠΎΡΠ΅ΡΠΈΡ
ΠΊΠΎΠΌΠΏΠΎΠ½Π΅ΡΠ½ΠΈ Π°Π»Π³ΠΎΡΠΈΡΠΌΠ° Π±ΠΈΡΠ°Π½Π΅ ΡΡ ΠΎΠ½Π΅ ΠΊΠΎΡΠ΅ ΡΡ
ΠΏΠΎΠΊΠ°Π·Π°Π»Π΅ ΡΠΏΠΎΡΠΎΠ±Π½ΠΎΡΡ Π·Π° ΡΠ½Π°ΠΏΡΠ΅ΡΠ΅Π½ΠΈ ΡΡΠ΅ΡΠΌΠ°Π½ Π½Π΅ΠΎΡΡΠΎΠ³ΠΎΠ½Π°Π»Π½ΠΎΡΡΠΈ Π½Π° ΡΠ΅Π»ΠΈΡΡΠΊΠΎΠΌ
Π½ΠΈΠ²ΠΎΡ, ΡΠ½ΡΡΠ°Ρ ΠΏΡΠΎΡΠ°ΡΡΠ½ΡΠΊΠ΅ ΠΌΡΠ΅ΠΆΠ΅, Π° Π½Π° ΠΌΠ΅ΡΡΠΈΠΌΠ° Π½Π° ΠΊΠΎΡΠΈΠΌΠ° ΡΠ΅ ΡΠΌΠ°ΡΡΠ°Π½ΠΎ ΠΏΠΎ-
ΡΡΠ΅Π±Π½ΠΎ ΡΠ²Π΅Π΄Π΅Π½Π΅ ΡΡ ΠΎΡΠΈΠ³ΠΈΠ½Π°Π»Π½Π΅ ΡΠΎΡΠΌΡΠ»Π°ΡΠΈΡΠ΅ ΠΊΠ°ΠΊΠΎ Π±ΠΈ ΡΠ΅ ΡΠ°ΡΠ½ΠΎΡΡ ΠΏΡΠΎΡΠ°ΡΡΠ½Π°
ΠΈ Π½ΡΠΌΠ΅ΡΠΈΡΠΊΠ° Π΅ΡΠΈΠΊΠ°ΡΠ½ΠΎΡΡ ΡΠ½Π°ΠΏΡΠ΅Π΄ΠΈΠ»Π΅ Π·Π° Π΄Π°ΡΠΈ ΡΠΈΠΏ ΡΡΡΡΡΠ°ΡΠ° ΠΈ ΠΏΡΠ΅Π΄ΡΡΠ°Π²ΡΠ°ΡΡ
ΠΎΡΠΈΠ³ΠΈΠ½Π°Π»Π½ΠΈ Π½Π°ΡΡΠ½ΠΈ Π΄ΠΎΠΏΡΠΈΠ½ΠΎΡ ΠΎΠ²Π΅ Π΄ΠΈΡΠ΅ΡΡΠ°ΡΠΈΡΠ΅. ΠΠΎΡΠ΅Π±Π½ΠΎ ΡΡ ΠΎΠ±ΡΠ°ΡΠ΅Π½Π΅ ΡΠ»Π΅-
Π΄Π΅ΡΠ΅ ΡΠ΅ΠΌΠ΅: i) ΠΏΡΠΎΡΠ΅Π΄ΡΡΠ° ΡΠ΅ΠΊΠΎΠ½ΡΡΡΡΠΊΡΠΈΡΠ΅ ΡΠ΅Π»ΠΈΡΡΠΊΠΈ ΡΠ΅Π½ΡΠΈΡΠ°Π½ΠΈΡ
Π³ΡΠ°Π΄ΠΈΡΠ΅Π½Π°ΡΠ°,
ΡΠΊΡΡΡΡΡΡΡΠΈ ΠΈ ΡΡΠ΅ΡΠΌΠ°Π½ Π³ΡΠ°Π΄ΠΈΡΠ΅Π½Π°ΡΠ° ΠΏΡΠΈΡΠΈΡΠΊΠ°, ii) Π½ΠΎΠ²ΠΈ Π³Π΅Π½Π΅ΡΠ°Π»ΠΈΠ·ΠΈΠ²Π°Π½ΠΈ ΠΏΡΠΈ-
ΡΡΡΠΏ Π°ΠΏΡΠΎΠΊΡΠΈΠΌΠ°ΡΠΈΡΠΈ Π΄ΠΈΡΡΠ·ΠΈΠΎΠ½ΠΎΠ³ ΡΠ»Π°Π½Π°, ΠΏΡΠΈΠΌΠ΅ΡΠΈΠ²ΠΎΠ³ Ρ ΠΏΡΠΈΡΡΡΡΠ²Ρ ΠΈΠ·ΡΠ°ΠΆΠ΅-
Π½ΠΈΡ
Π΄Π΅ΡΠΎΡΠΌΠ°ΡΠΈΡΠ° ΠΏΡΠΎΡΠ°ΡΡΠ½ΡΠΊΠ΅ ΠΌΡΠ΅ΠΆΠ΅.
ΠΠΈΡΠ΅ Π½ΡΠΌΠ΅ΡΠΈΡΠΊΠΈΡ
Π΅ΠΊΡΠΏΠ΅ΡΠΈΠΌΠ΅Π½Π°ΡΠ° ΡΠ΅ ΠΏΡΠΈΠΊΠ°Π·Π°Π½ΠΎ Π΄Π° Π±ΠΈ ΡΠ΅ Π΄Π΅ΠΌΠΎΠ½ΡΡΡΠΈΡΠ°Π»Π°
ΠΏΡΠΎΡΠ°ΡΡΠ½ΡΠΊΠ° ΠΏΡΠ΅ΡΠΈΠ·Π½ΠΎΡΡ ΠΈ Π΅ΡΠΈΠΊΠ°ΡΠ½ΠΎΡΡ ΠΏΡΠ΅Π΄Π»ΠΎΠΆΠ΅Π½Π΅ ΠΌΠ΅ΡΠΎΠ΄Π΅. ΠΠ΅ΡΠΈΡΠΈΠΊΠ°ΡΠΈΡΠ°
Π½ΡΠΌΠ΅ΡΠΈΡΠΊΠΎΠ³ Π°Π»Π³ΠΎΡΠΈΡΠΌΠ° ΡΠ΅ ΠΈΠ·Π²ΡΡΠ΅Π½Π° Π½Π° ΠΏΡΠΈΠΌΠ΅ΡΠΈΠΌΠ° ΡΠ°Π·Π»ΠΈΡΠΈΡΠΎΠ³ Π½ΠΈΠ²ΠΎΠ° ΠΊΠΎΠΌ-
ΠΏΠ»Π΅ΠΊΡΠ½ΠΎΡΡΠΈ ΠΈ Π½Π°ΠΌΠ΅Π½Π΅. ΠΠΎΡΠΈΡΠ΅ ΡΠ΅ ΡΠ΅ΠΊΠΎΠ½ΡΡΡΡΠΊΡΠΈΡΠΎΠΌ ΡΠ΅Π΄Π½ΠΎΡΡΠ°Π²Π½ΠΈΡ
ΡΠΈΠ½ΡΠ΅ΡΠΈΡ-
ΠΊΠΈΡ
ΡΡΠ½ΠΊΡΠΈΡΠ°, ΠΎΡΠΌΠΈΡΡΠ΅Π½ΠΈΡ
Π΄Π° ΠΈΡΡΠ°ΠΊΠ½Ρ ΠΎΠ΄ΡΠ΅ΡΠ΅Π½Π΅ Π½Π΅Π΄ΠΎΡΡΠ°ΡΠΊΠ΅ ΠΏΠΎΡΡΠΎΡΠ΅ΡΠΈΡ
Π°Π»-
Π³ΠΎΡΠΈΡΠ°ΠΌΠ° Π·Π° ΡΡΡΡΡΠ°ΡΠ° Ρ ΠΈΠ·ΡΠ°Π·ΠΈΡΠΎ Π½Π΅ΠΎΡΡΠΎΠ³ΠΎΠ½Π°Π»Π½ΠΈΠΌ Π³Π΅ΠΎΠΌΠ΅ΡΡΠΈΡΠ°ΠΌΠ°. Π’Π΅ΡΡΠΎΠ²ΠΈ ΡΡ
ΡΠ°ΠΊΠΎΡΠ΅ ΠΈΠ·Π²ΡΡΠ΅Π½ΠΈ Π½Π° Π°Π½Π°Π»ΠΈΡΠΈΡΠΊΠΈΠΌ ΡΠ΅ΡΠ΅ΡΠΈΠΌΠ° ΠΠ°Π²ΠΈΡΠ΅-Π‘ΡΠΎΠΊΡΠΎΠ²ΠΈΡ
ΡΠ΅Π΄Π½Π°ΡΠΈΠ½Π°,
Π·Π°ΡΠΈΠΌ ΡΡ ΠΏΡΠΈΠΊΠ°Π·Π°Π½ΠΈ ΡΠ΅Π·ΡΠ»ΡΠ°ΡΠΈ ΠΏΠΎΡΠ΅ΡΠ΅ΡΠ° ΡΠ° Π΄ΡΡΠ³ΠΈΠΌ Π½ΡΠΌΠ΅ΡΠΈΡΠΊΠΈΠΌ ΡΠΈΠΌΡΠ»Π°ΡΠΈ-
ΡΠ°ΠΌΠ°, ΠΈΠ·Π²Π΅Π΄Π΅Π½ΠΈΡ
ΡΠ° ΡΠ»ΠΈΡΠ½ΠΈΠΌ Π°Π»Π³ΠΎΡΠΈΡΠΌΠΈΠΌΠ°, Π²ΡΡΠ΅Π½Π° ΡΡ ΠΏΠΎΡΠ΅ΡΠ΅ΡΠ° ΡΠ° ΡΠ΅Π·ΡΠ»ΡΠ°-
ΡΠΈΠΌΠ° ΠΈΡΠΏΠΈΡΠΈΠ²Π°ΡΠ° Ρ Π°Π΅ΡΠΎΡΡΠ½Π΅Π»ΠΈΠΌΠ°, ΠΈ Π½Π°ΠΏΠΎΠΊΠΎΠ½ Π²ΡΡΠ΅Π½Π° ΡΡ ΠΏΠΎΡΠ΅ΡΠ΅ΡΠ° ΡΠΈΠΌΡΠ»Π°-
ΡΠΈΡΠ° ΡΠ° ΠΌΠ΅ΡΠ΅ΡΠΈΠΌΠ° Π½Π°Π΄ ΡΠ΅Π°Π»Π½ΠΈΠΌ ΠΊΠΎΠΌΠΏΠ»Π΅ΠΊΡΠ½ΠΈΠΌ Π±ΡΠ΄ΠΎΠ²ΠΈΡΠΈΠΌ ΡΠ΅ΡΠ΅Π½ΠΈΠΌΠ° Ρ ΡΠ΅Π°Π»-
Π½ΠΎΠΌ, Π°ΡΠΌΠΎΡΡΠ΅ΡΡΠΊΠΎΠΌ ΠΎΠΊΡΡΠΆΠ΅ΡΡ.
ΠΡΠΌΠ΅ΡΠΈΡΠΊΠΈ Π΅ΠΊΡΠΏΠ΅ΡΠΈΠΌΠ΅Π½ΡΠΈ ΠΏΠΎΠΊΠ°Π·ΡΡΡ Π΄Π° ΡΡ ΠΏΠΎΡΡΠΈΠ³Π½ΡΡΠ° Π·Π½Π°ΡΠ°ΡΠ½Π° ΡΠ½Π°ΠΏΡΠ΅-
ΡΠ΅ΡΠ° ΡΠ° ΠΏΡΠ΅Π΄Π»ΠΎΠΆΠ΅Π½ΠΎΠΌ Π½ΡΠΌΠ΅ΡΠΈΡΠΊΠΎΠΌ ΠΏΡΠΎΡΠ΅Π΄ΡΡΠΎΠΌ, Ρ ΠΎΠ΄Π½ΠΎΡΡ Π½Π° ΠΊΠΎΠ½Π²Π΅Π½ΡΠΈΠΎΠ½Π°Π»Π½Π΅
Π½ΡΠΌΠ΅ΡΠΈΡΠΊΠ΅ ΠΏΡΠΎΡΠ΅Π΄ΡΡΠ΅. Π’Π΅ΡΡΠΎΠ²ΠΈ Π°ΠΏΡΠΎΠΊΡΠΈΠΌΠ°ΡΠΈΡΠ΅ ΡΠ΅Π»ΠΈΡΡΠΊΠΈ ΡΠ΅Π½ΡΡΠΈΡΠ°Π½ΠΈΡ
Π³ΡΠ°-
Π΄ΠΈΡΠ΅Π½Π°ΡΠ° ΠΊΠΎΡΠΈΡΡΠ΅ΡΠΈ ΡΠΈΠ½ΡΠ΅ΡΠΈΡΠΊΠ° ΡΠ΅ΡΠ΅ΡΠ° ΡΡ ΠΏΠΎΠΊΠ°Π·Π°Π»ΠΈ Π΄Π° ΡΠ΅ ΠΏΡΠ΅Π΄Π»ΠΎΠΆΠ΅Π½ΠΈ ΠΏΡΠΈ-
ΡΡΡΠΏ ΡΠΏΠΎΡΠΎΠ±Π°Π½ Π΄Π° ΠΎΡΡΠ²Π°ΡΠΈ ΠΏΠΎΠΊΠ»Π°ΠΏΠ°ΡΠ΅ Π½Π° Π½ΠΈΠ²ΠΎΡ ΡΠ°ΡΡΠ½Π°ΡΡΠΊΠ΅ ΠΏΡΠ΅ΡΠΈΠ·Π½ΠΎΡΡΠΈ, ΡΠ°ΠΊ
ΠΈ Π½Π° ΠΈΠ·ΡΠ·Π΅ΡΠ½ΠΎ Π΄Π΅ΡΠΎΡΠΌΠΈΡΠ°Π½ΠΈΠΌ ΠΌΡΠ΅ΠΆΠ°ΠΌΠ°. Π£ ΡΠ΅ΡΡΠΎΠ²ΠΈΠΌΠ° ΠΊΠΎΡΠΈ ΡΠΊΡΡΡΡΡΡ ΡΡΡΡ-
ΡΠ°ΡΠ° ΡΠ° Π°Π½Π°Π»ΠΈΡΠΈΡΠΊΠΈΠΌ ΡΠ΅ΡΠ΅ΡΠΈΠΌΠ°, ΠΌΠ΅ΡΠΎΠ΄ ΡΠ΅ ΠΏΠΎΠΊΠ°Π·Π°ΠΎ ΠΎΡΠ΅ΠΊΠΈΠ²Π°Π½ΠΈ Π΄ΡΡΠ³ΠΈ ΡΠ΅Π΄ ΡΠ°Ρ-
Π½ΠΎΡΡΠΈ Π½Π° ΡΠ½ΠΈΡΠΎΡΠΌΠ½ΠΈΠΌ ΠΏΡΠ°Π²ΠΎΠ»ΠΈΠ½ΠΈΡΡΠΊΠΈΠΌ ΠΌΡΠ΅ΠΆΠ°ΠΌΠ°. ΠΠ° Π΄Π΅ΡΠΎΡΠΌΠΈΡΠ°Π½ΠΈΠΌ ΠΌΡΠ΅-
ΠΆΠ°ΠΌΠ°, Π½ΠΎΠ²Π΅ ΡΠ΅ΠΌΠ΅ Π·Π° Π΄ΠΈΡΠΊΡΠ΅ΡΠΈΠ·Π°ΡΠΈΡΡ Π΄ΠΈΡΡΠ·ΠΈΡΠ΅ ΡΡ ΠΏΠΎΠΊΠ°Π·Π°Π»Π΅ Π·Π½Π°ΡΠ°ΡΠ½ΠΎ ΠΏΠΎΠ±ΠΎΡ-
ΡΠ°ΡΠ΅ ΠΊΠ°ΠΊΠΎ Ρ ΠΏΡΠ΅ΡΠΈΠ·Π½ΠΎΡΡΠΈ ΠΏΡΠΎΡΠ°ΡΡΠ½Π°, ΡΠ°ΠΊΠΎ ΠΈ Ρ Π±ΡΠ·ΠΈΠ½ΠΈ ΠΊΠΎΠ½Π²Π΅ΡΠ³Π΅Π½ΡΠΈΡΠ΅, Ρ ΠΏΠΎ-
ΡΠ΅ΡΠ΅ΡΡ ΡΠ° Π΄ΡΡΠ³ΠΈΠΌ ΠΏΡΠΈΡΡΡΠΏΠΈΠΌΠ° ΠΊΠΎΡΠΈ ΡΡ ΡΠ°ΠΊΠΎΡΠ΅ ΡΠΊΡΡΡΠΈΠ²Π°Π»ΠΈ ΠΊΠΎΡΠ΅ΠΊΡΠΈΡΠ΅ Π½Π΅ΠΎΡ-
ΡΠΎΠ³ΠΎΠ½Π°Π»Π½ΠΎΡΡΠΈ. Π Π΅Π·ΡΠ»ΡΠ°ΡΠΈ ΡΡ ΠΏΠΎΠΊΠ°Π·Π°Π»ΠΈ Π΄Π° Π½ΠΈΡΠ΅ Π΄ΠΎΠ²ΠΎΡΠ½ΠΎ ΡΠ·Π΅ΡΠΈ Ρ ΠΎΠ±Π·ΠΈΡ ΡΠ°ΠΌΠΎ
ΠΈΡΠΊΠΎΡΠ΅Π½ΠΎΡΡ ΠΏΡΠΎΡΠ°ΡΡΠ½ΡΠΊΠΈΡ
ΡΠ΅Π»ΠΈΡΠ° ΡΠ½ΡΡΠ°Ρ ΠΌΡΠ΅ΠΆΠ΅, Π²Π΅Ρ Π΄Π° ΡΠ΅ ΠΏΠΎΡΡΠ΅Π±Π½ΠΎ ΡΠ·Π΅ΡΠΈ Ρ
ΠΎΠ±Π·ΠΈΡ ΠΏΠΎΡΠ°ΠΌ ΠΎΡΠΊΠ»ΠΎΠ½Π° ΡΠ°ΡΠΊΠ΅ ΠΏΡΠ΅ΡΠ΅ΠΊΠ°, ΠΊΠΎΡΠΈ ΡΠ΅ Π΄Π΅ΡΠΈΠ½ΠΈΡΠ°Π½ Ρ ΠΎΠ²ΠΎΡ Π΄ΠΈΡΠ΅ΡΡΠ°ΡΠΈΡΠΈ,
ΡΠΊΠΎΠ»ΠΈΠΊΠΎ ΠΏΠΎΡΡΠΎΡΠΈ ΠΏΠΎΡΡΠ΅Π±Π° Π·Π° Π²Π΅ΡΠΎΠΌ ΠΏΡΠ΅ΡΠΈΠ·Π½ΠΎΡΡΡ ΠΏΡΠΎΡΠ°ΡΡΠ½Π°. ΠΠ΅Π΄Π½ΠΎ ΠΎΠ΄ Π½Π°Ρ-
Π·Π½Π°ΡΠ°ΡΠ½ΠΈΡΠΈΡ
Π΄ΠΎΡΡΠΈΠ³Π½ΡΡΠ° ΡΠ΅ Π²Π΅Π·Π°Π½ΠΎ Π·Π° ΠΌΠΎΠ³ΡΡΠ½ΠΎΡΡ Π΄Π° ΡΠ΅ ΡΠ°ΡΠ½ΠΎ ΠΏΡΠ΅Π΄ΡΡΠ°Π²ΠΈ ΠΏΠΎΡΠ΅
ΠΏΡΠΈΡΠΈΡΠΊΠ°, Ρ ΡΠ»ΡΡΠ°ΡΠ΅Π²ΠΈΠΌΠ° Π½Π°Π³Π»ΠΈΡ
Π΄Π΅ΡΠΎΡΠΌΠ°ΡΠΈΡΠ°, ΠΊΠ°ΠΊΠ²Π΅ ΡΠ΅ ΡΠ΅ΡΡΠΎ Π²ΠΈΡΠ°ΡΡ Π½Π° ΠΌΡΠ΅-
ΠΆΠ°ΠΌΠ° ΠΊΠΎΡΠ΅ ΠΏΡΠ΅Π΄ΡΡΠ°Π²ΡΠ°ΡΡ ΡΠ΅Π°Π»Π½Π΅ ΠΊΠΎΠΌΠΏΠ»Π΅ΠΊΡΠ½Π΅ ΡΠΎΠΏΠΎΠ³ΡΠ°ΡΠΈΡΠ΅.
Π Π΅Π·ΡΠ»ΡΠ°ΡΠΈ ΠΏΡΠΈΠΊΠ°Π·Π°Π½ΠΈ Ρ Π΄ΠΈΡΠ΅ΡΡΠ°ΡΠΈΡΠΈ ΡΡ ΠΎΠ΄ ΠΏΡΠ°ΠΊΡΠΈΡΠ½ΠΎΠ³ Π·Π½Π°ΡΠ°ΡΠ° Ρ ΡΠ»ΡΡΠ°ΡΡ
ΡΠΈΠΌΡΠ»Π°ΡΠΈΡΠ΅ Π²Π΅ΡΡΠ° Π½Π°Π΄ ΠΊΠΎΠΌΠΏΠ»Π΅ΠΊΡΠ½ΠΈΠΌ ΡΠΎΠΏΠΎΠ³ΡΠ°ΡΠΈΡΠ°ΠΌΠ° Ρ Π°ΡΠΌΠΎΡΡΠ΅ΡΡΠΊΠΎΠΌ ΠΎΠΊΡΡ-
ΠΆΠ΅ΡΡ, ΡΠ° ΠΏΠΎΡΠ΅Π±Π½ΠΎΠΌ ΠΏΡΠΈΠΌΠ΅Π½ΠΎΠΌ Ρ Π΅Π½Π΅ΡΠ³ΠΈΡΠΈ Π²Π΅ΡΡΠ°.This disertation presents a new and substantially improved finite volume procedure
for simulation of incompressible flows on non-orthogonal grids. Cellcentered
least-squares gradients are obtained in a robust and highly accurate way.
A new discretization of the diffusive terms is employed, which is based on extension
of the original cell-face gradient interpolation and is more suitable for complex
grid distortions. A flexible flux-limited interpolation of dependent variables
on distorted computational grids is introduced. An efficient preconditioner
for Krylov method solution of linear systems is proposed, which substantially
improves the solution of Poisson equation for pressure correction. The pressurecorrection
algorithm is adapted for efficient convergence on highly complex grids
using a sequence of non-orthogonal corrector solutions and its effect on iteration
convergence is analyzed. The non-orthogonalities treated by current procedure
are more accustomed to numerical grids generated from a real complex terrain
elevation data. The main focus is on the simulation of atmospheric micro-scale
flows pertinent to wind energy application
Are subjective distributions in inflation expectations symmetric?
We conducted an anonymous survey in December 2013 asking around 200 economists worldwide to provide an interval (a to b) of average inflation in the US expected "over the next two years". The respondents were also instructed to give a probability of inflation being higher or lower than the mid-interval (a+b)/2. The aggregate distribution of inflation expectations we obtain closely resembles the outcome of the Survey of Professional Forecasters for 1Q2014. More importantly, we find that the subjective probability mass on either side of the mid-interval is not statistically different from 0.5, which means that the subjective distributions are symmetric. Our results align well with several papers evaluating the Survey of Professional Forecasters or similar data sets and finding no significant departures from symmetry
Solving fractional differential equations using fixed point results in generalized metric spaces of Perovβs type
In 1964, A. I. Perov generalized the Banach contraction principle introducing, following the work of Β―D. Kurepa, a new approach to fixed point problems, by defining generalized metric spaces (also known as vector valued metric spaces), and providing some actual results for the first time. Using the recent approach of coordinate representation for a generalized metric of Jachymski and Klima, we verify in this article some natural properties of generalized metric spaces, already owned by standard metric spaces. Among other results, we show that the theorems of Nemytckii (1936) and Edelstein (1962) are valid in generalized metric spaces, as well. A new application to fractional differential equations is also presented. At the end we state a few open questions for young researchers.Publisher's Versio
Some significant remarks on multivalued Perov type contractions on cone metric spaces with a directed graph
Using the approach of so-called c-sequences introduced by the fifth author in his recent work, we give much simpler and shorter proofs of multivalued Perov's type results with respect to the ones presented in the recently published paper by M. Abbas et al. Our proofs improve, complement, unify and enrich the ones from the recent papers. Further, in the last section of this paper, we correct and generalize the well-known Perov's fixed point result. We show that this result is in fact equivalent to Banach's contraction principle
Some significant remarks on multivalued Perov type contractions on cone metric spaces with a directed graph
Using the approach of so-called c-sequences introduced by the fifth author in his recent work, we give much simpler and shorter proofs of multivalued Perov's type results with respect to the ones presented in the recently published paper by M. Abbas et al. Our proofs improve, complement, unify and enrich the ones from the recent papers. Further, in the last section of this paper, we correct and generalize the well-known Perov's fixed point result. We show that this result is in fact equivalent to Banach's contraction principle
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