scholarly journals Convergence of the normalized solution of the Maurer-Cartan equation in the Barannikov-Kontsevich construction

2002 ◽  
Vol 54 (2) ◽  
pp. 309-328 ◽  
Author(s):  
Yuya ITAGAKI
Keyword(s):  
Normalized Solution

Complementary Method for Deriving Concentration of Diffusing Substance in a Medium for Multi-Dimensional Diffusion

2013 ◽  
Vol 30 (1) ◽  
pp. 29-38
Author(s):  
C.-L. Tsai ◽  
C.-C. Lin ◽  
H.-J. Lee ◽  
C.-H. Wang
Keyword(s):  
Boundary Conditions ◽  
Infinite Medium ◽  
Dimensional Case ◽  
Complementary Method ◽  
Dimensional Diffusion ◽  
Coordinate Direction ◽  
Normalized Solution

ABSTRACTConcentration of a diffusing substance in a medium was derived in various cases of uni-dimensional diffusion, including in a semi-infinite medium and a plate-shaped medium. Multi-dimensional diffusion involves boundary conditions in each coordinate direction. The algorithm dealing with uni-dimensional case becomes very complicated in multi-dimensional cases. This study proposes an algorithm, which is called the complementary method, that combines complementary functions of the normalized solution in uni-dimensional diffusion case by multiplication to solve those in various multi-dimensional diffusion cases with dramatically simplified mathematics. Besides, the complementary method is used to solve various kinds of boundary conditions for multi-dimensional diffusion.

Cavitation Bubble Collapse in Viscous, Compressible Liquids—Numerical Analysis

1965 ◽  
Vol 87 (4) ◽  
pp. 977-985 ◽  
Author(s):  
R. D. Ivany ◽  
F. G. Hammitt
Keyword(s):  
Surface Tension ◽  
High Pressures ◽  
Numerical Solutions ◽  
Compressible Liquid ◽  
Navier Stokes ◽  
Bubble Collapse ◽  
Navier Stokes Equation ◽  
Scaling Parameters ◽  
Collapse Behavior ◽  
Normalized Solution

Collapse of a spherical bubble in a compressible liquid, including the effects of surface tension, viscosity, and an adiabatic compression of gas within the bubble is investigated by numerical solutions of the hydrodynamic equations. A limiting value of shear viscosity causes the bubble collapse to slow down markedly, for both compressible and incompressible liquids, whereas moderate viscosities have very little effect on the rate of collapse. The inclusion of surface tension and viscosity introduces two scaling parameters into the solution, so that a single normalized solution is no longer sufficient to describe collapse behavior. The magnitude of the density changes calculated for the compressible liquid and the extremely rapid changes with time suggest that the usual Navier-Stokes equation of motion may not be appropriate. The possibility of liquid relaxational phenomenon and its contribution to sonoluminescence is considered. Shock waves or damagingly high pressures are not generated during collapse at a distance in the liquid equal to the initial radius from the center of collapse, although they will appear at such a distance if the bubble rebounds.

scholarly journals Complex Monge–Ampère equations on quasi-projective varieties

2017 ◽  
Vol 2017 (727) ◽  
Author(s):  
Eleonora Di Nezza ◽  
Chinh H. Lu
Keyword(s):  
Closed Subset ◽  
Projective Varieties ◽  
Right Hand ◽  
Normalized Solution ◽  
Monge Ampere

AbstractWe introduce generalized Monge–Ampère capacities and use these to study complex Monge–Ampère equations whose right-hand side is smooth outside a divisor. We prove, in many cases, that there exists a unique normalized solution which is smooth outside the divisor. Our results still hold if the divisor is replaced by any closed subset.

Locally finite groups and configurations

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Mahdi Meisami ◽  
Ali Rejali ◽  
Meisam Soleimani Malekan ◽  
Akram Yousofzadeh
Keyword(s):  
Finite Group ◽  
Positive Solution ◽  
Finite Groups ◽  
Discrete Group ◽  
Locally Finite Group ◽  
Finitely Generated ◽  
Locally Finite ◽  
Locally Finite Groups ◽  
Normalized Solution

Abstract Let 𝐺 be a discrete group. In 2001, Rosenblatt and Willis proved that 𝐺 is amenable if and only if every possible system of configuration equations admits a normalized solution. In this paper, we show independently that 𝐺 is locally finite if and only if every possible system of configuration equations admits a strictly positive solution. Also, we give a procedure to get equidecomposable subsets 𝐴 and 𝐵 of an infinite finitely generated or a locally finite group 𝐺 such that A ⊊ B A\subsetneq B , directly from a system of configuration equations not having a strictly positive solution.

scholarly journals Automated Normalized Solution for Finding Duplicate Records from Multiple Data Sources

2020 ◽  
Vol 9 (1) ◽  
pp. 834-837
Keyword(s):  
Information Fusion ◽  
Record Linkage ◽  
Information Reconciliation ◽  
Front End ◽  
Multiple Data ◽  
Other Information ◽  
Testing Issue ◽  
Normalized Solution ◽  
Standardization Methods ◽  
Paper Author

Information merging may be a testing issue clinched alongside information reconciliation. The convenience of information builds when it is joined Also combined for other information from various (Web) wellsprings. The guarantee from claiming enormous information hinges upon tending to a few enormous information coordination challenges, for example, such that record linkage toward scale, ongoing information fusion, What's more coordinating profound Web. In spite of significantly fill in need been directed with respect to these problems, there may be constrained worth of effort on making An uniform, standard record from an assembly for records relating of the similar genuine world substance. Author allude with this errand as document standardization. Such a record illustration, ‘coined normalized record, may be essential for both front end and back end provisions’. In this paper, author formalize those record standardization problem, available in-depth dissection from claiming standardization granularity levels Also for standardization types. We recommend a thorough structure to registering the normalized record. Those suggested schema incorporates a suit of shield from claiming record standardization methods, from credulous ones, which utilize best the data assembled starting with records themselves, to complex strategies, which comprehensively mine an assembly about copy records when selecting a quality for a trait of a normalized record.

scholarly journals Normalized solutions of supercritical nonlinear fractional Schrödinger equation with potential

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Songbai Peng ◽  
Aliang Xia
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Fractional Schrödinger Equation ◽  
Lack Of Compactness ◽  
Normalized Solutions ◽  
Nonlinear Fractional Schrödinger Equation ◽  
Normalized Solution ◽  
Physical Reasons ◽  
Fractional Schrodinger Equation

<p style='text-indent:20px;'>We are concerned with the following nonlinear fractional Schrödinger equation:</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$\begin{equation} (-\Delta)^s u+V(x)u+\omega u = |u|^{p-2}u\quad {\rm{in}}\,\,{\mathbb{R}}^N,\;\;\;\;\;\;({\textbf{P}})\end{equation}$ \end{document} </tex-math></disp-formula></p><p style='text-indent:20px;'>where <inline-formula><tex-math id="M1">\begin{document}$ s\in(0,1) $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M2">\begin{document}$ p\in\left(2+4s/N,2^*_s\right) $\end{document}</tex-math></inline-formula>, that is, the mass supercritical and Sobolev subcritical. Under certain assumptions on the potential <inline-formula><tex-math id="M3">\begin{document}$ V:{\mathbb{R}}^N\rightarrow {\mathbb{R}} $\end{document}</tex-math></inline-formula>, positive and vanishing at infinity including potentials with singularities (which is important for physical reasons), we prove that there exists at least one <inline-formula><tex-math id="M4">\begin{document}$ L^2 $\end{document}</tex-math></inline-formula>-normalized solution <inline-formula><tex-math id="M5">\begin{document}$ (u,\omega)\in H^s({\mathbb{R}}^N)\times{\mathbb{R}}^+ $\end{document}</tex-math></inline-formula> of equation (P). In order to overcome the lack of compactness, the proof is based on a new min-max argument and splitting lemma for nonlocal version.</p>

scholarly journals Normalized solutions for a coupled fractional Schrödinger system in low dimensions

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Meng Li ◽  
Jinchun He ◽  
Haoyuan Xu ◽  
Meihua Yang
Keyword(s):  
Coupling Parameter ◽  
Low Dimensions ◽  
Normalized Solutions ◽  
Normalized Solution ◽  
Schrödinger System

Abstract We consider the following coupled fractional Schrödinger system: $$ \textstyle\begin{cases} (-\Delta )^{s}u+\lambda _{1}u=\mu _{1} \vert u \vert ^{2p-2}u+ \beta \vert v \vert ^{p} \vert u \vert ^{p-2}u, \\ (-\Delta )^{s}v+\lambda _{2}v=\mu _{2} \vert v \vert ^{2p-2}v+\beta \vert u \vert ^{p} \vert v \vert ^{p-2}v \end{cases}\displaystyle \quad \text{in } {\mathbb{R}^{N}}, $$ { ( − Δ ) s u + λ 1 u = μ 1 | u | 2 p − 2 u + β | v | p | u | p − 2 u , ( − Δ ) s v + λ 2 v = μ 2 | v | 2 p − 2 v + β | u | p | v | p − 2 v in  R N , with $0< s<1$ 0 < s < 1 , $2s< N\le 4s$ 2 s < N ≤ 4 s and $1+\frac{2s}{N}< p<\frac{N}{N-2s}$ 1 + 2 s N < p < N N − 2 s , under the following constraint: $$ \int _{\mathbb{R}^{N}} \vert u \vert ^{2}\,dx=a_{1}^{2} \quad \text{and}\quad \int _{ \mathbb{R}^{N}} \vert v \vert ^{2}\,dx=a_{2}^{2}. $$ ∫ R N | u | 2 d x = a 1 2 and ∫ R N | v | 2 d x = a 2 2 . Assuming that the parameters $\mu _{1}$ μ 1 , $\mu _{2}$ μ 2 , $a_{1}$ a 1 , $a_{2}$ a 2 are fixed quantities, we prove the existence of normalized solution for different ranges of the coupling parameter $\beta >0$ β > 0 .

A new observation for the normalized solution of the Schrödinger equation

2020 ◽  
Vol 115 (3) ◽  
pp. 329-338
Author(s):  
Zuo Yang
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Normalized Solution

Fault Detection and Exclusion Using Normalized Solution Separation and Residual Monitoring Methods

Navigation ◽  
2003 ◽  
Vol 50 (3) ◽  
pp. 151-169 ◽  
Author(s):  
RYAN S. Y. YOUNG ◽  
GARY A. MCGRAW
Keyword(s):  
Fault Detection ◽  
Monitoring Methods ◽  
Normalized Solution
Sign in / Sign up

Export Citation Format

Share Document