scholarly journals On the Existence of Ground States for a Nonlinear Klein-Gordon-Maxwell Type System

2018 ◽  
Vol 61 (1) ◽  
pp. 1-14 ◽  
Author(s):  
Mathieu Colin ◽  
Tatsuya Watanabe
Keyword(s):  
Type System ◽  
Ground States ◽  
Klein Gordon

scholarly journals Finite dimensionality of a Klein-Gordon-Schrödinger type system

2009 ◽  
Vol 2 (1) ◽  
pp. 149-161
Author(s):  
Marilena N. Poulou ◽  
◽  
Nikolaos M. Stavrakakis ◽  
Keyword(s):  
Type System ◽  
Finite Dimensionality ◽  
Klein Gordon

scholarly journals Positive ground states for nonlinearly coupled Choquard type equations with lower critical exponents

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Huiling Wu
Keyword(s):  
Critical Exponents ◽  
Ground State ◽  
Type System ◽  
Ground States

AbstractWe study the coupled Choquard type system with lower critical exponents $$ \textstyle\begin{cases} -\Delta u+\lambda _{1}(x)u=\mu _{1}(I_{\alpha }* \vert u \vert ^{ \frac{N+\alpha }{N}}) \vert u \vert ^{\frac{\alpha }{N}-1}u+\beta (I_{\alpha }* \vert v \vert ^{ \frac{N+\alpha }{N}}) \vert u \vert ^{\frac{\alpha }{N}-1}u,\quad x\in {\mathbb{R}}^{N}, \\ -\Delta v+\lambda _{2}(x)v=\mu _{2}(I_{\alpha }* \vert v \vert ^{ \frac{N+\alpha }{N}}) \vert v \vert ^{\frac{\alpha }{N}-1}v+\beta (I_{\alpha }* \vert u \vert ^{ \frac{N+\alpha }{N}}) \vert v \vert ^{\frac{\alpha }{N}-1}v,\quad x\in {\mathbb{R}}^{N}, \\ u, v\in H^{1}({\mathbb{R}}^{N}), \end{cases} $$ { − Δ u + λ 1 ( x ) u = μ 1 ( I α ∗ | u | N + α N ) | u | α N − 1 u + β ( I α ∗ | v | N + α N ) | u | α N − 1 u , x ∈ R N , − Δ v + λ 2 ( x ) v = μ 2 ( I α ∗ | v | N + α N ) | v | α N − 1 v + β ( I α ∗ | u | N + α N ) | v | α N − 1 v , x ∈ R N , u , v ∈ H 1 ( R N ) , where $N\ge 3$ N ≥ 3 , $\mu _{1}, \mu _{2}, \beta >0$ μ 1 , μ 2 , β > 0 , and $\lambda _{1}(x)$ λ 1 ( x ) , $\lambda _{2}(x)$ λ 2 ( x ) are nonnegative functions. The existence of at least one positive ground state of this system is proved under certain assumptions on $\lambda _{1}$ λ 1 , $\lambda _{2}$ λ 2 .

scholarly journals Vortex ground states for Klein-Gordon-Maxwell-Proca type systems

2017 ◽  
Vol 58 (4) ◽  
pp. 041503 ◽  
Author(s):  
Pietro d’Avenia ◽  
Jarosław Mederski ◽  
Alessio Pomponio
Keyword(s):  
Ground States ◽  
Type Systems ◽  
Klein Gordon

Ultrastructural characteristics of sporidia of Ustilago

1989 ◽  
Vol 47 ◽  
pp. 786-787
Author(s):  
Patricia N. Hackney
Keyword(s):  
Electron Microscope ◽  
Type System ◽  
Tube Formation ◽  
High Voltage Electron Microscopy ◽  
Voltage Electron ◽  
University Of Wisconsin ◽  
Transmission Electron ◽  
Ustilago Hordei ◽  
Silene Alba ◽  
The University

Ustilago hordei and Ustilago violacea are yeast-like basidiomycete pathogens ofHordeum vulgare and Silene alba respectively. The mating type system in both species of Ustilago is bipolar, with alleles, A,a, (U.hordei) and a1, a2 (U.violacea) at a single locus. Haploid sporidia maintain the asexual phase by budding, while the sexual phase is initiated by conjugation tube formation between the mating types during budding and conjugation.For observation of budding, sporidia were prepared by culturing the four types on YEG (yeast extract glucose) broth for 24 hours. After centrifugation at 5000g cells were either left unmated or mated in a1/a2,A/a combinations. The sporidia were then mixed 1:1 with 4% agar and the resulting 1mm cubes fixed in 8% gluteraldehyde and post fixed in osmium tetroxide. After dehydration and embedding cubes were thin sectioned with a LKB ultratome and photographed in a Zeiss 9s transmission electron microscope or in an AE1 electron microscope of MK11 1MEV at the High Voltage Electron Microscopy Center of the University of Wisconsin-Madison.

Thermal comfort conditions in a classroom conditioned by a split-type system

2017 ◽  
Author(s):  
Rogério Vilain ◽  
Marcelo Pereira ◽  
Nathan Mendes ◽  
katia cordeiro ◽  
anastacio da silva junior
Keyword(s):  
Thermal Comfort ◽  
Type System

Ground states for the ising model with an external field on the Cayley tree

2018 ◽  
Vol 2018 (3) ◽  
pp. 147-155
Author(s):  
M.M. Rakhmatullaev ◽  
M.A. Rasulova
Keyword(s):  
Ising Model ◽  
External Field ◽  
Cayley Tree ◽  
Ground States
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