scholarly journals Uncountable dense categoricity in cats

2005 ◽  
Vol 70 (3) ◽  
pp. 829-860 ◽  
Author(s):  
Itay Ben-Yaacov
Keyword(s):  
Density Character ◽  
Complete Model ◽  
Abstract Theory

AbstractWe prove that under reasonable assumptions, every cat (compact abstract theory) is metric, and develop some of the theory of metric cats. We generalise Morley's theorem: if a countable Hausdorff cat T has a unique complete model of density character λ ≥ ω, then it has a unique complete model of density character λ for every λ ≥ ω.

scholarly journals Verification and Strategy Synthesis for Coalition Announcement Logic

2021 ◽  
Author(s):  
Natasha Alechina ◽  
Hans van Ditmarsch ◽  
Rustam Galimullin ◽  
Tuo Wang
Keyword(s):  
Model Checking ◽  
Proof Of Concept ◽  
Model Checker ◽  
Complete Model ◽  
Concept Model ◽  
The Family ◽  
Winning Strategies ◽  
Epistemic Goals

AbstractCoalition announcement logic (CAL) is one of the family of the logics of quantified announcements. It allows us to reason about what a coalition of agents can achieve by making announcements in the setting where the anti-coalition may have an announcement of their own to preclude the former from reaching its epistemic goals. In this paper, we describe a PSPACE-complete model checking algorithm for CAL that produces winning strategies for coalitions. The algorithm is implemented in a proof-of-concept model checker.

scholarly journals Orbital Stability of Solitary Waves to Double Dispersion Equations with Combined Power-Type Nonlinearity

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1398
Author(s):  
Natalia Kolkovska ◽  
Milena Dimova ◽  
Nikolai Kutev
Keyword(s):  
Solitary Waves ◽  
Orbital Stability ◽  
Second Derivative ◽  
Cubic Nonlinearity ◽  
Abstract Theory ◽  
Power Type ◽  
Analytical Formulas ◽  
Stability Of Solitary Waves ◽  
The Stability ◽  
Double Dispersion

We consider the orbital stability of solitary waves to the double dispersion equation utt−uxx+h1uxxxx−h2uttxx+f(u)xx=0,h1>0,h2>0 with combined power-type nonlinearity f(u)=a|u|pu+b|u|2pu,p>0,a∈R,b∈R,b≠0. The stability of solitary waves with velocity c, c2<1 is proved by means of the Grillakis, Shatah, and Strauss abstract theory and the convexity of the function d(c), related to some conservation laws. We derive explicit analytical formulas for the function d(c) and its second derivative for quadratic-cubic nonlinearity f(u)=au2+bu3 and parameters b>0, c2∈0,min1,h1h2. As a consequence, the orbital stability of solitary waves is analyzed depending on the parameters of the problem. Well-known results are generalized in the case of a single cubic nonlinearity f(u)=bu3.

scholarly journals Analytic semigroups generated by Dirichlet-to-Neumann operators on manifolds

2021 ◽  
Author(s):  
Tim Binz
Keyword(s):  
Boundary Conditions ◽  
Elliptic Operator ◽  
Compact Manifold ◽  
Analytic Semigroup ◽  
Continuous Functions ◽  
Analytic Semigroups ◽  
Abstract Theory ◽  
Neumann Operator ◽  
Wentzell Boundary Conditions ◽  
Dirichlet To Neumann Operator

AbstractWe consider the Dirichlet-to-Neumann operator associated to a strictly elliptic operator on the space $$\mathrm {C}(\partial M)$$ C ( ∂ M ) of continuous functions on the boundary $$\partial M$$ ∂ M of a compact manifold $$\overline{M}$$ M ¯ with boundary. We prove that it generates an analytic semigroup of angle $$\frac{\pi }{2}$$ π 2 , generalizing and improving a result of Escher with a new proof. Combined with the abstract theory of operators with Wentzell boundary conditions developed by Engel and the author, this yields that the corresponding strictly elliptic operator with Wentzell boundary conditions generates a compact and analytic semigroups of angle $$\frac{\pi }{2}$$ π 2 on the space $$\mathrm {C}(\overline{M})$$ C ( M ¯ ) .

ChemInform Abstract: Theory of Vibrational Circular Dichroism: trans-2,3-Dideuteriooxirane

ChemInform ◽  
1988 ◽  
Vol 19 (28) ◽  
Author(s):  
K. J. JALKANEN ◽  
P. J. STEPHENS ◽  
R. D. AMOS ◽  
N. C. HANDY
Keyword(s):  
Circular Dichroism ◽  
Vibrational Circular Dichroism ◽  
Abstract Theory ◽  
Circular Dichroïsm

On flexible link manipulators: modeling and analysis using the algebra of rotations

Robotica ◽  
1994 ◽  
Vol 12 (4) ◽  
pp. 371-382 ◽  
Author(s):  
F. Xi ◽  
R.G. Fenton
Keyword(s):  
Nonlinear Coupling ◽  
Flexible Link ◽  
Complete Model ◽  
Modeling And Analysis ◽  
Displacement Equation

SUMMARYIn this paper, a complete model of the elasto-kinematics is formulated in terms of a new kinematic notation, called the algebra of rotations. Based on this formulation, the elegant and concise expressions are derived for the displacement equation and especially the Jacobians governing the motion mapping between the manipulator tip and joint variables as well as link deflections. Introduction of the elasto-kinematics into the elasto-dynamics can directly take into consideration the nonlinear coupling between joint variables and link deflections, and thus improve the result of the elasto-dynamics.

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