All Solutions of Nonlinear Constrained Systems of Equations

2000 ◽  
pp. 641-666
Author(s):  
Christodoulos A. Floudas
Keyword(s):  
Constrained Systems ◽  
Systems Of Equations ◽  
All Solutions

Finding all solutions of nonlinearly constrained systems of equations

1995 ◽  
Vol 7 (2) ◽  
pp. 143-182 ◽  
Author(s):  
Costas D. Maranas ◽  
Christodoulos A. Floudas
Keyword(s):  
Constrained Systems ◽  
Systems Of Equations ◽  
All Solutions

Finding all solutions to polynomial systems and other systems of equations

1979 ◽  
Vol 16 (1) ◽  
pp. 159-176 ◽  
Author(s):  
C. B. Garcia ◽  
W. I. Zangwill
Keyword(s):  
Polynomial Systems ◽  
Systems Of Equations ◽  
All Solutions

Exogeneous factors are not necessary in attachment, spreading and polarization of hela cells

1978 ◽  
Vol 36 (2) ◽  
pp. 310-311
Author(s):  
W. Liebrich
Keyword(s):  
Hela Cells ◽  
Calf Serum ◽  
Glass Tube ◽  
Serum Free Medium ◽  
Nacl Solution ◽  
Free Medium ◽  
Minimum Essential Medium ◽  
Serum Free ◽  
All Solutions ◽  
Glass Support

HeLa cells were grown for 2-3 days in EAGLE'S minimum essential medium with 10% calf serum (S-MEM; Seromed, München) and then incubated for 24 hours in serum free medium (MEM). After detaching the cells with a solution of 0. 14 % EDTA and 0. 07 % trypsin (Difco, 1 : 250) they were suspended in various solutions (S-MEM = control, MEM, buffered salt solutions with or without Me++ions, 0. 9 % NaCl solution) and allowed to settle on glass tube slips (Leighton-tubes). After 5, 10, 15, 20, 25, 30, 1 45, 60 minutes 2, 3, 4, 5 hours cells were prepared for scanning electron microscopy as described by Paweletz and Schroeter. The preparations were examined in a Jeol SEM (JSM-U3) at 25 KV without tilting.The suspended spherical HeLa cells are able to adhere to the glass support in all solutions. The rate of attachment, however, is faster in solutions without serum than in the control. The latter is in agreement with the findings of other authors.

scholarly journals Universal Entanglement of Typical States in Constrained Systems

2020 ◽  
Vol 124 (5) ◽  
Author(s):  
S. C. Morampudi ◽  
A. Chandran ◽  
C. R. Laumann
Keyword(s):  
Constrained Systems

scholarly journals Oscillatory behavior of nonlinear Hilfer fractional difference equations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Tuğba Yalçın Uzun
Keyword(s):  
Difference Equations ◽  
Sufficient Conditions ◽  
Higher Order ◽  
Oscillatory Behavior ◽  
Fractional Difference ◽  
Fractional Difference Equations ◽  
All Solutions ◽  
Alpha Beta

AbstractIn this paper, we study the oscillation behavior for higher order nonlinear Hilfer fractional difference equations of the type $$\begin{aligned}& \Delta _{a}^{\alpha ,\beta }y(x)+f_{1} \bigl(x,y(x+\alpha ) \bigr) =\omega (x)+f_{2} \bigl(x,y(x+ \alpha ) \bigr),\quad x\in \mathbb{N}_{a+n-\alpha }, \\& \Delta _{a}^{k-(n-\gamma )}y(x) \big|_{x=a+n-\gamma } = y_{k}, \quad k= 0,1,\ldots,n, \end{aligned}$$ Δ a α , β y ( x ) + f 1 ( x , y ( x + α ) ) = ω ( x ) + f 2 ( x , y ( x + α ) ) , x ∈ N a + n − α , Δ a k − ( n − γ ) y ( x ) | x = a + n − γ = y k , k = 0 , 1 , … , n , where $\lceil \alpha \rceil =n$ ⌈ α ⌉ = n , $n\in \mathbb{N}_{0}$ n ∈ N 0 and $0\leq \beta \leq 1$ 0 ≤ β ≤ 1 . We introduce some sufficient conditions for all solutions and give an illustrative example for our results.

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