On the homotopy invariance of the boundedly controlled signature of a manifold over an open cone

1995 ◽  
pp. 285-300 ◽  
Author(s):  
Erik K. Pedersen ◽  
John Roe ◽  
Shmuel Weinberger
Keyword(s):  
Homotopy Invariance ◽  
Open Cone

scholarly journals Existence Theorems on Solvability of Constrained Inclusion Problems and Applications

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Teffera M. Asfaw
Keyword(s):  
Reflexive Banach Space ◽  
Existence Theorems ◽  
Maximal Monotone ◽  
Existence Of Solution ◽  
Existence Results ◽  
Uniformly Convex ◽  
Homotopy Invariance ◽  
Inclusion Problems ◽  
Compact Resolvents ◽  
Nonlinear Variational Inequality

LetXbe a real locally uniformly convex reflexive Banach space with locally uniformly convex dual spaceX⁎. LetT:X⊇D(T)→2X⁎be a maximal monotone operator andC:X⊇D(C)→X⁎be bounded and continuous withD(T)⊆D(C). The paper provides new existence theorems concerning solvability of inclusion problems involving operators of the typeT+Cprovided thatCis compact orTis of compact resolvents under weak boundary condition. The Nagumo degree mapping and homotopy invariance results are employed. The paper presents existence results under the weakest coercivity condition onT+C. The operatorCis neither required to be defined everywhere nor required to be pseudomonotone type. The results are applied to prove existence of solution for nonlinear variational inequality problems.

scholarly journals Homotopy invariance of the Conley index and local Morse homology in Hilbert spaces

2017 ◽  
Vol 263 (11) ◽  
pp. 7162-7186 ◽  
Author(s):  
Marek Izydorek ◽  
Thomas O. Rot ◽  
Maciej Starostka ◽  
Marcin Styborski ◽  
Robert C.A.M. Vandervorst
Keyword(s):  
Hilbert Spaces ◽  
Conley Index ◽  
Homotopy Invariance ◽  
Morse Homology

scholarly journals The strong Suslin reciprocity law

2021 ◽  
Vol 157 (4) ◽  
pp. 649-676
Author(s):  
Daniil Rudenko
Keyword(s):  
Rational Functions ◽  
Projective Curve ◽  
Main Ingredient ◽  
Homotopy Invariance ◽  
Reciprocity Law ◽  
Hyperbolic Volume ◽  
Scissors Congruence ◽  
Dehn Invariant ◽  
Contracting Homotopy ◽  
Invariance Theorem

We prove the strong Suslin reciprocity law conjectured by A. Goncharov. The Suslin reciprocity law is a generalization of the Weil reciprocity law to higher Milnor $K$ -theory. The Milnor $K$ -groups can be identified with the top cohomology groups of the polylogarithmic motivic complexes; Goncharov's conjecture predicts the existence of a contracting homotopy underlying Suslin reciprocity. The main ingredient of the proof is a homotopy invariance theorem for the cohomology of the polylogarithmic motivic complexes in the ‘next to Milnor’ degree. We apply these results to the theory of scissors congruences of hyperbolic polytopes. For every triple of rational functions on a compact projective curve over $\mathbb {C}$ we construct a hyperbolic polytope (defined up to scissors congruence). The hyperbolic volume and the Dehn invariant of this polytope can be computed directly from the triple of rational functions on the curve.

scholarly journals Stability and Hopf-Bifurcation Analysis of Delayed BAM Neural Network under Dynamic Thresholds

2009 ◽  
Vol 14 (4) ◽  
pp. 435-461 ◽  
Author(s):  
P. D. Gupta ◽  
N. C. Majee ◽  
A. B. Roy
Keyword(s):  
Hopf Bifurcation ◽  
Periodic Solutions ◽  
Global Bifurcation ◽  
Distributed Delay ◽  
Degree Theory ◽  
Homotopy Invariance ◽  
Normal Form Theory ◽  
Form Theory ◽  
Bam Neural Network ◽  
Uniqueness Of Equilibrium

In this paper the dynamics of a three neuron model with self-connection and distributed delay under dynamical threshold is investigated. With the help of topological degree theory and Homotopy invariance principle existence and uniqueness of equilibrium point are established. The conditions for which the Hopf-bifurcation occurs at the equilibrium are obtained for the weak kernel of the distributed delay. The direction and stability of the bifurcating periodic solutions are determined by the normal form theory and central manifold theorem. Lastly global bifurcation aspect of such periodic solutions is studied. Some numerical simulations for justifying the theoretical analysis are also presented.

scholarly journals The homotopy invariance of the Kuranishi space

1990 ◽  
Vol 34 (2) ◽  
pp. 337-367 ◽  
Author(s):  
William M. Goldman ◽  
John J. Millson
Keyword(s):  
Homotopy Invariance

scholarly journals The Catalytic Activities of Carbocyclic Fused Pyridineimine Nickel Complexes Analogues in Ethylene Polymerization by Modeling Study

Catalysts ◽  
2019 ◽  
Vol 9 (6) ◽  
pp. 520 ◽  
Author(s):  
Arfa Abrar Malik ◽  
Wenhong Yang ◽  
Zhifeng Ma ◽  
Wen-Hua Sun
Keyword(s):  
Energy Gap ◽  
Linear Regression Analysis ◽  
Cone Angle ◽  
Energy Difference ◽  
Multiple Linear Regression Analysis ◽  
Hammett Constant ◽  
Net Charge ◽  
Open Cone ◽  
Catalytic Activities ◽  
Bite Angle

In this work, two carbocyclic fused pyridineimine nickel analogue systems (Ni1 and Ni2) with different fused member rings were investigated to reveal the relationship between catalyst structure and reaction activity. Multiple linear regression analysis was performed by means of five electronic descriptors and two steric descriptors, including the Hammett constant (F), effective net charge (Qeff), energy difference (ΔE), HOMO–LUMO energy gap (Δε1, Δε2), open cone angle (θ), and bite angle (β). Very good values of correlation coefficient (R2) over 0.938 were obtained by using a combination of effective net charge (Qeff) and open cone angle (θ) for both individual analysis and comparisons between analogue systems. By analyzing the contribution of descriptors, it indicates that the dominant descriptor is effective net charge (Qeff) in the Ni1 system and open cone angle (θ) in Ni2 systems, respectively. This may explain the different variation trends of catalytic activities in two Ni complexes systems as a function of substituents.

scholarly journals Unbounded Fredholm Operators and Spectral Flow

2005 ◽  
Vol 57 (2) ◽  
pp. 225-250 ◽  
Author(s):  
Bernhelm Booss-Bavnbek ◽  
Matthias Lesch ◽  
John Phillips
Keyword(s):  
Hilbert Space ◽  
Separable Hilbert Space ◽  
Direct Methods ◽  
Spectral Flow ◽  
Surprising Result ◽  
Graph Distance ◽  
Manifolds With Boundary ◽  
Fredholm Operators ◽  
Homotopy Invariance ◽  
Definition Of

AbstractWe study the gap (= “projection norm” = “graph distance”) topology of the space of all (not necessarily bounded) self-adjoint Fredholm operators in a separable Hilbert space by the Cayley transformand direct methods. In particular, we show the surprising result that this space is connected in contrast to the bounded case. Moreover, we present a rigorous definition of spectral flow of a path of such operators (actually alternative but mutually equivalent definitions) and prove the homotopy invariance. As an example, we discuss operator curves on manifolds with boundary.

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