scholarly journals On compact leaves of a Morse form foliation

2011 ◽  
Vol 78 (1) ◽  
pp. 37-48 ◽  
Author(s):  
IRINA GELBUKH
Keyword(s):  
Morse Form

A New Test of Auditory-Visual Integration

1973 ◽  
Vol 36 (3_suppl) ◽  
pp. 1063-1066 ◽  
Author(s):  
Andrew H. Gregory ◽  
H. Margaret Gregory
Keyword(s):  
Reading Ability ◽  
The Other ◽  
Nonverbal Intelligence ◽  
Visual Integration ◽  
Morse Form ◽  
Highly Correlated

Two auditory-visual integration tests were given to 86 children from 6 yr. to 11 yr. One test was basically that developed by Birch; the other used Morse-type stimuli. The children were also given tests of nonverbal intelligence, reading and vocabulary. With age and intelligence partialled out, the Morse form of test was significantly more highly correlated with reading ability than the Birch test. Reasons are suggested as to why the Morse version may be a better test of some of the underlying skills involved in reading.

scholarly journals Number of minimal components and homologically independent compact leaves for a morse form foliation

2009 ◽  
Vol 46 (4) ◽  
pp. 547-557 ◽  
Author(s):  
Irina Gelbukh
Keyword(s):  
Betti Number ◽  
Sharp Estimate ◽  
Oriented Manifold ◽  
Morse Form

The numbers m ( ω ) of minimal components and c ( ω ) of homologically independent compact leaves of the foliation of a Morse form ω on a connected smooth closed oriented manifold M are studied in terms of the first non-commutative Betti number b ′ 1 ( M ). A sharp estimate 0 ≦ m ( ω ) + c ( ω ) ≦ b ′ 1 ( M ) is given. It is shown that all values of m ( ω ) + c ( ω ), and in some cases all combinations of m ( ω ) and c ( ω ) with this condition, are reached on a given M . The corresponding issues are also studied in the classes of generic forms and compactifiable foliations.

Structure of level surfaces of a Morse form

1988 ◽  
Vol 44 (1) ◽  
pp. 556-562 ◽  
Author(s):  
Ty Kuok Tkhang
Keyword(s):  
Morse Form

scholarly journals Incidence coefficients in the Novikov Complex for Morse forms: rationality and exponential growth properties

2021 ◽  
Vol 13 (4) ◽  
pp. 125-177
Author(s):  
Andrei Pajitnov
Keyword(s):  
Fundamental Group ◽  
Exponential Growth ◽  
Laurent Polynomials ◽  
Growth Properties ◽  
Boundary Operators ◽  
Morse Form ◽  
Homology Module ◽  
Dense Set ◽  
Refined Version ◽  
Novikov Complex

Let f : M → S 1 be a Morse map, v a transverse f -gradient. Theconstruction of the Novikov complex associates to these data a free chain complexC ∗ (f, v) over the ring Z[t]][t −1 ], generated by the critical points of f and computingthe completed homology module of the corresponding infinite cyclic covering of M .Novikov’s Exponential Growth Conjecture says that the boundary operators in thiscomplex are power series of non-zero convergence raduis.In [12] the author announced the proof of the Novikov conjecture for the case ofC 0 -generic gradients together with several generalizations. The proofs of the firstpart of this work were published in [13]. The present article contains the proofs ofthe second part.There is a refined version of the Novikov complex, defined over a suitable com-pletion of the group ring of the fundamental group. We prove that for a C 0 -genericf -gradient the corresponding incidence coefficients belong to the image in the Novikovring of a (non commutative) localization of the fundamental group ring.The Novikov construction generalizes also to the case of Morse 1-forms. In thiscase the corresponding incidence coefiicients belong to a certain completion of thering of integral Laurent polynomials of several variables. We prove that for a givenMorse form ω and a C 0 -generic ω-gradient these incidence coefficients are rationalfunctions.The incidence coefficients in the Novikov complex are obtained by counting thealgebraic number of the trajectories of the gradient, joining the zeros of the Morseform. There is V.I.Arnold’s version of the exponential growth conjecture, whichconcerns the total number of trajectories. We confirm this stronger form of theconjecture for any given Morse form and a C 0 -dense set of its gradients.We give an example of explicit computation of the Novikov complex.

A test for non-compactness of the foliation of a Morse form

1995 ◽  
Vol 50 (2) ◽  
pp. 444-445 ◽  
Author(s):  
I A Mel'nikova
Keyword(s):  
Morse Form

scholarly journals Presence of minimal components in a Morse form foliation

2005 ◽  
Vol 22 (2) ◽  
pp. 189-198 ◽  
Author(s):  
Irina Gelbukh
Keyword(s):  
Morse Form

scholarly journals Structure of a Morse form foliation on a closed surface in terms of genus

2011 ◽  
Vol 29 (4) ◽  
pp. 473-492 ◽  
Author(s):  
Irina Gelbukh
Keyword(s):  
Closed Surface ◽  
Morse Form

Analytic embedded atom method potentials for face-centered cubic metals

1998 ◽  
Vol 13 (7) ◽  
pp. 1919-1927 ◽  
Author(s):  
S. S. Pohlong ◽  
P. N. Ram
Keyword(s):  
Reasonable Agreement ◽  
Mean Square Displacement ◽  
Pair Potential ◽  
Embedded Atom Method ◽  
Face Centered Cubic ◽  
Embedded Atom ◽  
Phonon Spectra ◽  
Morse Form ◽  
Face Centered ◽  
Experimental Values

The universal form of embedding function suggested by Banerjea and Smith together with a pair-potential of the Morse form are used to obtain embedded atom method (EAM) potentials for fcc metals: Cu, Ag, Au, Ni, Pd, and Pt. The potential parameters are determined by fitting to the Cauchy pressure (C12 − C44)/2, shear constant GV = (C11 − C12 + 3C44)/5, and C44, the cohesive energy and the vacancy formation energy. The obtained parameters are utilized to calculate the unrelaxed divacancy binding energy and the unrelaxed surface energies of three low-index planes. The calculated quantities are in reasonable agreement with the experimental values except perhaps the divacancy energy in a few cases. In a further application, lattice dynamics of these metals are discussed using the present EAM potentials. On comparison with experimental phonons, the agreement is good for Cu, Ag, and Ni, while in the other three metals, Au, Pd, and Pt, the agreement is not so good. The phonon spectra are in reasonable agreement with the earlier calculations. The frequency spectrum and the mean square displacement of an atom in Cu are in agreement with the experiment and other calculated results.

scholarly journals On the structure of a Morse form foliation

2009 ◽  
Vol 59 (1) ◽  
pp. 207-220 ◽  
Author(s):  
I. Gelbukh
Keyword(s):  
Morse Form
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