Morse inequalities for the Koszul complex of multi-persistence

On Bernstein Type Inequalities for Complex Polynomial

In this paper, we establish some Bernstein type inequalities for the complex polynomial. Our results constitute generalizations and refinements of some well-known polynomial inequalities.

extensions of some polynomial inequalities to the polar derivative

توسیع تعدادی از نامساوی های چند جمله ای در مشتق قطبی

Witten’s Proof of Morse Inequalities

Both properties do not depend on the choice of coordinates. The index ind (x) is the number of negative eigenvalues of Hess (f) (x). Let mp = mp (f) be the number of critical points of index p. Let bp = bp (M) = dimH (M) be the dimension of the p de Rham cohomology group. 0→ Ω (M) d −→ Ω (M) d −→ ... d −→ Ω (M) d −→ 0 This is called the de Rham complex. Note that d = 0. If ω = dα, then dω = 0. ...

study of cohesive devices in the textbook of english for the students of apsychology by rastegarpour

this study investigates the cohesive devices used in the textbook of english for the students of psychology. the research questions and hypotheses in the present study are based on what frequency and distribution of grammatical and lexical cohesive devices are. then, to answer the questions all grammatical and lexical cohesive devices in reading comprehension passages from 6 units of 21units th...

Persistence in discrete Morse theory