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Perturbed Gradient Flow Trees and A -algebra Structures in Morse Cohomology

oriented manifold with the structure of an A -algebra by means of perturbed gradient flow trajectories. This approach is a variation on K. Fukaya's;

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Perturbed Gradient Flow Trees and A -algebra Structures in Morse Cohomology

oriented manifold with the structure of an A -algebra by means of perturbed gradient flow trajectories. This approach is a variation on K. Fukaya's;

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An Invitation to Morse Theory

edition also includes a new chapter on Morse-Smale flows and Whitney stratifications, many new exercises, and various corrections from the first;

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Dynamical Systems and Linear Algebra

starting point for a linear algebra for classes of time-varying linear systems, namely periodic, random, and perturbed (or controlled) systems. The;

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Morse Theory Of Gradient Flows, Concavity And Complexity On Manifolds With Boundary

maps.The geometric and combinatorial structures, arising from the interactions of vector flows with the boundary of the manifold, are surprisingly;

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Introduction to Categories, Homological Algebra and Sheaf Cohomology

Categories, homological algebra, sheaves and their cohomology furnish useful methods for attacking problems in a variety of mathematical;

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Local Cohomology

This second edition of a successful graduate text provides a careful and detailed algebraic introduction to Grothendieck's local cohomology;

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Math For Deep Learning

as well as how to implement data flow in a neural network, backpropagation, and gradient descent. You'll also use Python to work through the;

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From Calculus to Cohomology

De Rham cohomology is the cohomology of differential forms. This book offers a self-contained exposition to this subject and to the theory;

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Etale Cohomology Theory (Revised Edition)

Etale cohomology is an important branch in arithmetic geometry. This book covers the main materials in SGA 1, SGA 4, SGA 4 1/2 and SGA 5 on;

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Continuous Cohomology, Discrete Subgroups, and Representations of Reductive Groups

study of automorphic forms. The authors give a careful presentation of relative Lie algebra cohomology of admissible and of unitary $G$-modules;

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Discrete Morse Theory

Discrete Morse theory is a powerful tool combining ideas in both topology and combinatorics. Invented by Robin Forman in the mid 1990s;

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Representations and Cohomology

at algebraic and topological proofs of the finite generation of the cohomology ring of a finite group, and an algebraic approach to the;

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Group Cohomology & Algebraic Cycles

Group cohomology reveals a deep relationship between algebra and topology, and its recent applications have provided important insights;

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Origin of Turbulence

be composed of singularities of flow field. The mechanisms of flow stability and turbulent transition are described using the energy gradient;

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Cohomology of Quotients in Symplectic and Algebraic Geometry. (MN-31), Volume 31

These notes describe a general procedure for calculating the Betti numbers of the projective quotient varieties that geometric invariant;

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Twenty-Four Hours of Local Cohomology

and basic properties of local cohomology. Then it develops the theory in a number of different directions, and draws connections with topology;

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Differential Geometry and Topology

the geodesic flow. Smooth manifolds, Riemannian metrics, affine connections, the curvature tensor, differential forms, and integration on;

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Introduction To Homological Algebra

book provides a unified account of homological algebra as it exists today. The historical connection with topology, regular local rings, and;

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Cohomology of Groups and Algebraic K-theory

Cohomology of groups is a fundamental tool in many subjects of modern mathematics. One important generalized cohomology theory is the;

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Mechanics of Strain Gradient Materials

structures in terms of their elasticity, plasticity and fracturing. This book puts forward a unifying perspective to combine existing theories;

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Methods of Homological Algebra

This modern approach to homological algebra by two leading writers in the field is based on the systematic use of the language and ideas;

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Energy, Entropy, and the Flow of Nature

Energy, Entropy, and the Flow of Nature presents the essential principles of energetics (thermodynamics) in a straight-forward, easy to;

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Gradient Microstructure in Laser Shock Peened Materials

and the strengthening-toughing mechanism by gradient structures. The research has accumulated a large amount of experimental data, which has;

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Gradient Microstructure in Laser Shock Peened Materials

and the strengthening-toughing mechanism by gradient structures. The research has accumulated a large amount of experimental data, which has;

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Electromagnetic Theory and Computation

in electromagnetics, the finite element method, algorithms, and certain aspects of numerical linear algebra. A recurring theme is the formulation of and;

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Electromagnetic Theory and Computation

in electromagnetics, the finite element method, algorithms, and certain aspects of numerical linear algebra. A recurring theme is the formulation of and;

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