Braid groups in complex spaces
We describe the fundamental groups of ordered and unordered $k-$point sets in the n-dimensional complex space $C^n$ generating an affine subspace of fixed dimension.
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arXiv subjects
Saima Parveen
Publications and source records attributed to Saima Parveen.
Parameterized Stationary Solution for first order PDE
We analyze the existence of a parameterized stationary solution $z(λ,z_0)=\big(x(λ,z_0), p(λ,z_0),\,u(λ,z_0)\big)\in D\subseteq\mathbb{R}^{2n+1},\,λ\in B(0,a)\subseteq\mathop{\prod}\limits_{i=1}^{m}[-a_i,a_i]$, associated with a nonlinear first order PDE, $H_0(x,p(x),u(x))=\hbox{constant}\,\,(p(x)=\partial_x u(x))$ relying on (a) first integral $H\in\mathcal{C}^\infty\big(B(z_0,2ρ)\subseteq\mathbb{R}^{2n+1}\big)$ and the corresponding Lie algebra of characteristic fields is of the finite type; (b) gradient system in a Lie algebra finitely generated over orbits $(f.g.o;z_0)$ starting from $z_0\in D$ and their nonsingular algebraic representation.
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Gradient flows with jumps associated with nonlinear Hamilton-Jacobi equations with jumps
We analyze gradient flows with jumps generated by a finite set of complete vector fields in involution using some Radon measures $u\in \mathcal{U}_a$ as admissible perturbations. Both the evolution of a bounded gradient flow $\{x^u(t,ł)\in B(x^*,3\g)\subseteq \mbn: \,t\in[0,T],\,ł\in B(x^*,2\g)\}$ and the unique solution $ł=ψ^u(t,x)\in B(x^*,2\g)\subseteq \mbn$ of integral equation $x^u(t,ł)=x\in B(x^*,\g), \,t\in[0,T]$, are described using the corresponding gradient representation associated with flow and Hamilton-jacobi equations.
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Fundamental Group of Desargues Configuration Spaces
We compute the fundamental group of various spaces of Desargues configurations in complex projective spaces: planar and non-planar configurations, with a fixed center and also with an arbitrary center.
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Partial Differential Equations An Introduction
This book encompasses both traditional and modern methods treating partial differential equation (PDE) of first order and second order. There is a balance in making a selfcontained mathematical text and introducing new subjects. The Lie algebras of vector fields and their algebraic-geometric representations are involved in solving overdetermined of PDE and getting integral representation of stochastic differential equations (SDE). It is addressing to all scientists using PDE in treating mathematical methods.
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Braid groups in complex projective spaces
We describe the fundamental groups of ordered and unordered k point sets in complex projective space of dimension n generating a projective subspace of dimension i. We apply these to study connectivity of more complicated configurations of points.
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Hamilton-Jacobi equations with jumps: asymptotic stability
The asymptotic stability of a global solution satisfying Hamilton-Jacobi equations with jumps will be analyzed in dependence on the strong dissipativity of the jump control function and using orbits of the differentiable flows to describe the corresponding characteristic system.
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