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We study the problem of tumor growth and its monitoring ranging from the simple model for the radially symmetric to the more complex case being the radially non-symmetric one. In each case, we take killing rate of the cancer cells dependent on the concentration of the cells. A number of invariant reductions whose further analysis leads to exact solutions are obtained. Conservation laws for the model are also studied. 相似文献
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We describe the variety of Lagrangian subalgebras of the Drinfeld double for an arbitrary bialgebra structure on sl(2, R). We determine the irreducible components and the orbit structure under the natural action of the group SL(2, R) 相似文献
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E. M. Vechtomov 《Mathematical Notes》1997,62(5):575-580
The latticeA(X) of all possible subalgebras of the ring of all continuous ℝ-valued functions defined on an ℝ-separated spaceX is considered. A topological space is said to be a Hewitt space if it is homeomorphic to a closed subspace of a Tychonoff
power of the real line ℝ. The main achievement of the paper is the proof of the fact that any Hewitt spaceX is determined by the latticeA(X). An original technique of minimal and maximal subalgebras is applied. It is shown that the latticeA(X) is regular if and only ifX contains at most two points.
Translated fromMatematicheskie Zametki, Vol. 62, No. 5, pp. 687–693, November, 1997.
Translated by A. I. Shtern 相似文献
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Astha Chauhan Kajal Sharma Rajan Arora 《Mathematical Methods in the Applied Sciences》2020,43(15):8823-8840
In this work, Lie group theoretic method is used to carry out the similarity reduction and solitary wave solutions of (2 + 1)-dimensional Date–Jimbo–Kashiwara–Miwa (DJKM) equation. The equation describes the propagation of nonlinear dispersive waves in inhomogeneous media. Under the invariance property of Lie groups, the infinitesimal generators for the governing equation have been obtained. Thereafter, commutator table, adjoint table, invariant functions, and one-dimensional optimal system of subalgebras are derived by using Lie point symmetries. The symmetry reductions and some group invariant solutions of the DJKM equation are obtained based on some subalgebras. The obtained solutions are new and more general than the rest while known results reported in the literature. In order to show the physical affirmation of the results, the obtained solutions are supplemented through numerical simulation. Thus, the solitary wave, doubly soliton, multi soliton, and dark soliton profiles of the solutions are traced to make this research physically meaningful. 相似文献
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Leonid Makar-Limanov Ualbai Umirbaev 《Proceedings of the American Mathematical Society》2007,135(7):1969-1975
We prove an analog of the Bergman Centralizer Theorem for free Poisson algebras over an arbitrary field of characteristic 0. Some open problems are formulated.
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陈正新 《数学物理学报(B辑英文版)》2014,(3):814-828
Let P be a parabolic subalgebra of a general linear Lie algebra gl(n, F) over a field F, where n ≥ 3, F contains at least n different elements, and char(F) = 2. In this article, we prove that generalized derivations, quasiderivations, and product zero derivations of P coincide, and any generalized derivation of P is a sum of an inner derivation, a central quasiderivation, and a scalar multiplication map of P. We also show that any commuting automorphism of P is a central automorphism, and any commuting derivation of P is a central derivation. 相似文献
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Let F be a field of characteristic 0, Mn(F) the full matrix algebra over F, t the subalgebra of Mn(F) consisting of all upper triangular matrices. Any subalgebra of Mn(F) containing t is called a parabolic subalgebra of Mn(F). Let P be a parabolic subalgebra of Mn(F). A map φ on P is said to satisfy derivability if φ(x·y) = φ(x)·y+x·φ(y) for all x,y ∈ P, where φ is not necessarily linear. Note that a map satisfying derivability on P is not necessarily a derivation on P. In this paper, we prove that a map φ on P satisfies derivability if and only if φ is a sum of an inner derivation and an additive quasi-derivation on P. In particular, any derivation of parabolic subalgebras of Mn(F) is an inner derivation. 相似文献
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Orthogonal decomposition of the special linear Lie algebra over the complex numbers was studied in the early 1980s and attracted further attentions in the past decade due to its application in quantum information theory. In this paper, we study this decomposition problem of the special linear Lie algebra over a finite commutative ring with identity. 相似文献
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