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1.
We propose to reduce the (spectral) condition number of a given linear system by adding a suitable diagonal matrix to the system matrix, in particular by shifting its spectrum. Iterative procedures are then adopted to recover the solution of the original system. The case of real symmetric positive definite matrices is considered in particular, and several numerical examples are given. This approach has some close relations with Riley's method and with Tikhonov regularization. Moreover, we identify approximately the aforementioned procedure with a true action of preconditioning. 相似文献
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Yuliang Zhao 《中国科学:化学(英文版)》2018,61(12):1481-1482
正Living organisms have developed their unique strategies during the natural evolution for building hard tissues with minerals, including silica, calcium carbonate, calcium phosphate, and ferric oxide [1]. Such biomineralized materials generally have complex hierarchical structures with excellent mechanical properties. Although bioinspired approaches have led to the creation of well-defined synthetic structural materials ranging from micro to macro scales, the rational design of discrete biomimetic structures at the nanoscale remains a grand challenge. 相似文献
4.
JuHong Ge 《Nonlinear dynamics》2018,94(1):87-98
A five-neuron network model with multiple delays is proposed. This paper presents the combined effect of different delays on the dynamics of the proposed network. Pitchfork bifurcation is discussed in detail with the variation of the value of coupled weight or attenuation rate of internal neurons. By analyzing the corresponding characteristic equation, some stable criteria on delay-dependence and delay-independence are derived including multiple delays and coupled weights and the periodic oscillation arises bifurcated from the trivial equilibrium after the network loses its stability. Stable regions on delay-dependence are displayed in the two delayed parameter plane. It is shown that multiple delays can produce stability switching between resting state and periodic activity. Finally, theoretical results are justified by providing two illustrative examples. 相似文献
5.
It is shown that the countably infinite dimensional pointed vector space (the vector space equipped with a constant) over a finite field has infinitely many first order definable reducts. This implies that the countable homogeneous Boolean-algebra has infinitely many reducts. 相似文献
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Juan Manuel Cornejo Luiz F. Monteiro Hanamantagouda P. Sankappanavar Ignacio D. Viglizzo 《Mathematical Logic Quarterly》2020,66(4):409-417
We determine the number of non-isomorphic semi-Heyting algebras on an n-element chain, where n is a positive integer, using a recursive method. We then prove that the numbers obtained agree with those determined in [1]. We apply the formula to calculate the number of non-isomorphic semi-Heyting chains of a given size in some important subvarieties of the variety of semi-Heyting algebras that were introduced in [5]. We further exploit this recursive method to calculate the numbers of non-isomorphic semi-Heyting chains with n elements such that removing the mth element () we are left with a subalgebra. We also solve a related problem posed in [1] of determining the number of ways a semi-Heyting chain with elements can be extended to a n element semi-Heyting chain by adding a new element in the mth place. Finally we combine these results by finding a second way to calculate the numbers that provides some extra information. 相似文献
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Zinovy Reichstein 《Archiv der Mathematik》2018,111(5):449-455
We use a recent advance in birational geometry to prove new lower bounds on the essential dimension of some finite groups. 相似文献