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《Annals of Pure and Applied Logic》2022,173(8):103135
We further develop a forcing notion known as Coding with Perfect Trees and show that this poset preserves, in a strong sense, definable P-points, definable tight MAD families and definable selective independent families. As a result, we obtain a model in which , each of , , has a witness and there is a well-order of the reals. Note that both the complexity of the witnesses of the above combinatorial cardinal characteristics, as well as the complexity of the well-order are optimal. In addition, we show that the existence of a well-order of the reals is consistent with and each of the following: , , , where the smaller cardinal characteristics have co-analytic witnesses.Our methods allow the preservation of only sufficiently definable witnesses, which significantly differs from other preservation results of this type. 相似文献
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In this paper, we give the dimension and the minimum distance of two subclasses of narrow-sense primitive BCH codes over with designed distance for all , where q is a prime power and is a positive integer. As a consequence, we obtain an affirmative answer to two conjectures proposed by C. Ding in 2015. Furthermore, using the previous part, we extend some results of Yue and Hu [16], and we give the dimension and, in some cases, the Bose distance for a large designed distance in the range for , where if m is odd, and if m is even. 相似文献
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In this paper, we study the long-time behavior of solutions of a reaction–diffusion model in a one-dimensional river network, where the river network has two branches, and the water flow speeds in each branch are the same constant . We show the existence of two critical values and 2 with , and prove that when , the population density in every branch of the river goes to 1 as time goes to infinity; when , then, as time goes to infinity, the population density in every river branch converges to a positive steady state strictly below 1; when , the species will be washed down the stream, and so locally the population density converges to 0. Our result indicates that only if the water-flow speed is suitably small (i.e., ), the species will survive in the long run. 相似文献
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Minimal blocking sets in have size at most . This result is due to Bruen and Thas and the bound is sharp, sets attaining this bound are called unitals. In this paper, we show that the second largest minimal blocking sets have size at most , if , , or , , . Our proof also works for sets having at least one tangent at each of its points (that is, for tangency sets). 相似文献
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Yinan Guo 《Expositiones Mathematicae》2021,39(2):165-181
Analogs of Waring–Hilbert problem on Cantor sets are explored. The focus of this paper is on the Cantor ternary set . It is shown that, for each , every real number in the unit interval is the sum with each in and some . Furthermore, every real number in the interval can be written as , the sum of eight cubic powers with each in . Another Cantor set is also considered. More specifically, when is embedded into the complex plane , the Waring–Hilbert problem on has a positive answer for powers less than or equal to 4. 相似文献
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《Expositiones Mathematicae》2022,40(4):845-869
We make several observations relating the Lie algebra , associative 3-planes, and subalgebras. Some are likely well-known but not easy to find in the literature, while other results are new. We show that an element cannot have rank 2, and if it has rank 4 then its kernel is an associative subspace. We prove a canonical form theorem for elements of . Given an associative 3-plane in , we construct a Lie subalgebra of that is isomorphic to . This subalgebra differs from other known constructions of subalgebras of determined by an associative 3-plane. These are results of an NSERC undergraduate research project. The paper is written so as to be accessible to a wide audience. 相似文献
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