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21.
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给出了李color三系的Frattini子系的定义,得到了李color三系的Frattini子系的一些性质·特别的,证明了李color三系T有分解T=T_1⊕T_2⊕…⊕T_m,则φ(T)有分解φ(T)=φ(T_1)⊕φ(T_2)⊕…⊕φ(T_m). 相似文献
23.
For any integer n ≥ 2, let P(n) be the largest prime factor of n. In this paper, we prove that the number of primes p ≤ x with P(p-1) ≥ p~c is more than(1-c + o(1))π(x) for 0 c 1/2. This extends a recent result of Luca, Menares and Madariaga for1/4≤ c ≤1/2. We also pose two conjectures for further research. 相似文献
24.
Graphene is scientifically and commercially important because of its unique molecular structure which is monoatomic in thickness, rigorously two-dimensional and highly conjugated. Consequently, graphene exhibits exceptional electrical, optical, thermal and mechanical properties. Herein, we critically discuss the surface modification of graphene, the specific advantages that graphene-based materials can provide over other materials in sensor research and their related chemical and electrochemical properties. Furthermore, we describe the latest developments in the use of these materials for sensing technology, including chemical sensors and biosensors and their applications in security, environmental safety and diseases detection and diagnosis. 相似文献
25.
Various versions of representations of the percolation Reynolds number for porous media with isotropic and anisotropic flow properties are considered. The formulas are derived and the variants are analyzed with reference to model porous media with a periodic microstructure formed by systems of capillaries and packings consisting of spheres of constant diameter (ideal and fictitious porous media, respectively). A generalization of the Kozeny formula is given for determining the capillary diameter in an ideal porous medium equivalent to a fictitious medium with respect to permeability and porosity and it is shown that the capillary diameter is nonuniquely determined. Relations for recalculating values of the Reynolds number determined by means of formulas proposed earlier are given and it is shown that taking the microstructure of porous media into account, as proposed in [1, 2], makes it possible to explain the large scatter of the numerical values of the Reynolds number in processing the experimental data. 相似文献
26.
A second-order asymptotic expression for the profile of a capillary-gravity wave traveling over the charged surface of an ideal incompressible fluid is calculated analytically. Two types of steady-state profiles of nonlinear periodic capillary-gravity waves are found. For a certain fixed dimensionless surface charge the shape of the tops of the nonlinear waves changes: from blunt to pointed for short waves and from pointed to blunt for long waves. 相似文献
27.
Let be two monomial ideals of the polynomial ring . In this paper, we provide two lower bounds for the Stanley depth of . On the one hand, we introduce the notion of lcm number of , denoted by , and prove that the inequality holds. On the other hand, we show that , where denotes the order dimension of the lcm lattice of . We show that I and satisfy Stanley's conjecture, if either the lcm number of I or the order dimension of the lcm lattice of I is small enough. Among other results, we also prove that the Stanley–Reisner ideal of a vertex decomposable simplicial complex satisfies Stanley's conjecture. 相似文献
28.
Let 𝕂 be a field, and let R = 𝕂[x 1,…, x n ] be the polynomial ring over 𝕂 in n indeterminates x 1,…, x n . Let G be a graph with vertex-set {x 1,…, x n }, and let J be the cover ideal of G in R. For a given positive integer k, we denote the kth symbolic power and the kth bracket power of J by J (k) and J [k], respectively. In this paper, we give necessary and sufficient conditions for R/J k , R/J (k), and R/J [k] to be Cohen–Macaulay. We also study the limit behavior of the depths of these rings. 相似文献
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30.
In this paper, we determine the structures of the transfer ideal and its radical ideal for the ring of polynomials F p[x, y] under the action of dihedral group D2 p in the modular case. We mainly use Transfer variety, p order elements, and Hilbert’s Nullstellensatz Theorem. 相似文献