共查询到20条相似文献,搜索用时 62 毫秒
1.
Susumu Kubo 《Journal of Pure and Applied Algebra》2019,223(1):72-85
We consider tropical polynomials in nr variables, divided into n blocks of r variables, and especially r-symmetric tropical polynomials, which are invariant under the action of the symmetric group on the blocks. We define a set of basic r-symmetric tropical polynomials and show that the basic 2-symmetric tropical polynomials give coordinates on more efficiently than known polynomials. Moreover, we present special cases for where the basic polynomials separate orbits. 相似文献
2.
Multivariate incomplete polynomials are considered on compact 0-symmetric starlike domains. Problems of density and quantitative approximation properties of such polynomials are investigated. It is shown that density holds for a certain class of starlike domains which includes both convex and some nonconvex domains. On the other hand, a family of nonconvex starlike domains is also found for which density fails. In addition, it is also shown that on 0-symmetric convex bodies in $\mathbb{R}^{d}$ , continuous functions can be approximated by θ-incomplete polynomials with the rate O(ω 2(n ?1/(d+3))). Moreover, if the convex body is the intersection of simplexes with vertex at the origin, then this order improves to $O (\omega_{2}(f,1/\sqrt{n}) )$ . 相似文献
3.
For the long range interaction, we prove the global existence of renormalized solutions to the Boltzmann equation with incoming boundary condition. Furthermore, as Knudsen number ? goes to zero, the limit to the incompressible Navier–Stokes limit with homogeneous Dirichlet boundary condition is justified when the boundary data of the scaled Boltzmann equation is close to the Maxwellian with order in the sense of boundary relative entropy. 相似文献
4.
Peter P. Varju 《Constructive Approximation》2007,26(3):317-337
Let
be the boundary of a convex domain symmetric to the origin. The conjecture that any continuous even function can be uniformly
approximated by homogeneous polynomials of even degree on K is proven in the following cases: (a) if d = 2; (b) if K is twice
continuously differentiable and has positive curvature in every point; or (c) if K is the boundary of a convex polytope. 相似文献
5.
Relatively recently it was proved that if Γ is an arbitrary set, then any equivalent norm on can be approximated uniformly on bounded sets by polyhedral norms and smooth norms, with arbitrary precision. We extend this result to more classes of spaces having uncountable symmetric bases, such as preduals of the ‘discrete’ Lorentz spaces , and certain symmetric Nakano spaces and Orlicz spaces. We also show that, given an arbitrary ordinal number α, there exists a scattered compact space K having Cantor–Bendixson height at least α, such that every equivalent norm on can be approximated as above. 相似文献
6.
Jürgen Jost Lei Liu Miaomiao Zhu 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2019,36(2):365-387
For a sequence of coupled fields from a compact Riemann surface M with smooth boundary to a general compact Riemannian manifold with uniformly bounded energy and satisfying the Dirac-harmonic system up to some uniformly controlled error terms, we show that the energy identity holds during a blow-up process near the boundary. As an application to the heat flow of Dirac-harmonic maps from surfaces with boundary, when such a flow blows up at infinite time, we obtain an energy identity. 相似文献
7.
Xingfei Xiang 《Journal of Mathematical Analysis and Applications》2022,505(2):125518
In bounded convex domains, the regularity of a vector field u with its , in space and the tangential component or the normal component of u over the boundary in space, is established for . As an application, we derive an estimate for solutions to a Maxwell type system with an inhomogeneous boundary condition in convex domains. In contrast to the well-posed region of r in the space for the Maxwell type system in Lipschitz domains given by Kar and Sini (2016) [16], we extend the well-posed region to be optimal. 相似文献
8.
The so-called zero number diminishing property (or zero number argument) is a powerful tool in qualitative studies of one dimensional parabolic equations, which says that, under the zero- or non-zero-Dirichlet boundary conditions, the number of zeros of the solution of a linear equation is finite, non-increasing and strictly decreasing when there are multiple zeros (cf. Angenent (1988)). In this paper we extend the result to the problems with more general boundary conditions: sometime and at other times on the domain boundaries. Such results can be applied in particular to parabolic equations with Robin and free boundary conditions. 相似文献
9.
Sergey V. Astashkin 《Journal of Functional Analysis》2019,276(10):3205-3225
Let . A Banach lattice E is said to be disjointly homogeneous (resp. p-disjointly homogeneous) if two arbitrary normalized disjoint sequences from E contain equivalent in E subsequences (resp. every normalized disjoint sequence contains a subsequence equivalent in E to the unit vector basis of ). Answering a question raised in the paper [11], for each , we construct a reflexive p-disjointly homogeneous rearrangement invariant space on whose dual is not disjointly homogeneous. Employing methods from interpolation theory, we provide new examples of disjointly homogeneous rearrangement invariant spaces; in particular, we show that there is a Tsirelson type disjointly homogeneous rearrangement invariant space, which contains no subspace isomorphic to , , or . 相似文献
10.
11.
12.
13.
Mixed Oblique Extension Principles (MOEP) provide an important method to construct affine dual frames from refinable functions. This paper addresses MOEP under the setting of reducing subspaces of . We obtain an MOEP for (non)homogeneous affine dual frames and (non)homogeneous affine Parseval frames. 相似文献
14.
Linearized polynomials have attracted a lot of attention because of their applications in both geometric and algebraic areas. Let q be a prime power, n be a positive integer and σ be a generator of . In this paper we provide closed formulas for the coefficients of a σ-trinomial f over which ensure that the dimension of the kernel of f equals its σ-degree, that is linearized polynomials with maximum kernel. As a consequence, we present explicit examples of linearized trinomials with maximum kernel and characterize those having σ-degree 3 and 4. Our techniques rely on the tools developed in [24]. Finally, we apply these results to investigate a class of rank metric codes introduced in [8], to construct quasi-subfield polynomials and cyclic subspace codes, obtaining new explicit constructions to the conjecture posed in [37]. 相似文献
15.
A star edge coloring of a graph is a proper edge coloring such that every connected 2-colored subgraph is a path with at most 3 edges. Deng et al. and Bezegová et al. independently show that the star chromatic index of a tree with maximum degree is at most , which is tight. In this paper, we study the list star edge coloring of -degenerate graphs. Let be the list star chromatic index of : the minimum such that for every -list assignment for the edges, has a star edge coloring from . By introducing a stronger coloring, we show with a very concise proof that the upper bound on the star chromatic index of trees also holds for list star chromatic index of trees, i.e. for any tree with maximum degree . And then by applying some orientation technique we present two upper bounds for list star chromatic index of -degenerate graphs. 相似文献
16.
Nonintersecting Brownian bridges on the unit circle form a determinantal stochastic process exhibiting random matrix statistics for large numbers of walkers. We investigate the effect of adding a drift term μ to walkers on the circle conditioned to start and end at the same position. For each return time we show there exists a critical drift such that if for some integer m then the expected winding number for each walker is asymptotically m. In addition, we compute the asymptotic distribution of total winding numbers in the double-scaling regime in which the expected number of walkers with winding number not equal to m is finite. The method of proof is Riemann–Hilbert analysis of a certain family of discrete orthogonal polynomials with varying complex exponential weights. This is the first asymptotic analysis of such a class of polynomials. We determine asymptotic formulas for these polynomials as the degree of the polynomial grows large and demonstrate the emergence of a second band of zeros by a mechanism not previously seen for discrete orthogonal polynomials with real weights. 相似文献
17.
18.
19.
20.
We compute the second moment in the family of quadratic Dirichlet L–functions with prime conductors over when the degree of the discriminant goes to infinity, obtaining one of the lower order terms. We also obtain an asymptotic formula with the leading order term for the mean value of the derivatives of L–functions associated to quadratic twists of a fixed elliptic curve over by monic irreducible polynomials. As a corollary, we prove that there are infinitely many monic irreducible polynomials such that the analytic rank of the corresponding twisted elliptic curves is equal to 1. 相似文献