共查询到20条相似文献,搜索用时 31 毫秒
1.
We investigate k-uniform loose paths. We show that the largest Heigenvalues of their adjacency tensors, Laplacian tensors, and signless Laplacian tensors are computable. For a k-uniform loose path with length l ≥ 3 , we show that the largest H-eigenvalue of its adjacency tensor is ( ( 1 + 5 ) / 2 ) 2 / k when l = 3 and λ ( A ) = 3 1 / k when l = 4 , respectively. For the case of l ≥ 5 , we tighten the existing upper bound 2. We also show that the largest H-eigenvalue of its signless Laplacian tensor lies in the interval (2, 3) when l ≥ 5 . Finally, we investigate the largest H-eigenvalue of its Laplacian tensor when k is even and we tighten the upper bound 4. 相似文献
2.
Pascual JARA 《Frontiers of Mathematics in China》2015,10(1):91
Let A be a commutative ring. For any set p of prime ideals of A, we define a new ring Na(A, p ): the Nagata ring. This new ring has the particularity that we may transform certain properties relative to p to properties on the whole ring Na(A, p ); some of these properties are: ascending chain condition, Krull dimension, Cohen-Macaulay, Gorenstein. Our main aim is to show that most of the above properties relative to a set of prime ideals p (i.e., local properties) determine and are determined by the same properties on the Nagata ring (i.e., global properties). In order to look for new applications, we show that this construction is functorial, and exhibits a functorial embedding from the localized category (A, p )-Mod into the module category Na(A, p )-Mod. 相似文献
3.
Yuchao WANG 《Frontiers of Mathematics in China》2015,10(6):1449
value of a given binary linear form at prime arguments. Let λ1 and λ2 be positive real numbers such that λ1/λ2 is irrational and algebraic. For any (C, c) well-spaced sequence V and δ>0, let E(V , X, δ) denote the number of υ∈V with υ≤X for which the inequality | λ 1 p 1 + λ 2 ρ 2 − υ | < υ − δ has no solution in primes p1, p2. It is shown that for any ε>0,we have E(V , X, δ) «max(X 3 5 + 2 δ + ε , X 2 3 + 4 3 δ + ε ). 相似文献
4.
Complex Hermitian Clifford analysis emerged recently as a refinement of the theory of several complex variables, while at the same time, the theory of bicomplex numbers motivated by the bicomplex version of quantum mechanics is also under full development. This stimulates us to combine the Hermitian Clifford analysis with the theory of bicomplex number so as to set up the theory of bicomplex Hermitian Clifford analysis. In parallel with the Euclidean Clifford analysis, the bicomplex Hermitian Clifford analysis is centered around the bicomplex Hermitian Dirac operator | D : C ∞ ( R 4 n , W 4 n ) → C ∞ ( R 4 n , W 4 n ) , where W 4 n is the tensor product of three algebras, i.e., the hyperbolic quaternion B ^ , the bicomplex number B , and the Clifford algebra R n . The operator D is a square root of the Laplacian in R 4 n , introduced by the formula D | = ∑ j = 0 3 K j ? Z j with K j being the basis of B ^ , and ? Z j denoting the twisted Hermitian Dirac operators in the bicomplex Clifford algebra B ? R 0,4 n whose definition involves a delicate construction of the bicomplexWitt basis. The introduction of the operator D can also overturn the prevailing opinion in the Hermitian Clifford analysis in the complex or quaternionic setting that the complex or quaternionic Hermitiean monogenic functions are described by a system of equations instead of by a single equation like classical monogenic functions which are null solutions of Dirac operator. In contrast to the Hermitian Clifford analysis in quaternionic setting, the Poisson brackets of the twisted real Clifford vectors do not vanish in general in the bicomplex setting. For the operator D , we establish the Cauchy integral formula, which generalizes the Martinelli-Bochner formula in the theory of several complex variables. 相似文献
5.
Motivated by τ -tilting theory developed by T. Adachi, O. Iyama, I. Reiten, for a nite-dimensional algebra Λ with action by a nite group G; we introduce the notion of G-stable support τ -tilting modules. Then we establish bijections among G-stable support τ -tilting modules over Λ ; G-stable two-term silting complexes in the homotopy category of bounded complexes of nitely generated projective Λ -modules, and G-stable functorially nite torsion classes in the category of nitely generated left Λ -modules. In the case when Λ is the endomorphism of a G-stable cluster-tilting object T over a Hom-nite 2-Calabi-Yau triangulated category ℓ with a G-action, these are also in bijection with G-stable cluster-tilting objects in ℓ : Moreover, we investigate the relationship between stable support τ -tilitng modules over Λ and the skew group algebra Λ G: 相似文献
6.
Let G be a simple connected graph, and let d i be the degree of its i-th vertex. The sum-connectivity index of the graph G is defined as χ ( G ) = Σ v i v j ∈ E ( G ) ? ( d i + d j ) − 1 / 2 . We discuss the effect on χ(G) of inserting an edge into a graph. Moreover, we obtain the relations between sum-connectivity index and Randić index. 相似文献
7.
We consider anRd-valued discrete time branching random walk in an independent and identically distributed environment indexed by time n∈N.Let Wn(z)(z∈Cd)be the natural complex martingale of the process.We show necessary and sufficient conditions for the Lα-convergence of Wn(z)forα>1,as well as its uniform convergence region. 相似文献
8.
Let φ be a growth function, and let A : = - ( ? - i a ) ? ( ? - i a ) + V be a magnetic Schr?dinger operator on L 2 ( ? n ) , n ≥ 2 , where α : = ( α 1 , α 2 , ? , α n ) ∈ L l o c 2 ( ? n , ? n ) and 0 ≤ V ∈ L l o c 1 ( ? n ) . We establish the equivalent characterizations of the Musielak-Orlicz-Hardy space H A , φ ( ? n ) , defined by the Lusin area function associated with { e - t 2 A } t > 0 , in terms of the Lusin area function associated with { e - t A } t > 0 , the radial maximal functions and the nontangential maximal functions associated with { e - t 2 A } t > 0 and { e - t A } t > 0 , respectively. The boundedness of the Riesz transforms L k A - 1 / 2 , k ∈ { 1 , 2 , ? , n } , from H A , φ ( ? n ) to L φ ( ? n ) is also presented, where Lk is the closure of ? ? x k - i α k in L 2 ( ? n ) . These results are new even when φ ( x , t ) : = ω ( x ) t p for all x ∈ ? n and t ∈(0,+∞) with p ∈(0, 1] and ω ∈ A ∞ ( ? n ) (the class of Muckenhoupt weights on ? n ). 相似文献
9.
Let ■ be a k-uniform hypergraph on n vertices with degree sequence △= d1≥…≥ dn =δ. In this paper, in terms of degree di , we give some upper bounds for the Z-spectral radius of the signless Laplacian tensor (Q(■)) of ■. Some examples are given to show the efficiency of these bounds. 相似文献
10.
We study the exponential sums involving l:burmr coeffcients ot Maass forms and exponential functions of the form e(anZ), where 0 ≠ α∈R and 0 〈 β 〈 1. An asymptotic formula is proved for the nonlinear exponential sum ∑x〈n≤2x λg(n)e(αnβ), when β = 1/2 and |α| is close to 2√ q C Z+, where Ag(n) is the normalized n-th Fourier coefficient of a Maass cusp form for SL2 (Z). The similar natures of the divisor function 7(n) and the representation function r(n) in the circle problem in nonlinear exponential sums of the above type are also studied. 相似文献
11.
We extend Vandermonde matrices to generalized Vandermonde tensors. We call an mth order n-dimensional real tensor A = ( A i 1 i 2 ... i m ) a type-1 generalized Vandermonde (GV) tensor, or GV1 tensor, if there exists a vector v = ( v 1 , v 2 ... v n ) T such that A i 1 i 2 ... i m = v i 1 i 2 + i 3 + ... + i m - m + 1 , and call A a type-2 (mth order ndimensional) GV tensor, or GV2 tensor, if there exists an (m-1)th order tensor B = ( B i 1 i 2 ... i m - 1 ) such that A i 1 i 2 ... i m = B i 1 i 2 ... i m - 1 i m - 1 . In this paper, we mainly investigate the type-1 GV tensors including their products, their spectra, and their positivities. Applications of GV tensors are also introduced. 相似文献
12.
We introduce the generalized area operators by using nonnegative measures defined on upper half-spaces ? + n + 1 . The characterization of the boundedness and compactness of the generalized area operator from Lp(? n ) to Lq(? n ) is investigated in terms of s-Carleson measures with 1<p, q<+∞. In the case of p = q = 1, the weak type estimate is also obtained. 相似文献
13.
Consider a time-inhomogeneous branching random walk, generated by the point process Ln which composed by two independent parts: ‘branching’offspring Xn with the mean for and ‘displacement’ with a drift for , where the ‘branching’ process is supercritical for B>0 but ‘asymptotically critical’ and the drift of the ‘displacement’ is strictly positive or negative for but ‘asymptotically’ goes to zero as time goes to infinity. We find that the limit behavior of the minimal (or maximal) position of the branching random walk is sensitive to the ‘asymptotical’ parameter and . 相似文献
14.
Submanifolds in space forms satisfy the well-known DDVV inequality. A submanifold attaining equality in this inequality pointwise is called a Wintgen ideal submanifold. As conformal invariant objects, Wintgen ideal submanifolds are investigated in this paper using the framework of M?bius geometry. We classify Wintgen ideal submanfiolds of dimension m ≥ 3 and arbitrary codimension when a canonically defined 2-dimensional distribution ? 2 is integrable. Such examples come from cones, cylinders, or rotational submanifolds over super-minimal surfaces in spheres, Euclidean spaces, or hyperbolic spaces, respectively. We conjecture that if ? 2 generates a k-dimensional integrable distribution ? k and k<m, then similar reduction theorem holds true. This generalization when k = 3 has been proved in this paper. 相似文献
15.
Weili YAO 《Frontiers of Mathematics in China》2020,15(1):205-213
Let f be a holomorphic Hecke cusp form with even integral weight k≥2 for the full modular group,and letχbe a primitive Dirichlet character modulo q.Let Lf(s,χ)be the automorphic L-function attached to f andχ-We study the mean-square estimate of Lf(s,χ)and establish an asymptotic formula. 相似文献
16.
Shangquan BU 《Frontiers of Mathematics in China》2015,10(2):239
Using known operator-valued Fourier multiplier results on vectorvalued H?lder continuous function spaces, we completely characterize the wellposedness of the degenerate differential equations ( M u ) ' ( t ) = A u ( t ) + f ( t ) for t ∈ R in H?lder continuous function spaces C a ( R ; X ) by the boundedness of the M-resolvent of A, where A and M are closed operators on a Banach space X satisfying D ( A ) ? D ( M ) . 相似文献
17.
We establish sharp functional inequalities for time-changed symmetric -stable processes on with and , which yield explicit criteria for the compactness of the associated semigroups. Furthermore, when the time change is defined via the special function with we obtain optimal Nash-type inequalities, which in turn give us optimal upper bounds for the density function of the associated semigroups. 相似文献
18.
Let(C,E,s)be an extriangulated category with a proper classξof E-triangles,and W an additive full subcategory of(C,E,s).We provide a method for constructing a proper W(ξ)-resolution(resp.,coproper W(ξ)-coresolution)of one term in an E-triangle inξfrom that of the other two terms.By using this way,we establish the stability of the Gorenstein category GW(ξ)in extriangulated categories.These results generalize the work of Z.Y.Huang[J.Algebra,2013,393:142–169]and X.Y.Yang and Z.C.Wang[Rocky Mountain J.Math.,2017,47:1013–1053],but the proof is not too far from their case.Finally,we give some applications about our main results. 相似文献
19.
Xie-Bin CHEN 《Frontiers of Mathematics in China》2019,14(6):1117
We consider the problem of existence of a Hamiltonian cycle containing a matching and avoiding some edges in an n-cube , and obtain the following results. Let , and with . If M is a matching and every vertex is incident with at least two edges in the graph , then all edges of M lie on a Hamiltonian cycle in . Moreover, if or , then the upper bound of number of faulty edges tolerated is sharp. Our results generalize the well-known result for . 相似文献
20.
We consider a branching random walk on N with a random environment in time (denoted by ξ). Let Zn be the counting measure of particles of generation n, and let Zn(t) be its Laplace transform. We show the convergence of the free energy n-llog Zn(t), large deviation principles, and central limit theorems for the sequence of measures {Zn}, and a necessary and sufficient condition for the existence of moments of the limit of the martingale Zn(t)/E[Zn(t)ξ]. 相似文献