We investigate the characterization and the Carleson measure for Morrey type spaces JKp, where the weight function K:[0,∞)→[0,∞) is a right-continuous and nondecreasing function.
The present paper considered one problem which integer part of nonlinear form with mixed powers 2, 3, 4, 5 and prime variables represents prime infinitely. Using Davenport-Heilbronn method, we show that if λ1,λ2,λ3,λ4 are positive real numbers,at least one of the ratios λi/λj (1≤i< j≤4) is irrational, then there exist infinitely many primes p1,p2,p3,p4,p such that[λ1p12+λ2p23+λ3p34+λ4p45]=p.
In this paper, invariant subspaces of a class of second-order quadratic differential operators with variable coefficients are described. Applications of these invariant subspaces are discussed. Some examples are presented to illustrate their applications. In these examples, exact solutions of many nonlinear evolution equations with variable coefficients are constructed.
We consider the existence and multiplicity of solutions for a class of nonlinear impulsive problems when nonlinearity does not satisfy Ambrosetti-Rabinowitz condition. We obtain some new existence theorems of solutions by using critical theorems under Cerami condition.
Firstly, we introduce a kind of neural network operators by using a new smooth ramp function. We establish both the direct and converse results of approximation by the new operators, and thus give the essential approximation rate. Secondly, we use a linear combination of the new operators to improve the approximation rate for smooth functions. The uniform simultaneous approximation of the combination is also discussed. Finally, we introduce a new kind of neural network operators by using the Steklov functions, and establish both the direct and converse results of the approximation in Lp[a,b] spaces.
A new operation, skew product, of operator algebras is introduced. We show that reflexivity of operator algebras is preserved under the skew product. Thus many new reflexive algebras can be constructed. We also show that the skew product of two KS-algebras is, in general, not a KS-algebra.
Let m,n be non-zero integers with (m+n)(m-n)≠0, U an|mn(m+n)|-torsion free triangular algebra and D={dk}k∈N (m,n)-higher derivable map from U into itself. In this paper, it is shown that every (m,n)-higher derivable map on U is a higher derivation. As its application, we get that every (m,n)-higher derivable map on a nest algebra or an|mn(m+n)|-torsion free block upper triangular matrix algebra is a higher derivation.
We consider the existence of nodal solutions with two bubbles to the slightly subcritical problem with the fractional Laplacian
(-△)su=|u|p-1-εu，x∈Ω，
u=0，x∈∂Ω
where Ω is a smooth bounded domain in RN, N>2s, 0< s< 1, p=N+2s/N-2s and ε>0 is a small parameter, which can be seen as a nonlocal analog of the results of Bartsch, Micheletti, Pistoia[On the existence and the profile of nodal solutions of elliptic equations involving critical growth, Calc. Var. Partial Differential Equations, 2006, 3:265-282].
By Nevanlinna theory of the value distribution, and the theory of complex differential and complex difference, we will mainly investigate entire solutions with finite order of two types of systems of differential-difference equations, and obtain two results. It extends some results concerning complex differential (difference) equations to the systems of differential-difference equations.
An L(2, 1)-labeling of a graph G is an assignment of nonnegative integers to the vertices of G such that adjacent vertices receive numbers differed by at least 2, and vertices at distance 2 are assigned distinct numbers. The L(2, 1)-labeling number is the minimum range of labels over all such labeling. It was shown by Griggs and Yeh[Labelling graphs with a condition at distance 2, SIAM J. Discrete Math., 1992, 5:586-595] that the L(2,1)-labeling number of a tree is either Δ+1 or Δ+2. We give a complete characterization of L(2, 1)-labeling number for trees with maximum degree 3.
The symplectic structures on 3-Lie algebras and metric symplectic 3-Lie algebras are studied. For arbitrary 3-Lie algebra L, infinite many metric symplectic 3-Lie algebras are constructed. It is proved that a metric 3-Lie algebra (A,B) is a metric symplectic 3-Lie algebra if and only if there exists an invertible derivation D such that D∈DerB(A), and is also proved that every metric symplectic 3-Lie algebra (Ã,
) is a Tθ*-extension of a metric symplectic 3-Lie algebra (A,B,ω). Finally, we construct a metric symplectic double extension of a metric symplectic 3-Lie algebra by means of a special derivation.
