We develop a higher-order generalization of the LQ decomposition and show that this decomposition plays an important role in likelihood-based estimation and testing for separable, or Kronecker structured, covariance models, such as the multilinear normal model. This role is analogous to that of the LQ decomposition in likelihood inference for the multivariate normal model. Additionally, this hi...

Boujari [5] proved a fixed point theorem with an old version of the integraltype contraction , his proof is incorrect. In this paper, a new generalizationof integral type contraction is introduced. Moreover, a fixed point theorem isobtained.

We consider the free boundary problem of MHD in multi-dimensional case. This describes motion two incompressible fluids separated by a closed interface under action magnetic field. is overdetermined, and we find an equivalent system equations which uniquely solvable locally time Lp-Lq maximal regularity class, where 1<p,q<∞ 2/p+N/q<1. As result, original two-phase for time.

The one-sided Littlewood–Paley inequality for pairwise disjoint rectangles in R2 is proved for the Lp-metric, 0 < p ≤ 2. This result can be treated as an extension of Kislyakov and Parilov’s result (they considered the one-dimensional situation) or as an extension of Journé’s result (he considered disjoint parallelepipeds in Rn but his approach is only suitable for p ∈ (1, 2]). We combine Kisly...

In this work, we consider the Cauchy problem for u′ − Au = f with A the Laplacian operator on some Riemannian manifolds or a sublapacian on some Lie groups or some second order elliptic operators on a domain. We show the boundedness of the operator of maximal regularity f 7→ Au and its adjoint on appropriate Hardy spaces which we define and study for this purpose. As a consequence we reobtain t...

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A semideenite relaxation (?) for the problem of nding the maximum number (?) of edges in a complete bipartite subgraph of a bipartite graph ? = (V1 V2; E) is considered. For a large class of graphs, the relaxation is better than the LP-relaxation described in 8]. It is shown that (?) is bounded from above by the Lovv asz theta function (LQ(?)) of the graph LQ(?) related to the line graph of ?. ...

Let ωk φ( f, δ)w,Lq be the Ditzian–Totik modulus with weight w, M k be the cone of k-monotone functions on (−1, 1), i.e., those functions whose kth divided differences are nonnegative for all selections of k + 1 distinct points in (−1, 1), and denote E(X, Pn)w,q := sup f ∈X infP∈Pn ∥w( f − P)∥Lq , where Pn is the set of algebraic polynomials of degree at most n. Additionally, let wα,β (x) := (1...