— Suppose that G is a locally compact abelian group with a Haar measure μ. The δ-ball Bδ of a continuous translation invariant pseudo-metric is called d-dimensional if μ(B2δ′ ) 6 2μ(Bδ′ ) for all δ′ ⊂ (0, δ]. We show that if A is a compact symmetric neighborhood of the identity with μ(nA) 6 ndμ(A) for all n > d log d, then A is contained in an O(d log d)-dimensional ball, B, of positive radius ...

The principal result of this paper is the following Markov-type inequality for Müntz polynomials. Theorem (Newman’s Inequality on [a, b] ⊂ (0,∞)). Let Λ := (λj)j=0 be an increasing sequence of nonnegative real numbers. Suppose λ0 = 0 and there exists a δ > 0 so that λj ≥ δj for each j. Suppose 0 < a < b. Then there exists a constant c(a, b, δ) depending only on a, b, and δ so that ‖P ′‖[a,b] ≤ ...

in this paper we introduce the notions of g∗l-module and g∗l-module whichare two proper generalizations of δ-lifting modules. we give some characteriza tions and properties of these modules. we show that a g∗l-module decomposesinto a semisimple submodule m1 and a submodule m2 of m such that every non-zero submodule of m2 contains a non-zero δ-cosingular submodule.

The μ-value or structured singular value is a prominent mathematical tool to analyze and synthesize both the robustness performance of time-invariant systems. We establish new results concerning values for Hadamard product real square M-matrices. are obtained while considering set block diagonal uncertainties. targeted uncertainties two types, that is, pure scalar full-block eigenvalue perturba...

We analyze degenerate, second-order, elliptic operators H in divergence form on L2(R ×Rm). We assume the coefficients are real symmetric and a1Hδ ≥ H ≥ a2Hδ for some a1, a2 > 0 where Hδ = −∇x1 cδ1,δ′ 1(x1)∇x1 − cδ2,δ′ 2(x1)∇ 2 x2 . Here x1 ∈ R , x2 ∈ R m and cδi,δ′ i are positive measurable functions such that cδi,δ′ i(x) behaves like |x| δi as x→ 0 and |x| ′ i as x→ ∞ with δ1, δ ′ 1 ∈ [0, 1〉 a...

Catalytic tests to assess the performance of mixed perovskite-type oxides (La0.9Ca0.1FeO3-δ, La0.6Ca0.4FeO3-δ, Nd0.9Ca0.1FeO3-δ, Nd0.6Ca0.4FeO3-δ, Nd0.6Ca0.4Fe0.9Co0.1O3-δ, Nd0.6Ca0.4Fe0.97Ni0.03O3-δ, and LSF) with respect CO oxidation are presented as well characterization materials by XRD SEM. Perovskites a highly versatile class due their flexible composition ability incorporate dopants easi...

We give a new region of existence of solutions to the superhomogeneous Dirichlet problem (SR) −∆pu = v δ v > 0 in B, −∆qv = u μ u > 0 in B, u = v = 0 on ∂B, where B is the ball of radius R > 0 centered at the origin in R . Here δ, μ > 0 and ∆mu = div(|∇u| ∇u) is the m−Laplacian operator for m > 1.

We prove that the notion of rigidity (or relative property (T)) for inclusions of finite von Neumann algebras defined in [Po1] is equivalent to a weaker property, in which no “continuity constants” are required. The notion of relative property (T) (or rigidity) for inclusions of finite von Neumann algebras with countable decomposable center was introduced in ([P1]) by requiring that one of the ...

In this work, we provide an estimate of the Morse index radially symmetric sign changing bounded weak solutions u to semilinear fractional Dirichlet problem(−Δ)su=f(u) in B,u=0in RN∖B, where s∈(0,1), B⊂RN is unit ball centered at zero and nonlinearity f class C1. We prove that for s∈(1/2,1) any solution above problem has a greater than or equal N+1. If s∈(0,1/2], same conclusion holds under add...

We are interested in the investigation of the orthogonality (in the sense of Birkhoff) of the range of an elementary operator and its kernel. 1. Introduction. Let H be a separable infinite-dimensional complex Hilbert space and let B(H) denote the algebra of all bounded operators on H into itself. Given A, B ∈ B(H), we define the generalized derivation δ A,B : B(H) B(H) by δ A,B (X) = AX −XB and...