We use `p estimates together with Brascamp-Lieb inequalities to obtain bounds on the variance of the solution u" to the elliptic equation r" a(x="; ')r"u" = r" f . The variance is shown to be O("r) where the exponent r depends on the contrast of a(x; '). In two dimensions, we show that variance of the Greens function of the above elliptic operator is bounded. We also obtain decay rates for the ...

In the present article, we introduce Chlodowsky variant of $(p,q)$-Bernstein operators and compute the moments for these operators which are used in proving our main results. Further, we study some approximation properties of these new operators, which include the rate of convergence using usual modulus of continuity and also the rate of convergence when the function $f$ belongs to the class Li...

in the exterior domain Ω(1) := {x ∈ RN : ‖x‖ > 1}, where p > 1, x = (x1, . . . ,xN ) ∈ RN , N ≥ 2, Du= (∂u/∂x1, . . . ,∂u/∂xN ), ‖x‖ is usual Euclidean norm in RN . Throughout this paper we will assume that (A1) p ∈ C loc(Ω(1)), 0 < μ < 1, and p > 1 constant, (A2) A = (Aij(x))N×N is a real symmetric positive define matrix function with Aij ∈ C 1+μ loc (Ω(1)), i, j = 1, . . . ,N , and 0 < μ < 1....

Citation: Renna M, Signore A, Paradiso VM and Santamaria P (2018) Faba Greens, Globe Artichoke’s Offshoots, Crenate Broomrape and Summer Squash Greens: Unconventional Vegetables of Puglia (Southern Italy) With Good Quality Traits. Front. Plant Sci. 9:378. doi: 10.3389/fpls.2018.00378 Faba Greens, Globe Artichoke’s Offshoots, Crenate Broomrape and Summer Squash Greens: Unconventional Vegetables ...

we establish a sharp maximal function estimate for some vector-valued multilinear singular integral operators. as an application, we obtain the $(l^p, l^q)$-norm inequality for vector-valued multilinear operators.

We present a path integral formalism for quantising the spectral action of noncommutative geometry, based on the principle of summing over all Dirac operators. The approach is demonstrated on two simple finite noncommutative geometries. On the first, the graviton is described by a Higgs field, and on the second, it is described by a gauge field. We start with the partition function, and calcula...

ILP systems which use some form of Inverse Entailment (IE) are based on clause refinement through a hypotheses space bounded by a most specific clause. In this paper we give a new analysis of refinement operators in this setting. In particular, Progol’s refinement operator is revisited and discussed. It is known that Progol’s refinement operator is incomplete with respect to the general subsump...

In this paper we study matrices A = (aij) whose (i, j) -entry is a function of i/j; that is, aij = f(i/j) for some f : Q → C. We obtain a formula for the truncated determinants in the case where f is multiplicative, linking them to determinants of truncated Toeplitz matrices. We apply our formula to obtain several determinants of number-theoretic matrices. Mathematics Subject Classification 200...

Chiclana et al. [Chiclana, F., Herrera-Viedma, E., Herrera, F., Alonso, S. (2007). European Journal of Operational Research 182, 383–399] provided some IOWA operators for aggregating the individual fuzzy preference elations. The aim of this work is further to study their desired properties under group decision making problem with fuzzy preference relations. First, it is proved that the collecti...