Sentence examples for dual transform from inspiring English sources

To obtain an expression for the dual transform the Lagrangian function of (P1) is needed, which has the following form: (16).

We obtain new inversion formulas for the Radon transform and the corresponding dual transform acting on affine Grassmann manifolds of planes in Rn.

We show that this transform intertwines the actions of certain M n -invariant differential operators on G(p, n) and G(q, n), and we prove an inversion forM n -invarianttransform when n is odifferentialzing the Radoperatorsion formula, and obtaininG pn pandicular an inversion formula for the dual transform.

Starting with the study of the classical Laplace convolution and a cosine convolution, along with associated dual transforms, natural algebra homomorphisms are introduced which capture the convoluted semigroup and cosine function properties.

We also consider its dual transforms associated with the Schrödinger operator L defined by R ˜ = L − 1 / 2 ∇ and the higher order commutator R ˜ b m f ( x ) = ∫ R d ( b ( x ) − b ( y ) ) m K ˜ ( x, y ) f ( y ) d y, where K ˜ ( x, y ) is the kernel of R ˜ and m = 1, 2, …  .

Also, the dual Riesz transform associated with the Schrödinger operator L is defined by T ∗ = L − 1 2 ∇ and the commutator operator [ b, T ∗ ] ( f ) ( x ) = T ∗ ( b f ) ( x ) − b ( x ) T ∗ f ( x ), x ∈ R n. (2).

Motivated by [3], our aim is to establish the boundedness for the dual Riesz transform associated with Schrödinger operators and its commutators on weighted Morrey spaces related to the certain nonnegative potentials, where the condition on the potential is weaker than that in [3].

Dual SBP-RA21 and single SBP or UH-RA.21 display phage were produced from the double transformed DH5αF′ bacterial cells.

We describe the application of a dual beam Fourier transform infrared (FTIR) spectrometer and sampling system for simultaneous measurements of fluxes of several trace gases between the earth's surface and the atmosphere.

The Drive Gauge has dual functions: to transform Sora into a "Drive Form" or to summon a special character.

At the same time, we introduce the concept of non-marginal processing in multiband case: due to the presence of potentially strong common information between the various bands, we developed a denoising method based on dual-tree quaternionic transform that supports all spectral bands simultaneously.