We show how to determine the lowest order mixing of all scalar with twofermion two impurity BMN operators in the antisymmetric representation of SO(4). Differentiation on harmonic superspace allows one to derive two-loop anomalous dimensions of gauge invariant operators from this knowledge: the value for the second anomalous correction to the dimension is essentially the square of the two-fermi...

We show that the commutant lifting theorem for n-tuples of commuting contractions with regular dilations fails to be true. A positive answer is given for operators which ”double intertwine” given n-tuples of contractions. The commutant lifting theorem is one of the most important results of the Sz. Nagy—Foias dilation theory. It is usually stated in the following way: Theorem. Let T and T ′ be ...

Given a contraction A on Hilbert space $${\mathcal {H}}$$ , an operator T is said to be A-invariant if $$\langle Tx,x\rangle =\langle TAx,Ax\rangle $$ for every $$x\in {\mathcal such that $$\Vert Ax\Vert =\Vert x\Vert . In the special case in which both defect indices of are equal 1, we show compression unbounded linear transformation commutes with minimal unitary dilation A. This result was pr...

Here we study dilations of q-commuting tuples. In [BBD] the authors gave the correspondence between the two standard dilations of commuting tuples and here these results have been extended to q-commuting tuples. We are able to do this when q-coefficients ‘qij ’ are of modulus one. We introduce ‘maximal q-commuting subspace ’ of a n-tuple of operators and ‘standard q-commuting dilation’. Our mai...

background achalasia is the most recognized motor disorder of the esophagus.because it is an uncommon disease, most studies have reviewed small numbers of patients. here, we report demographic, clinical features and treatment outcomes in 700 achalasia patients. methods in all patients, diagnosis was established based on clinical, radiological, endoscopic and manometric criteria. a questionnaire...

A virtual element discretisation for the numerical approximation of three-field formulation linear poroelasticity introduced in R. Oyarzúa and Ruiz-Baier, (SIAM J. Numer. Anal. 54 2951–2973, 2016) is proposed. The treatment extended to include also transient case. Appropriate projector operators are they assist deriving energy bounds time-dependent discrete problem. Under standard assumptions o...

We propose a multiresolution representation for maximum intensity projection (MIP) volume rendering, based on morphological pyramids which allow progressive refinement and have the property of perfect reconstruction. The pyramidal analysis and synthesis operators are composed of morphological erosion and dilation, combined with dyadic downsampling for analysis and dyadic upsampling for synthesi...

We recently proposed a multiresolution representation for maximum intensity projection (MIP) volume rendering based on morphological adjunction pyramids which allow progressive refinement and have the property of perfect reconstruction. In this algorithm the pyramidal analysis and synthesis operators are composed of morphological erosion and dilation, combined with dyadic downsampling for analy...

This paper addresses extensions of the complex Ornstein-Uhlenbeck semigroup to operator algebras in free probability theory. If a1, . . . , ak are ∗-free R-diagonal operators in a II1 factor, then Dt(ai1 · · · ain) = e −ntai1 · · · ain defines a dilation semigroup on the non-self-adjoint operator algebra generated by a1, . . . , ak. We show that Dt extends (in two different ways) to a semigroup...

We establish the existence and uniqueness of finite free resolutions and their attendant Betti numbers for graded commuting d-tuples of Hilbert space operators. Our approach is based on the notion of free cover of a (perhaps noncommutative) row contraction. Free covers provide a flexible replacement for minimal dilations that is better suited for higher-dimensional operator theory. For example,...