This paper is devoted to GPU kernel optimization and performance analysis of three tensorproduct operators arising in finite element methods. We provide a mathematical background to these operations and implementation details. Achieving close-to-the-peak performance for these operators requires extensive optimization because of the operators’ properties: low arithmetic intensity, tiered structu...

The invariant projections of the energy-momentum tensors of Lagrangian densities for tensor fields over differentiable manifolds with contravariant and covariant affine connections and metrics [(Ln, g)-spaces] are found by the use of an non-null (non-isotropic) contravariant vector field and its corresponding projective metrics. The notions of rest mass density, momentum density, energy current...

A Banach space E has the Grothendieck property if every (linear bounded) operator from E into c0 is weakly compact. It is proved that, for an integer k > 1, every k-homogeneous polynomial from E into c0 is weakly compact if and only if the space P(kE) of scalar valued polynomials on E is reflexive. This is equivalent to the symmetric k-fold projective tensor product of E (i.e., the predual of P...

A quantization over a manifold can be seen as a way to construct a differential operator with prescribed principal symbol. The map from the space of principal symbols to the space of differential operators is moreover required to be a linear bijection. It is known that there is in general no natural quantization procedure. However, considering manifolds endowed with additional structures, such ...

This study examined Three Wishes (a projective technique commonly used with children) in boys with Duchenne muscular dystrophy (DMD), a fatal, progressive illness (n = 74). A reliable and parsimonious scoring system was developed to code wish type. Probands' responses were compared with unaffected siblings (n = 32) and a male comparison group (n = 43). Contrary to what was expected, the DMD gro...

One hundred and fifty-eight clinical psychologists practising in Britain completed a questionnaire concerning their use of and views about psychological assessment. The respondents reported spending on average slightly more than 50% of their working day on face-to-face clinical work and 13% of their time with clients on individual assessment. The results were compared to those of a similar surv...

This study examines whether coding open answers in a picture-based test, as to the extent they reflect the fear of being laughed at (i.e., gelotophobia), demonstrates sufficient validity to construct a semi-projective test for the assessment of gelotophobia. Previous findings indicate that cartoon stimuli depicting laughter situations (i.e., in the pilot version of the Picture-Geloph; Ruch et a...

We show that the numerical index of any operator ideal is less than or equal to minimum indices domain space and range space. Further, we compact operators weakly dual space, this result provides interesting examples. also a projective injective tensor product Banach spaces factors. Finally, if two has Daugavet property unit ball one factor slicely countably determined its contains point Fréche...

Abstract We consider real hypersurfaces M in complex projective space equipped with both the Levi-Civita and generalized Tanaka–Webster connections. Associated connection we can define a differential operator of first order. For any nonnull number k symmetric tensor field type (1,1) B on , (1,2) $$B^{(k)}_T$$ B</mml:m...

Throughout this paper we work over the base field C. The basic problem in algebraic geometry treated here is the filling-in problem (or degeneration problem). Given a smooth projective family X× → ∆×, we would like to know when we can fill in a reasonably nice special fiber X0 to form a projective family X → ∆, perhaps up to a finite base change on ∆×. For example, when can X0 be smooth? When c...