We investigate the complexity of the tree share model of Dockins et al., which is used to reason about shared ownership of resources in concurrent programs. We obtain the precise Berman complexity for the first-order theory of the Boolean algebra of tree shares with constants, which is STA(∗, 2 O(1) , n)-complete. For the first-order theory over the “relativization” multiplication operator on t...

Following Beurling’s theorem the natural compressions of multiplication operator in classical $$L^2$$ space are to model spaces and their orthogonal complements. Here, two possibly different considered, hence asymmetric truncated Toeplitz dual operators investigated. The main purpose paper is characterize which intertwine unilateral shift.

The aim of the present paper is to completely characterize boundedness and compactness a sum operator defined by some more complex products composition, multiplication, mth iterated radial derivative operators from Bloch-type spaces weighted-type on unit ball. In applications, all ball are also characterized.

We consider the C*-algebra, generated by multidimensional integral operators with homogeneous degree $$(-n)$$ kernels and of multiplication radial weak oscillating functions form $$|x|^{i\alpha }$$ . For this algebra, an operator symbolic calculus is constructed. In terms calculus, necessary sufficient conditions for Fredholm property are obtained.

A non-associative quantum mechanics is proposed in which the product of three and more operators can be non-associative one. The multiplication rules of the octonions define the multiplication rules of the corresponding operators with quantum corrections. The self-consistency of the operator algebra is proved for the product of three operators. Some properties of the non-associative quantum mec...

The border rank of the matrix multiplication operator for n× n matrices is a standard measure of its complexity. Using techniques from algebraic geometry and representation theory, we show the border rank is at least 2n2−n. Our bounds are better than the previous lower bound (due to Lickteig in 1985) of 2 n 2 + 2 −1 for all n≥ 3. The bounds are obtained by finding new equations that bilinear ma...

This paper focuses on the spectral properties of a bounded self-adjoint operator in L2(Rd) being sum convolution with an integrable kernel and multiplication by continuous potential converging to zero at infinity. We study both essential discrete spectra this operator. It is shown that spectrum union image potential. then provide number sufficient conditions for existence obtain lower upper bou...

We consider radial complex scaling/perfectly matched layer methods for scalar resonance problems in homogeneous exterior domains. introduce a new abstract framework to analyze the convergence of domain truncations and discretizations. Our theory requires rather minimal assumptions on scaling profile includes affine, smooth, unbounded profiles. report swift technique more technical one approxima...

It has been recently proposed that adults might solve single-digit addition and subtraction problems by rapidly moving through an ordered representation of numbers. In the present study, we tested whether these movements manifest themselves by on-line shifts of attention during arithmetic problem-solving. In two experiments, adult participants were presented with single-digit addition, subtract...

Abstract Diagonal (multiplication) operators acting between a particular class of countable inductive spectra Fréchet sequence spaces, called (LF)-spaces, are investigated. We prove results concerning boundedness, compactness, power and mean ergodicity. Furthermore, we determine when diagonal operator is Montel reflexive. analyze the in terms system weights defining spaces.