A tree is called k-decomposable if it has a spanning forest whose components are all of size k. Analogously, a tree is called T -decomposable for a fixed tree T if it has a spanning forest whose components are all isomorphic to T . In this paper, we use a generating functions approach to derive exact and asymptotic results on the number of k-decomposable and T -decomposable trees from a so-call...

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 provide an analytical expression for optimal Lewenstein-Sanpera decomposition of Bell decomposable states by using semi-definite programming. Also using the KarushKuhn-Tucker optimization method, the minimum relative entropy of entanglement of Bell decomposable states has been evaluated and it is shown that the same separable Bell decomposable state lying at the boundary of convex set of sep...

The Organic Grid is a biologically inspired and fully-decentralized approach to the organization of computation that is based on the autonomous scheduling of strongly mobile agents on a peer-to-peer network. Through the careful design of agent behavior, the emerging organization of the computation can be customized for different classes of applications. In this paper we report our experience in...

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...

A n-vertex graph is said to be decomposable if for any partition (λ1, . . . , λp) of the integer n, there exists a sequence (V1, . . . , Vp) of connected vertex-disjoint subgraphs with |Vi| = λi. In this paper, we focus on decomposable trees. We show that a decomposable tree has degree at most 4. Moreover, each degree-4 vertex of a decomposable tree is adjacent to a leaf. This leads to a polyno...

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...