Let $G$ be a strongly connected digraph with vertex set $\{v_1, v_2, \dots, v_n\}$. Denote by $D_{ij}$ the distance between vertices $v_i$ and $v_j$ in $G$. Two variant versions of matrix were proposed Yan Yeh (Adv. Appl. Math.), Bapat et al. (Linear Algebra Appl.) independently, one is $q$-distance matrix, other exponential matrix. Given nonzero indeterminate $q$, $\mathscr{D}_G=(\mathscr{D}_{...

Computation of the large sparse matrix exponential has been an important topic in many fields, such as network and finite-element analysis. The existing scaling squaring algorithm (SSA) is not suitable for computation it requires greater memories computational cost than actually needed. By introducing two novel concepts, i.e., real bandwidth bandwidth, to measure sparsity matrix, analyzed. It f...

A bstract By combining the KMOC-formalism with exponential representation of scattering matrix we show that two-body angle is given by corresponding element representation. This holds to all orders in Post-Minkowskian expansion gravity when restricted conservative sector. Once gravitational radiation taken into account new terms correcting this relationship appear starting at fourth order. syst...

In this paper, a class of multivariate matrix-exponential affine mixtures with marginals is proposed. The shown to possess various attractive properties such as closure under size-biased Esscher transform, order statistics, residual lifetime and higher equilibrium distributions. This allows for explicit calculations actuarial quantities interest. results are applied in wide range problems inclu...