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The metric dimension of the annihilating-ideal graph of a finite commutative ring
No full textWe determine the metric dimension of the annihilating-ideal graph of a local finite commutative principal ring and a finite commutative principal ring with two maximal ideals. We also find the bounds for the metric dimension of the annihilating-ideal graph of an arbitrary finite commutative principal ring.
http://dx.doi.org/10.1017/S000497271200033
A meshless local Galerkin integral equation method for solving a type of Darboux problems based on the radial basis functions
No full textThe main goal of this paper is to solve a class of Darboux problems by converting them into the two-dimensional nonlinear Volterra integral equation of the second kind. The scheme approximates the solution of these integral equations using the discrete Galerkin method together with local radial basis functions, which use a small set of data instead of all points in the solution domain. We also employ the Gauss–Legendre integration rule on the influence domains of shape functions to compute the local integrals appearing in the method. Since the scheme is constructed on a set of scattered points and does not require any background meshes, it is meshless. The error bound and the convergence rate of the presented method are provided. Some illustrative examples are included to show the validity and efficiency of the new technique. Furthermore, the results obtained demonstrate that this method uses much less computer memory than the method established using global radial basis functions.
doi:10.1017/S144618112100037
Numerical solutions to a fractional diffusion equation used in modelling dye-sensitized solar cells
No full textDye-sensitized solar cells consistently provide a cost-effective avenue for sources of renewable energy, primarily due to their unique utilization of nanoporous semiconductors. Through mathematical modelling, we are able to uncover insights into electron transport to optimize the operating efficiency of the dye-sensitized solar cells. In particular, fractional diffusion equations create a link between electron density and porosity of the nanoporous semiconductors. We numerically solve a fractional diffusion model using a finite-difference method and a finite-element method to discretize space and an implicit finite-difference method to discretize time. Finally, we calculate the accuracy of each method by evaluating the numerical errors under grid refinement.
doi:10.1017/S144618112100035
Fusion -categories with no line operators are grouplike
No full texthttp://dx.doi.org/10.1017/S000497271200033
Graphs determined by their -gain spectra
No full textAn undirected graph G is said to be determined by its T-gain spectrum (DTS) if every T-gain graph Φ = (H, T, φ) cospectral to G is switching equivalent to G. In this paper, we obtain the following results
(1) The complete graph Kn and the graph Kn, obtained from Kn by deleting an edge, are proved to be DTS.
(2) The star K1,n is DTS if and only if n ≤ 2.
(3) An odd path P2m+1 is not DTS if m ≥ 2.
(4) An operation is given for constructing cospectral T-gain graphs. As an application, a tree of arbitrary order (at least 5) is proved to be not DTS
Starlikeness and convexity of Cauchy transforms on regular polygons
No full textIf , let be an arbitrary regular -sided polygon. In this paper, we prove that the Cauchy transform of the normalized two-dimensional Lebesgue measure on is univalent and starlike but not convex in
The slot length of a family of matrices
No full textWe introduce the notion of the slot length of a family of matrices over an arbitrary field \DF. Using this definition it is shown that, if and and are complex matrices with unicellular and the pair irreducible, the slot length of satisfies , where both inequalities are sharp, for every . It is conjectured that the slot length of any irreducible pair of matrices, where , is at most . The slot length of a family of rank one complex matrices can equal
{\bf h}-minimum spanning lengths and an extension to Burnside's theorem on irreducibility
No full texthttp://dx.doi.org/10.1017/S000497271200033
The character graph of a finite group is perfect
No full texthttp://dx.doi.org/10.1017/S000497271200033
A harmonic sum over nontrivial zeros of the Riemann zeta-function
No full texthttp://dx.doi.org/10.1017/S000497271200033