Acta et Commentationes Universitatis Tartuensis de Mathematica

Quasi-Laplacian energy of fractal graphs

2023-08-25T09:02:40+00:00

Graph energy is a measurement of determining the structural information content of graphs. The first Zagreb index can be handled with its connection to graph energy. In this paper, a novel and significant application of the first Zagreb index to composite graphs based on fractal graphs is revealed, and by the relation between quasi-Laplacian energy and the vertex degrees of a graph, we derive closed-form formulas for the quasi-Laplacian energy of fractal graphs or namely R-graphs, R-vertex and edge join, R-vertex and edge corona, R-vertex and edge neighborhood graphs in terms of the corresponding energy, the first Zagreb indices, number of vertices and edges of the underlying graphs.

Asymmetric dynamic plastic response of stepped plates

2023-09-06T14:07:44+00:00

The dynamic plastic response of circular plates to asymmetric loading is studied. An approximate theoretical procedure is developed for the evaluation of asymmetrical residual de ections. The solution technique is based on the equality of the internal dissipation and the external work, respectively. Maximal residual de ections are defined for plates of piece-wise constant thickness.

On a generalization of the Nagumo–Brezis theorem

2023-09-10T08:34:18+00:00

We generalize the Nagumo–Brezis theorem to the category of MC^k-Fréchet manifolds. Then we will apply the obtained result to locate a critical value of a real-valued mapping over these manifolds.

Construction of continuous controlled K-g-fusion frames in Hilbert spaces

2023-10-06T13:26:51+00:00

We present the notion of continuous controlled K-g-fusion frame in a Hilbert space which is generalization of discrete controlled K-g-fusion frame.We discuss some characterizations of a continuous controlled K-g-fusion frame. A relationship between a continuous controlled K-g-fusion frame and a quotient operator has been studied. Finally, stability of a continuous controlled g-fusion frame has been described.

Statistical Killing vector fields on the Hopf hypersurfaces in the complex space forms

2024-02-12T09:47:01+00:00

Statistical Killing vector field is introduced and Hopf hypersurfaces of complex space forms with the condition of being structural statistical Killing vector field are studied. It is shown that these hypersurfaces have at most three distinct constant principal curvatures.

On h-almost conformal η-Ricci-Bourguignon soliton in a perfect fluid spacetime

2023-10-28T05:46:27+00:00

The primary object of the paper is to study h-almost conformal η-Ricci-Bourguignon soliton in an almost pseudo-symmetric Lorentzian Kähler spacetime manifold when some different curvature tensors vanish identically. We have also explored the conditions under which an h-almost conformal Ricci-Bourguignon soliton is steady, shrinking or expanding in different perfect fluids such as stiff matter, dust fluid, dark fluid and radiation fluid. We have observed in a perfect fluid spacetime with h-almost conformal η-Ricci-Bourguignon soliton to be a manifold of constant Riemannian curvature under some certain conditions. We have gone on to refine the classification of the potential function with respect to gradient h-almost conformal η-Ricci-Bourguignon soliton in a perfect uid spacetime with torse-forming vector field ξ. Finally, we have developed an example of h-almost conformal η-Ricci-Bourguignon soliton.

Equivalent Notions in the context of compatible Endo-Lie Algebras

2023-11-15T16:52:19+00:00

In this article, we introduce a notion of compatibility between two Endo-Lie algebras defined on the same linear space. Compatibility means that any linear combination of the two structures always induces a new Endo-Lie algebras structure. In this case of compatibility, we show that the notions of bialgebras, standard Manin triples and matched pairs are equivalent. We find this equivalence for the case of compatible Lie algebras since this is a particular case of compatible Endo-Lie algebras.

Stiffness parameter prediction for elastic supports of non-uniform rods

2024-02-03T08:46:58+00:00

The present research focuses on establishing the stiffness parameter of elastic springs placed at the ends of non-uniform rods. The governing equation for the longitudinal vibrations of the rod was solved using the Haar wavelet integration method. The calculated natural frequency parameters closely aligned with those available in the literature. The normalised values of the first ten natural frequency parameters were used in the feature vector to predict the stiffness parameter of the springs. A feedforward neural network with two hidden layers made accurate predictions when the range of each natural frequency parameter
within its domain exceeded one. The insights garnered from this study contribute to the design, optimisation and assessment of diverse engineering applications.

The poroelastic layer with an axisymmetric cylindrical hole under different types of loading

2024-03-07T08:49:17+00:00

The exact solution of the poroelastic axisymmetric problem for a layer with a cylinderical hole is constructed under assumptions of Biot's model. The calculations provided by derived explicit formulas for full stress and pore pressure allow to state some important dependencies between the poroelastic stress state of the layer and type of poroelastic materials, loading types and height of the layer.

A refinement of a lemma by Aron, Cascales, and Kozhushkina on Asplund operators

2024-01-11T12:55:28+00:00

We prove a refinement of a lemma by Aron, Cascales, and Kozhushkina on Asplund operators. Refinements of a Bishop–Phelps–Bollobás type theorem for Asplund operators with values in spaces C₀(L) by the same authors, and an extension of this theorem for Asplund operators with values in uniform algebras by Cascales, Guirao, and Kadets, follow.