Calculation

On the structure of almost Ricci-Bourguignon solitons in Lorentzian para-Kenmotsu geometry

2025-10-15T10:21:23+00:00

This paper investigates almost Ricci-Bourguignon solitons on Lorentzian para-Kenmotsu (LP-Kenmotsu) manifolds. We show that when the soliton vector field coincides with the timelike vector field, the manifold admits an Einstein structure with constant scalar curvature, and the soliton is classified as shrinking or expanding depending on the soliton parameter. In the gradient case, the structure reduces either to an Einstein manifold or a gradient $u^\#$-Yamabe soliton. For manifolds of constant scalar curvature, we establish that the geometry is locally isometric to a Lorentzian hyperbolic space, while the Ricci-Bourguignon condition further yields a gradient conformal structure. These results provide a classification of almost Ricci-Bourguignon solitons in the LP-Kenmotsu setting and open avenues for exploring their role in Lorentzian paracontact geometry and spacetime models inspired by general relativity.

$\widetilde{L_r}-$finite type null hypersurfaces in generalized Robertson-Walker spacetimes

2025-12-08T10:30:57+00:00

This paper explores the $\widetilde{L_r}$-finite type null hypersurfaces within generalized Robertson-Walker spacetimes, where $\widetilde{L_r}$ stands for the linearized operator of the first variation of the $(r+1)-$th mean curvature arising from normal variations of the hypersurface equipped with its rigged Riemannian structure. We provide necessary and/or sufficient conditions characterizing $\widetilde{L_r}$-$p$-type and $\widetilde{L_r}$-null-$p$-type null hypersurfaces $(p=1,2)$, followed by various examples.

A computational benchmark of standardized lattice-based post-quantum signature schemes

2025-12-12T13:19:02+00:00

This article provides an expanded computational evaluation of three standardized lattice-based post-quantum signature schemes—ML-DSA-44, ML-DSA-65 and Falcon-512—using reference implementations from the Open Quantum Safe (liboqs) project. Unlike prior benchmarking efforts that rely on optimized implementations or hardware-specific tuning, this work focuses on reproducible baseline performance on a conventional CPU platform. We measure key generation, signing and verification times across 5,000 iterations and analyze the effect of message length on signing cost. Results confirm that ML-DSA variants achieve significantly faster signing and key generation, whereas Falcon-512 produces substantially smaller keys and signatures. The study further highlights the computational dominance of lattice operations over hashing, explaining the weak dependence of signing cost on message size. These findings aim to support system architects evaluating the practical feasibility of standardized post-quantum signature algorithms.

Multiplicative Lebesgue spaces

2025-12-16T11:09:15+00:00

This study introduces Lebesgue spaces of multiplicative functions defined from the set of real numbers to the set of geometric real numbers; it is demonstrated that these spaces constitute multiplicative normed spaces, and multiplicative versions of Minkowski's and H\"{o}lder's inequalities are established.

The surfaces with idempotent shape operator matrix defined along a surface curve

2025-12-07T13:53:56+00:00

In this study, we investigate surfaces in differential geometry whose shape operator is idempotent. Such an algebraic constraint on the operator imposes strict geometric restrictions on the surface, particularly on its curvature functions. We classify surfaces according to the values of their Gaussian curvature, mean curvature, and principal curvatures when the shape operator matrix defined along a surface curve satisfies $S^{2}=S$.

The results show that the idempotency condition leads to three distinct geometric cases depending on whether the geodesic torsion vanishes. These classifications provide insight into the structure of flat, minimal, elliptic, and umbilical surfaces.