The paper derives optimal inequalities for bi-slant submanifolds in metallic Riemannian space forms.
problem Understanding geometric properties of bi-slant submanifolds in metallic Riemannian product space forms.
method Deriving generalized Wintgen inequality, optimal inequalities involving δ-invariants, Ricci curvature, shape operator invariants, and generalized normalized δ-Casorati curvatures.
result Established optimal inequalities for bi-slant submanifolds in metallic Riemannian product space forms.
We consider submanifolds into Riemannian manifold with metallic structures. We obtain some new results for hypersurfaces in these spaces and we express the fundamental theorem of submanifolds into products spaces in terms of metallic structures. Moreover, we define new structures called complex metallic structures. We …
The paper characterizes metallic pseudo-Riemannian manifolds using conjugate connections and tensor structures.
problem Characterizing metallic pseudo-Riemannian manifolds.
method Using conjugate connections and tensor structures, the paper derives new characterizations and conditions for these manifolds.
result A necessary and sufficient condition for a non-integrable metallic pseudo-Riemannian manifold to be a quasi metallic pseudo-Riemannian manifold is derived.
Study properties of specific submanifolds in metallic Riemannian spaces.
problem Characterize warped product pointwise bi-slant submanifolds.
method Analyze in locally metallic Riemannian manifolds with examples in Euclidean spaces.
result Construct examples of warped product pointwise bi-slant submanifolds.
The aim of our paper is to focus on some properties of submanifolds in Riemannian manifolds endowed with endomorphisms that generalize the Golden Riemannian structure, named metallic Riemannian structures. We focus on the properties of the structure induced on submanifolds, named by us Σ-metallic Riemannian structure…
In this paper, we study the existence of proper warped product submanifolds in metallic (or Golden) Riemannian manifolds and we discuss about semi-invariant, semi-slant and, respectively, hemi-slant warped product submanifolds in metallic and Golden Riemannian manifolds. Also, we provide some examples of warped product…
Review of metallic Riemannian geometry advances.
problem No specific problem stated; focuses on advancements.
method No specific method mentioned; focuses on review of advances.
result Rich potential and diverse applications of metallic Riemannian geometry.
We characterize the metallic structure on the product of two metallic manifolds in terms of metallic maps and provide a necessary and sufficient condition for the warped product of two locally metallic Riemannian manifolds to be locally metallic. The particular case of product manifolds is discussed and an example of m…
The aim of our paper is to focus on some properties of slant and semi-slant submanifolds of metallic Riemannian manifolds. We give some characterizations for submanifolds to be slant or semi-slant submanifolds in metallic or Golden Riemannian manifolds and we obtain integrability conditions for the distributions involv…
The Metallic Ratio is fascinating topic that continually generated news ideas. A Riemannian manifold endowed with a Metallic structure will be called a Metallic Riemannian manifold. The main purpose of the present paper is to study the geometry of transversal lightlike submanifolds and radical transversal lightlike sub…
In this paper, we introduce metallic maps between metallic Riemannian manifolds, provide an example and obtain certain conditions for such maps to be totally geodesic. We also give a sufficient condition for a map between metallic Riemannian manifolds to be harmonic map. Then we investigate the constancy of certain map…
The aim of our paper is to focus on some properties of hemi-slant submanifolds in metallic (and Golden) Riemannian manifolds. We give some characterizations for submanifolds to be hemi-slant submanifolds in metallic (or Golden) Riemannian manifolds and we obtain integrability conditions for the distributions involved. …
Properties of invariant, anti-invariant and slant isometrically immersed submanifolds of metallic Riemannian manifolds are given with a special view towards the induced Σ-structure. Examples of such metallic manifolds are also given.
Study characterizes submanifolds in metallic semi-Riemannian manifolds with specific connections.
problem Characterizing submanifolds in metallic semi-Riemannian manifolds.
method Introduces and analyzes invariant and screen semi-invariant lightlike submanifolds with a quarter symmetric non-metric connection.
result Characterizes integrability and parallelism of distributions in these submanifolds.
We study the properties of a generalized metallic, a generalized product and a generalized complex structure induced on the generalized tangent bundle of M by a metallic Riemannian structure (J,g) on M, providing conditions for their integrability with respect to a suitable connection. Moreover, by using methods …
In this paper, we study metallic structures, i.e. polynomial structures with the structure polynomial Q(J)=J2−aJ−bI on manifolds using the metallic ratio, which is a generalization of the Golden proportion. We investigate for integrability and parallelism conditions of metallic structures. Also, we gi…
In our article, we introduce and study lightlike hypersurfaces of a metallic semi-Riemannian manifold. We examine some geometric properties of invariant lightlike hypersurfaces. We show that the induced structure on an invariant lightlike hypersurface is also metallic. We also define screen semi-invariant lightlike hyp…
We give necessary and sufficient conditions for the real distributions defined by a metallic pseudo-Riemannian structure to be integrable and geodesically invariant, in terms of associated tensor fields to the metallic structures and of adapted connections. In the integrable case, we prove a Chen-type inequality for th…
The concept of harmonic metallic structure on a metallic pseudo-Riemannian manifold is introduced. In the case of compact manifolds we prove that harmonicity of a metallic structure J, with J2=pJ+qI and p2+4q=0, is equivalent to dJ=0. Conditions for a harmonic metallic structure to be preserved by harmoni…
Study geodesic X-ray transform and streaking artifacts on simple surfaces or spaces of constant curvature.
problem Streaking artifacts in CT images due to metal regions.
method Geodesic X-ray transform on nontrapping compact Riemannian manifolds with strictly convex boundaries.
result Streaking artifacts result from conormal singularities along common tangent geodesics.
In the present paper, we introduce screen transversal lightlike submanifolds of metallic semi-Riemannian manifolds with its subclasses, namely screen transversal anti-invariant, radical screen transversal and isotropic screen transversal lightlike submanifolds, and give an example. We show that there do not exist co-is…
A new unsupervised method removes CT metal artifacts using beta-CycleGAN and attention.
problem Metal artifact reduction in computed tomography (CT) images.
method Unsupervised learning using a beta-CycleGAN architecture with attention mechanism.
result Improved metal artifact removal that preserves image details.
A RL approach optimizes metal AM process parameters for consistent melt pool depth.
problem Optimizing process parameters for metal additive manufacturing to ensure repeatability and control microstructure.
method A Reinforcement Learning (RL) framework based on Q-learning is applied to find optimal laser power and scan velocity combinations.
result The RL framework learns optimal process parameters without prior knowledge, providing a model-free approach.
The purpose of the present work is to study the complete and horizontal lifts of the metallic structure on tangent bundles with respect to almost product structure. We also establish fundamental formulae related to integrability and horizontal lifts of metallic structures on tangent bundles. Moreover, the study reveale…
In this article, we introduce some metallic structures on the tangent bundle of a P-Sasakian manifold by complete lift, horizontal lift and vertical lift of a P-Sasakian structure (φ,η,ξ) on tangent bundle. Then we investigate the integrability and parallelity of these metallic structures.
Improved MF-DFA model analyzes precious metals market efficiency and multifractality.
problem Analyze price fluctuations in precious metals market.
method Proposed Bi-OSW-MF-DFA method compared to MF-DFA.
result Bi-OSW-MF-DFA method shows better efficiency in precious metals market analysis.
This study examines local co-movements in energy, agriculture, and metal markets using copulas.
problem Identifying local dependencies and asymmetries in energy, agriculture, and metal markets.
method Non-parametric mixture copula and copula-based local Kendall's tau approach.
result Increased co-movements in extreme situations, asymmetric local dependence, and diversification potential.
The assessment of co-movement among metals is crucial to better understand the behaviors of the metal prices and the interactions with others that affect the changes in prices. In this study, both Wavelet Analysis and VARMA (Vector Autoregressive Moving Average) models are utilized. First, Multiple Wavelet Coherence (M…
A new HOM model improves forecasting of Indian base metal prices.
problem Improving accuracy in predicting base metal prices in the Indian market.
method A Higher Order Markovian (HOM) model with varying order based on market delay.
result The HOM model consistently outperforms the standard Markovian model in forecasting.
Modeling precious metals market making using nested Ornstein-Uhlenbeck processes.
problem Navigating liquidity provided by futures contracts in spot precious metals.
method Nested Ornstein-Uhlenbeck process for EFP spread modeling, Hamilton-Jacobi-Bellman equation approximation.
result Maximizing expected P&L while minimizing inventory risk in near real-time.
New periodic solutions found in 2n-body problem, braids of pseudo-Anosov type with stretch factors as metallic ratios.
problem Periodic solutions of the 2n-body problem and their braid types.
method Analyzing braid types and stretch factors associated with pseudo-Anosov braids.
result Braids from new periodic solutions are of pseudo-Anosov type with stretch factors as metallic ratios.
MetAL improves graph classification models with fewer labeled data.
problem Efficiently selecting unlabeled graph instances for training.
method Formulates AL as bilevel optimization, uses meta-learning to approximate model performance.
result MetAL outperforms existing AL algorithms on multiple graph datasets.
The paper establishes new Casorati inequalities for various Riemannian maps and submersions.
problem Developing new inequalities for Riemannian maps and submersions.
method Using general forms of Casorati inequalities, the paper derives inequalities for specific Riemannian spaces.
result The paper provides new Casorati inequalities for Riemannian maps and submersions.
New model predicts grain boundary migration in metals.
problem Anisotropic grain boundary migration in polycrystals.
method Level set-finite element formulation based on thermodynamics and mechanics.
result First analytical solution for anisotropic grain boundary configurations.
Study on Riemannian Poisson warped product spaces and their properties.
problem Characterizing and understanding Riemannian Poisson warped product spaces.
method Formal treatment of Killing and 2-Killing 1-forms on Riemannian Poisson manifolds, including Bochner type results.
result Characterization of 2-Killing 1-form on (R2,g,Π) and Bochner type results on compact spaces. Study develops ensemble machine learning framework for predicting groundwater heavy metal pollution.
problem Statistical complexity and spatial heterogeneity of heavy metal contamination in groundwater.
method Nested cross-validated ensemble machine learning with response transformations (raw, log, Gaussian copula).
result Copula-based models with DBSCAN clustering diagnostics provide the most reliable and interpretable assessments of groundwater contamination.
We have measured the dissimilarities among several printed characters of a single page in the Gutenberg 42-line bible and we prove statistically the existence of several different matrices from which the metal types where constructed. This is in contrast with the prevailing theory, which states that only one matrix per…
Paper studies quaternionic space forms and Riemannian maps inequalities.
problem Investigate DDVV-type inequality for quaternionic space forms.
method Analyze Riemannian maps from quaternionic space forms to manifolds.
result Derived inequality with equality conditions discussed.
Physics-informed neural network identifies and characterizes surface cracks in metals.
problem Identifying and characterizing surface-breaking cracks in metals using ultrasound.
method Physics-informed neural network (PINN) trained with ultrasonic surface wave data and adaptive activation functions.
result PINN accurately estimates the speed of sound and identifies crack locations in metals.
Novikov's problem of semiclassical orbits of quasi-electrons in a normal metal leads to a correspondance between 3-ply periodic functions in R and fractals in R P^2. These fractals are the complement of infinitely many open sets labeled by integer 2-cycles of T^3. Here we present a characterization of the fractal point…
Novel data acquisition schemes have been an emerging need for scanning microscopy based imaging techniques to reduce the time in data acquisition and to minimize probing radiation in sample exposure. Varies sparse sampling schemes have been studied and are ideally suited for such applications where the images can be re…
The paper classifies submanifolds in pseudo-Riemannian space forms.
problem Characterizing and classifying totally umbilical submanifolds.
method Classification of congruent classes of totally umbilical submanifolds in non-flat pseudo-Riemannian space forms.
result Some moduli spaces of isometric immersions between space forms are non-Hausdorff.
The study classifies quasi-minimal surfaces in 4D pseudo-Riemannian space-forms with positive nullity.
problem Characterizing surfaces in pseudo-Riemannian space forms with positive nullity.
method Analyzing the relative null space and classifying quasi-minimal surfaces.
result Classifications of quasi-minimal surfaces with positive relative nullity.
Researchers provide explicit parametrizations for Sasakian space forms.
problem Understanding homogeneous contact Riemannian structures on Sasakian space forms.
method Explicit parametrizations of all homogeneous structures.
result Detailed descriptions of all homogeneous structures in 3D Sasakian space forms.
A deep learning algorithm designs low-cost SPP films.
problem Designing SPP films with high accuracy and low cost.
method Guided deep learning algorithm with low-cost sample replacement.
result Deep CNN learns to replace precious metals with ordinary metals, reducing cost.
Survey on smooth function and form density in Riemannian Sobolev spaces.
problem Density of smooth functions and forms in Sobolev spaces on Riemannian manifolds.
method Careful examination of weak covariant derivatives and partial derivatives.
result Equivalence of weak covariant derivatives to weak partial derivatives.
Deep RL optimizes processing paths to desired material structures.
problem Optimizing processing paths to achieve desired material properties.
method Deep reinforcement learning guided by structure representations and reward signals.
result Algorithm learns to find optimal paths to target structures in material space.
We introduce and begin the study of new knot energies defined on knot diagrams. Physically, they model the internal energy of thin metallic solid tori squeezed between two parallel planes. Thus the knots considered can perform the second and third Reidemeister moves, but not the first one. The energy functionals consid…