Generalized numbers, arithmetic operators, and derivative operators, grouped in four classes based on symmetry features, are introduced. Their building element is the pair of q-logarithm/q-exponential inverse functions. Some of the objects were previ...
The Calogero–Leyvraz Lagrangian framework, associated with the dynamics of a charged particle moving in a plane under the combined influence of a magnetic field as well as a frictional force, proposed by Calogero and Leyvraz, has some special f...
This paper introduces a broad class of Mirror Descent (MD) and Generalized Exponentiated Gradient (GEG) algorithms derived from trace-form entropies defined via deformed logarithms. Leveraging these generalized entropies yields MD and GEG algorithms...
By using the symmetry of the Dunkl Laplacian operator, we prove a sharp Shannon-type inequality and a logarithmic Sobolev inequality for the Dunkl transform. Combining these inequalities, we obtain a new, short proof for Heisenberg-type uncertainty p...
This study explores the swelling behavior of strong expansive soil from the Nanyang Section II canal bed of the South-to-North Water Diversion Middle Route Project, with practical relevance to foundation engineering. A total of 45 one-dimensional swe...
This study presents the adoption of locally constrained regression models (LCRMs) with logarithmic transformations in order to model the flow stress behavior of the high-temperature deformation of 5005 aluminum alloy. Hot tensile tests for 5005 alumi...
We illustrate some financial applications of the Tsallis and Kaniadakis deformed exponential. The minimization of the corresponding deformed divergence is discussed as a criterion to select a pricing measure in the valuation problems of incomplete ma...
The work is devoted to the results of processing electromagnetic radiation signals obtained during laboratory loading of marble and diabase samples using a technique for determining the parameters of microcracks, developed and published by the author...
The axiomatic structure of the κ-statistcal theory is proven. In addition to the first three standard Khinchin–Shannon axioms of continuity, maximality, and expansibility, two further axioms are identified, namely the self-duality axiom a...
A paper was published (Harsha and Subrahamanian Moosath, 2014) in which the authors claimed to have discovered an extension to Amari's \(\alpha\)-geometry through a general monotone embedding function. It will be pointed out here that this so-called...
Kaniadakis deformed κ-mathematics is an area of mathematics that has found relevance in the analysis of complex systems. Specifically, the mathematical framework in the context of a first-order decay κ-differential equation is investigate...
We discuss an approach to the problem of calculating the local topological index of vector fields given on complex spaces or varieties with singularities developed by the author over the past few years. Our method is based on the study of the homolog...
In this paper, we studied the Picard–Fuchs systems and equations which appear in the theory of Gauss–Manin systems and connections associated with deformations of isolated singularities. Among other things, we describe some interesting pr...
We study the convexity or concavity of certain trace functions for the deformed logarithmic and exponential functions, and in this way obtain new trace inequalities for deformed exponentials that may be considered as generalizations of Peierls–Bogoly...
An effective Hamiltonian finite element method is presented in this paper to investigate the three-dimensional dynamic responses of a towed cable-payload system with large deformation. The dynamics of a flexible towed system moving in a medium is a c...
Based on dilatometric tests, the effect of various values of previous deformation on the kinetics of austenite transformations during the cooling of 100Cr6 steel has been studied. Dilatometric tests have been performed with the use of the optical dil...
Noncommutative geometry is an established potential candidate for including quantum phenomena in gravitation. We outlined the formalism of Hopf algebras and its connection to the algebra of infinitesimal diffeomorphisms. Using a Drinfeld twist, we de...
A Ti-AZ31 composite was severely plastically deformed by rotary swaging at room temperature up to a logarithmic deformation strain of 2.98. A value far beyond the forming limit of pure AZ31 when being equivalently deformed. It is observed, that the m...
The deformed wavelet transform is a new addition to the class of wavelet transforms that heavily rely on a pair of generalized translation and dilation operators governed by the well-known Dunkl transform. In this study, we adapt the symmetrical prop...
Coal mine waste rocks, mainly broken gangue, can be used as filling materials to backfill into goafs. Under the overburden load, the backfill body is vulnerable to compressive deformation and particle breakage. With the increase in mining depth, the...
Due to the long-term deformation settlement of foundations, issues such as damage and functional failure of buildings and structures have long been a concern in the engineering field. The creep of soil is one of the primary causes leading to long-ter...
Schrödinger equations with non-Hermitian, but PT -symmetric quantum potentials V ( x ) found, recently, a new field of applicability in classical optics. The potential acquired there a new physical role of an “anomalous” refraction index...
This paper systematically presents the λ-deformation as the canonical framework of deformation to the dually flat (Hessian) geometry, which has been well established in information geometry. We show that, based on deforming the Legendre dualit...
General load cells have typically constant sensitivity throughout the measurement range, which is acceptable for common force measurement systems. However, it is not adequate for high-performance control and high-stroke applications such as robotic s...
Magnesium sheet metal alloys offer a deformation asymmetry, which is strongly related to grain size and texture. In order to predict deformation behavior as well as to provide methods to eliminate anisotropy and yield asymmetry, a lot of effort is in...
To study the hot deformation behavior of and obtain the optimal hot processing parameters for 2219 aluminum alloy, a new, precise constitutive model based on the partial derivative of flow data was constructed and hot processing maps were constructed...
The paper defines and studies new semi-Riemannian generalized Fisher metrics and Fisher-like metrics, associated with entropies and divergences. Examples of seven such families are provided, based on exponential PDFs. The particular case when the bas...
Coal matrix deformation is one of the main controlling factors for coal reservoir permeability changes in nitrogen foam fracturing. The characteristics and mechanism of coal matrix deformation during the process of adsorption/desorption were studied...
Offshore monopile foundations endure complex loads during service. They bear vertical loads from the superstructure’s self-weight and lateral cyclic loads (e.g., wind, waves), while near-coastal seabeds are usually sloped. To resolve these issu...
To address the problem of surface subsidence caused by the compression of filling gangue in deep mines, a layered compaction test was designed based on the zonation of the failure of the overburden in the goaf and layered property of the filling gang...
Atmospheric Phase Screen (APS) is a major noise that suppresses the accuracy of InSAR deformation time series products. Several correction methods have been developed to perform APS reduction in the InSAR analysis, in which an algorithm called Common...
The amplitude-dependent internal friction of continuously-cast and rolled AZ31 magnesium alloy was measured in this study. Samples were annealed and quenched step by step; immediately after the treatment, the amplitude dependence of the logarithmic d...
We present the main features of the mathematical theory generated by the κ-deformed exponential function exp k (x) = ( 1 + k 2 x 2 + kx) 1 k , with 0 ≤ κ < 1, developed in the last twelve years, which turns out to be a...
In the seismic response analysis of liquefiable sites, the existing soil dynamic constitutive model is challenging to simulate saturated sand’s post-liquefaction deformation, and the current pore-water pressure buildup model cannot reflect the...
The polyphosphoric acid (PPA) modified asphalt binder is a potential choice as one of the pavement materials for its excellent high-temperature performance and low cost. To further analyze the influences of temperature and load on the service life of...
In the world of generalized entropies—which, for example, play a role in physical systems with sub- and super-exponential phase space growth per degree of freedom—there are two ways for implementing constraints in the maximum entropy prin...
To study the deformation characteristics of crushed gangue under different water content conditions, the confined compaction test of crushed gangue was carried out under five different water content conditions by using a universal material testing ma...
In this paper, we discuss a few simple methods for computing the local topological index and its various analogs for vector fields and differential forms given on complex varieties with singularities of different types. They are based on properties o...
This paper researches the issues related to the print quality in flexography, especially the influence of the print run and inadequate printing settings on dot deformation. Dot deformation can lead to inconsistencies in print quality, such as a loss...
To achieve the purposes of disposing industry solid wastes and enhancing the sustainability of subgrade life-cycle service performance in seasonally frozen regions compared to previous research of modified silty clay (MSC) composed of oil shale ash (...
Time-series observations from Sentinel-1 A/B InSAR spanning November 2014 to July 2021 were used to study the late post-seismic deformation velocity field arising from the Kokoxili earthquake. The deformation velocity caused by the interseismic slip...
In underground tunnels or caverns, time-dependent deformation or failure of rock mass, such as extending cracks, gradual rock falls, etc., are a costly irritant and a major safety concern if the time-dependent damage of surrounding rock is serious. T...
The hot deformation behavior of selected non-alloyed carbon steels was investigated by isothermal continuous uniaxial compression tests. Based on the analysis of experimentally determined flow stress curves, material constants suitable for predicting...
This study investigates the elevated-temperature mechanical and viscoelastic properties of a PDMS–silica-based superhydrophobic nanocomposite coating using nanoindentation and a nano-dynamic mechanical analysis over a temperature range of 24 &d...
In the field of slope landslide prevention and monitoring in open-pit mines, addressing the lag issues associated with the traditional GNSS inverse-velocity method, this study introduces a novel strategy that integrates high-spatiotemporal-resolution...
The yielding transition, structural relaxation, and mechanical properties of metallic glasses subjected to repeated loading are examined using molecular dynamics simulations. We consider a poorly annealed Cu-Zr amorphous alloy periodically deformed i...
Metal matrix nanocomposites (MMNCs) reinforced by carbon nanotubes (CNTs) are good candidates to produce structural components in the mobility industry, given their unique properties. The manufacture of these components can involve plastic deformatio...
The void of the cracked rock mass of the goaf is the main water storage space of underground reservoirs, which is in a time-space dynamic evolution process. Before the formation of the underground reservoir, the water storage space was primarily affe...
On 22 July 2020, an Mw 6.3 earthquake occurred in Nima County, central Qinghai-Tibet Plateau, China. We used the synthetic aperture radar interferometry (InSAR) technique with Sentinel-1 images to retrieve the line of sight (LOS) coseismic deformatio...
The origin of the photoplethysmography (PPG) signal is a debatable topic, despite plausible models being addressed. One concern revolves around the correlation between the mechanical waveform’s pulsatile nature and the associated biomechanism....
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