SELECTION OF FREE PARAMETER FOREL-2 ALGORITHM IN THE PROBLEM OF AUTOMATIC GROUPING OF INDUSTRIAL PRODUCTS BY HOMOGENEOUS PRODUCTION BATCHES

Исследуется проблема влияния полуавтоматического подбора свободного параметра в задаче автоматической группировки промышленной продукции по однородным производственным партиям полупроводниковых приборов, основанной на модели FOREL-2 для задач p-медиан и k-средних. The author considers the problem impact of semi-automatic selection free parameter in the problem of automatic grouping of industrial products by homogeneous production batches based on the FOREL-2 model. We provide a comparative automatic grouping quality assessment results with models of FOREL-2, p-median and k-means.

Parameter N Analysis on the Rational-Talbot Algorithm for Numerical Inversion of Laplace Transform

This article investigates the numerical inversion of the Laplace Transform by the Rational-Talbot method and analyzes the influence on the variation of the free parameter N established by the technique when applied to certain functions. The set of elementary functions, for which the method is tested, has exponential and oscillatory characteristics. Based on the results obtained, it was concluded that the Rational-Talbot method is e cient for the inversion of decreasing exponential functions. At the same time, to perform the inversion process effectively for trigonometric forms, the algorithm requires a greater amount of terms in the sum. For higher values of N, the technique works well. In fact, this is observed in inverting the functions transform, that combine trigonometric and polynomial factors. The method numerical results have a good precision for the treatment of decreasing exponential functions when multiplied by trigonometric functions.

Slowly rotating black holes in the novel Einstein–Maxwell-scalar theory

We investigate a slowly rotating black hole solution in a novel Einstein–Maxwell-scalar theory, which is prompted by the classification of general Einstein–Maxwell-scalar theory. The gyromagnetic ratio of this black hole is calculated, and it increases as the second free parameter $$\beta $$ β increases, but decreases with the increasing parameter $$\gamma \equiv \frac{2 \alpha ^{2}}{1+\alpha ^2}$$ γ ≡ 2 α 2 1 + α 2 . In the Einstein–Maxwell-dilaton (EMD) theory, the parameter $$\beta $$ β vanishes but the free parameter $$\alpha $$ α governing the strength of the coupling between the dilaton and the Maxwell field remains. The gyromagnetic ratio is always less than 2, the well-known value for a Kerr–Newman (KN) black hole as well as for a Dirac electron. Scalar hairs reduce the magnetic dipole moment in dilaton theory, resulting in a drop in the gyromagnetic ratio. However, we find that the gyromagnetic ratio of two can be realized in this Einstein–Maxwell-scalar theory by increasing $$\beta $$ β and the charge-to-mass ratio Q/M simultaneously (recall that the gyromagnetic ratio of KN black holes is independent of Q/M). The same situation also applies to the angular velocity of a locally non-rotating observer. Moreover, we analyze the period correction for circular orbits in terms of charge-to-mass ratio, as well as the correction of the radius of the innermost stable circular orbits. It is found the correction increases with $$\beta $$ β but decreases with Q/M. Finally, the total radiative efficiency is investigated, and it can vanish once the effect of rotation is considered.

A Physical Model for the Quasar Luminosity Function Evolution between Cosmic Dawn and High Noon

Modeling the evolution of the number density distribution of quasars through the quasar luminosity function (QLF) is critical to improving our understanding of the connection between black holes, galaxies, and their halos. Here we present a novel semiempirical model for the evolution of the QLF that is fully defined after the specification of a free parameter, the internal duty cycle, ε DC, along with minimal other assumptions. All remaining model parameters are fixed upon calibration against the QLF at two redshifts, z = 4 and z = 5. Our modeling shows that the evolution at the bright end results from the stochasticity in the median quasar luminosity versus halo mass relation, while the faint end shape is determined by the evolution of the halo mass function (HMF) with redshift. Additionally, our model suggests the overall quasar density is determined by the evolution of the HMF, irrespective of the value of ε DC. The z ≥ 4 QLFs from our model are in excellent agreement with current observations for all ε DC, with model predictions suggesting that observations at z ≳ 7.5 are needed to discriminate between different ε DC. We further extend the model at z ≤ 4, successfully describing the QLF between 1 ≤ z ≤ 4, albeit with additional assumptions on Σ and ε DC. We use the existing measurements of quasar duty cycle from clustering to constrain ε DC, finding ε DC ∼ 0.01 or ε DC ≳ 0.1 dependent on observational data sets used for reference. Finally, we present forecasts for future wide-area surveys with promising expectations for the Nancy Grace Roman Telescope to discover N ≳ 10, bright, m UV < 26.5 quasars at z ∼ 8.

Gravastars in a non-minimally coupled gravity with electromagnetism

In this paper we investigate the gravitational vacuum stars which called gravastars in the non-minimally coupled models with electromagnetic and gravitational fields. We consider two non-minimal models and find the corresponding spherically symmetric exact solutions in the interior of the star consisting of the dark energy condensate. Our models turn out to be Einstein–Maxwell model at the outside of the star and the solutions become the Reissner–Nordström solution. The physical quantities of these models are continuous and non-singular in some range of parameters and the exterior geometry continuously matches with the interior geometry at the surface. We calculate the matter mass, the total gravitational mass, the electric charge and redshift of the star for the two models. We notice that these quantities except redshift are dependent of a subtle free parameter, k, of the model. We also remark a wide redshift range from zero to infinity depending on one free parameter, $$\beta $$ β , in the second model.

The signature of the quadratic generalized uncertainty principle on the newtonian gravity and galaxy mass profile

In this study, we discuss the corrections implies by the presence of the general uncertainty principle (GUP) on Newton’s law of gravity by virtue of Verlinde’s proposal. We argue here that GUP leads to twofold modification, namely on the equipartition theorem and the holographic relation (Bekenstein-Hawking formula). Hence, following Verlinde’s proposal, we obtain quantum corrections term to the Newtonian gravity. In addition, we also report the quantum corrected mass profile of the galaxy. We restricted our derivation to first order in the GUP’s free parameter and compared it analytically with the other relevant works.

Geometric Constraints of Visual Space

Perspective space has been introduced as a computational model of visual space. The model is based on geometric features of visual space. The model has proven to describe a range of phenomena related to the visual perception of distance and size. Until now, the model lacks a mathematical description that holds for complete 3D space. Starting from a previously derived equation for perceived distance in the viewing direction, the suitability of various functions is analyzed. Functions must fulfill the requirement that straight lines, oriented in whatever direction in physical space, transfer to straight lines in visual space. A second requirement is that parallel lines oriented in depth in physical space, converge to a finite vanishing point in visual space. A rational function for perceived distance, compatible with the perspective-space model of visual space, satisfies the requirements. The function is unique. Analysis of alternative functions shows there is little tolerance for deviations. Conservation of the straightness of lines constrains visual space to having a single geometry. Visual space is described by an analytical function having one free parameter, that is, the distance of the vanishing point.

New Analytical Approach to Operational Assessment of Fractured Well Productivity with Variable Permeability

Requirements of targeted optimization are imposed on the hydraulic fracturing operations carried out in the conditions of borderline economic efficiency of fields taking into account geological and technological features. Consequently, the development of new analytical tools foranalyzing and planning the productivity of fractured wells, taking into account the structuralfeatures of the productive reservoir and inhomogeneous distribution of the fracture conductivity, is becoming highly relevant. The paper proposes a new approach of assessing the vertical hydraulic fracture productivityin a rectangular reservoir in a pseudo-steady state, based on reservoir resistivity concept described in the papers of Meyer et al. However, there is a free parameter in the case of modeling the productivity of a hydraulic fracture by the concept. The parameter describes the distribution of the inflow along the plane of the fracture. This paper presents a systematic approach to determining of the parameter. The resulting model allows to conduct an assessment of the influence of various complications in the fracture on the productivity index. During the research a method of determining the free parameter was developed,it was based on the obtained dependence of the inflow distribution on the coordinate along the fracture of finite conductivity. The methodology allowed to refine existent analytical solution of the Meyer et al. model, which, in turn, allowed to assess the influence of different fracture damages in the hydraulic fracture on the productivity index of the well. The work includes the cases of the presence of fracture damages at the beginning and at the end of the fracture. A hydraulic fracture model was built for each of the types of damages, it was based on the developed method, and also the solution of dimensionless productivity ratio was received. The results of the obtained solution were confirmed by comparison with the numerical solutions of commercial simulators and analytical models available in the literature. The advantage of the methodology is the resulting formulas for well productivity are relatively simple, even for exotic cases ofvariable conductivity fractures. The approaches and algorithms described in the paper assume the calculation of the productivity of a hydraulic fracture with variable conductivity and the presence of other complicatingfactors.The methodology of the paper can be used for analysis and diagnosis problems with formation hydraulic fracturing. The efficiency of the calculations allows using the presented methodology to solve inverse problems of determining the efficiency of the hydraulic fracturing operation.

Constraints on Non-Flat Starobinsky f(R) Dark Energy Model

We study the viable Starobinsky f(R) dark energy model in spatially non-flat FLRW backgrounds, where f(R)=R−λRch[1−(1+R2/Rch2)−1] with Rch and λ representing the characteristic curvature scale and model parameter, respectively. We modify CAMB and CosmoMC packages with the recent observational data to constrain Starobinsky f(R) gravity and the density parameter of curvature ΩK. In particular, we find the model and density parameters to be λ−1<0.283 at 68% C.L and ΩK=−0.00099−0.0042+0.0044 at 95% C.L, respectively. The best χ2 fitting result shows that χf(R)2≲χΛCDM2, indicating that the viable f(R) gravity model is consistent with ΛCDM when ΩK is set as a free parameter. We also evaluate the values of AIC, BIC and DIC for the best fitting results of f(R) and ΛCDM models in the non-flat universe.

Evidence for profile changes in PSR J1713+0747 using the uGMRT

ABSTRACT PSR J1713+0747 is one of the most precisely timed pulsars in the international pulsar timing array experiment. This pulsar showed an abrupt profile shape change between 2021 April 16, (MJD 59320) and 2021 April 17 (MJD 59321). In this paper, we report the results from multi-frequency observations of this pulsar carried out with the upgraded Giant Metrewave Radio Telescope (uGMRT) before and after the event. We demonstrate the profile change seen in Band 5 (1260 MHz–1460 MHz) and Band 3 (300 MHz–500 MHz). The timing analysis of this pulsar shows a disturbance accompanying this profile change followed by a recovery with a time-scale of ∼159 days. Our data suggest that a model with chromatic index as a free parameter is preferred over models with combinations of achromaticity with DM bump or scattering bump. We determine the frequency dependence to be ∼ν+1.34.