Polynomials of Least Deviation from Zero in Sobolev p-Norm

The first part of this paper complements previous results on characterization of polynomials of least deviation from zero in Sobolev p-norm ($$1<p<\infty $$ 1 < p < ∞ ) for the case $$p=1$$ p = 1 . Some relevant examples are indicated. The second part deals with the location of zeros of polynomials of least deviation in discrete Sobolev p-norm. The asymptotic distribution of zeros is established on general conditions. Under some order restriction in the discrete part, we prove that the n-th polynomial of least deviation has at least $$n-\mathbf {d}^*$$ n - d ∗ zeros on the convex hull of the support of the measure, where $$\mathbf {d}^*$$ d ∗ denotes the number of terms in the discrete part.

Finite size spectrum of the staggered six-vertex model with Uq($$ \mathfrak{sl} $$(2))-invariant boundary conditions

The finite size spectrum of the critical ℤ2-staggered spin-1/2 XXZ model with quantum group invariant boundary conditions is studied. For a particular (self-dual) choice of the staggering the spectrum of conformal weights of this model has been recently been shown to have a continuous component, similar as in the model with periodic boundary conditions whose continuum limit has been found to be described in terms of the non-compact SU(2, ℝ)/U(1) Euclidean black hole conformal field theory (CFT). Here we show that the same is true for a range of the staggering parameter. In addition we find that levels from the discrete part of the spectrum of this CFT emerge as the anisotropy is varied. The finite size amplitudes of both the continuous and the discrete levels are related to the corresponding eigenvalues of a quasi-momentum operator which commutes with the Hamiltonian and the transfer matrix of the model.

The quantum-mechanical Coulomb propagator in an L2 function representation

The quantum-mechanical Coulomb propagator is represented in a square-integrable basis of Sturmian functions. Herein, the Stieltjes integral containing the Coulomb spectral function as a weight is evaluated. The Coulomb propagator generally consists of two parts. The sum of the discrete part of the spectrum is extrapolated numerically, while three integration procedures are applied to the continuum part of the oscillating integral: the Gauss–Pollaczek quadrature, the Gauss–Legendre quadrature along the real axis, and a transformation into a contour integral in the complex plane with the subsequent Gauss–Legendre quadrature. Using the contour integral, the Coulomb propagator can be calculated very accurately from an L$$^2$$ 2 basis. Using the three-term recursion relation of the Pollaczek polynomials, an effective algorithm is herein presented to reduce the number of integrations. Numerical results are presented and discussed for all procedures.

Uncertainties in Adoption of Model-Based Definition and Enterprise for High-Value Manufacturing

The world is adopting digital technologies at a rapid pace which are the key enablers to improve every walk of life in the modern era. This quest for digitization has equal rigor within the manufacturing industry. 2D drawings have been used historically to define the specifications of a product for manufacturing. The evolution in digital technologies has made it possible to improve the way of representing these specifications in the form of 3D models which is known as Model-Based Definition (MBD). However, the 2D representation is still the authoritative source within the industry for engineering definition and related documents in the product lifecycle. Though MBD has been adopted in design, discrete part manufacturing, and inspection stages to some extent, the industry heavily relies on the conventional 2D representation of product definition. The digitization process of product definition lies within the adoption of MBD as the authoritative source for all the enterprise activities which is referred to as Model- based Enterprise (MBE). However, there are several uncertainties and risks in this process. In this work, it is ascertained to formulate the key uncertainties in the transformation towards MBD/E. These uncertainties are categorized and analyzed further for visualization.

Vivianite formation as indicator of human impact in porous sediments

Environmental geological survey of a chemical works situated in NE Hungary has been performed for decades. Up till now, several hundreds of drillings of different depths as well as engineering geological soundings have been carried out in the area. Vivianite has been found in a discrete part of a drilling in a gray, silty bed at the depth 6.8–8.5 m. Vivianite was analyzed using X-ray powder diffraction (XRPD), thermal analysis (TG/DTG), and scanning electron microscopic and energy dispersive spectrometry (SEM–EDS) techniques. To demonstrate the spatial distribution of hydrochemical parameters and selected chemical constituents the available data concerning drillings and hydrochemical analyses were collected and evaluated, and field measurements were also performed. For mapping the distribution of relevant physico-chemical parameters and chemical constituents kriging interpolation method was used. Archive aerial photographs demonstrate that a coffered, earth-bedded reservoir for storing huge amounts of extracted plant debris is situated in the vicinity of the drilling. Our study suggests that orthophosphate derived from decomposing biomass entered the groundwater and accumulated within the lowest permeability zone of the intact bedrock. Therefore, the discrete appearance of vivianite in the drilling can be regarded, at least partly, the result of a man-induced mineralogical process.

A Class of Exponentiated Regression Model for Non Negative Censored Data with an Application to Antibody Response to Vaccine

In this paper, an asymmetric regression model for censored non-negative data based on the centred exponentiated log-skew-normal and Bernoulli distributions mixture is introduced. To connect the discrete part with the continuous distribution, the logit link function is used. The parameters of the model are estimated by using the likelihood maximum method. The score function and the information matrix are shown in detail. Antibody data from a study of the measles vaccine are used to illustrate applicability of the proposed model, and it was found the best fit to the data with respect to an others models used in the literature.

Optimal Placement and Sizing of D-STATCOM in Radial and Meshed Distribution Networks Using a Discrete-Continuous Version of the Genetic Algorithm

In this paper, we propose a new discrete-continuous codification of the Chu–Beasley genetic algorithm to address the optimal placement and sizing problem of the distribution static compensators (D-STATCOM) in electrical distribution grids. The discrete part of the codification determines the nodes where D-STATCOM will be installed. The continuous part of the codification regulates their sizes. The objective function considered in this study is the minimization of the annual operative costs regarding energy losses and installation investments in D-STATCOM. This objective function is subject to the classical power balance constraints and devices’ capabilities. The proposed discrete-continuous version of the genetic algorithm solves the mixed-integer non-linear programming model that the classical power balance generates. Numerical validations in the 33 test feeder with radial and meshed configurations show that the proposed approach effectively minimizes the annual operating costs of the grid. In addition, the GAMS software compares the results of the proposed optimization method, which allows demonstrating its efficiency and robustness.

Optimal Integration of Photovoltaic Sources in Distribution Networks for Daily Energy Losses Minimization Using the Vortex Search Algorithm

This paper deals with the optimal siting and sizing problem of photovoltaic (PV) generators in electrical distribution networks considering daily load and generation profiles. It proposes the discrete-continuous version of the vortex search algorithm (DCVSA) to locate and size the PV sources where the discrete part of the codification defines the nodes. Renewable generators are installed in these nodes, and the continuous section determines their optimal sizes. In addition, through the successive approximation power flow method, the objective function of the optimization model is obtained. This objective function is related to the minimization of the daily energy losses. This method allows determining the power losses in each period for each renewable generation input provided by the DCVSA (i.e., location and sizing of the PV sources). Numerical validations in the IEEE 33- and IEEE 69-bus systems demonstrate that: (i) the proposed DCVSA finds the optimal global solution for both test feeders when the location and size of the PV generators are explored, considering the peak load scenario. (ii) In the case of the daily operative scenario, the total reduction of energy losses for both test feeders are 23.3643% and 24.3863%, respectively; and (iii) the DCVSA presents a better numerical performance regarding the objective function value when compared with the BONMIN solver in the GAMS software, which demonstrates the effectiveness and robustness of the proposed master-slave optimization algorithm.

A micromechanically calibrated numerical model reproducing earthquake cycle in the lab

&lt;p&gt;In this communication, we present a novel numerical framework which consists in a direct coupling between a discrete micromechanical modelling of rock damaging processes and a continuous modelling of elastic deformation and acoustic waves. It includes a polygon-based conforming Discrete Element Method (DEM) with a cohesive zone model (CZM, [1]) for the discrete part and a meshfree formulation for the continuum part. This framework is applied to the numerical reproduction of sawcut triaxial tests performed in the lab on marble samples under seismogenic conditions [2]. Realistic boundary conditions (in terms of the elasticity of the loading system, of the absorption of the elastic waves and of the fluid pressure applied on the lateral boundaries) are introduced. Constitutive laws (in the continuum part) and micromechanical parameters (in the discrete part) are calibrated by performing independant simulations based on experimental results found in the literature [3].&lt;/p&gt;&lt;p&gt;Upon loading, this model provides information on the system behavior that nicely complement the experimental data, such as (i) the progressive damaging of the contacting surfaces, leading to the emission of granular matter in the interface, to the formation of a gouge layer, and to a modification of the interface rheology, (ii) the space and time distribution and statistics and the detailed kinematics of the slip events related to the interface evolution, and (iii) the acoustic wave emission and propagation in the medium associated with such events.&lt;/p&gt;&lt;p&gt;The model shows that, depending on the experimental conditions (confining pressure, loading rate, surface roughness, etc.), and without relying to any prior choice of slip- or rate-dependent friction laws, a large number of sliding regimes can emerge from this system. This includes large stress drops, regular stick-slip, or stable sliding. This model thus provides an unprecedented view of both local and global phenomena at stake during lab earthquakes, at sampling rates in both space and time which remain out of reach for experimental instrumentation.&lt;/p&gt;&lt;p&gt;[1]. Mollon, G. (2015). &amp;#8220;A numerical framework for discrete modelling of friction and wear using Voronoi polyhedrons&amp;#8221;, Tribology International, 90, 343-355&lt;br&gt;[2]. Aubry, J. (2019). &amp;#8220;S&amp;#233;ismes au laboratoire: friction, plasticit&amp;#233; et bilan &amp;#233;nerg&amp;#233;tique&amp;#8221;, PhD Thesis, Ecole Normale Sup&amp;#233;rieure.&lt;br&gt;[3]. Fredrich, J. T.; Evans, B. &amp; Wong, T.-F., (1989). &amp;#8220;Micromechanics of the brittle to plastic transition in Carrara marble&amp;#8221;, Journal of Geophysical Research: Solid Earth, &lt;span&gt;&lt;/span&gt;&lt;/p&gt;