Gravity field forward modelling using tesseroids accelerated by Taylor series expansion and symmetry relations

How economic inequality shapes social class stereotyping

This paper considers the layout design problem of a single block order-picking rack-based warehouse that employs turnover-based storage assignment in both vertical and horizontal dimensions. An analytical expression for vertical travel distance is derived which is incorporated in the pick distance model. The effect of inventory staggering on storage space requirement is considered in arriving at warehouse dimensions. A model that incorporates area cost along with handling cost in optimizing warehouse design is developed and a solution algorithm is presented. The analytical model for vertical travel and the optimization model are applied to data from a real life case. It was found that the model would offer considerable operational cost savings, especially when space costs are high. Computational experiments show that the effect of inventory staggering is quite significant in the estimated storage space. Experiments also demonstrated the importance of segregating products based on turnover in the vertical dimension.

The design of the development of learning methods involves the pattern of organizing elements or components in the curriculum. the development of learning materials listening to correlated core-based learning with the application of listening in action methods seen from two dimensions, namely horizontal and vertical dimensions. The horizontal dimension is related to the compilation of the scope of learning content. This spatial arrangement is often integrated with the learning and teaching process. The vertical dimension concerns the compilation of material sequences based on the order of difficulty. Arranged materials start from the easy ones, then go to the more difficult ones, or start with the basic ones followed by the continuation. This development describes in detail about the components that must be present in each listening learning material that can be used for the learning process. The design of the development of the listening learning material consists of several components, including the objectives of the curriculum, teaching materials or the material or content of the curriculum, teaching strategies or teaching methods, teaching media and teaching evaluation and improving teaching. These components are related to each other in the development of learning materials listening to correlated core-based learning by applying listening in action methods.

The vertical dimension is one of the important aspects that affect facial appearance, because it is related in facial height ratio. The vertical occlusal dimension is the height of the lower face measured from two points (infra-nasal and gnation points) when the maxillary and mandibular teeth were occlusion in the maximum intercuspal position. In complex cases, tooth wear can result in a decrease in facial height because the predominant wear on the anterior teeth encourages downward movement of the condyles when the intercuspal is maximum so that the vertical di-mension decreases. In addition, factors that cause a decrease in the vertical dimension are loss of posterior teeth accompanied by skeletal disharmony or accompanied by tooth abrasion and migration. The purpose of this paper is to explain how to restore the decreased occlusal vertical dimensions. Things that need to be considered are di-vided into two, extraorally and intraorally. Extraoral considerations are in the form of a large reduction in OVD, fa-cial esthetics and conditions of the temporomandibular joint. The parameters considered intraoral were the remain-ing tooth structure and occlusion. It was concluded that tooth wear due to functional and parafunctional activities can result in dimensional changes in facial morphology as well as a decrease in the occlusal vertical dimension. Correct OVD rehabilitation is an important factor in the success of rehabilitation treatment.

The accurate computation of gravitational effects from topographic and atmospheric masses is one of the core issues in gravity field modeling. Using gravity forward modeling based on Newton’s integral, mass distributions are generally decomposed into regular mass bodies, which can be represented by rectangular prisms or polyhedral bodies in a rectangular coordinate system, or tesseroids in a spherical coordinate system. In this study, we prefer the latter representation because it can directly take the Earth’s curvature into account, which is particularly beneficial for regional and global applications. Since the volume integral cannot be solved analytically in the case of tesseroids, approximation solutions are applied. However, one well-recognized issue of these solutions is that the accuracy decreases as the computation point approaches the tesseroid. To overcome this problem, we develop a method that can precisely compute the gravitational potential $$\left( V\right) $$ and vector $$\left( V_x, V_y, V_z\right) $$ on the tesseroid surface. In addition to considering a constant density for the tesseroid, we further derive formulas for a linearly varying density. In the near zone (up to a spherical distance of 15 times the horizontal tesseroid dimension from the computation point), the gravitational effects of the tesseroids are computed by Gauss–Legendre quadrature using a two-dimensional adaptive subdivision technique to ensure high accuracy. The tesseroids outside this region are evaluated by means of expanding the integral kernel in a Taylor series up to the second order. The method is validated by synthetic tests of spherical shells with constant and linearly varying density, and the resulting approximation error is less than $$10^{-4}\,\hbox {m}^2\,\hbox {s}^{-2}$$ for V, $$10^{-5}\,\hbox {mGal}$$ for $$V_x$$ , $$10^{-7}\,\hbox {mGal}$$ for $$V_y$$ , and $$10^{-4}\,\hbox {mGal}$$ for $$V_z$$ . Its practical applicability is then demonstrated through the computation of topographic reductions in the White Sands test area and of global atmospheric effects on the Earth’s surface using the US Standard Atmosphere 1976.

An experimental study to investigate thermal-induced damage to SSRL-designed beryllium foil windows was performed at LLNL's Laser Welding Research Facility. The primary goal of this study was to determine the threshold at which thermal-stress-induced damage occurs in these commonly used vacuum barriers. An Nd:Yag pulsed laser with cylindrical optics and a carefully designed test cell provided a test environment that closely resembles the actual beamline conditions at SSRL. Tests performed on two beryllium window geometries, with different vertical aperture dimensions but equal foil thicknesses of 0.254 mm, resulted in two focused total-power thresholds at which incipient damage was determined. For a beam spot size similar to that of the Beamline-X Wiggler Line, onset of surface damage for a 5-mm by 25-mm aperture window was observed at 170 W after 174,000 laser pulses (1.2-ms pulse at 100 pps). A second window with double the vertical aperture dimension (10 mm by 25 mm) was observed to have surface cracking after 180,000 laser pulses with 85 W impinging its front surface. It failed after approximately 1,000,000 pulses. Another window of the same type (10 mm by 25 mm) received 2,160,000 laser pulses at 74.4 W, and subsequent metallographic sectioning revealed no signs of through-thickness damage. Comparison of windows with equal foil thicknesses and aperture dimensions has effectively identified the heat flux limit for incipient failure. The data show that halving the aperture's vertical dimension allows doubling the total incident power for equivalent onsets of thermal-induced damage.

Introduction Experiments on humans and animals indicate that auditory localization develops through the association of sets of monaural and binaural cues and locations in space: this calibration process in guided by vision (Knudsen, 1989).The auditory system lacks a straightforward correspondence between external spatial locations and sensory receptive fields (Ahveninen et al ., 2014), so the development of auditory localization is more complex than visual localization. Aim The main aim is to assess if the development of audio spatial localization in sighted humans:Differs for horizontal and vertical dimensionsDepends on: a)Type of sound: static or motion b)Type of task: verbal or motor Results and DiscussionWe tested audio spatial localization for horizontal and vertical dimensions in sighted humans taking into consideration both the type of sound (static or motion) and the type of response requested by the task (verbal or motor). In audio spatial localization, sighted humans show enhanced sensitivity for the horizontal dimension, irrespective of the type of sound and the type of task. The static sound condition tend to be easier than the sound motion condition and motor responses more accurate than verbal responses. Developmental improvement between 10-15 years of age. Future direction: since vision has a predominant role in the maturation of space cognition in the brain, we aim to assess the development of audio spatial localization for horizontal and vertical dimensions in blind humans.

The density and performance of integrated circuits have increased by many orders of magnitude through the process of device scaling. As pointed out in the overview chapter, the long channel relations are not strictly valid for horizontal dimensions that are comparable to the vertical dimensions. In this example, the operating voltage is kept constant. The horizontal dimension, L eff , and the vertical dimension, T ax , will be separately scaled to approximately two-thirds of the established process values. The two scaling factors are not identical, but are in the typical scaling range. The result of this reduction is then established. Comparison with the long-channel scaling assumptions is possible, and the importance of secondary physical effects can be seen. Device width will not be scaled, the current drive capability will be expressed for a fixed width. Breakdown and punchthrough voltages must be sufficiently greater than the supply voltage so that reliability is not a problem. For this example, power density is not a limitation.

Taylor series, a fundamental concept in mathematics, expresses a function as an infinite sum of terms which is calculated from the values of its derivatives at a single point. Its applications span various fields, notably physics and finance, where it simplifies complex functions for analysis and problem-solving. This study employs a qualitative approach, reviewing existing literature on Taylor series applications. It analyzes case studies in physics, such as approximating motion equations, and in finance, like option pricing models. The method includes mathematical derivations and simulations to demonstrate efficacy. Findings indicate that Taylor series significantly enhance computational efficiency and accuracy. In physics, it aids in predicting particle behavior under varying forces. In finance, it provides valuable insights into the pricing of derivatives and risk assessment. The Taylor series proves to be an indispensable tool in both physics and finance, facilitating complex calculations and improving analytical capabilities. Its versatility underscores the importance of mathematical foundations in real-world applications.

Abstract. Several alternative gravity forward modelling methodologies and associated numerical codes with their own advantages and limitations are available for the solid Earth community. With upcoming state-of-the-art lithosphere density models and accurate global gravity field data sets, it is vital to understand the opportunities and limitations of the various approaches. In this paper, we discuss the four widely used techniques: global spherical harmonics (GSH), tesseroid integration (TESS), triangle integration (TRI), and hexahedral integration (HEX). A constant density shell benchmark shows that all four codes can produce similar precise gravitational potential fields. Two additional shell tests were conducted with more complicated density structures: laterally varying density structures and a crust–mantle interface density. The differences between the four codes were all below 1.5 % of the modelled gravity signal suitable for reproducing satellite-acquired gravity data. TESS and GSH produced the most similar potential fields (<0.3 %). To examine the usability of the forward modelling codes for realistic geological structures, we use the global lithosphere model WINTERC-G that was constrained, among other data, by satellite gravity field data computed using a spectral forward modelling approach. This spectral code was benchmarked against the GSH, and it was confirmed that both approaches produce a similar gravity solution with negligible differences between them. In the comparison of the different WINTERC-G-based gravity solutions, again GSH and TESS performed best. Only short-wavelength noise is present between the spectral and tesseroid forward modelling approaches, likely related to the different way in which the spherical harmonic analysis of the varying boundaries of the mass layer is performed. The spherical harmonic basis functions produce small differences compared to the tesseroid elements, especially at sharp interfaces, which introduces mostly short-wavelength differences. Nevertheless, both approaches (GSH and TESS) result in accurate solutions of the potential field with reasonable computational resources. Differences below 0.5 % are obtained, resulting in residuals of 0.076 mGal standard deviation at 250 km height. The biggest issue for TRI is the characteristic pattern in the residuals that is related to the grid layout. Increasing the resolution and filtering allow for the removal of most of this erroneous pattern, but at the expense of higher computational loads with respect to the other codes. The other spatial forward modelling scheme, HEX, has more difficulty in reproducing similar gravity field solutions compared to GSH and TESS. These particular approaches need to go to higher resolutions, resulting in enormous computation efforts. The hexahedron-based code performs less than optimal in the forward modelling of the gravity signature, especially with a laterally varying density interface. Care must be taken with any forward modelling software as the approximation of the geometry of the WINTERC-G model may deteriorate the gravity field solution.

The paper considers discourse analysis instruments for investigation of political communications. The research is based upon example of communist movement discourse. Ideological conflicts within communist organizations appeal to the legacy of theorists of the past century. Participants in disputes identify themselves with certain trends and oppose their positions to those of their opponents. However, scientific analysis of these divisions is hampered by the lack of an adequate methodological apparatus. Postmodern versions of discourse analysis dissolve material relations into language games. Critical approaches fix grammatical structures but do not trace the connection between the text and the class positions of its producers. Historiographical narratives select quotations according to a pre-established scheme. These limitations give rise to the need for a different tool. The article develops materialist discourse analysis as a method for identifying power interests in symbolic space. The theoretical basis consists of W. Lippmann's propositions on stereotypes, G. Lasswell's categories of political communication, and M. Foucault's procedures for discourse control. The analytical scheme divides discourse into two dimensions: vertical and horizontal. The vertical dimension is broken down into deep, middle, and surface levels. The horizontal dimension includes the center and the periphery. The center is determined by the referential core of discourse. The scientific novelty of materialistic discourse analysis lies in considering discourse not as a language game, but as a socially conditioned objectified interest that reproduces relations of domination. The vertical dimension shows the transformation of interests into political formulas. The horizontal dimension shows the mechanism of competition for the meanings of words, the use of external, internal, and social control procedures. The referential core of discourse allows us to track this struggle for meaning. The effectiveness of the method has been tested on V. I. Lenin's 1923 text “Better Less, But Better.” The reference core of the discourse is the provisions of Karl Marx's Critique of the Gotha Program. The procedure made it possible to identify the points of convergence between the two discourses, their differences, and Lenin's specific innovations. The latter include an emphasis on the quality of personnel, the problem of retaining power in an agrarian country, and criticism of the growing bureaucracy. The proposed method helps to analyze political texts and reconstruct ideological discourses and political formulas.

Several alternative gravity forward modelling methodologies and associated numerical codes with their own advantages and limitations are available for the Solid Earth community. With the upcoming state-of-the-art lithosphere density models and accurate global gravity field data sets it is vital to understand the opportunities and limitations of the various approaches. In this paper, we discuss the four widely used techniques: global spherical harmonics (GSH), tesseroid integration (TESS), triangle integration (TRI), and hexahedral integration (HEX). A constant density shell benchmark shows that all four codes can produce similar precise gravitational potential fields. Two additional shell tests were conducted with more complicated density structures: lateral varying density structures and a Moho density interface between crust and mantle. The differences between the four codes were all below 1.5 percent of the modeled gravity signal suitable for reproducing satellite-acquired gravity data. TESS and GSH produced the most similar potential fields (< 0.3 percent). To examine the usability of the forward modelling codes for realistic geological structures, we use the global lithosphere model WINTERC-G, that was constrained, among other data, by satellite gravity field data computed using a spectral forward modeling approach. This spectral code was benchmarked against the GSH and it was confirmed that both approaches produce similar gravity solution with negligible differences between them. In the comparison of the different WINTERC-G-based gravity solutions, again GSH and TESS performed best. Only short-wavelength noise is present between the spectral and tesseroid forward modelling approaches, likely related to the different way in which the spherical harmonic analysis of the varying boundaries of the mass layer is performed. The Spherical harmonic basis functions produces small differences compared to the tesseroid elements especially at sharp interfaces, which introduces mostly short-wavelength differences. Nevertheless, both approaches (GSH and TESS) result in accurate solutions of the potential field with reasonable computational resources. Differences below 0.5 percent are obtained, resulting in residuals of 0.076 mGal standard deviation at 250 km height. The biggest issue for TRI is the characteristic pattern in the residuals that is related to the grid layout. Increasing the resolution and filtering allows for the removal of most of this erroneous pattern, but at the expense of higher computational loads with respect to the other codes. The other spatial forward modelling scheme HEX has more difficulty in reproducing similar gravity field solutions compared to GSH and TESS. These particular approaches need to go to higher resolutions, resulting in enormous computation efforts. The hexahedron-based code performs less than optimal in the forward modelling of the gravity signature, especially of a lateral varying density interface. Care must be taken with any forward modelling software as the approximation of the geometry of the WINTERC-G model may deteriorate the gravity field solution.

The popularization of electricity-gas systems leads to increasing demand for state management of systems. However, the existence of neglected measurement correlations brings uncertainties to the electricity-gas systems state estimation. In this paper, an interval state estimation method that considers measurement correlations existing in the electricity-gas systems is presented. We derive the linear measurement model for the electricity-gas systems through Taylor series expansion and estimate the measurement variance-covariance matrix with measurement correlations. The system parameter matrix and the measurement variance-covariance matrix containing measurement correlations are combined into an interval, and the interval state matrix considering measurement correlations is constructed. Then, the linear equations for the state estimation interval considering measurement correlations are established based on the measurement containing correlations and interval state matrix; as a result, the electricity-gas system state estimation model containing measurement correlations is established. In addition, a method for determining the range of state estimation intervals is proposed. Numerical tests on an integrated electricity-gas system comprising a 10-node natural gas network and IEEE 30-bus system indicate that the proposed approach has more advantages over the UT+KO approach in computation accuracy and computation efficiency.

Clinical accuracy and responsiveness of 3D software for measuring facial dimensions at altered vertical dimensions.

Many abstract bipolar concepts are usually represented by metaphors on vertical dimensions (e.g. positive-up, negative-down). However, several studies have found an asymmetry in the way in which individuals process bipolar dimensions, with +polarities being stronger than -polarities. The current research focused on moral metaphors on a vertical dimension (e.g. moral-up and immoral-down) and examined the asymmetric representation of moral and immoral concepts. The first experiment showed a distinct metaphorical association between morality and vertical space, consistent with earlier research. The second experiment showed that moral and immoral words are processed differently depending on whether they are used as metaphorically congruent or incongruent vertical cues. 'Moral-up' association modulated the amplitudes of the N1, P2, and late positive-going potential during the processing of moral words, whereas the 'immoral-down' association only modulated the amplitudes of the late positive-going potential induced during the processing of immoral words. These results suggest that asymmetry in the processing of vertically represented morality metaphors is reflected in the time course of the representation of these bipolar concepts, with the 'moral-up' association having an earlier effect than the 'immoral-down' association.