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The switching impulse discharge characteristics are the basis for determining the minimum approach distance in equipotential live working (EPLW) gap. The discharge mechanism of the EPLW gap is not fully deterministic currently. In this study, two actual EPLW gaps and two simplified gaps including sphere–plane gap and bundle conductor + rod-plane gap are established, and the discharge mechanism of these gaps is investigated. The result indicates that the discharge characteristics of sim-worker's back and feet are similar to the simplified electrode. For the sim-worker's back, the streamer inception time delay, inception voltage, injected charge, and transition time are 93.3 μs, 765 kV, 6.19 μC, and 44.7 μs, respectively. The current waveforms of the sim-worker's back and the sphere electrode (R = 0.3 m) exhibit similar characteristics, both containing single pulse, and streamer length nearly half the gap. For the sim-worker's feet, the corresponding values are 28.5 μs, 307 kV, 0.67 μC, and 81.6 μs, similar to the bundle conductor + rod electrode (R = 5 cm), with multiple pulse current waveforms and streamer length of 0.49 m, also similar to the bundle conductor + rod electrode (R = 5 cm). The result can contribute to lineman safety protection and simplified gap design for live working. [ABSTRACT FROM AUTHOR]

This study explores the dynamics of self-assembly and mesophase formation through molecular dynamics simulations of hexagonal and lamellar systems using a simplified coarse-grained model. We focus on characterizing the order–disorder transitions driven by temperature variations and emphasize the often overlooked disordered regime, which serves as a precursor to periodic mesoscale ordering. Our findings not only underscore the morphological richness of the disordered regime, comparable to that of its periodic counterparts, but also reveal the presence of clustering regimes within isotropic phases, thus corroborating prior experimental and theoretical observations. By employing the dynamic correlation coefficient, this work introduces a novel approach to understanding the fundamental mechanisms of mesophase formation, providing new insights into the complex dynamics of self-assembly. [ABSTRACT FROM AUTHOR]

Policy-guided Monte Carlo is an adaptive method to simulate classical interacting systems. It adjusts the proposal distribution of the Metropolis–Hastings algorithm to maximize the sampling efficiency, using a formalism inspired by reinforcement learning. In this work, we first extend the policy-guided method to deal with a general state space, comprising, for instance, both discrete and continuous degrees of freedom, and then apply it to a few paradigmatic models of glass-forming mixtures. We assess the efficiency of a set of physically inspired moves whose proposal distributions are optimized through on-policy learning. Compared to conventional Monte Carlo methods, the optimized proposals are two orders of magnitude faster for an additive soft sphere mixture but yield a much more limited speed-up for the well-studied Kob–Andersen model. We discuss the current limitations of the method and suggest possible ways to improve it. [ABSTRACT FROM AUTHOR]

One method for computationally determining phase boundaries is to explicitly simulate a direct coexistence between the two phases of interest. Although this approach works very well for fluid–fluid coexistences, it is often considered to be less useful for fluid–crystal transitions, as additional care must be taken to prevent the simulation boundaries from imposing unwanted strains on the crystal phase. Here, we present a simple adaptation to the direct coexistence method that nonetheless allows us to obtain highly accurate predictions of fluid–crystal coexistence conditions, assuming that a fluid–crystal interface can be readily simulated. We test our approach on hard spheres, the screened Coulomb potential, and a 2D patchy-particle model. In all cases, we find excellent agreement between the direct coexistence approach and (much more cumbersome) free-energy calculation methods. Moreover, the method is sufficiently accurate to resolve the (tiny) free-energy difference between the face-centered cubic and hexagonally close-packed crystal of hard spheres in the thermodynamic limit. The simplicity of this method also ensures that it can be trivially implemented in essentially any simulation method or package. Hence, this approach provides an excellent alternative to free-energy based methods for the precise determination of phase boundaries. [ABSTRACT FROM AUTHOR]

We evaluate depletion forces in molecular dynamics simulation of a binary mixture of spheres (depleted particles) and rods (depletant particles) for a wide range of densities for both species. This evaluation was carried out using a recently proposed least squares fitting algorithm. We found that the restriction of the rods' rotational degrees of freedom, when the distance between two spheres is less than the rods length, creates a shallow, and apparently linear, attractive force ramp. For intersphere distances smaller than the rods' diameter, a much stronger attractive force is found, and a large repulsive barrier appears between these aforementioned regimes, roughly at the distance of the rods' thickness. The evaluated forces are validated via a comparison of the pairwise correlation functions obtained from molecular dynamics simulation of a mono-disperse sphere fluid, using the evaluated effective forces, against the original (full system) pairwise correlation functions. Agreement is excellent. We also record the angular pairwise correlation function, using the P2(x) Legendre polynomial, and find that for high densities of both species, a local nematic ordering starts to appear. This nematic order may be a factor in the small differences found between original and effective pairwise correlation functions at high densities of rods. [ABSTRACT FROM AUTHOR]

School libraries are trusted institutions that can empower students to participate in the civic sphere. Cognizant of the need to create a space where students could engage in civil discourse about political issues, one school librarian began ProjectCiv, a semiregular, bipartisan discussion that exposes students to different perspectives and builds background knowledge about controversial topics. This article explains the purpose of ProjectCiv, why it was created, how it operates, and how it has increased opportunities for civic engagement for the participants. These opportunities have given students a chance to exhibit the civic dispositions that are a focus of ProjectCiv discussions. Examples of students' civic engagement are detailed and explained. [ABSTRACT FROM AUTHOR]

Using particle-resolved computer simulations, we investigate the effect of friction on the packing structure of hard-sphere mixtures with two kinds of particles under external compression. We first show that increasing friction between the particles results in a more disordered and less efficient packing of the local structure on the nearest neighbor scale. It is also found that standard two-point correlation functions, i.e., radial distribution function and static structure factor, show basically no detectable changes beyond short-range distances upon varying inter-particle friction. Further analysis of the structure using a four-point correlation method reveals that these systems have on the intermediate-range scale a three-dimensional structure with an icosahedral/dodecahedral symmetry that exhibits a pronounced dependence on friction: small friction gives rise to an orientational order that extends to larger distances. Our results also demonstrate that composition plays a role in that the degree of structural order and the structural correlation length are mainly affected by the friction coefficients associated with the more abundant species. [ABSTRACT FROM AUTHOR]

A system associated with several number of weak interactions supports numerous number of stable structures within a narrow range of energy. Often, a deterministic search method fails to locate the global minimum geometry as well as important local minimum isomers for such systems. Therefore, in this work, the stochastic search technique, namely parallel tempering, has been executed on the quantum chemical surface of the CNO(‐)(H2O)n system for n=1–8 to generate global minimum as well as several number of local minimum isomers. IR spectrum can act as the fingerprint property for such system to be identified. Thus, IR spectroscopic features have also been included in this work. Vertical detachment energy has also been calculated to obtain clear information about number of water molecules in several spheres around the central anion. In addition, in a real experimental scenario, not only the global but also the local minimum isomers play an important role in determining the average value of a particular physically observable property. Therefore, the relative conformational populations have been determined for all the evaluated structures for the temperature range between 20K and 400K. Further to understand the phase change behavior, the configurational heat capacities have also been calculated for different sizes. [ABSTRACT FROM AUTHOR]

There are a number of known constructions of quasimorphisms on Hamiltonian groups. We show that on surfaces many of these quasimorphisms are not compatible with the Hofer norm in a sense they are not continuous and not Lipschitz. The only exception known to the author is the Calabi quasimorphism on a sphere [M. Entov and L. Polterovich, Calabi quasimorphism and quantum homology, Int. Math. Res. Not. 2003 (2003) 1635–1676] and induced quasimorphisms on genus-zero surfaces (e.g. [P. Biran, M. Entov and L. Polterovich, Calabi quasimorphisms for the symplectic ball, Commun. Contemp. Math. 6 (2004) 793–802]). [ABSTRACT FROM AUTHOR]

In the contemporary landscape of technological advancements, the burgeoning demand for portable electronics and flexible wearable devices has necessitated the development of energy storage systems with superior volumetric performance. Tungsten oxide (WO3), known for its high density and theoretical capacitance, is a promising electrode material for supercapacitors. However, low conductivity and poor cycling stability are still the key bottlenecks for its application. Herein, a novel composite comprising hollow porous WO3 spheres (HPWS) derived by template method was electrostatic self-assembled on the surface of the Ti3C2T x nanosheets. The resulting electrodes exhibited ultra-high volumetric capacitance of 1930 F cm−3 at 1 A g−1 and rate capability of 46% at 50 A g−1, attributed to enhanced ion accessibility from microporous structure and electron transport from conductive network of Ti3C2T x even at a high packing density of 3.86 g cm−3. Utilizing HPWS/Ti3C2T x as the negative electrode and porous carbon as the positive electrode, the assembled asymmetric supercapacitor achieved an energy density of 31 Wh kg−1 at a power density of 650 W kg−1 with over 107% capacitance retention after 5000 cycles. This work provides a promising approach for developing next-generation supercapacitors with ultra-high volumetric capacitance. [ABSTRACT FROM AUTHOR]

The widely accepted globalization of innovation entails two interrelated undertheorized aspects: (1) the capacity of certain firms to orchestrate transnational innovation systems appropriating successful results, which some have explained with the concept of corporate innovation systems (CIS), and (2) the co-existence of such globalization with those CIS and national innovation systems. I address these matters analysing US Big Tech artificial intelligence (AI) CIS showing that they combine multiple mechanisms to co-produce and appropriate AI. I propose 'frenemy' to describe Microsoft's strategy because many Chinese organizations and even direct competitors integrate its CIS. 'University' symbolises Google's strategy, given its focus on fundamental AI, its central place in the AI research field and appropriation mechanisms that are not translating into clear business advantages. 'Secrecy' defines Amazon's strategy, maximizing knowledge inflows while minimizing outflows. Facebook, with the narrowest AI CIS, exhibits an 'application-centred' strategy. Ultimately, this paper contributes to understanding the multiple mechanisms used by leading corporations for controlling and shaping frontier transnational knowledge production and appropriation. By doing so, it advances our knowledge of the interplay between different innovation spheres (national, global and corporate) and highlights the dangers of CIS's encroachment of national and global systems. [ABSTRACT FROM AUTHOR]

In the present paper, I enlarge William Stern's value theory and link it to his teachings about signs and symbols. People come with dynamic self-value (which is derived from their needs and goal hierarchies), which they radiate into different action spheres, within which they make use of specific signs and tools. Therefore, by altering their psychic systems, the action spheres and tools combine to create a specific service value for each person. In the second part, I criticize Stern's value theory for not emphasizing social-historical features in his general theoretical framework. This is compared to Vygotsky, for example, who emphasized that action spheres come with a particular cultural-historical situation, so that we get a glimpse not only into a person's self-value but also into the social conditions under which they act. [ABSTRACT FROM AUTHOR]

In Wolf's EPWH, the importance of debt for scaffolding the expansion of the capitalist mode of production was shown repeatedly, despite not being treated as a distinct phenomenon. In the forty years that have gone by since the publication of the book, financial debt has gained centrality in global accumulation processes. The advancing frontier of financialization, reminiscent of that of earlier capitalist expansion, as well as its effects on particular groups and localities, has been a recurrent object of analysis in recent anthropological scholarship, often with a focus on the sphere of circulation and consumption. This article contends that the Wolfian conceptual toolkit, and particularly the notion of labor, should be brought back into the equation for addressing debt and credit relations in contemporary times. [ABSTRACT FROM AUTHOR]

The spherical radial basis function (SRBF) approach, widely used in gravity modeling, is theoretically surveyed from a viewpoint of random field theory. Let the gravity potential be a random field which is represented as an integral functional of another random field, namely an isotropic Gaussian random field (IGRF) on a sphere inside the Bjerhammar sphere with the SRBF as the integral kernel. When the integration is approximated by a discrete sum within a local region, one gets the widely applicable SRBF model. With this theoretical study, the following two findings are made. First, the IGRF implies a Gaussian prior on the spherical harmonic coefficients (SHCs) of the gravity potential; for this prior the SHCs are independent with each other and their variances are degree-only dependent. This should be reminiscent of two well-known priors, namely the power-law Kaula's rule and the asymptotic power-law Tscherning-Rapp model. Second, the IGRF-SRBF representation is non-unique. Benefiting from this redundant representation, one can employ a simple IGRF, e.g., the simplest white field, and then design the SRBF accordingly to represent a potential with desired prior statistical properties. This can simplify the corresponding SRBF modeling significantly; to be more specific, the regularization matrix in parameter estimation of the SRBF modeling can be chosen to be a diagonal matrix, or even the naïve identity matrix. [ABSTRACT FROM AUTHOR]

A central problem in low-dimensional topology asks which homology three-spheres bound contractible four-manifolds or homology four-balls. In this paper, we address this question for plumbed three-manifolds and we present two new infinite families. We consider most of the classical examples from around the 1980s by reproving that they all bound Mazur manifolds. We also show that several well-known families bound possibly different types of four-manifolds, called Poénaru homology four-balls. To unify classical and new results in a fairly simple way, we modify Mazur's argument and work with Poénaru manifolds. [ABSTRACT FROM AUTHOR]

In a long-forgotten essay, Alvin Gouldner defended the distinctive contributions of Romantic social science. Today, half a century later, very few would risk making a similar plea. Owing to its deconstruction, the discourse of Romanticism has increasingly fallen out of favor in the social sciences, meaning social scientists have progressively come to see Romanticism as less a resource for critique than a bourgeois ideology warranting critical scrutiny. Yet the truth is quite a bit more complicated. For despite its disapproval at the level of social science's explicit culture, Romanticism continues to serve, at the level of implicit culture, as a potent resource for social analysis. We start with a clarification of what we mean by Romanticism. While Romanticism may be an amorphous and multifaceted structure of thought and feeling, like Gouldner, we do not think it lacks coherence. Thus, we outline what we take to be the core dimensions of the 'Romantic syndrome', and then survey some of its key figures in Western social thought. Next, we move to a discussion of three select studies about the infiltration of Romanticism into the capitalist heartland—the sphere of work. We demonstrate how, consistent with our argument that Romanticism has become increasingly symbolically polluted within social science, each of these studies critiques the Romantic turn at work, while nevertheless anchoring their critiques in Romanticism, albeit in increasingly implicit fashion. We conclude by offering some reflections on why Romanticism continues to haunt contemporary social science—and why this matters. [ABSTRACT FROM AUTHOR]

The present work is devoted to discuss the transient wave propagation in an isotropic homogenous thermoelastic spherical body with voids due to harmonically varying heat sources in the context of nonlocal thermoelasticity. The constitutive relations and the governing equations are resolved by applying harmonic variations in time and transformed into coupled ordinary differential equations. The outer and the inner surfaces of the sphere are kept stress-free and free from void concentration. A harmonically varying heat source is supplied on the inner surface along the radial direction and the outer surface is assumed to be isothermal. Numerical simulations are implemented to the analytical results with the support of MATLAB software tool. Numerically, generated data are presented graphically for the field variables of interest (temperature, stresses, cubical dilation, displacement and void volume fraction field) and at the end analysis of these results are given. [ABSTRACT FROM AUTHOR]

We consider here the problem of a three-dimensional (3D) body subjected to an arbitrarily oriented and remotely applied stationary heat flux. The body includes a non-conductive inhomogeneity (or pore) having the shape of two intersecting spheres with different radii. Using toroidal coordinates, the steady-state temperature field and the heat flux have been expressed in terms of Mehler–Fock transforms. Then, by imposing Neumann BCs at the surface of the spheres, a system of two Fredholm integral equations is obtained and solved based on Gauss–Laguerre quadrature rule. It is shown that the components of the resistivity contribution tensor exhibit a non-monotonic trend with the distance between sphere centers. In particular, if the inhomogeneity has a symmetric dumbbell-shape, then the extrema of the resistivity contribution tensor components occur when the two overlapping spheres have the same size. Differently, when the inhomogeneity has a lenticular shape, then these extrema are attained for a non-symmetric configuration, namely, for different radii of the intersecting spheres. [ABSTRACT FROM AUTHOR]

We study weighted sums of free identically distributed self-adjoint random variables with weights chosen randomly from the unit sphere and show that the Kolmogorov distance between the distribution of such a weighted sum and Wigner's semicircle law is of order n - 1 2 with high probability. Replacing the Kolmogorov distance by a weaker pseudometric, we obtain a rate of convergence of order n - 1 , thus providing a free analog of the Klartag-Sodin result in classical probability theory. Moreover, we show that our ideas generalize to the setting of sums of free non-identically distributed bounded self-adjoint random variables leading to a new rate of convergence in the free central limit theorem. [ABSTRACT FROM AUTHOR]

For any s∈[−∞,0] and oriented homology 3-sphere Y, we introduce a homology cobordism invariant r s ​ (Y)∈(0, ∞]. The values {r s ​ (Y)} are included in the critical values of the SU(2)-Chern–Simons functional of Y, and we show a negative definite cobordism inequality and a connected sum formula for r s ​. As applications, we obtain several new results on the homology cobordism group. First, we give infinitely many homology 3-spheres which cannot bound any definite 4-manifold. Next, we show that if the 1-surgery of S 3 along a knot has the Frøyshov invariant negative, then all positive 1/n-surgeries along the knot are linearly independent in the homology cobordism group. In another direction, we use {r s ​} to define a filtration on the homology cobordism group which is parametrized by [0, ∞]. Moreover, we compute an approximate value of r s ​ for the hyperbolic 3-manifold obtained by 1/2-surgery along the mirror of the knot 5 2 ​. [ABSTRACT FROM AUTHOR]

In this paper, we obtain new upper bounds for the Lieb–Thirring inequality on the spheres of any dimension greater than 2. As far as we have checked, our results improve previous results found in the literature for all dimensions greater than 2. We also prove and exhibit an explicit new upper bound for the Lieb–Thirring inequality on SO(3). We also discuss these estimates in the case of general compact Lie groups. Originally developed for estimating the sums of moments of negative eigenvalues of the Schrödinger operator in L 2 (R n) , these inequalities have applications in quantum mechanics and other fields. [ABSTRACT FROM AUTHOR]

We present a novel topology-preserving 3D medial axis computation framework based on volumetric restricted power diagram (RPD), while preserving the medial features and geometric convergence simultaneously, for both 3D CAD and organic shapes. The volumetric RPD discretizes the input 3D volume into sub-regions given a set of medial spheres. With this intermediate structure, we convert the homotopy equivalency between the generated medial mesh and the input 3D shape into a localized contractibility checking for each restricted element (power cell, power face, power edge), by checking their connected components and Euler characteristics. We further propose a fractional Euler characteristic algorithm for efficient GPU-based computation of Euler characteristic for each restricted element on the fly while computing the volumetric RPD. Compared with existing voxel-based or point-cloud-based methods, our approach is the first to adaptively and directly revise the medial mesh without globally modifying the dependent structure, such as voxel size or sampling density, while preserving its topology and medial features. In comparison with the feature preservation method MATFP [Wang et al. 2022], our method provides geometrically comparable results with fewer spheres and more robustly captures the topology of the input 3D shape. [ABSTRACT FROM AUTHOR]

In this article, we explore why the Myanmar-based insurgency organisation known as the United League of Arakan (ULA) supports the Kyaukphyu Special Economic Zone (KSEZ): a controversial Belt and Road Initiative (BRI) project. We argue that the ULA's support for the KSEZ is rooted in a biopolitics that benefits the ULA by attractively showcasing its insurgent aims and by effectively boosting its local authority. The ULA's pro-KSEZ policy partially explains why the KSEZ, unlike other BRI projects in junta-led Myanmar, has enjoyed moderate success. Despite its biopolitical benefits, the ULA's pro-KSEZ policy has marginalised certain anti-KSEZ actors in the rebel organisation's sphere of control. The resulting fragmentation may both destabilise the ULA's hard-fought social order and undermine the prospects of the KSEZ. Our examination of the ULA–KSEZ relationship empirically contributes to BRI-in-Myanmar research, which has heretofore paid little attention to rebel-controlled societies' significant influence on foreign-led domestic development projects. [ABSTRACT FROM AUTHOR]

The argument I defend in this paper challenges whether Waldron's explanation of the conditions required for a moral right to satisfy its autonomy-promoting function is the best one available. It questions the suitability of Waldron's preferred taxonomy of moral action, where acts are divided into: (1) those that are morally required; (2) those that are morally prohibited; and (3) those that are morally indifferent, advocating instead for a binary classification consisting of: (a) actions that admit of reasonable moral disagreement; and (b) actions that do not admit of reasonable moral disagreement. My claim is that the protective sphere moral rights set up in organizing the moral relations among persons is applicable only to the former category—namely, actions that admit of reasonable moral disagreement. Actions that do not admit of reasonable moral disagreement will either: (b') not normally demand a right against interference in the first place (if the action is unquestionably permissible); or (b") fail to admit of a right against interference at all (if the action is unquestionably impermissible). This competing explanation allows us to preserve the autonomy-promoting conception of moral rights Waldron endorses while avoiding a number of its suspect implications. [ABSTRACT FROM AUTHOR]

In this paper, we present a candidate of a vector space basis for the noncommutative algebra 풪(Sq4n−1) of the quantum symplectic sphere for every n ≥ 1. The algebra 풪(Sq4n−1) is defined as a certain subalgebra of the quantum symplectic group 풪(SPq(2n)). A nontrivial application of the Diamond Lemma is used to construct the vector space basis and the conjecture is supported by computer experiments for n = 1, 2,…, 8. [ABSTRACT FROM AUTHOR]

Let SO(m, 1) be the group of orientation preserving isometries of the m-dimensional real hyperbolic space ℍℝm, and let SU(n, 1) be the group of holomorphic isometries of the n-dimensional complex hyperbolic space ℍℂn. The group SU(n, 1) is naturally a subgroup of PSL(n + 1, ℂ), so it acts on ℙℂn preserving a ball that serves as a model for ℍℂn. We consider discrete subgroups of SO(m, 1) with limit set an (m − 1)-dimensional real sphere and we look at their action on ℙℂn for n ≥ m via the natural embedding of SO(m, 1) into SU(n, 1). We describe the Kulkarni limit set of these set of these actions and show that this is a real semi-algebraic set in ℙℂn. We also show that the Kulkarni region of discontinuity can only have either one or three connected components. We use Sylvester’s law of inertia when n = m. In the other cases, we use some suitable projections of the n-dimensional complex projective space to the m-dimensional complex projective space. [ABSTRACT FROM AUTHOR]

Unique continuation is one of the most important properties for the solution of partial differential equation, which means the local information of the solution can determine the global one. In this paper, we discuss a special unique continuation for Helmholtz equations on a sphere in ℝ3$$ {\mathbb{R}}^3 $$, which is different with the classical unique continuation. The unique continuation holds only on the sphere and may not be extended to the domain in ℝ3$$ {\mathbb{R}}^3 $$. A Hölder type conditional stability of unique continuation is proved by complex extension method. Then a Tikhonov regularized scheme is proposed and the convergence rate is obtained by using the conditional stability estimate. Numerical examples are presented to show the performance of the scheme. It should be remarked here that our results may be applied to the problem of recovering a far field pattern with its local information. [ABSTRACT FROM AUTHOR]

A PT-symmetric non-Hermitian photonic system composed of specifically designed metal structures is used to conduct arbitrary polarization transition from the equator and generate polarization vortices with exceptional point on the Poincaré sphere's poles, which induces unidirectional hyperbolic polaritons propagation due to the break of mirror symmetry. [Display omitted] [ABSTRACT FROM AUTHOR]

The synthesis and characterization of a gadolinium-based contrast agent conjugated to 3-phosphoglycerate (Gd-3PG) are reported. The synthetic steps are optimized to incorporate a selective deprotection strategy for a primary tert-butyl dimethyl silyl (TBS) hydroxyl over a secondary one. The relaxivity of Gd-3PG shows characteristic improvement, likely due to secondary sphere effects and/or an increase in molecular weight (5.39 ± 0.14 mM−1 s−1 at 1.4 T and 37 °C). Michaelis–Menten enzymatic kinetics was measured on the modified 3PG-arm and it showed similar activity to the native 3PG metabolite, Km = 240 ± 30 μM. This agent and future versions of this type of GBCA, which are conjugated to glycolytic metabolites, were designed to monitor in vivo allosteric regulatory events in glycolytic processes. [ABSTRACT FROM AUTHOR]

In this study, a system for measuring the positional accuracy of industrial robots using 3D vision and networking technology has been proposed. The 3D vision system comprises a charge-coupled device (CCD) module, a reference sphere module, and a signal processing module. The reference sphere module serves as the sensing object, while the CCD module captures displacement images of the reference sphere module. The signal processing module receives and processes signals from the CCD module. It utilizes a self-developed Visual C + + interface to calculate the X, Y, Z, θx, and θy (five-degree-of-freedom, 5-DOF) positional accuracy of the industrial robot. Experimental results demonstrate that the linear accuracy (X, Y, Z) and angular accuracy (θx, θy) of the 3D vision system are approximately 3 μm and 0.15°, respectively. Additionally, a networking architecture connects the controller of the machine tool with the industrial robot to enable synchronized motion path planning. The industrial robot can be calibrated using the high-precision machine tool equipped with the 3D vision-based positional accuracy measurement system. [ABSTRACT FROM AUTHOR]

We prove that in any rank one symmetric space of non-compact type M ∈ { ℝ ⁢ H n , ℂ ⁢ H m , ℍ ⁢ H m , 핆 ⁢ H 2 } {M\in\{\mathbb{R}H^{n},\mathbb{C}H^{m},\mathbb{H}H^{m},\mathbb{O}H^{2}\}} , geodesic spheres are uniformly quantitatively stable with respect to small C 1 {C^{1}} -volume preserving perturbations. We quantify the gain of perimeter in terms of the W 1 , 2 {W^{1,2}} -norm of the perturbation, taking advantage of the explicit spectral gap of the Laplacian on geodesic spheres in M. As a consequence, we give a quantitative proof that for small volumes, geodesic spheres are isoperimetric regions among all sets of finite perimeter. [ABSTRACT FROM AUTHOR]

In this paper, we consider proper holomorphic maps of ball complements and differences in complex euclidean spaces of dimension at least two. Such maps are always rational, which naturally leads to a related problem of classifying rational maps taking concentric spheres to concentric spheres, what we call m-fold sphere maps; a proper map of the difference of concentric balls is a two-fold sphere map. We prove that proper maps of ball complements are in one to one correspondence with polynomial proper maps of balls taking infinity to infinity. We show that rational m-fold sphere maps of degree less than m (or polynomial maps of degree m or less) must take all concentric spheres to concentric spheres and we provide a complete classification of them. We prove that these degree bounds are sharp. [ABSTRACT FROM AUTHOR]

The fundamental group of the complement of a locally flat surface in a 4‐manifold is called the knot group of the surface. In this article, we prove that two locally flat 2‐spheres in CP2$\mathbb {C}P^2$ with knot group Z2$\mathbb {Z}_2$ are ambiently isotopic if they are homologous. This combines with work of Tristram and Lee–Wilczyński, as well as the classification of Z$\mathbb {Z}$‐surfaces, to complete a proof of the statement: a class d∈H2(CP2)≅Z$d \in H_2(\mathbb {C}P^2) \cong \mathbb {Z}$ is represented by a locally flat sphere with abelian knot group if and only if |d|∈{0,1,2}$|d| \in \lbrace 0,1,2\rbrace$; and this sphere is unique up to ambient isotopy. [ABSTRACT FROM AUTHOR]

In this article, we give a unified method to derive the classical characteristic functions of all elliptical and related distributions in terms of Bessel functions. The approach is based on the stochastic representation of an elliptical random variable and the characteristic function of uniform distribution on the unit sphere surface in ℝn. In particular, we present the simple closed form of characteristic functions for commonly used distributions such as multivariate t, Pearson Type II, Pearson Type VII, Kotz type, and Bessel distributions. Some extensions are also being investigated. [ABSTRACT FROM AUTHOR]

In this work, the theory of the modified unit sphere representation (mUSR) has been proposed as a computational tool suitable for the three‐dimensional representation of the pure electric‐dipole [βλμν(−2ω;ω,ω)] as well as of the mixed electric‐dipole/magnetic‐dipole [ αJλμν(−2ω;ω,ω) and βJλμν(−2ω;ω,ω)] or electric‐dipole/electric‐quadrupole [ αKλμνo(−2ω;ω,ω) and βKλμνo(−2ω;ω,ω)] first hyperpolarizabilities. These five quantities are Cartesian tensors and they are responsible for the chiral signal in the chiroptical version of the hyper‐Rayleigh scattering (HRS) spectroscopy, namely the HRS optical activity (HRS‐OA) spectroscopy. For the first time, for each hyperpolarizability, alongside with the three‐dimensional representation of the whole (i.e., reducible) Cartesian tensors, the mUSRs are developed for each of the irreducible Cartesian tensors (ICTs) that constitute them. This scheme has been applied to a series of three (chiral) hexahelicene molecules containing different degrees of electron‐withdrawing (quinone) groups and characterized by the same (positive) handedness. For these molecules, the mUSR shows that, upon substitution, the most remarkable qualitative and semi‐quantitative (enhancement of the molecular responses) effects are obtained for the pure electric‐dipole and for the mixed electric‐dipole/magnetic‐dipole hyperpolarizabilities. [ABSTRACT FROM AUTHOR]

In this paper, we classify the solutions of the following elliptic equation in R + 4 { (− Δ) 2 u (x) = e 4 u (x) in R + 4 , ∂ u ∂ ν = 0 on ∂ R + 4 , ∂ (− Δ u) ∂ ν = e 3 u on ∂ R + 4. Under some assumptions, we will show that, on the boundary of R + 4 , the solutions must have the following form u (x ′ , 0) = ln ⁡ C (ε) ε 2 + | x ′ − x 0 ′ | 2 , where C is a positive constant depending only on ε and x 0 ′ is a fixed point on ∂ R + 4. [ABSTRACT FROM AUTHOR]

Sphere partition function integral for abelian Calabi–Yau GLSM is equal to the pairing of the I-function with its complex conjugate, where the real structure is essentially constructed from Iritani’s integral structure on the cohomology of the target. [ABSTRACT FROM AUTHOR]

ABSTRACT This research aims to analyse the complex connections between students' engagement in extracurricular activities (ECAs), their sense of school belonging, and the cumulative effects on their psychological well‐being and academic performance. The results based on a sample of 892 students reveal that active engagement in ECAs does not influence students' academic outcomes directly. Instead, the benefits derived from ECAs primarily manifest in non‐academic spheres, particularly in enhancing well‐being. Moreover, ECAs yield positive psychological well‐being and academic performance only when students have a low sense of school belonging. At higher levels, the positive impact of ECAs diminishes, and it may even detrimentally affect academic performance. This study offers a different viewpoint to address the dilemma surrounding ECAs and practical implications in the development of institutional policies. [ABSTRACT FROM AUTHOR]

This paper examines how the European Union (EU) has discursively framed the European Neighbourhood Policy (ENP) since 2003 and explores frames and frame alignment over time. The study argues that the EU embeds the ENP with relatively fixed frame-issues and unstable framings that get aligned when the Union feels urged to respond to external/internal dynamics and deepen engagement with partner countries’ political elites to tackle external challenges/threats. The study argues that the EU has consistently utilized the security frame as the main pillar in crafting the ENP discourse. Even though the ENP incorporates a variety of priority spheres – policy frame areas – for cooperation between the EU and the ‘neighbours’ within the ENP, security frame issues top the EU-led priority list in the neighborhood. Accordingly, the study argues that the neighbors and the neighborhood are conceived in terms of security. Furthermore, it claims that the EU-led frames are interlinked with each other mainly through the security frame. Security policy-frame infiltrates majority of the ENP-driven policy issues, which explains its elevated frequency across the ENP documents. To explain the process the research introduces the concept of frame alignment to explain the changes in EU-driven framings, linking discursive instability with internal and external environmental factors. [ABSTRACT FROM AUTHOR]

This article attempts to explain the peculiar role of Isaac Newton in the poetry of Friedrich Schiller. I show that Newtonian ideas appear from the earliest poems in Anthologie auf das Jahr 1782 wherein gravity is used mainly as a metaphor for love. Newton is made a culprit, in Schiller's cosmological poems, for the destruction of the spheres and for the poet's despair in the ‘empty’, Newtonian universe. I chart the changing role of Newton in the later poetry of Schiller, where it is mainly his Opticks that interests the poet, who at this point has a thoroughly negative idea of the scientist, probably inspired by Goethe. Newton's famous experiment with the prism is figured as being the opposite of the poetry with which Schiller sought to unify (rather than refract) nature. [ABSTRACT FROM AUTHOR]

Background: The aim was to compare bias and precision for 177Lu-SPECT activity-concentration estimation using a dual-headed Anger SPECT system and a ring-configured CZT SPECT system. This was investigated for imaging at 208 keV and 113 keV, respectively. Methods: Phantom experiments were performed on a GE Discovery 670 system with 5/8" NaI(Tl) crystal (dual-headed Anger system) and a GE StarGuide (ring-configured CZT system). Six spheres (1.2 mL to 113 mL) in a NEMA PET body phantom were filled with 99mTc and 177Lu, separately. Mean relative errors and coefficients of variation (CV) in estimated sphere activity concentration were studied over six timeframes of 10 min each for the two systems. For 177Lu, similar acquisitions were also performed for an anthropomorphic phantom with two spheres (10 mL and 25 mL) in a liver with non-radioactive background and a sphere-to-background ratio of 15:1. Tomographic reconstruction was performed using OS-EM with 10 subsets with compensation for attenuation, scatter, and distance-dependent spatial resolution. For the Anger system, up to 40 iterations were used and for the ring-configured CZT system up to 30 iterations were used. Results: The two systems showed similar mean relative errors and CVs for 177Lu when using an energy window around 208 keV, while the ring-configured system demonstrated a lower bias for a similar CV compared to the Anger system for 99mTc and for 177Lu when using an energy window around 113 keV. However, total activity in the phantom tended to be overestimated in both systems for these cases. Conclusions: The ring-configured CZT system is a viable alternative to the dual-headed Anger system equipped with medium-energy collimators for 177Lu-SPECT and shows a potential advantage for activity-concentration estimation when operated at 113 keV. However, further consideration of the preservation of total activity is warranted. [ABSTRACT FROM AUTHOR]

For plane wave scattering by an obstacle, the optical theorem relates the scattering cross section to the far-field scattered field in the forward direction. This simple and useful result fails to hold when the incident field is not a plane wave. "Failures" of this kind are explored. For scattering by a sphere, an explicit formula for the scattering cross section is obtained, applicable to arbitrary incident fields. [ABSTRACT FROM AUTHOR]

During performing multiple tasks of a redundant manipulator, the obstacles affect the sequential order of task areas and the joint trajectories. The end-effector is constrained to visit multiple task areas with an optimal anti-collision path, while the joints are required to move smoothly and avoid predefined obstacles. A special encoding genetic algorithm (SEGA) is proposed for multitask-based anti-collision trajectory planning. Firstly, the spatial occupancy relationship between obstacles and manipulator is developed utilizing the theory of spherical enclosing box and spatial superposition. The obstacles are detected according to the relative position relationship between linear segments and spheres. Secondly, each joint trajectory between adjacent task areas is depicted with a sixth-degree polynomial. Additionally, each joint trajectory is improved via optimizing the unknown six-order coefficient. By searching for optimal sequential order of task areas, optimal collision detection results, and optimal joint trajectories, the multitask-based anti-collision trajectory planning problem is transformed into a parameter optimization problem. In SEGA, the cost function consists of two parts, including the end-effector path length and the variation of joint angles. Moreover, each chromosome consists of three categories of genes, including the sequential order of task areas, the sequential order of joint configurations corresponding to task areas, and the unknown coefficients for anti-collision joint trajectories. Finally, numerical simulations are carried out to verify the proposed method. [ABSTRACT FROM AUTHOR]

We review and present several challenging model classes arising in the context of finding optimized object packings (OP). Except for the smallest and/or simplest general OP model instances, it is not possible to find their exact (closed-form) solution. Most OP problem instances become increasingly difficult to handle even numerically, as the number of packed objects increases. Specifically, here we consider classes of general OP problems that can be formulated in the framework of nonlinear optimization. Research experience demonstrates that—in addition to utilizing general-purpose nonlinear optimization solver engines—the insightful exploitation of problem-specific heuristics can improve the quality of numerical solutions. We discuss scalable OP problem classes aimed at packing general circles, spheres, ellipses, and ovals, with numerical (conjectured) solutions of non-trivial model instances. In addition to their practical relevance, these models and their various extensions can also serve as constrained global optimization test challenges. [ABSTRACT FROM AUTHOR]

This structural study examines over 102 coordinate Cu(I) complexes with compositions such as C-Cu-Y (Y=HL, OL, NL, SL, SiL, BL, PL, Cl, Br, I, AlL, or SnL), N-Cu-Y (Y=OL, Cl), S-Cu-Y (Y=Cl, Br, I), P-Cu-Y (Y=Cl, I), and Se-Cu-Y (Y=Br, I). These complexes crystallize into three different crystal classes: monoclinic (seventy-two instances), triclinic (twenty-eight instances), and orthorhombic (eight instances). The Cu-L bond length increases with the covalent radius of the ligating atom. There are two possible geometries for coordination number two: linear and bent. A total of 21 varieties of inner coordination spheres exist, categorized into two hetero-types (C-Cu-Y, i.e., organometallic compounds and X-Cu-Y, i.e., coordination compounds). The structural parameters of hetero Cu(I) complexes were compared with trans-X-Cu (I)-X (homo) complexes and analyzed. The maximum deviations from linearity (180.0°) are, on average, 10.3° for Br-Cu(I)-Br, 16.6° for C-Cu(I)-Sn, and 35.5° for P-Cu(I)-I. These results indicate that ligand properties influence deviation from linearity, increasing in the order of hard < borderline < soft. [ABSTRACT FROM AUTHOR]

Does deliberation produce any lasting effects? "America in One Room" was a national field experiment in which more than 500 randomly selected registered voters were brought from all over the country to deliberate on five major issues facing the country. A pre-post control group was also surveyed on the same questions after the weekend and about a year later. There were significant differences in voting intention and in actual voting behavior a year later among the deliberators compared to the control group. This article accounts for these differences by showing how deliberation stimulated a latent variable of political engagement. If deliberation has lasting effects on political engagement, then it provides a rationale for attempts to scale the deliberative process to much larger numbers. The article considers methods for doing so in the context of the broader debate about mini-publics, isolated spheres of deliberation situated within a largely non-deliberative society. [ABSTRACT FROM AUTHOR]

Humans build mental models of the world and utilize them for various cognitive tasks. The exact form of cognitive maps is not fully understood, especially for novel and complex environments beyond the flat Euclidean environment. To address this gap, we investigated path integration —a critical process underlying cognitive mapping—and spatial-memory capacity on the spherical (non-Euclidean) and planar (Euclidean) environments in young healthy adults (N = 20) using immersive virtual reality. We observed a strong Euclidean bias during the path-integration task on the spherical surface, even among participants who possessed knowledge of non-Euclidean geometry. Notably, despite this bias, participants demonstrated reasonable navigation ability on the sphere. This observation and simulation suggest that humans navigate nonflat surfaces by constructing locally confined Euclidean maps and flexibly combining them. This insight sheds light on potential neural mechanisms and behavioral strategies for solving complex cognitive tasks. [ABSTRACT FROM AUTHOR]

To reconsider the meaning of justice in a planetary frame is both a necessity in our time of multiple entangled crises and an endeavour that seeks convergence and synthesis where there might instead be irreconcilable differences. We invited scholars from diverse disciplinary backgrounds to share their perspectives on the scope, scale, and purpose of planetary justice and received a variety of responses – all highly worthwhile in their own right. What we can conclude from this new milestone in the literature on planetary justice is that people emphasize different justice concerns and operate with different ontologies. Are the Earth system and the pluriverse opposing frameworks or somehow reconcilable? What concerns should be prioritized is also contested. Can there be a decolonial, multispecies, Earth systemic, justice that begins with the self and where matter is included in our sphere of justice? However, one agreement seems to be that planetary justice is inevitably ecosocial justice. [ABSTRACT FROM AUTHOR]

Given a set T ⊆ R n and a nonnegative function r defined on T, we consider the power of x ∈ R n with respect to the sphere with center t ∈ T and radius r t , that is, p r x , t : = x - t 2 - r 2 t , with · denoting the Euclidean distance. The corresponding power cell of s ∈ T is the set C T r (s) : = { x ∈ R n : p r (x , s) ≤ p r (x , t) , for all t ∈ T }. We study the structure of such cells and investigate the assumptions on r that allow for generalizing known results on classical Voronoi cells. [ABSTRACT FROM AUTHOR]

Conversations about accessibility and representation in US theatre have increased over the past decade but few articles address how these topics might be incorporated into our classrooms and educational rehearsal spaces. Using as a case study the rehearsal and production processes devised for the Broadway musical How to Dance in Ohio this Note considers how access initiatives implemented in the nonprofit and professional theatre spheres might be adapted and included in US theatre pedagogical practices for introducing students to comprehensive and holistic approaches to disability inclusion and accordant access initiatives. [ABSTRACT FROM AUTHOR]