Femtosecond relaxation kinetics of highly excited \mathrm{M}_{\mathrm{Na}}^{**} states in CaF2 at 3.2 eV and 4.7 eV

Femtosecond (fs) laser pulses at variable delay times allowed us to track the fast non-radiative transitions between the manifold of highly excited $\mathrm{M}_{\mathrm{Na}}^{**}$ states to the lower lying fluorescent $\mathrm{M}_{\mathrm{Na}}^{*}$ state in CaF₂. Two distinct $\mathrm{M}_{\mathrm{Na}}^{**}$ states of the manifold at 3.16?eV ( $\mathrm{M}_{\mathrm{Na}2}^{**}$ ) and 4.73?eV ( $\mathrm{M}_{\mathrm{Na}3}^{**}$ ) were populated using the second (SH) and third harmonics (TH) of fs laser light at 785?nm. The population kinetics of the fluorescent $\mathrm{M}_{\mathrm{Na}}^{*}$ state in the 2?eV excitation energy range was revealed by depleting its fluorescence centered at 740?nm using fundamental near infrared (NIR) fs laser pulses. The related time constants for $\mathrm{M}_{\mathrm{Na}2,3}^{**}{\sim}{>} \mathrm{M}_{\mathrm{Na}}^{*}$ relaxation amounted to 1.0±0.14?ps and 3.0±0.3?ps upon SH and TH excitation, respectively.     

Noncommutative products of Euclidean spaces

We present natural families of coordinate algebras on noncommutative products of Euclidean spaces \({\mathbb {R}}^{N_1} \times _{\mathcal {R}} {\mathbb {R}}^{N_2}\). These coordinate algebras are quadratic ones associated with an \(\mathcal {R}\)-matrix which is involutive and satisfies the Yang–Baxter equations. As a consequence, they enjoy a list of nice properties, being regular of finite global dimension. Notably, we have eight-dimensional noncommutative euclidean spaces \({\mathbb {R}}^{4} \times _{\mathcal {R}} {\mathbb {R}}^{4}\). Among these, particularly well behaved ones have deformation parameter \(\mathbf{u} \in {\mathbb {S}}^2\). Quotients include seven spheres \({\mathbb {S}}^{7}_\mathbf{u}\) as well as noncommutative quaternionic tori \({\mathbb {T}}^{{\mathbb {H}}}_\mathbf{u} = {\mathbb {S}}^3 \times _\mathbf{u} {\mathbb {S}}^3\). There is invariance for an action of \({{\mathrm{SU}}}(2) \times {{\mathrm{SU}}}(2)\) on the torus \({\mathbb {T}}^{{\mathbb {H}}}_\mathbf{u}\) in parallel with the action of \(\mathrm{U}(1) \times \mathrm{U}(1)\) on a ‘complex’ noncommutative torus \({\mathbb {T}}^2_\theta \) which allows one to construct quaternionic toric noncommutative manifolds. Additional classes of solutions are disjoint from the classical case.     

Background-free detection of trapped ions

We demonstrate a Doppler cooling and detection scheme for ions with low-lying D levels which almost entirely suppresses scattered laser light background, while retaining a high fluorescence signal and efficient cooling. We cool a single ion with a laser on the $^{2}\mathrm{S}_{\mbox{\tiny$1/2$}}\leftrightarrow {^{2}\mathrm{P}}_{\mbox{\tiny$1/2$}}$ transition as usual, but repump via the $^{2}\mathrm{P}_{\mbox{\tiny$3/2$}}$ level. By filtering out light on the cooling transition and detecting only the fluorescence from the $^{2}\mathrm{P}_{\mbox{\tiny$3/2$}}\rightarrow {^{2}\mathrm{S}}_{\mbox{\tiny$1/2$}}$ decays, we suppress the scattered laser light background count rate to 1 s^?1 while maintaining a signal of 29000 s^?1 with moderate saturation of the cooling transition. This scheme will be particularly useful for experiments where ions are trapped in close proximity to surfaces, such as the trap electrodes in microfabricated ion traps, which leads to high background scatter from the cooling beam.     

Nonsingular black holes in quadratic Palatini gravity

We find that if general relativity is modified at the Planck scale by a Ricci-squared term, electrically charged black holes may be nonsingular. These objects concentrate their mass in a microscopic sphere of radius $r_{\mathrm{core}}\approx N_{q}^{1/2}l_{\mathrm{P}}/3$ , where l _P is the Planck length and N _q is the number of electric charges. The singularity is avoided if the mass of the object satisfies the condition $M_{0}^{2}\approx m_{\mathrm{P}}^{2} \alpha_{\mathrm{em}}^{3/2} N_{q}^{3}/2$ , where m _P is the Planck mass and α _em is the fine-structure constant. For astrophysical black holes this amount of charge is so small that their external horizon almost coincides with their Schwarzschild radius. We work within a first-order (Palatini) approach.     

Selectivity of anion exchange membrane modified with polyethyleneimine

Previous works have been made on the improvement of selectivity of ion exchange membranes using adsorption of polyelectrolyte on the surface of the materials. The modification of the surface material in the case of an anion exchange membrane concerns the hydrophilic/hydrophobic balance properties and its relationship with the hydration state. Starting from this goal, the AMX membrane has been modified, in this work, by adsorption of polyethyleneimine on its surface. Many conditions of modification of the AMX membrane surface were studied. A factorial experimental design was used for determining the influent parameters on the AMX membrane modification. The results obtained have shown that the initial concentration of polyethyleneimine and the pH of solution were the main influent parameters on the adsorption of polyethyleneimine on the membrane surface. Competitive ion exchange reactions were studied for the modified and the unmodified membrane involving $ {\text{C}}{{\text{l}}^{ - }} $ , $ {\text{NO}}_3^{ - } $ and $ {\text{SO}}_4^{{2 - }} $ ions. All experiments were carried out at constant concentration of 0.3?mol?L^?1 and at 25?°C. Ion exchange isotherms for the binary systems $ \left( {{\text{C}}{{\text{l}}^{ - }}/{\text{NO}}_3^{ - }} \right) $ , $ \left( {{\text{C}}{{\text{l}}^{ - }}/{\text{SO}}_4^{{2 - }}} \right) $ and $ \left( {{\text{NO}}_3^{ - }/{\text{SO}}_4^{{2 - }}} \right) $ were studied. The obtained results show that chloride was the most sorbed and the selectivity order both for the modified membrane and the unmodified one is: $ {\text{Cl}} > {\text{NO}}_3^{ - } > {\text{SO}}_4^{{2 - }} $ , under the experimental conditions. Selectivity coefficients $ {\text{K}}_{{{\text{C}}{{\text{l}}^{ - }}}}^{{{\text{NO}}_3^{ - }}} $ , $ {\text{K}}_{{2{\text{C}}{{\text{l}}^{ - }}}}^{{{\text{SO}}_4^{{2 - }}}} $ and $ {\text{K}}_{{2{\text{NO}}_3^{ - }}}^{{{\text{SO}}_4^{{2 - }}}} $ for the three binary systems and for the two membranes were determined. It was also observed that for the modified membrane the selectivity towards sulfate ion decrease and the modified membrane became more selective towards monovalent anions.     

Measurement of all Deuteron Analyzing Powers for {\overrightarrow{d} + p} Elastic Scattering at 294 MeV/Nucleon

We have measured all deuteron analyzing powers ${(A_{y}^{d}, A_{yy}, A_{xx}, A_{xz})}$ for deuteron-proton elastic scattering at 294 MeV/nucleon in order to study the properties of three nucleon forces (3 NFs). Measurement was made at in an angular range of ${\theta_{{\rm c.m.}} = 35.6^{\circ} - 163.0^{\circ}}$ . Obtained data were compared with Faddeev calculations with and without the 3 NFs. At ${\theta_{{\rm c.m.}}\lesssim 120^{\circ}}$ all the data have general agreement with the calculations, while the measured data at ${\theta_{{\rm c.m.}} \gtrsim 120^{\circ}}$ are not explained by any theoretical calculations. These results were consistent with those at 250 MeV/nucleon.     

Antihydrogen formation via antiproton scattering on positronium between the $e^{-} +\bar {H}(n = 2)$ and e−+H̄(n=3)$e^{-}+\bar {H}(n = 3)$ thresholds

The charge exchange reaction \(\bar {\mathrm {p}} + \text {Ps} \rightarrow \mathrm {e}^{-} + \bar {\mathrm {H}} \), of interest for the future experiments (GBAR, AEGIS, ATRAP, ...) aiming to produce antihydrogen atoms, is investigated in the energy range between the \(\mathrm {e}^{-}+\bar {\mathrm {H}}(n = 2)\) and \(\mathrm {e}^{-}+\bar {\mathrm {H}}(n = 3)\) thresholds. An ab-initio method based on the solution of the Faddeev-Merkuriev equations is used. Special focus is put on the impact of the Feshbach resonances and the Gailitis-Damburg oscillations, appearing in the vicinity of the \(\bar {\mathrm {p}} +\text {Ps}(n = 2)\) threshold, on the \(\bar {\mathrm {H}}\) production cross section.     

The Polyanalytic Ginibre Ensembles

For integers n,q=1,2,3,…?, let Pol _n,q denote the ${\mathbb{C}}$ -linear space of polynomials in z and $\bar{z}$ , of degree ≤n?1 in z and of degree ≤q?1 in $\bar{z}$ . We supply Pol _n,q with the inner product structure of $$\begin{aligned} L^2 \bigl({\mathbb{C}},\mathrm{e}^{-m|z|^2} {\mathrm{d}}A \bigr),\quad \mbox {where } {\mathrm{d}}A(z)=\pi^{-1}{\mathrm{d}}x {\mathrm{d}}y,\ z= x+ {\mathrm{i}}y; \end{aligned}$$ the resulting Hilbert space is denoted by Pol _m,n,q . Here, it is assumed that m is a positive real. We let K _m,n,q denote the reproducing kernel of Pol _m,n,q , and study the associated determinantal process, in the limit as m,n→+∞ while n=m+O(1); the number q, the degree of polyanalyticity, is kept fixed. We call these processes polyanalytic Ginibre ensembles, because they generalize the Ginibre ensemble—the eigenvalue process of random (normal) matrices with Gaussian weight. There is a physical interpretation in terms of a system of free fermions in a uniform magnetic field so that a fixed number of the first Landau levels have been filled. We consider local blow-ups of the polyanalytic Ginibre ensembles around points in the spectral droplet, which is here the closed unit disk $\bar{\mathbb{D}}:=\{z\in{\mathbb{C}}:|z|\le1\}$ . We obtain asymptotics for the blow-up process, using a blow-up to characteristic distance m ^?1/2; the typical distance is the same both for interior and for boundary points of $\bar{\mathbb{D}}$ . This amounts to obtaining the asymptotical behavior of the generating kernel K _m,n,q . Following (Ameur et al. in Commun. Pure Appl. Math. 63(12):1533–1584, 2010), the asymptotics of the K _m,n,q are rather conveniently expressed in terms of the Berezin measure (and density) For interior points |z|<1, we obtain that ${\mathrm{d}}B^{\langle z\rangle}_{m,n,q}(w)\to{\mathrm{d}}\delta_{z} $ in the weak-star sense, where δ _z denotes the unit point mass at z. Moreover, if we blow up to the scale of m ^?1/2 around z, we get convergence to a measure which is Gaussian for q=1, but exhibits more complicated Fresnel zone behavior for q>1. In contrast, for exterior points |z|>1, we have instead that ${\mathrm{d}}B^{\langle z\rangle}_{m,n,q}(w) \to{\mathrm{d}}\omega(w,z, {\mathbb{D}}^{e}) $ , where ${\mathrm{d}}\omega(w,z,{\mathbb{D}}^{e})$ is the harmonic measure at z with respect to the exterior disk ${\mathbb{D}}^{e}:= \{w\in{\mathbb{C}}:\, |w|>1\}$ . For boundary points, |z|=1, the Berezin measure ${\mathrm{d}}B^{\langle z\rangle}_{m,n,q}$ converges to the unit point mass at z, as with interior points, but the blow-up to the scale m ^?1/2 exhibits quite different behavior at boundary points compared with interior points. We also obtain the asymptotic boundary behavior of the 1-point function at the coarser local scale q ^1/2 m ^?1/2.     

An analytical expression for the specific capacity of lithium ion cells

The concentration of lithium ions in the cathode of lithium ion cells has been obtained by solving the materials balance equation $$\frac{{\partial c}}{{\partial t}} = \varepsilon ^{1/2} D\frac{{\partial ^2 c}}{{\partial x^2 }} + \frac{{aj_n (1--t_ + )}}{\varepsilon }$$ by Laplace transform. On the assumption that the cell is fully discharged when there are zero lithium ions at the current collector of the cathode, the discharge timet _d is obtained as $$\tau = \frac{{r^2 }}{{\pi ^2 \varepsilon ^{1/2} }}\ln \left[ {\frac{{\pi ^2 }}{{r^2 }}\left( {\frac{{\varepsilon ^{1/2} }}{J} + \frac{{r^2 }}{6}} \right)} \right]$$ which, when substituted into the equationC=It _d /M, whereI is the discharge current andM is the mass of the separator and positive electrode, an analytical expression for the specific capacity of the lithium cell is given as $$C = \frac{{IL_c ^2 }}{{\pi {\rm M}D\varepsilon ^{1/2} }}\ln \left[ {\frac{{\pi ^2 }}{2}\left( {\frac{{FDc_0 \varepsilon ^{3/2} }}{{I(1 - t_ + )L_c }} + \frac{1}{6}} \right)} \right]$$      

On Blow-up Profile of Ground States of Boson Stars with External Potential

We study minimizers of the pseudo-relativistic Hartree functional \({\mathcal {E}}_{a}(u):=\Vert (-\varDelta +m^{2})^{1/4}u\Vert _{L^{2}}^{2}+\int _{{\mathbb {R}}^{3}}V(x)|u(x)|^{2}\mathrm{d}x-\frac{a}{2}\int _{{\mathbb {R}}^{3}}(\left| \cdot \right| ^{-1}\star |u|^{2})(x)|u(x)|^{2}\mathrm{d}x\) under the mass constraint \(\int _{{\mathbb {R}}^3}|u(x)|^2\mathrm{d}x=1\). Here \(m>0\) is the mass of particles and \(V\ge 0\) is an external potential. We prove that minimizers exist if and only if a satisfies \(0\le a<a^{*}\), and there is no minimizer if \(a\ge a^*\), where \(a^*\) is called the Chandrasekhar limit. When a approaches \(a^*\) from below, the blow-up behavior of minimizers is derived under some general external potentials V. Here we consider three cases of V: trapping potential, i.e. \(V\in L_{\mathrm{loc}}^{\infty }({\mathbb {R}}^3)\) satisfies \(\lim _{|x|\rightarrow \infty }V(x)=\infty \); periodic potential, i.e. \(V\in C({\mathbb {R}}^3)\) satisfies \(V(x+z)=V(x)\) for all \(z\in \mathbb {Z}^3\); and ring-shaped potential, e.g. \( V(x)=||x|-1|^p\) for some \(p>0\).     

Study of the ion exchange equilibrium of Cl−, NO_3^{ - } , and SO_4^{{2 - }} ions on the AMX membrane

Equilibrium between the ion exchange membrane and solutions of anions at various valences has been the subject of this investigation. Competitive ion exchange reactions were studied on a strong base anion exchange membrane AMX manufactured by Tokuyama, commercialized by Eurodia, involving Cl^?, $ {\text NO}_3^{ - } $ and $ {\text SO}_4^{{2 - }} $ ions. Solution concentrations studied were 0.05 and 0.1 M for all the systems reported. Experiments were performed with sodium as the counter ion, and the temperature was kept constant (T?=?298 K). Ionic exchange isotherms for the binary systems— $ {{\text Cl}^{ - }}/{\text NO}_3^{ - } $ , $ {{\text Cl}^{ - }}/{\text SO}_4^{{2 - }} $ , and $ {\text NO}_3^{ - }/{\text SO}_4^{{2 - }} $ —were established. The obtained results show that the sulfate was the most strongly sorbed, and the selectivity order is $ {\text SO}_4^{{2 - }} > {\text NO}_3^{ - } > {{\text Cl}^{ - }} $ at 0.05 M and $ {\text NO}_3^{ - } > {\text SO}_4^{{2 - }} > {{\text Cl}^{ - }} $ at 0.1 M under the experimental conditions. Selectivity coefficients $ K_{{{{{\text Cl} }^{ - }}}}^{{{\text NO}_3^{ - }}} $ , $ K_{{2{{{\text Cl} }^{ - }}}}^{{{\text SO}_4^{{2 - }}}} $ , and $ K_{{2{\text NO}_3^{ - }}}^{{{\text SO}_4^{{2 - }}}} $ for the three binary systems were determined. All the results given by this membrane were compared with those obtained, in the same conditions, with the RPA membrane (produced by RHONE POULENC). Ternary equilibrium data were taken for $ {{\text Cl}^{ - }}/{\text NO}_3^{ - }/{\text SO}_4^{{2 - }} $ . The prediction of the ternary system based only on the binary data was consistent with the experimental data obtained for this system. The good agreement between the experimental and the predicted data showed that the proposed framework can be considered as an effective method to predict many ternary systems from binary systems.     

Polarized angular distributions in the decays of the 3D2 state of charmonium produced in unpolarized proton–antiproton annihilation

Using the helicity formalism, we calculate the combined angular distribution functions of the polarized gamma photons and electron in the triple cascade process $\bar{\mathrm{p}}\mathrm{p}\to{}^{3}\mathrm{D}_{\mathrm{2}}\to\chi_{\mathrm{\mathrm{{J}}}}+\gamma_{\mathrm{1}}\to(\psi +\gamma_{\mathrm{2}})+\gamma_{\mathrm{1}}\to(\mathrm{e}^{+}+\mathrm{e}^{-})+\gamma_{\mathrm{1}}+\gamma_{\mathrm{2}}\ (\mathrm{{J}}=0,1,2)$ , when $\bar{\mathrm{p}}$ and p are unpolarized. We also present the partially integrated angular distribution functions in different cases. Our results show that by measuring the two-particle angular distribution of γ ₁ and γ ₂ and that of γ ₂ and e^? with the polarization of either one of the two particles, one can determine the relative magnitudes as well as the relative phases of all the helicity amplitudes in the two radiative decay processes ³D₂→χ _J+γ ₁ and χ _J→ψ+γ ₂.     

Predicting leptonic CP violation in the light of the Daya Bay result on θ 13

In the light of the recent Daya Bay result $\theta_{13}^{\mathrm{DB}}=8.8^{\circ}\pm0.8^{\circ}$ , we reconsider the model presented in Meloni et?al. (J. Phys.?G 38:015003, 2011), showing that, when all neutrino oscillation parameters are taken at their best fit values of Schwetz et?al. (New J. Phys. 10:113011,?2008) and where $\theta_{13}=\theta_{13}^{\mathrm{DB}}$ , the predicted values of the CP phase are ????±??/4.     

Dispersion dependence of two-photon absorption transition on frequency in Si PIN photodetector

The variation of two-photon absorption (TPA) coefficient \(\beta _{\mathrm{TPA}} (\omega )\) of Si excited at difference photon energy was investigated. The TPA coefficient was measured by using a picosecond pulsed laser with the wavelength could be tuned in a wide photon-energy range. An equivalent RC circuit model was adapted to derive the TPA coefficient \(\beta _{\mathrm{TPA}} (\omega )\) . The results showed that \(\beta _{\mathrm{TPA}} (\omega )\) varied from \(4.2 \times 10^{-4}\) to \(1.17 \times 10^{-3 }\)  cm/GW in the transparent wavelength region \(1.80<\lambda <1.36\,\upmu \) m of Si. The increasing tendency of \(\beta _{\mathrm{TPA}} (\omega )\) with the incident photon energy can be qualitatively interpreted as the photon energy increases from \(E_{\mathrm{ig}}/2\) to nearly \(E_{\mathrm{ig}}\) , the electrons excited from the valance band find an increasing availability of conduction band states. Comparing with the high-energy side transitions, the TPA coefficient in low-energy side is about 10 times too small. This can be attributed that the TPA transition in low-energy side is the process of photon-assisted electron transitions from valence to conduction band occurring between different points in k-space, while is direct transition in high-energy side.     

A measurement of the branching ratio∑ +→pγ/∑ +→pπ 0⋆

In an experiment performed in the CERN SPS hyperon beam we have obtained a value for the branching ratio $${{\Sigma ^ + \to p\gamma } \mathord{\left/ {\vphantom {{\Sigma ^ + \to p\gamma } {\Sigma ^ + \to p\pi }}} \right. \kern-\nulldelimiterspace} {\Sigma ^ + \to p\pi }}^0 of\left( {2.46_{ - 0.35}^{ + 0.30} } \right) \times 10^{ - 3} ,$$ corresponding to a branching ratio $${{\Sigma ^ + \to p\gamma } \mathord{\left/ {\vphantom {{\Sigma ^ + \to p\gamma } {\Sigma ^ + \to all}}} \right. \kern-\nulldelimiterspace} {\Sigma ^ + \to all}}of\left( {1.27_{ - 0.18}^{ + 0.16} } \right) \times 10^{ - 3} .$$ This result is discussed in the context of present understanding of hyperon radiative decays.     

Relationship of the Williams-Poulios and Manning-Rosen Potential Energy Models for Diatomic Molecules

By employing the dissociation energy and the equilibrium bond length for a diatomic molecule as explicit parameters, we generate an improved form of the Williams-Poulios potential energy model. It is found that the negative Williams-Poulios potential model is equivalent to the Manning-Rosen potential model for diatomic molecules. We observe that the Manning-Rosen potential is superior to the Morse potential in reproducing the interaction potential energy curves for the \({{a}^{3} \Sigma_{{\rm u}}^{+}}\) state of the ⁶Li₂ molecule and the \({{X}^{1} \sum^{+}}\) state of the SiF⁺ molecule.     

Electrical properties of ferroelectric-gate FETs with SrBi2Ta2O9 formed using MOCVD technique

Ferroelectric-gate?field-effect?transistors?(FeFETs) with a Pt/SrBi₂Ta₂O₉/Hf-Al-O/Si gate stack were fabricated using the metal-organic chemical vapor deposition (MOCVD) technique to prepare the SrBi₂Ta₂O₉ (SBT) ferroelectric layer. A?good threshold voltage (V _th) distribution was found for more than 90?n-channel FeFETs in one chip with a 170?nm SBT layer owing to the good film uniformity of the SBT layer deposited by MOCVD. The average memory window $(V_{\mathrm{w}}^{\mathrm{av}})$ and the standard deviations (σ _thl,σ _thr) of the left- and right-side branches of the drain-gate voltage curves of the FeFETs yielded a $V_{\mathrm{w}}^{\mathrm{av}}/(\sigma_{\mathrm{thl}} + \sigma_{\mathrm{thr}})$ value of 5.45, indicating that the FeFETs can be adapted for large-scale-integration. The electric field, the energy band profile in the gate stack, and the gate leakage current were also investigated at high gate voltages. We found that the effect of Fowler–Nordheim tunneling appeared under these conditions. Because of the tunneling injection and trapping of electrons into the gate insulators, the operation voltage ranges of the FeFETs were limited by this tunneling.     

On the similarity solution of evolution equation u t =H(x,t, u,u x,u xx , ...)

Let $$\begin{gathered} u^* = u + \in \eta (x,{\text{ }}t,{\text{ }}u), \hfill \\ \hfill \\ \hfill \\ x^* = x + \in \xi (x, t, u{\text{),}} \hfill \\ \hfill \\ \hfill \\ {\text{t}}^{\text{*}} = {\text{ }}t + \in \tau {\text{(}}x,{\text{ }}t,{\text{ }}u), \hfill \\ \end{gathered}$$ be an infinitesimal invariant transformation of the evolution equation u _t =H(x,t,u,?u/?x,...,? ⁿ :u/?x ⁿ . In this paper we give an explicit expression for \(\eta ^{X^i }\) in the ‘determining equation’ $$\eta ^T = \sum\limits_{i = 1}^n {{\text{ }}\eta ^{X^i } {\text{ }}\frac{{\partial H}}{{\partial u_i }} + \eta \frac{{\partial H}}{{\partial u_{} }} + \xi \frac{{\partial H}}{{\partial x}} + \tau } \frac{{\partial H}}{{\partial t}},$$ where u _i =? ⁱ u/?x ⁱ . By using this expression we derive a set of equations with η, ξ, τ as unknown functions and discuss in detail the cases of heat and KdV equations.     

On the Quasi-linear Elliptic PDE {-\nabla \cdot ( \nabla{u}/ \sqrt{1-| \nabla{u} |^2}) = 4 \pi \sum_k a_k \delta_{s_k}} in Physics and Geometry

It is shown that for each finite number N of Dirac measures ${\delta_{s_n}}$ supported at points ${s_n \in {\mathbb R}^3}$ with given amplitudes ${a_n \in {\mathbb R} \backslash\{0\}}$ there exists a unique real-valued function ${u \in C^{0, 1}({\mathbb R}^3)}$ , vanishing at infinity, which distributionally solves the quasi-linear elliptic partial differential equation of divergence form ${-\nabla \cdot ( \nabla{u}/ \sqrt{1-| \nabla{u} |^2}) = 4 \pi \sum_{n=1}^N a_n \delta_{s_n}}$ . Moreover, ${u \in C^{\omega}({\mathbb R}^3\backslash \{s_n\}_{n=1}^N)}$ . The result can be interpreted in at least two ways: (a) for any number N of point charges of arbitrary magnitude and sign at prescribed locations s _n in three-dimensional Euclidean space there exists a unique electrostatic field which satisfies the Maxwell-Born-Infeld field equations smoothly away from the point charges and vanishes as |s| ?? ??; (b) for any number N of integral mean curvatures assigned to locations ${s_n \in {\mathbb R}^3 \subset{\mathbb R}^{1, 3}}$ there exists a unique asymptotically flat, almost everywhere space-like maximal slice with point defects of Minkowski spacetime ${{\mathbb R}^{1, 3}}$ , having lightcone singularities over the s _n but being smooth otherwise, and whose height function vanishes as |s| ?? ??. No struts between the point singularities ever occur.