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.     

The Charmonium-Molecule Hybrid Structure of the X(3872)

In order to understand the structure of the X(3872) the effects of the ${{\rm c\overline{c}}}$ charmonium core state coupling to the ${D^0\overline{D}^{*0}}$ and D ⁺ D ^*? molecule states are studied. The obtained structure of the X(3872) is about 9 % of ${{\rm c}\overline{{\rm c}}}$ charmonium, 75 % of the isoscalar ${D\overline{D}}$ molecule and 16 % of the isovector ${D\overline{D}}$ molecule which explains observed properties of the X(3872) well.     

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.     

The Lie–Rinehart Universal Poisson Algebra of Classical and Quantum Mechanics

The Lie–Rinehart algebra of a (connected) manifold ${\mathcal {M}}$ , defined by the Lie structure of the vector fields, their action and their module structure over ${C^\infty({\mathcal {M}})}$ , is a common, diffeomorphism invariant, algebra for both classical and quantum mechanics. Its (noncommutative) Poisson universal enveloping algebra ${\Lambda_{R}({\mathcal {M}})}$ , with the Lie–Rinehart product identified with the symmetric product, contains a central variable (a central sequence for non-compact ${{\mathcal {M}}}$ ) ${Z}$ which relates the commutators to the Lie products. Classical and quantum mechanics are its only factorial realizations, corresponding to Z  =  i z, z  =  0 and ${z = \hbar}$ , respectively; canonical quantization uniquely follows from such a general geometrical structure. For ${z =\hbar \neq 0}$ , the regular factorial Hilbert space representations of ${\Lambda_{R}({\mathcal{M}})}$ describe quantum mechanics on ${{\mathcal {M}}}$ . For z  =  0, if Diff( ${{\mathcal {M}}}$ ) is unitarily implemented, they are unitarily equivalent, up to multiplicity, to the representation defined by classical mechanics on ${{\mathcal {M}}}$ .     

{{\psi(3S)}} and {{\Upsilon(5S)}} Originating in Heavy Meson Molecules: A Coupled Channel Analysis Based on an Effective Vector Quark–Quark Interaction

In our previous coupled channel analysis based on the Cornell effective quark–quark interaction, it was indicated that the ${\psi(3S)}$ solution corresponding to ${\psi(4040)}$ originates from a ${{\rm D}^{^{*}}\overline{{\rm D}}^{*}}$ channel state. In this article, we report on a simultaneous analysis of the ${\psi}$ - and ${\Upsilon}$ -family states. The most conspicuous outcome is a finding that the ${\Upsilon(5S)}$ solution corresponding to ${\Upsilon(10860)}$ originates from a ${{\rm B}^{*}\overline{{\rm B}}^{*}}$ channel state, very much like ${\psi(3S)}$ . Some other characteristics of the result, including the induced very large S–D mixing and relation of some of the solutions with newly observed heavy quarkonia-like states are discussed.     

Fomenko–Mischenko Theory, Hessenberg Varieties, and Polarizations

The symmetric algebra ${S(\mathfrak{g})}$ over a Lie algebra ${\mathfrak{g}}$ has the structure of a Poisson algebra. Assume ${\mathfrak{g}}$ is complex semisimple. Then results of Fomenko–Mischenko (translation of invariants) and Tarasov construct a polynomial subalgebra ${{\mathcal {H}} = {\mathbb C}[q_1,\ldots,q_b]}$ of ${S(\mathfrak{g})}$ which is maximally Poisson commutative. Here b is the dimension of a Borel subalgebra of ${\mathfrak{g}}$ . Let G be the adjoint group of ${\mathfrak{g}}$ and let ? = rank ${\mathfrak{g}}$ . Using the Killing form, identify ${\mathfrak{g}}$ with its dual so that any G-orbit O in ${\mathfrak{g}}$ has the structure (KKS) of a symplectic manifold and ${S(\mathfrak{g})}$ can be identified with the affine algebra of ${\mathfrak{g}}$ . An element ${x\in \mathfrak{g}}$ will be called strongly regular if ${\{({\rm d}q_i)_x\},\,i=1,\ldots,b}$ , are linearly independent. Then the set ${\mathfrak{g}^{\rm{sreg}}}$ of all strongly regular elements is Zariski open and dense in ${\mathfrak{g}}$ and also ${\mathfrak{g}^{\rm{sreg}}\subset \mathfrak{g}^{\rm{ reg}}}$ where ${\mathfrak{g}^{\rm{reg}}}$ is the set of all regular elements in ${\mathfrak{g}}$ . A Hessenberg variety is the b-dimensional affine plane in ${\mathfrak{g}}$ , obtained by translating a Borel subalgebra by a suitable principal nilpotent element. Such a variety was introduced in Kostant (Am J Math 85:327–404, 1963). Defining Hess to be a particular Hessenberg variety, Tarasov has shown that ${{\rm{Hess}}\subset \mathfrak{g}^{\rm{sreg}}}$ . Let R be the set of all regular G-orbits in ${\mathfrak{g}}$ . Thus if ${O\in R}$ , then O is a symplectic manifold of dimension 2n where n = b ? ?. For any ${O\in R}$ let ${O^{\rm{sreg}} = \mathfrak{g}^{\rm{sreg}} \cap O}$ . One shows that O ^sreg is Zariski open and dense in O so that O ^sreg is again a symplectic manifold of dimension 2n. For any ${O\in R}$ let ${{\rm{Hess}}(O) = {\rm{Hess}}\cap O}$ . One proves that Hess(O) is a Lagrangian submanifold of O ^sreg and that $${\rm{Hess}} = \sqcup_{O\in R}{\rm{Hess}}(O).$$ The main result of this paper is to show that there exists simultaneously over all ${O\in R}$ , an explicit polarization (i.e., a “fibration” by Lagrangian submanifolds) of O ^sreg which makes O ^sreg simulate, in some sense, the cotangent bundle of Hess(O).     

On the {{\mathcal{N}}=2} Superconformal Index and Eigenfunctions of the Elliptic RS Model

We define an infinite sequence of superconformal indices, ${{\mathcal{I}}_n}$ , generalizing the Schur index for ${{\mathcal{N}}=2}$ theories. For theories of class ${{\mathcal{S}}}$ we then suggest a recursive technique to completely determine ${{\mathcal{I}}_n}$ . The information encoded in the sequence of indices is equivalent to the ${{\mathcal{N}}=2}$ superconformal index depending on a maximal set of fugacities. Mathematically, the procedure suggested in this note provides a perturbative algorithm for computing a set of eigenfunctions of the elliptic Ruijsenaars–Schneider model.     

Singular $$ \mathcal{R}$$ -Matrices and Drinfeld's Comultiplication

We compute the $\mathcal{R}$ -matrix which intertwines two dimensional evaluation representations with Drinfeld comultiplication for ${\text{U}}_q \left( {\widehat{{\text{sl}}}_{\text{2}} } \right)$ . This $\mathcal{R}$ -matrix contains terms proportional to the δ-function. We construct the algebra $A\left( \mathcal{R} \right)$ generated by the elements of the matrices L^±(z) with relations determined by $\mathcal{R}$ . In the category of highest-weight representations, there is a Hopf algebra isomorphism between $A\left( \mathcal{R} \right)$ and an extension $\overline {\text{U}} _q \left( {\widehat{{\text{sl}}}_{\text{2}} } \right)$ of Drinfeld's algebra.     

Non-Almost Periodicity of Parallel Transports for Homogeneous Connections

Let ${\cal A}$ be the affine space of all connections in an SU(2) principal fibre bundle over ?³. The set of homogeneous isotropic connections forms a line l in ${\cal A}$ . We prove that the parallel transports for general, non-straight paths in the base manifold do not depend almost periodically on l. Consequently, the embedding $l \hookrightarrow {\cal A}$ does not continuously extend to an embedding $\overline{l} \hookrightarrow \overline{\cal A}$ of the respective compactifications. Here, the Bohr compactification $\overline{l}$ corresponds to the configuration space of homogeneous isotropic loop quantum cosmology and $\overline{\cal A}$ to that of loop quantum gravity. Analogous results are given for the anisotropic case.     

Charmonium and Meson–Molecule Hybrid Tetraquarks

In the X (3872) decay, both of the ${{J/{\psi\pi\pi}}}$ and ${{J/{\psi\pi\pi\pi}}}$ branching fractions are observed experimentally, and their sizes are comparable to each other. In order to clarify the mechanism to cause such a large isospin violation, we investigate X(3872) employing a model of coupled-channel two-meson scattering with a ${{\rm c}\bar{c}}$ core. The two-meson states consist of ${{D^0\overline{D}^{*0}}}$ , D ⁺ D ^*?, ${{J/{\psi\rho}}}$ , and ${{J/{\psi\omega}}}$ . The effects of the ρ and ω meson width are also taken into account. We calculate the transfer strength from the ${{{\rm c}\bar{c}}}$ core to the final two-meson states. It is found that very narrow ${{J/{\psi\rho}}}$ and ${{J/{\psi\omega}}}$ peaks appear very close to the ${{D^0\overline{D}^{*0}}}$ threshold for a wide range of variation in the parameter sets. The size of the ${{J/{\psi\rho}}}$ peak is almost the same as that of ${{J/{\psi\omega}}}$ , which is consistent with the experiments. The large width of the ρ meson makes the originally small isospin violation by about five times larger.     

Theoretical study of collision and collision-free radiative lifetimes of {{\text{S}}_2}\left( {{{\text{B}}^3}\Sigma_{\text{u}}^{-} \left( {{\upsilon^{\prime}} = 0 - 9} \right)} \right)

We calculate multireference configuration-interaction wavefunctions and the potential-energy curves for the $ {B^3}\Sigma_u^{-} $ and $ {X^3}\Sigma_g^{-} $ states of the collision-free S₂ molecule and the T-shape collision complex S₂?CHe using cc-pVQZ basis sets. We obtain the transition dipole moments of the $ {{\text{S}}_2}\left( {{B^3}\Sigma_u^{-} \to {X^3}\Sigma_g^{-} } \right) $ and the Franck?CCondon factors between the vibrational levels of this two states. We evaluate the radiative lifetimes of $ {{\text{S}}_2}\left( {{B^3}\Sigma_u^{-} \left( {{\upsilon^{\prime}} = 0 - 9} \right)} \right) $ levels of the collision complex and the collision-free molecule and compare them with the experiments. The collision provides little change in the radiative lifetimes of $ {{\text{S}}_2}\left( {{B^3}\Sigma_u^{-} \left( {{\upsilon^{\prime}} = 0 - 9} \right)} \right) $ according to the previous calculations. We obtain excellent agreement between the theoretical results and the experiments. The data calculated are very useful in the study of the microwave-driven high-pressure sulfur lamp and an S₂ laser pumped by a transverse fast discharge.     

On Gravitational Effects in the Schrödinger Equation

The Schrödinger  equation for a particle of rest mass $m$ and electrical charge $ne$ interacting with a four-vector potential $A_i$ can be derived as the non-relativistic limit of the Klein–Gordon  equation $\left( \Box '+m^2\right) \varPsi =0$ for the wave function $\varPsi $ , where $\Box '=\eta ^{jk}\partial '_j\partial '_k$ and $\partial '_j=\partial _j -\mathrm {i}n e A_j$ , or equivalently from the one-dimensional  action $S_1=-\int m ds +\int neA_i dx^i$ for the corresponding point particle in the semi-classical approximation $\varPsi \sim \exp {(\mathrm {i}S_1)}$ , both methods yielding the equation $\mathrm {i}\partial _0\varPsi \approx \left( \frac{1}{2m}\eta ^{\alpha \beta }\partial '_{\alpha }\partial '_{\beta } + m + n e\phi \right) \varPsi $ in Minkowski  space–time  , where $\alpha ,\beta =1,2,3$ and $\phi =-A_0$ . We show that these two methods generally yield equations  that differ in a curved background  space–time   $g_{ij}$ , although they coincide when $g_{0\alpha }=0$ if $m$ is replaced by the effective mass $\mathcal{M}\equiv \sqrt{m^2-\xi R}$ in both the Klein–Gordon  action $S$ and $S_1$ , allowing for non-minimal coupling to the gravitational  field, where $R$ is the Ricci scalar and $\xi $ is a constant. In this case $\mathrm {i}\partial _0\varPsi \approx \left( \frac{1}{2\mathcal{M}'} g^{\alpha \beta }\partial '_{\alpha }\partial '_{\beta } + \mathcal{M}\phi ^{(\mathrm g)} + n e\phi \right) \varPsi $ , where $\phi ^{(\mathrm g)} =\sqrt{g_{00}}$ and $\mathcal{M}'=\mathcal{M}/\phi ^{(\mathrm g)} $ , the correctness of the gravitational  contribution to the potential having been verified to linear order $m\phi ^{(\mathrm g)} $ in the thermal-neutron beam interferometry experiment due to Colella et al. Setting $n=2$ and regarding $\varPsi $ as the quasi-particle wave function, or order parameter, we obtain the generalization of the fundamental macroscopic Ginzburg-Landau equation of superconductivity to curved space–time. Conservation of probability and electrical current requires both electromagnetic gauge and space–time  coordinate conditions to be imposed, which exemplifies the gravito-electromagnetic analogy, particularly in the stationary case, when div ${{\varvec{A}}}=\hbox {div}{{\varvec{A}}}^{(\mathrm g)}=0$ , where ${{\varvec{A}}}^{\alpha }=-A^{\alpha }$ and ${{\varvec{A}}}^{(\mathrm g)\alpha }=-\phi ^{(\mathrm g)}g^{0\alpha }$ . The quantum-cosmological Schrödinger  (Wheeler–DeWitt) equation is also discussed in the $\mathcal{D}$ -dimensional  mini-superspace idealization, with particular regard to the vacuum potential $\mathcal V$ and the characteristics of the ground state, assuming a gravitational  Lagrangian   $L_\mathcal{D}$ which contains higher-derivative  terms up to order $\mathcal{R}^4$ . For the heterotic superstring theory  , $L_\mathcal{D}$ consists of an infinite series in $\alpha '\mathcal{R}$ , where $\alpha '$ is the Regge slope parameter, and in the perturbative approximation $\alpha '|\mathcal{R}| \ll 1$ , $\mathcal V$ is positive semi-definite for $\mathcal{D} \ge 4$ . The maximally symmetric ground state satisfying the field equations is Minkowski  space for $3\le {\mathcal {D}}\le 7$ and anti-de Sitter  space for $8 \le \mathcal {D} \le 10$ .     

Experimental and theoretical determination of transition dipole moments of ethyl 5-(4-aminophenyl)- and 5-(4-dimethylaminophenyl)-3-amino-2,4-dicyanobenzoate

The absorption and fluorescence transition dipole moments ( $\hat M_{ge}$ and $\hat M_{eg}$ ) for ethyl 5-(4-aminophenyl)-3-amino-2, 4-dicyanobenzoate (EAADCy) and ethyl 5-(4-dimethylaminophenyl)-3-amino-2, 4-dicyanobenzoate (EDMAADCy) have been determined on the basis of the steady-state and time-resolved spectroscopic measurements and semiempirical quantum-chemical calculations. The values of the transition dipole moments of perpendicular and flattened forms of the investigated molecules were estimated as a function of the solvent polarity. Noted differences between the absorption and emission transition dipole moments (i.e., ${{\hat M_{ge} } \mathord{\left/ {\vphantom {{\hat M_{ge} } {\hat M_{eg} }}} \right. \kern-0em} {\hat M_{eg} }} \ne 1$ ) confirm that the change of the electronic and molecular structure take place in the excited state.     

Muonic Anti-hydrogen {(\bar{\rm H}_{\mu}}) Formation in Low-energy Three-body Reactions

A few-body type computation is performed for a three-charge-particle collision with participation of a slow antiproton ${\bar{\rm{p}}}$ and a muonic muonium atom (true muonium), i.e. a bound state of two muons ${(\mu^{+}\mu^{-})}$ in its ground state. The total cross section of the following reaction ${\bar{\rm p}+(\mu^{+}\mu^{-}) \rightarrow \bar{\rm{H}}_{\mu} + \mu^{-}}$ , where muonic anti-hydrogen ${\bar{\rm{H}}_{\mu}=(\bar{\rm p}\mu^{+})}$ is a bound state of an antiproton and positive muon, is computed in the framework of a set of coupled two-component Faddeev-Hahn-type equation. A better known negative muon transfer low energy three-body reaction: ${{\rm t}^{+} + ({\rm d}^{+}\mu^{-})\rightarrow ({\rm t}^{+}\mu^{-}) + {\rm d}^{+}}$ is also computed as a test system. Here, t⁺ is triton and d⁺ is deuterium.     

Analysis of the \frac{1} {2}^ - and \frac{3} {2}^ - heavy and doubly heavy baryon states with QCD sum rules

In this article, we study the $\frac{1} {2}^ -$ and $\frac{3} {2}^ -$ heavy and doubly heavy baryon states $\Sigma _Q \left( {\frac{1} {2}^ - } \right)$ , $\Xi '_Q \left( {\frac{1} {2}^ - } \right)$ , $\Omega _Q \left( {\frac{1} {2}^ - } \right)$ , $\Xi _{QQ} \left( {\frac{1} {2}^ - } \right)$ , $\Omega _{QQ} \left( {\frac{1} {2}^ - } \right)$ , $\Sigma _Q^* \left( {\frac{3} {2}^ - } \right)$ , $\Xi _Q^* \left( {\frac{3} {2}^ - } \right)$ , $\Omega _Q^* \left( {\frac{3} {2}^ - } \right)$ , $\Xi _{QQ}^* \left( {\frac{3} {2}^ - } \right)$ and $\Omega _{QQ}^* \left( {\frac{3} {2}^ - } \right)$ by subtracting the contributions from the corresponding $\frac{1} {2}^ +$ and $\frac{3} {2}^ +$ heavy and doubly heavy baryon states with the QCD sum rules in a systematic way, and make reasonable predictions for their masses.     

Exploring the nuclear potential of antihyperons with antiprotons at {\overline{\rm\bf P}}{\rm\bf ANDA}

A schematic Monte Carlo simulation is used to examine the potential of the ${\overline{\rm P}} {\rm ANDA}$ experiment to extract information on the interaction of antihyperons in nuclei by exclusive hyperon-antihyperon pair production close to threshold in antiproton nucleus interactions. Due to energy and momentum conservation event-by-event transverse momentum correlations of the produced hyperon and antihyperons contain information on the difference between their potentials. It is demonstrated that for ${{\Lambda}{\overline{\Lambda}}}$ and ${{{\Xi}}{{\overline{\Xi}}}}$ pairs produced at antiproton momenta of 1.66 GeV/c and 2.9 GeV/c, respectively, the asymmetry is sufficiently sensitive even if the density as well as the momentum dependencies of the potentials are considered.     

Finite W-Superalgebras and Truncated Super Yangians

Let ${Y_{m|n}^{\ell}}$ be the super Yangian of general linear Lie superalgebra for ${\mathfrak{gl}_{m|n}}$ . Let ${e \in \mathfrak{gl}_{m\ell|n\ell}}$ be a “rectangular” nilpotent element and ${\mathcal{W}_e}$ be the finite W-superalgebra associated to e. We show that ${Y_{m|n}^{\ell}}$ is isomorphic to ${\mathcal{W}_e}$ .     

A brief review of antimatter production

In this article, we present a brief review of the discoveries of kinds of antimatter particles, including positron ( $ \bar e $ ), antiproton ( $ \bar p $ ), antideuteron ( $ \bar d $ ) and antihelium-3 ( $ ^3 \overline {He} $ ). Special emphasis is put on the discovery of the antihypertriton( $ \frac{3} {\Lambda }\overline H $ ) and antihelium-4 nucleus ( $ ^4 \overline {He} $ , or $ \bar \alpha $ ) which were reported by the RHIC-STAR experiment very recently. In addition, brief discussions about the effort to search for antinuclei in cosmic rays and study of the longtime confinement of the simplest antimatter atom, antihydrogen are also given. Moreover, the production mechanism of anti-light nuclei is introduced.