Photoreflectance spectroscopy of the chalcopyrite semiconductor <Emphasis Type="Bold">AgInS</Emphasis><Subscript>2</Subscript> for ordinary and extraordinary rays

Photoreflectance spectra have been measured on the chalcopyrite semiconductor silver indium disulfide (\(\hbox {AgInS}_{2}\)) for light polarization \({\varvec{E}}\) perpendicular (\({\varvec{E}} \bot {c}\)) and parallel to the c-axis (\({\varvec{E}} \vert \vert {c}\)) at temperature between 10 and 300 K. The measured photoreflectance spectra revealed distinct structures at 1.8–2.1 eV. The lowest bandgap energies \(E_{0A}\), \(E_{0B}\), and \(E_{0C}\) of \(\hbox {AgInS}_{2}\) show unusual temperature dependence at low temperatures (\(\le\)140 K). The \(E_{0\alpha }\) (\(\alpha =A, B, C\)) is found to increase with increasing temperature from 10 to \(\sim\)140 K and decreases with a further increase in temperature. This result has been successfully explained by taking into account the effects of thermal expansion and electron–phonon interaction. The spin–orbit and crystal-field splitting parameters of \(\hbox {AgInS}_{2}\) are determined to be \(\Delta _{{\mathrm{so}}}=38\) meV and \(\Delta _{{\mathrm{cr}}}=-168\) meV at T = 10 K, respectively, and are discussed from an aspect of the electronic energy band structure consequences. The temperature dependence of spin–orbit and crystal-field splitting parameters of \(\hbox {AgInS}_{2}\) was also presented.     

One-dimensional backreacting holographic <Emphasis Type="Italic">p</Emphasis>-wave superconductors

We analytically and numerically study the properties of one-dimensional holographic p-wave superconductors in the presence of backreaction. We employ the Sturm–Liouville eigenvalue problem for the analytical calculation and the shooting method for the numerical investigations. We apply the \(\hbox {AdS}_{{3}}\)/\(\hbox {CFT}_{{2}}\) correspondence and determine the relation between the critical temperature \(T_{c}\) and the chemical potential \(\mu \) for different values of the mass m of a charged spin-1 field \(\rho _{\mu }\) and backreacting parameters. We observe that the data of both analytical and numerical studies are in good agreement. We find that increasing the backreaction and the mass parameter causes the greater values for \({T_{c}}/{\mu }\). Thus, it makes the condensation harder to form. In addition, the analytical and numerical approaches show that the value of the critical exponent \( \beta \) is 1 / 2, which is the same as in the mean field theory. Moreover, both methods confirm the existence of a second order phase transition.     

Regularity of the Speed of Biased Random Walk in a One-Dimensional Percolation Model

We consider biased random walks on the infinite cluster of a conditional bond percolation model on the infinite ladder graph. Axelson-Fisk and Häggström established for this model a phase transition for the asymptotic linear speed \(\overline{\hbox {v}}\) of the walk. Namely, there exists some critical value \(\lambda _{\hbox {c}}>0\) such that \(\overline{\hbox {v}}>0\) if \(\lambda \in (0,\lambda _{\hbox {c}})\) and \(\overline{\hbox {v}}=0\) if \(\lambda \ge \lambda _{\hbox {c}}\). We show that the speed \(\overline{\hbox {v}}\) is continuous in \(\lambda \) on \((0,\infty )\) and differentiable on \((0,\lambda _{\hbox {c}}/2)\). Moreover, we characterize the derivative as a covariance. For the proof of the differentiability of \(\overline{\hbox {v}}\) on \((0,\lambda _{\hbox {c}}/2)\), we require and prove a central limit theorem for the biased random walk. Additionally, we prove that the central limit theorem fails to hold for \(\lambda \ge \lambda _{\hbox {c}}/2\).     

Isospin analysis of charmless <Emphasis Type="Italic">B</Emphasis>-meson decays

We discuss the determination of the CKM angle \(\alpha \) using the non-leptonic two-body decays \(B\rightarrow \pi \pi \), \(B\rightarrow \rho \rho \) and \(B\rightarrow \rho \pi \) using the latest data available. We illustrate the methods used in each case and extract the corresponding value of \(\alpha \). Combining all these elements, we obtain the determination \(\alpha _\mathrm{dir}={({86.2}_{-4.0}^{+4.4} \cup {178.4}_{-5.1}^{+3.9})}^{\circ }\). We assess the uncertainties associated to the breakdown of the isospin hypothesis and the choice of the statistical framework in detail. We also determine the hadronic amplitudes (tree and penguin) describing the QCD dynamics involved in these decays, briefly comparing our results with theoretical expectations. For each observable of interest in the \(B\rightarrow \pi \pi \), \(B\rightarrow \rho \rho \) and \(B\rightarrow \rho \pi \) systems, we perform an indirect determination based on the constraints from all the other observables available and we discuss the compatibility between indirect and direct determinations. Finally, we review the impact of future improved measurements on the determination of \(\alpha \).     

Ionic liquid-functionalized magnetic nanostructures as an efficient catalyst for the synthesis of 6H-chromeno[4,3-b]quinolin-6-ones

A novel imidazole ionic liquid (IL)-functionalized \(\hbox {silica}@\gamma \)-\(\hbox {Fe}_{2}\hbox {O}_{3}\) (\(\hbox {IL-SiO}_{2}@\hbox {MNP}\)) is prepared by the functionalization of \(\hbox {SiO}_{2}@\hbox {MNP}\) by 1-butyl-3-(3-trimethoxypropyl)-1H-imidazol-3-ium chloride as the IL moiety. The catalyst is characterized by transmission electron microscopy, scanning electron microscope, vibrating sample magnetometer, dynamic light scattering and Fourier transform infrared spectroscopy. \(\hbox {IL-SiO}_{2}@\hbox {MNP}\) showed good activity in the synthesis of 6H-chromeno[4,3-b]quinolin-6-one derivatives via multicomponent reaction of 4-hydroxycoumarin, anilines and benzaldehydes. The nanocatalyst is magnetically separable and easily recoverable and showed successful activity up to 10 runs.     

Synthesis of new quinazolin-2,4-diones as anti-<Emphasis Type="Italic">Leishmania mexicana</Emphasis> agents

The quinazolin-2,4-dione moiety is found in many compounds with important biological activities making it a target for its synthesis. In this work, a one-pot three-step synthesis of new quinazolin-2,4-diones from phthalic anhydrides and their activity against Leishmania mexicana are described. The new quinazolin-2,4-diones were isolated with yields in the range of 32–70 %. All compounds displayed lower cytotoxicity in RAW 264.7 macrophage over miltefosine. Compound 6,7-dichloro-3-phenylquinazoline-2,4(1H,3H)-dione (6e) displayed an attractive profile which includes anti-Leishmania mexicana activity (\(\hbox {IC}_{50} = 6.05\) \(\upmu \)M), much lower cytotoxic activity (\(\hbox {CC}_{50} = 111\) \(\upmu \)M) and a high selective index (\(\text {SI} = 18.35\)) proving to be superior to miltefosine.     

First-principle calculations of structural,electronic, optical,elastic and thermal properties of $$\hbox {MgXAs}_{2}$$ ($$\hbox {X}=\hbox {Si}, \hbox {Ge}$$X=Si,Ge) compounds

First-principle calculations on the structural, electronic, optical, elastic and thermal properties of the chalcopyrite \(\hbox {MgXAs}_{2}\) (\(\hbox {X}=\hbox {Si}, \hbox {Ge}\)) have been performed within the density functional theory (DFT) using the full-potential linearized augmented plane wave (FP-LAPW) method. The obtained equilibrium structural parameters are in good agreement with the available experimental data and theoretical results. The calculated band structures reveal a direct energy band gap for the interested compounds. The predicted band gaps using the modified Becke–Johnson (mBJ) exchange approximation are in fairly good agreement with the experimental data. The optical constants such as the dielectric function, refractive index, and the extinction coefficient are calculated and analysed. The independent elastic parameters namely, \(C_{11}\), \(C_{12}\), \(C_{13}\), \(C_{33}\), \(C_{44}\) and \(C_{66 }\) are evaluated. The effects of temperature and pressure on some macroscopic properties of \(\hbox {MgSiAs}_{2}\) and \(\hbox {MgGeAs}_{2}\) are predicted using the quasiharmonic Debye model in which the lattice vibrations are taken into account.     

Synthesis and evaluation of bile acid amides of $$\alpha $$-cyanostilbenes as anticancer agents

A series of amino-substituted \(\alpha \)-cyanostilbene derivatives and their bile acid (cholic and deoxycholic acid) amides were designed and synthesized. A comparative study on the anticancer and antibacterial activity evaluation on the synthesized analogs was carried against the human osteosarcoma (HOS) cancer cell line, and two gram ?ve (E. coli and S. typhi) and two gram \(+\)ve (B. subtilis and S. aureus) bacterial strains. All the cholic acid \(\alpha \)-cyanostilbene amides showed an \(\hbox {IC}_{50}\) in the range 2–13 \(\upmu \hbox {M}\) against human osteosarcoma cells (HOS) with the most active analog (6g) possessing an \(\hbox {IC}_{50}\) of \(2\,\upmu \hbox {M}\). One of the amino-substituted \(\alpha \)-cyanostilbene, 4e, was found to possess an \(\hbox {IC}_{50}\) of \(3\,\upmu \hbox {M}\). An increase in the number of cells at the sub-\(\hbox {G}_{1}\) phase of the cell was observed in the in vitro cell cycle analysis of two most active compounds in the series (4e, 6g) suggesting a clear indication toward induction of apoptotic cascade. With respect to antibacterial screening, amino-substituted \(\alpha \)-cyanostilbenes were found to be more active than their corresponding bile acid amides. The synthesized compounds were also subjected to in silico study to predict their physiochemical properties and drug-likeness score.     

The envelope travelling wave solutions to the Gerdjikov–Ivanov model

Valence universal multireference coupled cluster (VUMRCC) method via eigenvalue independent partitioning has been applied to estimate the effect of three-body transformed Hamiltonian (\(\widetilde{{H}}_3\)) on ionisation potentials through full connected triple excitations \(S_{3}^{(1,0) }\). \(\widetilde{H}_3 \) is constructed using CCSDT1-A model of Bartlett et al for the ground-state calculation. Contribution of transformed Hamiltonian through full connected triples \(\overline{\widetilde{H}_3 S_3^{\left( {1,0} \right) }}\) involves huge amount of computational operations that is time-consuming. Investigation on \(\hbox {Cl}_{2}\) and \(\hbox {F}_{2}\) molecules using cc-pVDZ and cc-pVTZ basis sets shows that the above effect varies from 0.001 eV to around 0.5 eV, suggesting that inclusion of \(\overline{\widetilde{H} _3 S_3^{\left( {1,0} \right) } }\) is essential for highly accurate calculations.     

On quantum analogue of dynamical stabilisation of inverted harmonic oscillator by time periodical uniform field

Quantum analogue of stabilised forced oscillations around an unstable equilibrium position is explored by solving the non-stationary Schrödinger equation (NSE) of the inverted harmonic oscillator (IHO) driven periodically by spatial uniform field of frequency \(\Omega \), amplitude \(F_{0}\) and phase \(\phi \), i.e. the system with the Hamiltonian of \(\hat{{H}}=(\hat{{p}}^{2}/2m)-(m\omega ^{2}x^{2}/2)-F_0 x\sin \) \(\left( {\Omega t+\phi } \right) \). The NSE has been solved both analytically and numerically by Maple 15 in dimensionless variables \(\xi = x\sqrt{m\omega /\hbar }\hbox {, }f_0 =F_0 /\omega \sqrt{\hbar m\omega }\) and \(\tau =\omega t\). The initial condition (IC) has been specified by the wave function (w.f.) of a generalised Gaussian type which suits well the corresponding quantum IC operator. The solution obtained demonstrates the non-monotonous behaviour of the coordinate spreading \(\sigma \left( \tau \right) \hbox { =}\sqrt{\big ( {\overline{\Delta \xi ^{2}\big ( \tau \big )} } \big )}\) which decreases first from quite macroscopic values of \(\sigma _{0} =2^{12,\ldots ,25}\) to minimal one of \(\sim \!(1/\sqrt{2})\) at times \(\tau <\tau _0 =0.125\ln \!\left( {16\sigma _0^4 +1} \right) \) and then grows back unlimitedly. For certain phases \(\phi \) depending on the \(\Omega /\omega \) ratio and \(n=\log _2\!\sigma _0 \), the mass centre of the packet \(\xi _{\mathrm {av}}( \tau )= \overline{\hat{{x}}(\tau )} \cdot \sqrt{m\omega /\hbar }\) delays approximately two natural ‘periods’ \(\sim \!(4\pi /\omega )\) in the area of the stationary point and then escapes to ‘\(+\)’ or ‘?’ infinity in a bifurcating way.  For ‘resonant’ \(\Omega =\omega \), the bifurcation phases \(\phi \) fit well with the regression formula of Fermi–Dirac type of argument n with their asymptotic \(\phi ( {\Omega ,n\rightarrow \infty } )\) obeying the classical formula \(\phi _{\mathrm {cl}} ( \Omega )=-\hbox {arctg} \, \Omega \) for initial energy \(E = 0\) in the wide range of \(\Omega =2^{-4},...,2^{7}\).     

Strange quark star with Tolman IV background

In this paper, using the optical emission spectroscopy (OES) technique, the optical characteristics of a radiofrequency (RF) plasma jet are examined. The \(\hbox {Ar}/\hbox {O}_{2}\) mixture is taken as the operational gas and, the Ar percentage in the \(\hbox {Ar}/\hbox {O}_{2}\) mixture is varied from 70% to 95%. Using the optical emission spectrum analysis of the RF plasma jet, the excitation temperature is determined based on the Boltzmann plot method. The electron density in the plasma medium of the RF plasma jet is obtained by the Stark broadening of the hydrogen Balmer \(H_{\beta }\). It is mostly seen that, the radiation intensity of Ar 4p\(\rightarrow \)4s transitions at higher argon contributions in \(\hbox {Ar}/\hbox {O}_{2}\) mixture is higher. It is found that, at higher Ar percentages, the emission intensities from atomic oxygen (O) are higher and, the line intensities from the argon atoms and ions including O atoms linearly increase. It is observed that the quenching of \(\hbox {Ar}^{*}\) with \(\hbox {O}_{2}\) results in higher O species with respect to \(\hbox {O}_{2}\) molecules. In addition, at higher percentages of Ar in the \(\hbox {Ar}/\hbox {O}_{2}\) mixture, while the excitation temperature is decreased, the electron density is increased.     

Holography of massive M2-brane theory: non-linear extension

We investigate the gauge/gravity duality between the \(\mathcal{N} = 6\) mass-deformed ABJM theory with \(\hbox {U}_k(N)\times \hbox {U}_{-k}(N)\) gauge symmetry and the 11-dimensional supergravity on LLM geometries with SO(2,1)\(\times \)SO(4)/\({\mathbb {Z}}_k\) \(\times \)SO(4)/\({\mathbb {Z}}_k\) isometry, in terms of a KK holography, which involves quadratic order field redefinitions. We establish the quadratic order KK mappings for various gauge invariant fields in order to obtain the canonical 4-dimensional gravity equations of motion and to reduce the LLM solutions to an asymptotically AdS\(_4\) gravity solutions. The non-linearity of the KK maps indicates that we can observe the true purpose of the non-linear KK holography of the LLM solutions. We read the vacuum expectation value of conformal dimension two operator from the asymptotically AdS\(_4\) gravity solutions. For the LLM solutions which are represented by square-shaped Young diagrams, we compare the vacuum expectation value obtained from the holographic procedure with the result obtained from the field theory, which is given by \(\langle \mathcal{O}^{(\Delta =2)}\rangle =\sqrt{k}N^{\frac{3}{2}}f_{(\Delta =2)}+\mathcal{O}(N)\), where \(f_{\Delta }\) is independent of N. Based on this result, we examine the gauge/gravity duality in the large N limit and finite k. We also show that the vacuum expectation values of the massive KK graviton modes are vanishing as expected by the supersymmetry.     

Tracking iron oxide nanoparticles in plant organs using magnetic measurements

Common bean plants were grown in soil and irrigated with water solutions containing different concentrations of \(\hbox{Fe}_3\hbox{O}_4\) nanoparticles (NPs) with a mean diameter close to 10 nm. No toxicity on plant growth has been detected as a consequence of Fe deficiency or excess in leaves. In order to track the \(\hbox{Fe}_3\hbox{O}_4\) NPs, magnetization measurements were performed in soils and in three different dried organs of the plants: roots, stems, and leaves. Some magnetic features of both temperature and magnetic field dependence of magnetization M(T, H) arising from \(\hbox{Fe}_3\hbox{O}_4\) NPs were identified in all the three organs of the plants. Based on the results of saturation magnetization \(M_\mathrm{s}\) at 300 K, the estimated number of \(\hbox{Fe}_3\hbox{O}_4\) NPs was found to increase from 2 to 3 times in leaves of common bean plants irrigated with solutions containing magnetic material. The combined results indicated that M(T, H) measurements, conducted in a wide range of temperature and applied magnetic fields up to 70 kOe, constitute a useful tool through which the uptake, translocation, and accumulation of magnetic nanoparticles by plant organs may be monitored and tracked.     

X-ray spectra and valence states of cations in nanostructured half-doped $$\hbox {La}_{0.5}\hbox {Ca}_{0.5}\hbox {MnO}_{3}$$ manganite

Soft X-ray absorption (XAS) and emission (XES) spectroscopies were applied to determine valence states of manganese ions in nanostructured powder of half-doped \(\hbox {La}_{0.5}\hbox {Ca}_{0.5}\hbox {MnO}_{3}\) manganite obtained by milling in a ball mill. XAS spectra were measured both in surface-sensitivity total electron-yield and in bulk-sensitivity total fluorescence-yield modes. O K\(_{\upalpha }\) XES and O 1s XAS spectra characterized the occupied and unoccupied partial O 2p densities of states are compared with band-structure calculations made using the TB-LMTO-ASA codes. Experimental Mn 2p, Ca 2p, and La 3\(d\) XAS spectra are compared with results of crystal field atomic multiplet calculations. For the nanostructured system of \(\hbox {La}_{0.5}\hbox {Ca}_{0.5}\hbox {MnO}_{3}\), concentrations of Mn\(^{4+}\) ions are found to be increased with increasing the time of milling.     

Likelihood analysis of the pMSSM11 in light of LHC 13-TeV data

We use MasterCode to perform a frequentist analysis of the constraints on a phenomenological MSSM model with 11 parameters, the pMSSM11, including constraints from \(\sim 36\)/fb of LHC data at 13 TeV and PICO, XENON1T and PandaX-II searches for dark matter scattering, as well as previous accelerator and astrophysical measurements, presenting fits both with and without the \((g-2)_\mu \) constraint. The pMSSM11 is specified by the following parameters: 3 gaugino masses \(M_{1,2,3}\), a common mass for the first-and second-generation squarks \(m_{\tilde{q}}\) and a distinct third-generation squark mass \(m_{\tilde{q}_3}\), a common mass for the first-and second-generation sleptons \(m_{\tilde{\ell }}\) and a distinct third-generation slepton mass \(m_{\tilde{\tau }}\), a common trilinear mixing parameter A, the Higgs mixing parameter \(\mu \), the pseudoscalar Higgs mass \(M_A\) and \(\tan \beta \). In the fit including \((g-2)_\mu \), a Bino-like \(\tilde{\chi }^0_{1}\) is preferred, whereas a Higgsino-like \(\tilde{\chi }^0_{1}\) is mildly favoured when the \((g-2)_\mu \) constraint is dropped. We identify the mechanisms that operate in different regions of the pMSSM11 parameter space to bring the relic density of the lightest neutralino, \(\tilde{\chi }^0_{1}\), into the range indicated by cosmological data. In the fit including \((g-2)_\mu \), coannihilations with \(\tilde{\chi }^0_{2}\) and the Wino-like \(\tilde{\chi }^\pm _{1}\) or with nearly-degenerate first- and second-generation sleptons are active, whereas coannihilations with the \(\tilde{\chi }^0_{2}\) and the Higgsino-like \(\tilde{\chi }^\pm _{1}\) or with first- and second-generation squarks may be important when the \((g-2)_\mu \) constraint is dropped. In the two cases, we present \(\chi ^2\) functions in two-dimensional mass planes as well as their one-dimensional profile projections and best-fit spectra. Prospects remain for discovering strongly-interacting sparticles at the LHC, in both the scenarios with and without the \((g-2)_\mu \) constraint, as well as for discovering electroweakly-interacting sparticles at a future linear \(e^+ e^-\) collider such as the ILC or CLIC.     

Strong decay of $$\Lambda _c(2940)$$ as a 2 P state in the $$\Lambda _c$$Λc family

Considering the mass, parity and \(D^0 p\) decay mode, we tentatively assign the \(\Lambda _c(2940)\) as the \(P-\)wave states with one radial excitation. Then, via studying the strong decay behavior of the \(\Lambda _c(2940)\) within the \(^3P_0\) model, we obtain that the total decay widths of the \(\Lambda _{c1}(\frac{1}{2}^-,2P)\) and \(\Lambda _{c1}(\frac{3}{2}^-,2P)\) states are 16.27 and 25.39 MeV, respectively. Compared with the experimental total width \(27.7^{+8.2}_{-6.0}\pm 0.9^{+5.2}_{-10.4}~\mathrm {MeV}\) measured by LHCb Collaboration, both assignments are allowed, and the \(J^P=\frac{3}{2}^-\) assignment is more favorable. Other \(\lambda \)-mode \(\Sigma _c(2P)\) states are also investigated, which are most likely to be narrow states and have good potential to be observed in future experiments.     

Theoretical analysis of somatostatin receptor 5 with antagonists and agonists for the treatment of neuroendocrine tumors

We report on SSTR5 receptor modeling and its interaction with reported antagonist and agonist molecules. Modeling of the SSTR5 receptor was carried out using multiple templates with the aim of improving the precision of the generated models. The selective SSTR5 antagonists, agonists and native somatostatin SRIF-14 were employed to propose the binding site of SSTR5 and to identify the critical residues involved in the interaction of the receptor with other molecules. Residues Q2.63, D3.32, Q3.36, C186, Y7.34 and Y7.42 were found to be highly significant for their strong interaction with the receptor. SSTR5 antagonists were utilized to perform a 3D quantitative structure–activity relationship study. A comparative molecular field analysis (CoMFA) was conducted using two different alignment schemes, namely the ligand-based and receptor-based alignment methods. The best statistical results were obtained for ligand-based (\({q}^{2} = 0.454\), \({r}^{2}\) = 0.988, noc = 4) and receptor-guided methods (docked mode 1:\({q}^{2} = 0.530\), \({r}^{2} = 0.916\), noc = 5), (docked mode 2:\({q}^{2}\) = 0.555, \({r}^{2 }= 0.957\), noc = 5). Based on CoMFA contour maps, an electropositive substitution at \(\hbox {R}^{1}\), \(\hbox {R}^{2}\) and \(\hbox {R}^{4}\) position and bulky group at \(\hbox {R}^{4}\) position are important in enhancing molecular activity.     

On non-consensus motions of dynamical linear multiagent systems

The first-principle density functional theory (DFT) calculations were employed to investigate the electronic structures, magnetic properties and half-metallicity of \(\text {Ti}_{2}\text {IrZ}\) (Z \(=\) B, Al, Ga, and In) Heusler alloys with \(\text {AlCu}_{2}\text {Mn}\)- and \(\text {CuHg}_{2}\text {Ti}\)-type structures within local density approximation and generalised gradient approximation for the exchange correlation potential. It was found that \(\text {CuHg}_{2}\text {Ti}\)-type structure in ferromagnetic state was energetically more favourable than \(\text {AlCu}_{2}\text {Mn}\)-type structure in all compounds except \(\text {Ti}_{2}\text {IrB}\) which was stable in \(\text {AlCu}_{2}\text {Mn}\)-type structure in non-magnetic state. \(\text {Ti}_{2}\text {IrZ}\) (Z \(=\) B, Al, Ga, and In) alloys in \(\text {CuHg}_{2}\text {Ti}\)-type structure were half-metallic ferromagnets at their equilibrium lattice constants. Half-metallic band gaps were respectively equal to 0.87, 0.79, 0.75, and 0.73 eV for \(\text {Ti}_{2}\text {IrB}\), \(\text {Ti}_{2}\text {IrAl}\), \(\text {Ti}_{2}\text {IrGa}\), and \(\text {Ti}_{2}\text {IrIn}\). The origin of half-metallicity was discussed for \(\text {Ti}_{2}\text {IrGa}\) using the energy band structure. The total magnetic moments of \(\text {Ti}_{2}\text {IrZ}\) (Z \(=\) B, Al, Ga, and In) compounds in \(\text {CuHg}_{2}\text {Ti}\)-type structure were obtained as \(2\mu _{\mathrm{B}}\) per formula unit, which were in agreement with Slater–Pauling rule (\(M_{\mathrm{tot}} =Z_{\mathrm{tot}}-\)18). All the four compounds were half-metals in a wide range of lattice constants indicating that they may be suitable and promising materials for future spintronic applications.     

$$\varvec{B^0\rightarrow K^{*0}\mu ^+\mu ^-}$$ decay in the aligned two-Higgs-doublet model

In the aligned two-Higgs-doublet model, we perform a complete one-loop computation of the short-distance Wilson coefficients \(C_{7,9,10}^{(\prime )}\), which are the most relevant ones for \(b\rightarrow s\ell ^+\ell ^-\) transitions. It is found that, when the model parameter \(\left| \varsigma _{u}\right| \) is much smaller than \(\left| \varsigma _{d}\right| \), the charged scalar contributes mainly to chirality-flipped \(C_{9,10}^\prime \), with the corresponding effects being proportional to \(\left| \varsigma _{d}\right| ^2\). Numerically, the charged-scalar effects fit into two categories: (A) \(C_{7,9,10}^\mathrm {H^\pm }\) are sizable, but \(C_{9,10}^{\prime \mathrm {H^\pm }}\simeq 0\), corresponding to the (large \(\left| \varsigma _{u}\right| \), small \(\left| \varsigma _{d}\right| \)) region; (B) \(C_7^\mathrm {H^\pm }\) and \(C_{9,10}^{\prime \mathrm {H^\pm }}\) are sizable, but \(C_{9,10}^\mathrm {H^\pm }\simeq 0\), corresponding to the (small \(\left| \varsigma _{u}\right| \), large \(\left| \varsigma _{d}\right| \)) region. Taking into account phenomenological constraints from the inclusive radiative decay \(B\rightarrow X_{s}{\gamma }\), as well as the latest model-independent global analysis of \(b\rightarrow s\ell ^+\ell ^-\) data, we obtain the much restricted parameter space of the model. We then study the impact of the allowed model parameters on the angular observables \(P_2\) and \(P_5'\) of \(B^0\rightarrow K^{*0}\mu ^+\mu ^-\) decay, and we find that \(P_5'\) could be increased significantly to be consistent with the experimental data in case B.     

Equilibration in the Kac Model Using the GTW Metric $$d_2$$

We use the Fourier based Gabetta–Toscani–Wennberg metric \(d_2\) to study the rate of convergence to equilibrium for the Kac model in 1 dimension. We take the initial velocity distribution of the particles to be a Borel probability measure \(\mu \) on \(\mathbb {R}^n\) that is symmetric in all its variables, has mean \(\vec {0}\) and finite second moment. Let \(\mu _t(dv)\) denote the Kac-evolved distribution at time t, and let \(R_\mu \) be the angular average of \(\mu \). We give an upper bound to \(d_2(\mu _t, R_\mu )\) of the form \(\min \left\{ B e^{-\frac{4 \lambda _1}{n+3}t}, d_2(\mu ,R_\mu )\right\} ,\) where \(\lambda _1 = \frac{n+2}{2(n-1)}\) is the gap of the Kac model in \(L^2\) and B depends only on the second moment of \(\mu \). We also construct a family of Schwartz probability densities \(\{f_0^{(n)}: \mathbb {R}^n\rightarrow \mathbb {R}\}\) with finite second moments that shows practically no decrease in \(d_2(f_0(t), R_{f_0})\) for time at least \(\frac{1}{2\lambda }\) with \(\lambda \) the rate of the Kac operator. We also present a propagation of chaos result for the partially thermostated Kac model in Tossounian and Vaidyanathan (J Math Phys 56(8):083301, 2015).