Search of the neutrino-less double beta decay of $$^{}$$Se into the excited states of $$^{}$$Kr with CUPID-0

The CUPID-0 experiment searches for double beta decay using cryogenic calorimeters with double (heat and light) read-out. The detector, consisting of 24 ZnSe crystals 95\(\%\) enriched in \(^{82}\)Se and two natural ZnSe crystals, started data-taking in 2017 at Laboratori Nazionali del Gran Sasso. We present the search for the neutrino-less double beta decay of \(^{82}\)Se into the 0\(_1^+\), 2\(_1^+\) and 2\(_2^+\) excited states of \(^{82}\)Kr with an exposure of 5.74 kg\(\cdot \)yr (2.24\(\times \)10\(^{25}\) emitters\(\cdot \)yr). We found no evidence of the decays and set the most stringent limits on the widths of these processes: \(\varGamma \)(\(^{82}\)Se \(\rightarrow ^{82}\)Kr\(_{0_1^+}\))8.55\(\times \)10\(^{-24}\) yr\(^{-1}\), \(\varGamma \) (\(^{82}\) Se \(\rightarrow ^{82}\) Kr \(_{2_1^+}\))\(\,{<}\,6.25 \,{\times }\,10^{-24}\) yr\(^{-1}\), \(\varGamma \)(\(^{82}\)Se \(\rightarrow ^{82}\)Kr\(_{2_2^+}\))8.25\(\times \)10\(^{-24}\) yr\(^{-1}\) (90\(\%\) credible interval).     

Rapid communication: $$K_{S}^{0}$$ Production from beryllium target using 120 $$\hbox {GeV}/\hbox {c}$$GeV/c protons beam interactions at the MIPP experiment

We have measured the cross-section for the \(K_{S}^{0}\) production from beryllium target using 120 \(\hbox {GeV}/\hbox {c}\) protons beam interactions at the main injector particle production (MIPP) experiment at Fermilab. The data were collected with target having a thickness of 0.94% of the nuclear interaction length. The \(K_{S}^{0}\) inclusive differential cross-section in bins of momenta is presented covering momentum range from \(0.4\,\hbox {GeV}/\hbox {c}\) to \(30\,\hbox {GeV}/\hbox {c}\). The measured inclusive \(K_{S}^{0}\) production cross-section amounts to \(39.54\pm 1.46\delta _{\mathrm {stat}}\pm 6.97\delta _{\mathrm {syst}}\) mb and the value is compared with the prediction of FLUKA hadron production model.     

$$\varvec{B^0\rightarrow K^{*0}\mu ^+\mu ^-}$$ 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.     

Decay widths of the spin-2 partners of the <Emphasis Type="Italic">X</Emphasis>(3872)

We consider the X(3872) resonance as a \(J^\mathrm{{PC}}=1^{++}\) \(D\bar{D}^*\) hadronic molecule. According to heavy quark spin symmetry, there will exist a partner with quantum numbers \(2^{++}\), \(X_{2}\), which would be a \(D^*\bar{D}^*\) loosely bound state. The \(X_{2}\) is expected to decay dominantly into \(D\bar{D}\), \(D\bar{D}^*\) and \(\bar{D} D^*\) in d-wave. In this work, we calculate the decay widths of the \(X_{2}\) resonance into the above channels, as well as those of its bottom partner, \(X_{b2}\), the mass of which comes from assuming heavy flavor symmetry for the contact terms. We find partial widths of the \(X_{2}\) and \(X_{b2}\) of the order of a few MeV. Finally, we also study the radiative \(X_2\rightarrow D\bar{D}^{*}\gamma \) and \(X_{b2} \rightarrow \bar{B} B^{*}\gamma \) decays. These decay modes are more sensitive to the long-distance structure of the resonances and to the \(D\bar{D}^{*}\) or \(B\bar{B}^{*}\) final state interaction.     

The decays of $$\bar{B}^0$$, $$\bar{B}^0_s$$B¯s0 and $$B^-$$B- into $$\eta _c$$ηc plus a scalar or vector meson

We investigate the decays of \(\bar{B}^0_s\), \(\bar{B}^0\) and \(B^-\) into \(\eta _c\) plus a scalar or vector meson in a theoretical framework by taking into account the dominant process for the weak decay of \(\bar{B}\) meson into \(\eta _c\) and a \(q\bar{q}\) pair. After hadronization of this \(q\bar{q}\) component into pairs of pseudoscalar mesons we obtain certain weights for the pseudoscalar meson-pseudoscalar meson components. In addition, the \(\bar{B}^0\) and \(\bar{B}^0_s\) decays into \(\eta _c\) and \(\rho ^0\), \(K^*\) are evaluated and compared to the \(\eta _c\) and \(\phi \) production. The calculation is based on the postulation that the scalar mesons \(f_0(500)\), \(f_0(980)\) and \(a_0(980)\) are dynamically generated states from the pseudoscalar meson-pseudoscalar meson interactions in S-wave. Up to a global normalization factor, the \(\pi \pi \), \(K \bar{K}\) and \(\pi \eta \) invariant mass distributions for the decays of \(\bar{B}^0_s \rightarrow \eta _c \pi ^+ \pi ^-\), \(\bar{B}^0_s \rightarrow \eta _c K^+ K^-\), \(\bar{B}^0 \rightarrow \eta _c \pi ^+ \pi ^-\), \(\bar{B}^0 \rightarrow \eta _c K^+ K^-\), \(\bar{B}^0 \rightarrow \eta _c \pi ^0 \eta \), \(B^- \rightarrow \eta _c K^0 K^-\) and \(B^- \rightarrow \eta _c \pi ^- \eta \) are predicted. Comparison is made with the limited experimental information available and other theoretical calcualtions. Further comparison of these results with coming LHCb measurements will be very valuable to make progress in our understanding of the nature of the low lying scalar mesons, \(f_0(500), f_0(980)\) and \(a_0(980)\).     

Fabrication and photoresponse of n-$$\hbox {WS}_{2}/$$p-V$$_{0.25}$$0.25W$$_{0.75}$$0.75Se$$_{2}$$2 van der Waals heterojunction

Excitation functions for \(\alpha \)-induced reactions on natural vanadium were measured in the energy range up to 20 MeV. The stacked-foil activation technique was used. The experimental results were compared with the theoretical calculations using EMPIRE-3.1, EMPIRE-3.2.2 and TENDL 2015, and with earlier experimental results. Thick target yields were calculated for the production of \(^{54}\hbox {Mn}\) and for the associated impurity \(^{52}\hbox {Mn}\).     

Spin-label Order Parameter Calibrations for Slow Motion

Calibrations are given to extract orientation order parameters from pseudo-powder electron paramagnetic resonance line shapes of ¹⁴N-nitroxide spin labels undergoing slow rotational diffusion. The nitroxide z-axis is assumed parallel to the long molecular axis. Stochastic-Liouville simulations of slow-motion 9.4-GHz spectra for molecular ordering with a Maier–Saupe orientation potential reveal a linear dependence of the splittings, \(2A_{\hbox{max} }\) and \(2A_{\hbox{min} }\), of the outer and inner peaks on order parameter \(S_{zz}\) that depends on the diffusion coefficient \(D_{{{\text{R}} \bot }}\) which characterizes fluctuations of the long molecular axis. This results in empirical expressions for order parameter and isotropic hyperfine coupling: \(S_{zz} = s_{1} \times \left( {A_{\hbox{max} } - A_{\hbox{min} } } \right) - s_{o}\) and \(a_{o}^{{}} = \tfrac{1}{3}\left( {f_{\hbox{max} } A_{\hbox{max} } + f_{\hbox{min} } A_{\hbox{min} } } \right) + \delta a_{o}\), respectively. Values of the calibration constants \(s_{1}\), \(s_{\text{o}}\), \(f_{\hbox{max} }\), \(f_{\hbox{min} }\) and \(\delta a_{o}\) are given for different values of \(D_{{{\text{R}} \bot }}\) in fast and slow motional regimes. The calibrations are relatively insensitive to anisotropy of rotational diffusion \((D_{{{\text{R}}//}} \ge D_{{{\text{R}} \bot }} )\), and corrections are less significant for the isotropic hyperfine coupling than for the order parameter.     

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.     

Scattering of kinks of the sinh-deformed $$\varphi ^4$$ model

We consider the scattering of kinks of the sinh-deformed \(\varphi ^4\) model, which is obtained from the well-known \(\varphi ^4\) model by means of the deformation procedure. Depending on the initial velocity \(v_\mathrm {in}\) of the colliding kinks, different collision scenarios are realized. There is a critical value \(v_\mathrm {cr}\) of the initial velocity, which separates the regime of reflection (at \(v_\mathrm {in}>v_\mathrm {cr}\)) and that of a complicated interaction (at \(v_\mathrm {in}<v_\mathrm {cr}\)) with kinks’ capture and escape windows. Besides that, at \(v_\mathrm {in}\) below \(v_\mathrm {cr}\) we observe the formation of a bound state of two oscillons, as well as their escape at some values of \(v_\mathrm {in}\).     

Virtual depth by active background suppression: revisiting the cosmic muon induced background of <Emphasis Type="SmallCaps">Gerda</Emphasis> Phase II

In-situ production of radioisotopes by cosmic muon interactions may generate a non-negligible background for deep underground rare event searches. Previous Monte Carlo studies for the Gerda experiment at Lngs identified the delayed decays of \(^{77}\)Ge and its metastable state \(^{77m}\)Ge as dominant cosmogenic background in the search for neutrinoless double beta decay of \(^{76}\)Ge. This might limit the sensitivity of next generation experiments aiming for increased \(^{76}\)Ge mass at background-free conditions and thereby define a minimum depth requirement. A re-evaluation of the \(^{77(m)}\)Ge background for the Gerda experiment has been carried out by a set of Monte Carlo simulations. The obtained \(^{77(m)}\)Ge production rate is (\(0.21\pm 0.01\)) nuclei/(kg\(\cdot \)year). After application of state-of-the-art active background suppression techniques and simple delayed coincidence cuts this corresponds to a background contribution of \((2.7\pm 0.3)\times 10^{-6}\) cts/(keV\(\cdot \)kg\(\cdot \)year). The suppression achieved by this strategy equals an effective muon flux reduction of more than one order of magnitude. This virtual depth increase opens the way for next generation rare event searches.     

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.     

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.     

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 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 \(\Omega =2^{-4},...,2^{7}\).     

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.     

Exotic tetraquark states with the $$qq\bar{Q}\bar{Q}$$ configuration

In this work, we study systematically the mass splittings of the \(qq\bar{Q}\bar{Q}\) (\(q=u\), d, s and \(Q=c\), b) tetraquark states with the color-magnetic interaction by considering color mixing effects and estimate roughly their masses. We find that the color mixing effect is relatively important for the \(J^P=0^+\) states and possible stable tetraquarks exist in the \(nn\bar{Q}\bar{Q}\) (\(n=u\), d) and \(ns\bar{Q}\bar{Q}\) systems either with \(J=0\) or with \(J=1\). Possible decay patterns of the tetraquarks are briefly discussed.     

Test the mergers of the primordial black holes by high frequency gravitational-wave detector

The black hole could have a primordial origin if its mass is less than \(1M_\odot \). The mergers of these black hole binaries generate stochastic gravitational-wave background (SGWB). We investigate the SGWB in high frequency band \(10^{8}\)–\(10^{10}\,\mathrm {Hz}\). It can be detected by high frequency gravitational-wave detector. Energy density spectrum and amplitude of the SGWB are derived. The upper limit of the energy density spectrum is around \(10^{-7}\). Also, the upper limit of the amplitude ranges from \(10^{-31.5}\) to \(10^{-29.5}\). The fluctuation of spacetime origin from gravitational wave could give a fluctuation of the background electromagnetic field in a high frequency gravitational-wave detector. The signal photon flux generated by the SGWB in the high frequency band \(10^{8}\)–\(10^{10}\,\mathrm {Hz}\) is derived, which ranges from 1 to \(10^2\,\mathrm {s^{-1}}\). The comparison between the signal photon flux generated by relic gravitational waves (RGWs) and the SGWB is also discussed in this paper. It is shown that the signal photon flux generated by the RGW, which is predicted by the canonical single-field slow-roll inflation models, is sufficiently lower than the one generated by the SGWB in the high frequency band \(10^{8}\)–\(10^{10}\,\mathrm {Hz}\). Our results indicate that the SGWB in the high frequency band \(10^{8}\)–\(10^{10}\,\mathrm {Hz}\) is more likely to be detected by the high frequency gravitational-wave detector.     

Gibbs Measures Over Locally Tree-Like Graphs and Percolative Entropy Over Infinite Regular Trees

Consider a statistical physical model on the d-regular infinite tree \(T_{d}\) described by a set of interactions \(\Phi \). Let \(\{G_{n}\}\) be a sequence of finite graphs with vertex sets \(V_n\) that locally converge to \(T_{d}\). From \(\Phi \) one can construct a sequence of corresponding models on the graphs \(G_n\). Let \(\{\mu _n\}\) be the resulting Gibbs measures. Here we assume that \(\{\mu _{n}\}\) converges to some limiting Gibbs measure \(\mu \) on \(T_{d}\) in the local weak\(^*\) sense, and study the consequences of this convergence for the specific entropies \(|V_n|^{-1}H(\mu _n)\). We show that the limit supremum of \(|V_n|^{-1}H(\mu _n)\) is bounded above by the percolative entropy \(H_{\textit{perc}}(\mu )\), a function of \(\mu \) itself, and that \(|V_n|^{-1}H(\mu _n)\) actually converges to \(H_{\textit{perc}}(\mu )\) in case \(\Phi \) exhibits strong spatial mixing on \(T_d\). When it is known to exist, the limit of \(|V_n|^{-1}H(\mu _n)\) is most commonly shown to be given by the Bethe ansatz. Percolative entropy gives a different formula, and we do not know how to connect it to the Bethe ansatz directly. We discuss a few examples of well-known models for which the latter result holds in the high temperature regime.     

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.