Dynamic Logic Assigned to Automata

A dynamic logic B can be assigned to every automaton Open image in new window without regard if Open image in new window is deterministic or nondeterministic. This logic enables us to formulate observations on Open image in new window in the form of composed propositions and, due to a transition functor T, it captures the dynamic behaviour of Open image in new window . There are formulated conditions under which the automaton Open image in new window can be recovered by means of B and T.     

Pitowsky’s Kolmogorovian Models and Super-determinism

In an attempt to demonstrate that local hidden variables are mathematically possible, Pitowsky constructed “spin- Open image in new window functions” and later “Kolmogorovian models”, which employs a nonstandard notion of probability. We describe Pitowsky’s analysis and argue (with the benefit of hindsight) that his notion of hidden variables is in fact just super-determinism (and accordingly physically not relevant). Pitowsky’s first construction uses the Continuum Hypothesis. Farah and Magidor took this as an indication that at some stage physics might give arguments for or against adopting specific new axioms of set theory. We would rather argue that it supports the opposing view, i.e., the widespread intuition “if you need a non-measurable function, it is physically irrelevant”.     

Monte Carlo Glauber model with meson cloud: predictions for 5.44 TeV Xe + Xe collisions

We study, within the Monte-Carlo Glauber model, centrality dependence of the midrapidity charged multiplicity density \(dN_{ch}/d\eta \) and of the anisotropy coefficients \(\varepsilon _{2,3}\) in Pb + Pb collisions at \(\sqrt{s}=5.02\) TeV and in Xe + Xe collisions at \(\sqrt{s}=5.44\) TeV. Calculations are performed for versions with and without nucleon meson cloud. The fraction of the binary collisions, \(\alpha \), has been fitted to the data on \(dN_{ch}/d\eta \) in Pb + Pb collisions. We obtain \(\alpha \approx 0.09(0.13)\) with (without) meson cloud. The effect of meson cloud on the \(dN_{ch}/d\eta \) is relatively small. For Xe + Xe collisions for 0–5% centrality bin we obtain \(dN_{ch}/d\eta \approx 1149\) and 1134 with and without meson cloud, respectively. We obtain \(\varepsilon _2(\mathrm {Xe})/\varepsilon _2(\mathrm {Pb})\sim 1.45\) for most central collisions, and \(\varepsilon _2(\mathrm {Xe})/\varepsilon _2(\mathrm {Pb})\) close to unity at Open image in new window . We find a noticeable increase of the eccentricity in Xe + Xe collisions at small centralities due to the prolate shape of the Xe nucleus. The triangularity in Xe + Xe collisions is bigger than in Pb + Pb collisions at Open image in new window . We obtain \(\varepsilon _3(\text{ Xe })/\varepsilon _3(\text{ Pb })\sim 1.3\) at Open image in new window .     

Temperature Effect of Hydrogen-Like Impurity on the Ground State Energy of Strong Coupling Polaron in a RbCl Quantum Pseudodot

We study the ground state energy and the mean number of LO phonons of the strong-coupling polaron in a RbCl quantum pseudodot (QPD) with hydrogen-like impurity at the center. The variations of the ground state energy and the mean number of LO phonons with the temperature and the strength of the Coulombic impurity potential are obtained by employing the variational method of Pekar type and the quantum statistical theory (VMPTQST). Our numerical results have displayed that the absolute value of the ground state energy increases (decreases) when the temperature increases at lower (higher) temperature regime, the mean number of the LO phonons increases with increasing temperature, the absolute value of ground state energy and the mean number of LO phonons are increasing functions of the strength of the Coulombic impurity potential.     

Supersymmetric Quantum Mechanics with Lévy Disorder in One Dimension

We consider the Schrödinger equation with a random potential of the form

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where w is a Lévy noise. We focus on the problem of computing the so-called complex Lyapunov exponent

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where N is the integrated density of states of the system, and γ is the Lyapunov exponent. In the case where the Lévy process is non-decreasing, we show that the calculation of Ω reduces to a Stieltjes moment problem, we ascertain the low-energy behaviour of the density of states in some generality, and relate it to the distributional properties of the Lévy process. We review the known solvable cases—where Ω can be expressed in terms of special functions—and discover a new one.

     

The dielectric constant of liquid metals

The dielectric constant of a liquid metal is calculated with the temperature Green's functions technique in the frequency rangeω _P Ω?ξ ₀ andΩ ξ ₀, whereξ ₀ is the resistivity relaxation frequency, andω _P the plasma frequency. The electron scattering is described in the Born approximation using the empirical dynamical structure factor ofVan Hove and a screened electron-ion pseudopotential. At low frequencies (?Ω ?_F=Fermi energy) the result can be identified with Drude's classical formula introducing an effective number of electrons per ion. For?Ω～?_F, however, the result differs in form.     

Ratiometric Detection of Water in Acetonitrile with 9-Hydroxybenzo[<Emphasis Type="Italic">b</Emphasis>]Quinolizinium as Fluorosolvatochromic Probe

The solvatochromic 9-hydroxybenzo[b]quinolizinium ion is shown to operate as fluorescent probe for the detection of water in acetonitrile. The dual fluorescence of this photoacid and its dependence on the content of water in the medium enable the ratiometric analysis of the fluorescence data.

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g-factors of rotational states in 176Hf, 177Hf,and 180Hf

g-factors of rotational states in ¹⁷⁶Hf and ¹⁸⁰Hf were measured with the twelve detector IPAC-apparatus of our laboratory [1]. The natural radioactivity 3.78 · 10¹⁰y ¹⁷⁶Lu and the 5.5 h isomer ^180mHf were used which populate the ground-state rotational bands of ¹⁷⁶Hf and ¹⁸⁰Hf. The integral rotations of γ-γ directional correlations in strong external magnetic fields and in static hyperfine fields of (Lu → Hf)Fe₂ and HfFe₂ were observed. The following results were obtained: The hyperfine field in (Lu → Hf)Fe₂ was calibrated by observing the integral rotation of the 9/2^? first excited state of ¹⁷⁷Hf populated in the decay of 6.7d ¹⁷⁷Lu. The g-factor of this state was redetermined in an external magnetic field as Finally the g-factor of the 2 ₁ ⁺ state of ¹⁷⁶Hf was derived from the measured g(2 ₁ ⁺ ) of ¹⁸⁰Hf by use of the precisely known ratio g(2 ₁ ⁺ , ¹⁷⁶Hf)/g(2₁ ⁺, ¹⁸⁰Hf) [2] as      

Effect of interaction of external surfaces on the symmetry and lattice distortion of CdSe nanocrystals by molecular dynamics simulations

The effect of interaction of low-index atomic planes, (100), (110), and (111) terminating CdSe platelet nanocrystals is examined using molecular dynamics (MD) simulations. Asymmetry of the environment of atoms at the end surface layers leads to anisotropic deformation of the cubic lattice and to a relative shift of Cd and Se sub-lattices. Interference of distortions of the crystal lattice originating at the terminal surfaces leads to changes of symmetry of the CdSe lattice in the whole sample volume. In the models, 2–3 nm thick, for all types of surfaces under examination, the initial cubic lattice symmetry gets lost in the whole sample volume.

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The effects of magnetic field and hydrogen-like impurity on RbCl quantum pseudodot qubit

By using a variational method of Pekar type, we investigate the effects of the hydrogen-like impurity and magnetic field on the electron’s probability density (PD) and oscillating frequency (OF) of a RbCl quantum pseudodot qubit. Numerical results indicate that (1) the PD oscillates periodically; (2) the crest of the PD will decrease with increasing the cyclotron frequencies and the Coulombic impurity potential strength; (3) as the cyclotron frequency of the magnetic field and the strength of the Coulombic impurity potential increases, PD’s peaks will occur more frequently; (4) besides, Figs. 1b and 2b clearly show that in a single period the PD will decrease with increasing the cyclotron frequency and the Coulombic impurity potential strength when \( t > 1.8\;\text{fs} \); whereas the changing law is just the opposite when \( t < 1.8\;\text{fs} \); (5) the OF is an aggrandizing function of the strength of the Coulombic impurity potential, whereas it is a decaying one of the cyclotron frequencies of the magnetic field. The coherence of qubit is crucial to the investigations of quantum information and quantum computation, where the electron’s PD, the OF and the coherence time are the physical quantities representing the properties of coherence. Our research results fine that by changing the cyclotron frequency of the magnetic field and the strength of the Coulombic impurity potential one can adjust the electron’s PD and the OF.

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Fig. 1 The PD \( \text{Q}\left( {r,t} \right) \) versus the time \( t \) and the cyclotron frequency of the magnetic field \( \omega_{c} \) with \( \text{V}_{0} = 10.0\,\text{meV, r}_{0} = 1.0\,\text{nm, }\beta \text{ = 1.0}\,\text{meV} \cdot \text{nm} \) and \( x = y = z = 1.0\,\text{nm} \)

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Fig. 2 The PD \( \text{Q}\left( {r,t} \right) \) versus the time \( t \) and strength of the Coulombic impurity potential \( \beta \) with \( \text{V}_{0} = 10.0\,\text{meV, r}_{0} = 1.0\,\text{nm,} \, \omega_{c} \text{ = 2.0}\, \times \text{10}^{13}\,\text{Hz} \) and \( x = y = z = 1.0\,\text{nm} \)

     

Phase diagrams and cluster expansions for low temperature models

Low temperature phase diagrams of two-dimensional quantum field models are constructed. Let lie in an (r?1)-dimensional space of perturbations of a polynomial withr degenerate minima. Perform a scaling and assume λ«1. We constructk distinct states on \(\left( {\begin{array}{*{20}c} r \\ k \\ \end{array} } \right)\) hypersurfaces of codimensionk?1 in the space of perturbations. An expansion is used to exhibit exponential clustering of the Schwinger functions of each of these states. At the core of the construction is a general technique for finding the thermodynamically stable phases from a collection of competing minima. We draw on ideas of Pirogov and Sinai [24] for this problem.     

Likelihood analysis of the minimal AMSB model

We perform a likelihood analysis of the minimal anomaly-mediated supersymmetry-breaking (mAMSB) model using constraints from cosmology and accelerator experiments. We find that either a wino-like or a Higgsino-like neutralino LSP, \(\tilde{\chi }^0_{1}\), may provide the cold dark matter (DM), both with similar likelihoods. The upper limit on the DM density from Planck and other experiments enforces \(m_{\tilde{\chi }^0_{1}} \lesssim 3 \,\, \mathrm {TeV}\) after the inclusion of Sommerfeld enhancement in its annihilations. If most of the cold DM density is provided by the \(\tilde{\chi }^0_{1}\), the measured value of the Higgs mass favours a limited range of \(\tan \beta \sim 5\) (and also for \(\tan \beta \sim 45\) if \(\mu > 0\)) but the scalar mass \(m_0\) is poorly constrained. In the wino-LSP case, \(m_{3/2}\) is constrained to about \(900\,\, \mathrm {TeV}\) and \(m_{\tilde{\chi }^0_{1}}\) to \(2.9\pm 0.1\,\, \mathrm {TeV}\), whereas in the Higgsino-LSP case \(m_{3/2}\) has just a lower limit \(\gtrsim 650\,\, \mathrm {TeV}\) (\(\gtrsim 480\,\, \mathrm {TeV}\)) and \(m_{\tilde{\chi }^0_{1}}\) is constrained to \(1.12 ~(1.13) \pm 0.02\,\, \mathrm {TeV}\) in the \(\mu >0\) (\(\mu <0\)) scenario. In neither case can the anomalous magnetic moment of the muon, \((g-2)_\mu \), be improved significantly relative to its Standard Model (SM) value, nor do flavour measurements constrain the model significantly, and there are poor prospects for discovering supersymmetric particles at the LHC, though there are some prospects for direct DM detection. On the other hand, if the \(\tilde{\chi }^0_{1}\) contributes only a fraction of the cold DM density, future LHC Open image in new window -based searches for gluinos, squarks and heavier chargino and neutralino states as well as disappearing track searches in the wino-like LSP region will be relevant, and interference effects enable \(\mathrm{BR}(B_{s, d} \rightarrow \mu ^+\mu ^-)\) to agree with the data better than in the SM in the case of wino-like DM with \(\mu > 0\).     

Anti-inflammatory/infection PLA nanoparticles labeled with technetium 99m for in vivo imaging

Despite advancements in treatment of infectious diseases, opportunistic pathogens continue to pose a worldwide threat. Identifying a source of infection/inflammation is often challenging which highlights the need of improved diagnostic agents. Using a model of local S. aureus infection, here we evaluated the potential of betamethasone or dexamethasone loaded in poly (lactic acid) nanoparticles and radiolabeled with 99mTc to detect an infection/inflammation site in vivo. A betamethasone and dexamethasone nanoparticles (NPs) with 200 and 220 nm in size, respectively, were created with a 98% 99mTc radiolabeling efficiency. When injected in infected mice, betamethasone NPs presented a higher accumulation in the infected hind paw in comparison with dexamethasone NPs. Our results suggest that this nanosystem may be a valid nanoradiopharmaceutical for the detection of inflammation/infection foci in vivo.

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Graphical abstract Nanoradiopharmaceutical for inflammation

     

Dual Fluorescence and Solvatochromic Study on 3-Acyl Coumarins

Electronic absorption and emission spectra of 3-acetyl coumarin, 3-(bromoacetyl) coumarin and 3-(di bromoacetyl) coumarin have been recorded at room temperature in thirteen solvents with different polarities. Both ground and excited state dipole moments have been calculated for both locally excited and charge transfer transitions by using the solvatochromic method. Excited state dipole moments of all the three compounds are higher than their ground state values. DFT calculations have been profound to estimate their ground and excited state dipole moments. The estimated change in dipole moment by the application of microscopic solvent polarity parameter and bulk solvent polarity methods are in close agreement. Concentration dependent dual fluorescence has been observed in the emission spectra of all the three compounds.

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Graphical Abstract Dual fluorescence of 3-acetyl coumarin (I) in different solvents.

     

Motions of vortex patches

An evolution equation describing the motion of vortrex patches is established. The existence of steady solutions of this equation is proved. These solutions arem-fold symmetric regions of constant vorticity ω₀ and are uniformly rotating with angular velocity Ω in the range $$\tilde \Omega _{m - 1}< \tilde \Omega \leqslant \tilde \Omega _m (\tilde \Omega = \Omega /\omega _0 ,m \geqslant 2)$$ where \(\tilde \Omega _m = (m - 1)/2m\) . We call this class, ofm-fold symmetric rotating regionsD, the class of them-waves of Kelvin. Any may be regarded as a simply connected region which is a stationary configuration of the Euler equations in two dimensions. If then any magnification, rotation or reflection is also in with the same angular velocity Ω ofD. The angular velocity \(\Omega _m = \tilde \Omega _m \omega _0 \) corresponds only to the circle solution, which is a trivial member of every class ,m?2. The class corresponds to the rotating ellipses of Kirchoff. Other properties of the class are established.     

Green synthesis of fluorescent carbon dots for sensitive detection of Fe<Superscript>2+</Superscript> and hydrogen peroxide

In this paper, the green synthesis of fluorescent carbon dots (CDs) via one-step hydrothermal treatment of cornstalk was investigated. This approach is facile, economical, and effective. The obtained CDs with an average diameter of 5.2 nm possess many excellent properties such as emitting blue fluorescence under UV light (365 nm), high monodispersity, good stability, excellent water dispersibility, and absolute quantum yield of 7.6%. Then, these CDs were used as sensing probes for the detection of Fe²⁺ and H₂O₂ with detection limits as low as 0.18 and 0.21 μM, respectively. This sensing platform shows advantages such as high selectivity, good precision, rapid operation, and avoiding the precipitation of iron oxyhydroxides.

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Effect of the surface on the internal structure of CdSe crystal lattice based on molecular dynamics simulations

The results of molecular dynamics (MD) simulations of CdSe crystals terminated by low-index atomic planes, (100), (110) and (111), are presented. The effect of the crystal termination on the atomic arrangement (interatomic distances) at the surface and underneath the surface is examined. It is shown that the crystal lattice is distorted in lateral and normal directions to the depth of up to about 2 nm from the surface. The exact characteristic of the changes of interatomic distances is specific to the type of the atomic plane terminating the crystal lattice. At some surfaces, the very last monoatomic layer loses the long-range ordering and becomes quasi amorphous. The atoms group into randomly distributed pairs or short linear groups.

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On the Exact Evaluation of the Face-Centred Cubic Lattice Green Function

The mathematical properties of the lattice Green function

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are investigated, where w=w ₁+iw ₂ lies in a complex plane which is cut from w=?1 to w=3, and {? ₁,? ₂,? ₃} is a set of integers with ? ₁+? ₂+? ₃ equal to an even integer. In particular, it is proved that G(2n,0,0;w), where n=0,1,2,…, is a solution of a fourth-order linear differential equation of the Fuchsian type with four regular singular points at w=?1,0,3 and ∞. It is also shown that G(2n,0,0;w) satisfies a five-term recurrence relation with respect to the integer variable n. The limiting function

$G^{-}(2n,0,0;w_1)\equiv\lim_{\epsilon\rightarrow0+}G(2n,0,0;w_1-\mathrm{i}\epsilon) =G_{\mathrm{R}}(2n,0,0;w_1)+\mathrm{i}G_{\mathrm {I}}(2n,0,0;w_1) ,\nonumber $

where w ₁∈(?1,3), is evaluated exactly in terms of ₂ F ₁ hypergeometric functions and the special cases G ^?(2n,0,0;0), G ^?(2n,0,0;1) and G(2n,0,0;3) are analysed using singular value theory. More generally, it is demonstrated that G(? ₁,? ₂,? ₃;w) can be written in the form

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where Open image in new window are rational functions of the variable ξ, K(k _?) and E(k _?) are complete elliptic integrals of the first and second kind, respectively, with

$k_{-}^2\equiv k_{-}^2(w)={1\over2}- {2\over w} \biggl(1+{1\over w} \biggr)^{-{3\over2}}- {1\over2} \biggl(1-{1\over w} \biggr ) \biggl(1+{1\over w} \biggr)^{-{3\over2}} \biggl(1-{3\over w} \biggr)^{1\over2}\nonumber $

and the parameter ξ is defined as

$\xi\equiv\xi(w)= \biggl(1+\sqrt{1-{3\over w}} \,\biggr)^{-1} \biggl(-1+\sqrt{1+{1\over w}} \,\biggr) .\nonumber $

This result is valid for all values of w which lie in the cut plane. The asymptotic behaviour of G ^?(2n,0,0;w ₁) and G(2n,0,0;w ₁) as n→∞ is also determined. In the final section of the paper a new ₂ F ₁ product form for the anisotropic face-centred cubic lattice Green function is given.

     

PAC study of O-H and O-D in Ta

A PAC experiment was performed on a¹⁸¹HfTa sample which contained ～ 0. 1 at. oxygen and ～1 at. hydrogen. At low temperature a new quadrupole interaction withν _Q=470 MHz, η=0.95 was found. This interaction is attributed to an O-H complex. At 55 K this interaction disappears and the well known oxygen frequency shows up, indicating a breakup of the O-H pair at 55 K. With deuterium instead of hydrogen the same frequency but a different (105 K) breakup temperature was found.     

Selective debenzylation of 1-benzyloxy-4-methoxy benzene over 5-sulfosalicylic acid-functionalized ordered mesoporous silica (SBA-15/SFSA) catalyst

5-Sulfosalicylic acid (SFSA) functionalized mesoporous silica nanocomposites (SBA/APTS/SFSA) were synthesized by post grafting technique for selective debenzylation of 1-benzyloxy-4-methoxy benzene. The uniform incorporation of SFSA inside the mesoporous SBA-15 framework was confirmed by standard characterization techniques (PXRD, adsorption studies, FT-IR, etc.). Total surface area, pore size and pore volume of the SBA/APTS/SFSA catalysts decreased with increase in the concentration of SFSA confirming the uniform insertion of SFSA into mesoporous SBA-15 matrix. Catalytic activity studies showed highest conversion and selectivity of the desired product on SBA/APTS/SFSA catalyst compared to homogeneous SFSA and other solid support (Al₂O₃ and SiO₂). All the reaction parameters such as reaction time, reaction temperature and catalyst weight were optimized under environmental friendly conditions. Finally, the possible mechanism of the reaction was explained.

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