On generalized Leibniz triangles and q-Gaussians

Generalized Leibniz triangles have been used in nonextensive statistical mechanics as theoretical models that yield q  -Gaussians (q<1$q<1$) as attractors. We study such triangles from a probability point of view. Our results show that one can get any distribution on [0,1]$[0,1]$ (or any distribution that has a compact support, after a linear transform) from such triangles, including q  -Gaussians with q<1$q<1$. Next we propose conceptual models that are triangular arrays of row-wise exchangeable random variables and yield q  -Gaussians for q<1$q<1$ and q?1$q?1$ as attractors, via laws of large numbers and central limit theorems, respectively.     

π‐Aryl/heteroaryl conjugated coumarin‐thiazoles: Synthesis,optical spectral and nonlinear optic properties

A series of π‐aryl/heteroaryl conjugated coumarin‐thiazole systems 8a‐f has been synthesized by using Hantzsch thiazole protocol and Wittig olefination as the keys. In the UV‐Visible spectra of 8a‐f , a main absorption band associated with a dominant π‐π* transition is observed in the region of 338 to 390 nm. Qualitatively, the values of λ_max have been found to correlate satisfactory with the donor/acceptor characteristics of the π‐attached chromophores. Marked changes observed in the absorption maxima of 8a under acidic conditions are rationalized on the basis of mono‐or bis‐protonation and modification of the donor/acceptor properties of chromophores undergoing protonation. The emission spectra of 8a‐f , obtained by exciting the molecules at their main absorption bands showed emission maxima in the region of 429 nm to 537 nm, with relatively high Stokes shifts of 145 and 171 nm being observed for 8a and 8e , carrying a π‐donor, dimethylaminophenyl and a π‐acceptor, p‐nitrophenyl chromophore, respectively. Although, the first hyperpolarisability β, measured by the hyper‐Reileigh scattering (HRS) technique are modest (12 to 23 × 10^?30 esu), all the compounds exhibited complete transparency in the frequency doubling region at 532 nm and showed high thermal stability (T_d from 330 to 365 °C).     

New PCT probes featuring N-phenylmonoaza-18-crown-6 and aryl/pyridyl oxadiazoles: optical spectral studies of solvent effects and selected metal ions

Aryl/pyridyl oxadiazole chromophores 6, 8 and 10, carrying N-phenyl aza-18-crown-6 have been synthesized as new photo-induced charge transfer (PCT) probes. While, the absorption spectra of the hosts experienced a slight negative solvatochromism, however the emission bands were dramatically red shifted (Stokes shifts up to 178 nm) in solvents of increasing polarity. Among the metal ions tested, Li⁺, Na⁺, K⁺ and Mg²⁺ did not appreciably perturbed the optical properties of the hosts. On the other hand, Ba²⁺ and to a lesser extent Ca²⁺ induced marked blue shifts in both the absorption and emission spectra of the hosts. The magnitude of cation induced spectral blue shifts corresponded with the increasing acceptor strength of the attached aryl/pyridyl groups in the host molecules. The blue shifts and the stability constants were found to follow the order Ba²⁺ > Ca²⁺ ? Mg²⁺ > Na⁺ > Li⁺ > K⁺. Competitive experiments performed with a matrix of ions also revealed superior binding affinity of Ba²⁺ with all the hosts examined. Noteworthily, the deep yellow solution (λ_max, 386 nm) of the host 10 was completely bleached (λ_max, 320 nm), in the company of Ba²⁺ thereby allowing the naked eye detection of this ion.     

Optically transparent and thermally stable nonlinear optic chromophores featuring a thieno[2,3-b]thiophene donor

A thieno[2,3-b]thiophene core has been utilized as a π-donor component to design two series of push-pull thienothiophenes by introducing various acceptor groups either via olefinic or aza-spacers. The molecules show a UV-visible cut-off wavelength below the second harmonic generation (SHG) at λ/2 of 532 nm, thereby conforming to the nonlinearity-transparency trade-off. Second order molecular nonlinearity, β measured by Hyper-Rayleigh scattering technique was found in the range of 9.58-47.66×10⁻³⁰ esu, while the Kurtz powder technique produced signals of the order of 0.43-1.02 U. Thermal decomposition temperatures measured by differential scanning calorimetry revealed decomposition temperatures≥275 °C, indicating high thermal stability.     

Dipyridyl/pyridinium thieno[2,3-b]thiophenes as new atropisomeric systems. Synthesis, conformational analysis and energy minimization

Synthesis of a new class of cofacially oriented dipyridyl(pyridinium)lthieno[2,3-b]thiophenes with or without -CO₂Et and -COMe substituents at C2, and C5 positions of thieno[2,3-b]thiophene ring was readily accomplished using a double Dieckman cyclization protocol as the key step. While C2/C5 substituted dipyridylthieno[2,3-b]thiophenes exhibited syn/anti atropisomerism at least up to 70 °C with Arrhenius energy of activation (ΔG^≠) in the range of 17-18 kcal/mol, on the other hand unsubstituted dipyridylthieno[2,3-b]thiophene and its bis-N-quaternized salt were found to show free conformational rotation with an estimated ΔG^≠ of lower than 10 kcal/mol. Conformational energy minimization using AM1 protocol revealed a slight preference for the anti over syn isomers. Compared to the unsubstituted dipyridylthieno[2,3-b]thiophenes, higher energy barriers to rotation (3.7-5.1 kcal/mol) in substituted dipyridylthieno[2,3-b]thiophenes can be attributed to steric encumbrance resulting from -CO₂Et and -COMe substituents located on the non-rotating thienothiophene platform.     

Nonlinear statistical coupling

By considering a nonlinear combination of the probabilities of a system, a physical interpretation of Tsallis statistics as representing the nonlinear coupling or decoupling of statistical states is proposed. The escort probability is interpreted as the coupled probability, with Q=1−q defined as the degree of nonlinear coupling between the statistical states. Positive values of Q have coupled statistical states, a larger entropy metric, and a maximum coupled-entropy distribution of compact-support coupled-Gaussians. Negative values of Q have decoupled statistical states and for −2<Q<0 a maximum coupled-entropy distribution of heavy-tail coupled-Gaussians. The conjugate transformation between the heavy-tail and compact-support domains is shown to be for coupled-Gaussian distributions. This conjugate relationship has been used to extend the generalized Fourier transform to the compact-support domain and to define a scale-invariant correlation structure with heavy-tail limit distribution. In the present paper, we show that the conjugate is a mapping between the source of nonlinearity in non-stationary stochastic processes and the nonlinear coupling which defines the coupled-Gaussian limit distribution. The effects of additive and multiplicative noise are shown to be separable into the coupled-variance and the coupling parameter Q, providing further evidence of the importance of the generalized moments.     

A Novel Scheme for Quantum Teleportation of N-Particle Generalized Bell-Type States Using Minimal Entanglement Resources

In this paper, we present an efficient scheme for the teleportation of an arbitrary N-particle generalized Bell-type state using a single Bell pair as entanglement channel. For odd and even N-particle states the scheme slightly differs and it is discussed in detail for the simplest cases, 3 and 4 particle states. Further, we have compared the quantum cost of our scheme with other teleportation schemes which use a single Bell pair as entanglement channel.

     

Cubic Auto-Catalysis Reactions in Three-Dimensional Nanofluid Flow Considering Viscous and Joule Dissipations Under Thermal Jump

In this problem, simultaneous effects of Joule and viscous dissipationin three-dimensional flow of nanoliquid have been addressed in slip flow regime under timedependent rotational oscillations. Silver nanoparticles are submerged in the base fluid (water)due to their chemical and biological features. To increment the novelty, effects of cubicautocatalysis chemical reactions and radiative heat transfer have been incorporated in therelated boundary layer equations. Dimensionless partial differential system is solved byemploying the proposed implicit finite difference approach. Convergence conditions andstability criteria are obtained to ensure the convergence and accuracy of solutions.A comparative analysis is proposed for no-slip nanofluid flow (NSNF) and slip nanofluid flow(SNF). Variations in skin-friction coefficients, Sherwood and Nusselt numbers against physicalparameters are tabulated. It is investigated that velocity slip and temperature jump significantlycontrol drag forces and rate of heat transfer.     

On Hardy Inequality in Variable Lebesgue Spaces with Mixed Norm

In this paper a two-weight boundedness of multidimensional Hardy operator and its dual operator acting from one weighted variable Lebesgue spaces with mixed norm into other weighted variable Lebesgue spaces with mixed norm spaces is proved. In particular, a new type two-weight criterion for multidimensional Hardy operator is obtained.