Limit cycles in a forced Lorenz system

We consider a Lorenz system where the control parameter is sinusoidally modulated. Limit cycles appear where previously there were strange attractors. Perturbation theory is used to estimate the critical amplitude of the modulation for which limit cycles appear.     

Nature of Nonlocality in Triangle Network based on Elegant Joint Measurement

Defining nonlocality in a no-input closed quantum network scenario is a new area of interest nowadays. Gisin, in [Entropy 21, 325 (2019)], proposed a possible condition for non-tri-locality of the trivial no-input closed network scenario, triangle network, by introducing a new kind of joint measurement bases and a probability bound. In [npj Quantum Information (2020) 6:70] they found a shred of numerical evidence in support of Gisin's probability bound. Now based on that probability bound, it finds the nature of the correlation in a triangle network scenario. This study observes how far the probability lies from that Gisin's bound with every possible combination of entangled and local pure states distributed from three independent quantum sources. Here, it uses the generalized Elegant Joint Measurements bases for each party and find that there is a dependency of non-locality on the entanglement of these joint measurement bases. It also checks the probability bound for the polygon structure.     

Rational Landen transformations on

The Landen transformation preserves the value of an elliptic integral, and its iteration produces the classical arithmetic-geometric mean AGM. We present analogous transformations for rational functions integrated over the whole real line.

     

Thermal analysis of a drug-polymeric excipient solid system

Differential scanning calorimetry has been applied to the study of the solid system cross-linked polyvinylpyrrolidone/trimethoprim.Different results have been systematically obtained on co-ground and not co-ground mixtures, suggesting some type of interaction to take place between components as a consequence of co-grinding.A simple phenomenological model of the interaction is proposed, which quite satisfactorily agrees with thermal data.

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Zusammenfassung Das feste System von vernetztem Polyvinyl-pyrolidin/Trimethoprim wurde mittels DSC untersucht. Unterschiedliche Ergebnisse wurden systematisch für zusammen und nicht zusammen verriebene Mischungen gefunden, was auf eine Wechselwirkung zwischen Komponenten beim Verreiben hindeutet. Ein einfaches phänomenologisches Modell dieser Wechselwirkung wird vorgeschlagen, das mit thermischen Daten befriedigend übereinstimmt.

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This work has been partially supported by Ministero Pubblica Istruzione (Fondi 60%).     

Synthesis,Crystal Structure,Spectral and Thermal Studies of (<Emphasis Type="Italic">E</Emphasis>)-4-Dimethamino[(1-phenylethyl)iminomethyl]benzyne

Abstract  

Schiff-base compound (E)-4-dimethamino[(1-phenylethyl)iminomethyl]benzyne was synthesized and characterized by elemental analyses (CHN), FT-IR and ¹H-NMR spectroscopic techniques and thermogravimetric analyses (TG). Crystal structure of the title compound was obtained by single crystal X-ray diffraction. The title compound crystallizes in the monoclinic space group P2₁ with unit cell parameters: a = 8.5283(2), b = 6.0699(2), c = 13.6997(4) Ǻ, β = 91.471(2)°, V = 708.94(4) Ǻ³ and Z = 2.     

Hájek-Inagaki convolution representation theorem for randomly stopped locally asymptotically mixed normal experiments

Under suitable regularity conditions imposed on a general discrete time-parameter stochastic process, the Hájek-Inagaki convolution representation theorem is established for randomly stopped locally asymptotically mixed normal experiments. D. Bhattacharya: On leave from Visva-Bharati University, Santiniketan, India.     

The Development of Bulky Palladium NHC Complexes for the Most-Challenging Cross-Coupling Reactions

Palladium‐catalyzed cross‐coupling reactions enable organic chemists to form C? C bonds in targeted positions and under mild conditions. Although phosphine ligands have been intensively researched, in the search for even better cross‐coupling catalysts attention has recently turned to the use of N‐heterocyclic carbene (NHC) ligands, which form a strong bond to the palladium center. PEPPSI (pyridine‐enhanced precatalyst preparation, stabilization, and initiation) palladium precatalysts with bulky NHC ligands have established themselves as successful alternatives to palladium phosphine complexes. This Review shows the success of these species in Suzuki–Miyaura, Negishi, and Stille–Migita cross‐couplings as well as in amination and sulfination reactions.     

Cd(ii)-triggered excimer-monomer conversion of a pyrene derivative: time dependent red-shift of monomer emission with cell staining application

An efficient fluorescent probe (E)-N1-((E)-2-((pyren-7-yl)methyleneamino)ethyl)-N2-((pyren-7-yl)methylene)ethane-1,2-diamine (L) has been synthesized by a facile one-step condensation reaction. L can selectively detect Cd(2+) in presence of other common metal ions in 0.1 M HEPES buffered DMSO-water (4?:?1, v/v) medium. The detection limit of Cd(2+) is 1.8 × 10(-8) M. Cd(2+) can effectively convert the excimer emission of L into its monomer emission which in turn exhibits a time-dependent red-shift.     

About the fastest growth of the Order Parameter in models of percolation

The growth of the average size 〈_smax〉$〈s_{max}〉$ of the largest component at the percolation threshold _pc(N)$p_c\left(N\right)$ on a graph of size N$N$ has been defined as 〈_smax(_pc(N),N)〉∼N^χ$〈s_{max}(p_c\left(N\right),N)〉\sim N^{\chi }$. Here we argue that the precise value of the ‘growth exponent’ χ$\chi$ indicates the nature of percolation transition; χ<1$\chi <1$ or χ=1$\chi =1$ determines if the transition is continuous or discontinuous. We show that a related exponent η=1−χ$\eta =1-\chi$ which describes how the average maximal jump sizes in the Order Parameter decays on increasing the system size, is the single exponent that describes the finite-size scaling of a number of distributions related to the fastest growth of the Order Parameter in these problems. Excellent quality scaling analysis are presented for the two single peak distributions corresponding to the Order Parameters at the two ends of the maximal jump, the bimodal distribution constructed by the weighted average of these distributions and for the distribution of the maximal jump in the Order Parameter.