The coherent state and anharmonic oscillator description of nonlinear oscillation

A perturbation solution of the nonlinear oscillation of the form $$\ddot x + \omega ^2 x + bx^2 + ax^3 = 0$$ is obtained, using the coherent states constructed out of quantum oscillator states. The equation of the spine obtained here is compared with that obtained by using an averaging procedure. It is found that the equation obtained in the present case is simpler and different from the other. Also the method used here has the distinct advantage that it is suitable for any nonlinear oscillator containing both even and odd higher order terms.     

Computing roadmaps of semi-algebraic sets on a variety

We consider a semi-algebraic set defined by polynomials in variables which is contained in an algebraic variety . The variety is assumed to have real dimension the polynomial and the polynomials defining have degree at most . We present an algorithm which constructs a roadmap on . The complexity of this algorithm is . We also present an algorithm which, given a point of defined by polynomials of degree at most , constructs a path joining this point to the roadmap. The complexity of this algorithm is These algorithms easily yield an algorithm which, given two points of defined by polynomials of degree at most , decides whether or not these two points of lie in the same semi-algebraically connected component of and if they do computes a semi-algebraic path in connecting the two points.

     

Fluorogenic Probe Using a Mislow–Evans Rearrangement for Real‐Time Imaging of Hydrogen Peroxide

Hydrogen peroxide (H₂O₂) mediates the biology of wound healing, apoptosis, inflammation, etc. H₂O₂ has been fluorometrically imaged with protein‐ or small‐molecule‐based probes. However, only protein‐based probes have afforded temporal insights within seconds. Small‐molecule‐based electrophilic probes for H₂O₂ require many minutes for a sufficient response in biological systems. Here, we report a fluorogenic probe that selectively undergoes a [2,3]‐sigmatropic rearrangement (seleno‐Mislow‐Evans rearrangement) with H₂O₂, followed by acetal hydrolysis, to produce a green fluorescent molecule in seconds. Unlike other electrophilic probes, the current probe acts as a nucleophile. The fast kinetics enabled real‐time imaging of H₂O₂ produced in endothelial cells in 8 seconds (much earlier than previously shown) and H₂O₂ in a zebrafish wound healing model. This work may provide a platform for endogenous H₂O₂ detection in real time with chemical probes.     

Gold Metallodrugs to Target Coronavirus Proteins: Inhibitory Effects on the Spike-ACE2 Interaction and on PLpro Protease Activity by Auranofin and Gold Organometallics**

Gold complexes have a long tradition in medicine and for many examples antirheumatic, anticancer or anti-infective effects have been confirmed. Herein, we evaluated the lead compound Auranofin and five selected gold organometallics as inhibitors of two relevant drug targets of severe acute respiratory syndrome coronaviruses (SARS-CoV). The gold metallodrugs were effective inhibitors of the interaction of the SARS-CoV-2 spike protein with the angiotensin converting enzyme 2 (ACE2) host receptor and might thus interfere with the viral entry process. The gold metallodrugs were also efficient inhibitors of the papain-like protease (PLpro) of SARS-CoV-1 and SARS-CoV-2, which is a key enzyme in the viral replication. Regarding PLpro from SARS-CoV-2, the here reported inhibitors are among the very first experimentally confirmed examples with activity against this target enzyme. Importantly, the activity of the complexes against both PLpro enzymes correlated with the ability of the inhibitors to remove zinc ions from the labile zinc center of the enzyme. Taken together, the results of this pilot study suggest further evaluation of gold complexes as SARS-CoV antiviral drugs.     

Fluorescence Turn on Sensor for Sulfate Ion in Aqueous Medium Using Tripodal-Cu2+ Ensemble

We report the selective recognition of sulfate anion in aqueous medium at biological pH 7.2 over the other interfering anions based on naphthoic acid bearing tripodal ligand by applying fluorescence turn off-on mechanism. The carboxylic acid groups in the ligand enhance the solubility in water and enable it to form complex with copper salt. Thus formed L-Cu²⁺ ensemble quench the fluorescence of the parent ligand and in turn recognize sulfate anion via revival of fluorescence intensity. The 1:2 stoichiometry was confirmed by ESI mass spectral data and Job’s plot. The average binding constant was found to be 6.2?×?10⁸ M^?2.

Zero-sum risk-sensitive stochastic games on a countable state space

Infinite horizon discounted-cost and ergodic-cost risk-sensitive zero-sum stochastic games for controlled Markov chains with countably many states are analyzed. Upper and lower values for these games are established. The existence of value and saddle-point equilibria in the class of Markov strategies is proved for the discounted-cost game. The existence of value and saddle-point equilibria in the class of stationary strategies is proved under the uniform ergodicity condition for the ergodic-cost game. The value of the ergodic-cost game happens to be the product of the inverse of the risk-sensitivity factor and the logarithm of the common Perron–Frobenius eigenvalue of the associated controlled nonlinear kernels.     

Conductivity and dielectric relaxation of gelatin films with glycerol as plasticizer

Gelatin films complexed with ionic salts are of current interest as potential solid polymer electrolytes. However, even without salt, gelatin films are found to have quite high ionic conductivity at room temperature (around 30 °C), when plasticized with an adequate fraction of glycerol. In the present work, the admittance and dielectric properties of gelatin are studied as a function of glycerol content and temperature. An enhancement in the ionic conductivity by four orders of magnitude to ～9.13?×?10^?3 S/m at room temperature is obtained by adding 35.71 wt% of glycerol. This enhancement appears to be correlated with the changes in the local microstructure on plasticizer addition. Admittance and dielectric relaxation have been studied to understand the dynamics of the charge carriers. Differential scanning calorimetry, X-ray diffraction and scanning electron microscopy are also done.     

On the relative strength of split,triangle and quadrilateral cuts

Integer programs defined by two equations with two free integer variables and nonnegative continuous variables have three types of nontrivial facets: split, triangle or quadrilateral inequalities. In this paper, we compare the strength of these three families of inequalities. In particular we study how well each family approximates the integer hull. We show that, in a well defined sense, triangle inequalities provide a good approximation of the integer hull. The same statement holds for quadrilateral inequalities. On the other hand, the approximation produced by split inequalities may be arbitrarily bad.     

Influence of heterogeneity of confined water on photophysical behavior of acridine with amines: a time-resolved fluorescence and laser flash photolysis study

The photophysical behavior of acridine (Acr) shows facilitated water-assisted protonation equilibrium between its deprotonted (Acr* ～ 10 ns) and protonated forms (AcrH(+*) ～ 28 ns) within confined region of ordered water molecules inside AOT/H(2)O/n-heptane reverse micelles (RMs). The time-resolved-area-normalized-emission spectra confirm both Acr* and AcrH(+*), while time-resolved-emission spectra depict time evolution between them. Quenching of AcrH(+*) with N,N-dimethylaniline (DMA) is a purely diffusion-controlled bimolecular quenching with linear Stern-Volmer (S-V) plot, while nonlinearity arises with triethylamine (TEA) that forms ground state complex with AcrH(+) (AcrH(+)··H(2)O··TEA) indicating both static and dynamic quenching. Transient intermediates, DMA(?+) and AcrH(?) infer photoinduced electron transfer from DMA to Acr, while those from AcrH(+)··H(2)O··TEA complex suggest water mediated excited-state proton transfer (ESPT) between AcrH(+) and TEA. The ESPT becomes faster in larger RMs due to enhanced mobility of hydronium ions in AcrH(+)··H(2)O··TEA, which reduces in smaller RMs as water becomes much more constrained owing to stronger complexation by excess confinement.