Stochastic resonance with different periodic forces in overdamped two coupled anharmonic oscillators

We study the stochastic resonance phenomenon in the overdamped two coupled anharmonic oscillators with Gaussian noise and driven by different external periodic forces. We consider (i) sine, (ii) square, (iii) symmetric saw-tooth, (iv) asymmetric saw-tooth, (v) modulus of sine and (vi) rectified sinusoidal forces. The external periodic forces and Gaussian noise term are added to one of the two state variables of the system. The effect of each force is studied separately. In the absence of noise term, when the amplitude $f$ of the applied periodic force is varied cross-well motion is realized above a critical value ($f_{\mathrm{c}}$) of $f$. This is found for all the forces except the modulus of sine and rectified sinusoidal forces.Stochastic resonance is observed in the presence of noise and periodic forces. The effect of different forces is compared. The logarithmic plot of mean residence time $\tau_{\mathrm{MR}}$ against $1/(D - D_{\mathrm{c}})$ where $D$ is the intensity of the noise and $D_{\mathrm{c}}$ is the value of $D$ at which cross-well motion is initiated shows a sharp knee-like structure for all the forces. Signal-to-noise ratio is found to be maximum at the noise intensity $D=D_{\mathrm{max}}$ at which mean residence time is half of the period of the driving force for the forces such as sine, square, symmetric saw-tooth and asymmetric saw-tooth waves. With modulus of sine wave and rectified sine wave, the $SNR$ peaks at a value of $D$ for which sum of $\tau_{MR}$ in two wells of the potential of the system is half of the period of the driving force. For the chosen values of $f$ and $\omega$, signal-to-noise ratio is found to be maximum for square wave while it is minimum for modulus of sine and rectified sinusoidal waves.Comment: 13 figures,27 page

Simultano UV-spektrofotometrijsko određivanje ramiprila, acetilsalicilne kiseline i atorvastatin kalcija u kapsulama primjenom kemometrijskih metoda

In the present work, three different spectrophotometric methods for simultaneous estimation of ramipril, aspirin and atorvastatin calcium in raw materials and in formulations are described. Overlapped data was quantitatively resolved by using chemometric methods, viz. inverse least squares (ILS), principal component regression (PCR) and partial least squares (PLS). Calibrations were constructed using the absorption data matrix corresponding to the concentration data matrix. The linearity range was found to be 1-5, 10-50 and 2-10 µg mL–1 for ramipril, aspirin and atorvastatin calcium, respectively. The absorbance matrix was obtained by measuring the zero-order absorbance in the wavelength range between 210 and 320 nm. A training set design of the concentration data corresponding to the ramipril, aspirin and atorvastatin calcium mixtures was organized statistically to maximize the information content from the spectra and to minimize the error of multivariate calibrations. By applying the respective algorithms for PLS 1, PCR and ILS to the measured spectra of the calibration set, a suitable model was obtained. This model was selected on the basis of RMSECV and RMSEP values. The same was applied to the prediction set and capsule formulation. Mean recoveries of the commercial formulation set together with other figures of merit (calibration sensitivity, selectivity, limit of detection, limit of quantification and analytical sensitivity) were estimated. Validity of the proposed approaches was successfully assessed for analyses of drugs in the various prepared physical mixtures and formulations.U radu su opisane tri različite spektrofotometrijske metode za određivanje ramiprila, acetilsalicilne kiseline i atorvastatin kalcija u sirovinama i formulacijama. Preklapanje podataka kvantitativno je riješeno pomoću kemometrijskih metoda, tj. metodama inverznih najmanjih kvadrata (ILS), regresije glavnog sastojka (PCR) i djelomičnih najmanjih kvadrata (PLS). Kalibracije su postavljene pomoću matrice podataka za apsorpciju koja odgovara matrici pripadajućih koncentracija. Područje linearnosti za ramipril iznosilo je 1–5, za acetilsalicilnu kiselinu 10–50, a za atorvastatin kalcij 2–10 µg mL–1. Matrica s apsorbancijama dobivena je mjerenjem apsorbancije nultog reda na valnim duljinama između 210 i 320 nm. Set podataka za koncentracije ramiprila, acetilsalicilne kiseline i atorvastatin kalcija u smjesi statistički je tako organiziran da osigura maksimalnu količinu informacije u spektrima i minimalizira grešku multivarijantnih kalibracija. Primjenom odgovarajućih algoritama za PLS, PCR i ILS na snimljene spektre kalibracijskog seta dobiven je dobar model, koji je odabran na temelju RMSECV i RMSEP vrijednosti. Isti model je primijenjen i na set s predviđenim vrijednostima i na kapsule sa smjesom ove tri ljekovite tvari. Određena je srednja vrijednost povrata za komercijalnu formulaciju te ostale analitičke izvedbene značajke (kalibracijska osjetljivost, selektivnost, granica dokazivanja, granica određivanja i analitička osjetljivost). Potvrđena je primjenjljivost predloženih metoda u analizama lijekova u fizičkim smjesama i u gotovim ljekovitim oblicima