scholarly journals Erratum: Determination of Third‐Order Elastic Coefficients in Crystals

1965 ◽  
Vol 36 (10) ◽  
pp. 3364-3364
Author(s):  
K. Brugger
Keyword(s):  
Third Order ◽  
Elastic Coefficients

A multitechnique investigation of the second order NLO response of a 10,20-diphenylporphyrinato nickel(II) complex carrying a phenylethynyl based push-pull system in the 5- and 15-positions

2004 ◽  
Vol 08 (11) ◽  
pp. 1311-1324 ◽  
Author(s):  
Maddalena Pizzotti ◽  
Elisabetta Annoni ◽  
Renato Ugo ◽  
Silvia Bruni ◽  
Silvio Quici ◽  
...  
Keyword(s):  
Ab Initio ◽  
Planar Structure ◽  
Third Order ◽  
Incident Wavelength ◽  
Pull System ◽  
Nlo Response ◽  
Self Consistent ◽  
Order Of Magnitude ◽  
Zero Frequency

A multitechnique investigation of the determination of the order of magnitude of the second and third order NLO response of [5-[(4-dimethylaminophenyl)ethynyl]-15-[(4-nitrophenyl)ethynyl]-10,20-diphenylporphyrinato]nickel(II) (1) is reported with the aim to produce self consistent evidence for a significant NLO response of this kind of push-pull porphyrin chromophore. The experimental multitechnique approach is based on the EFISH technique, working with a non-resonant incident wavelength of 1.907 μm, on the solvatochromic method and finally on a vibrational method, avoiding any fluorescence or resonance interference. A theoretical MNDO-TDHF evaluation of the zero-frequency quadratic and cubic hyperpolarizabilities of an ab initio optimized planar structure is also reported. The order of magnitude of the quadratic hyperpolarizability of (1) at zero frequency (β0), was found to be significantly lower than that reported for the corresponding Cu (II) or Zn (II) complexes with the same push-pull porphyrin chromophore.

scholarly journals DETERMINATION OF THE ENERGY GAP OF C60 MOLECULE USING THIRD-ORDER DERIVATIVE ABSORPTION SPECTROSCOPY

1998 ◽  
Vol 47 (2) ◽  
pp. 208
Author(s):  
ZHAO MING-SHAN ◽  
DAI ZUO-XIAO ◽  
LI YI ◽  
LI GUO-HUA ◽  
BU YU-XIANG ◽  
...  
Keyword(s):  
Absorption Spectroscopy ◽  
Energy Gap ◽  
Order Derivative ◽  
Third Order

Third-Order Elastic Coefficients of Crystals

1951 ◽  
Vol 83 (6) ◽  
pp. 1274-1275 ◽  
Author(s):  
Fausto G. Fumi
Keyword(s):  
Third Order ◽  
Elastic Coefficients

The Elastic Coefficients of the Theory of Consolidation

1957 ◽  
Vol 24 (4) ◽  
pp. 594-601
Author(s):  
M. A. Biot ◽  
D. G. Willis
Keyword(s):  
Nonlinear Systems ◽  
Shear Modulus ◽  
Physical Interpretation ◽  
Compressible Fluid ◽  
Elastic Solid ◽  
Fluid Content ◽  
Alternate Forms ◽  
Elastic Coefficients ◽  
Methods Of Measurement

Abstract The theory of the deformation of a porous elastic solid containing a compressible fluid has been established by Biot. In this paper, methods of measurement are described for the determination of the elastic coefficients of the theory. The physical interpretation of the coefficients in various alternate forms is also discussed. Any combination of measurements which is sufficient to fix the properties of the system may be used to determine the coefficients. For an isotropic system, in which there are four coefficients, the four measurements of shear modulus, jacketed and unjacketed compressibility, and coefficient of fluid content, together with a measurement of porosity appear to be the most convenient. The porosity is not required if the variables and coefficients are expressed in the proper way. The coefficient of fluid content is a measure of the volume of fluid entering the pores of a solid sample during an unjacketed compressibility test. The stress-strain relations may be expressed in terms of the stresses and strains produced during the various measurements, to give four expressions relating the measured coefficients to the original coefficients of the consolidation theory. The same method is easily extended to cases of anisotropy. The theory is directly applicable to linear systems but also may be applied to incremental variations in nonlinear systems provided the stresses are defined properly.

scholarly journals A NEW VALIDATED THIRD ORDER DERIVATIVE SPECTROSCOPIC METHOD FOR SIMULTANEOUS ESTIMATION OF METOPROLOL SUCCINATE AND RAMIPRIL IN TABLET DOSAGE FORM

2020 ◽  
pp. 54-59
Author(s):  
ALEKHYA B. ◽  
M. SINDHUSHA ◽  
SORAJ K. RAUL ◽  
GOPAL K. PADHY
Keyword(s):  
Quantitative Analysis ◽  
Dosage Form ◽  
Spectroscopic Method ◽  
Simultaneous Estimation ◽  
Third Order ◽  
Metoprolol Succinate ◽  
Zero Crossing ◽  
Ich Guidelines ◽  
Tablet Dosage

Objective: The objective of the present work is to develop and validate a new UV derivative spectrophotometric method for simultaneous estimation of metoprolol succinate and ramipril in methanol: water (50:50v/v). Methods: “Zero crossing technique” was chosen for quantitative determination. The zero-crossing points (ZCP’s) were found to be 209 nm where metoprolol succinate was quantified and 211 nm where ramipril was quantified. This method was then subjected to accuracy, linearity, sensitivity and reproducibility according to ICH guidelines to ensure and confirm its validity. Results: The method was found to be obeying Beer’s law in the range of 10-50 µg/ml and 5-25 µg/ml for metoprolol succinate and ramipril, respectively. The % recoveries were observed between the range of 99.2-100.2 for metoprolol succinate and 99.57-99.86 for ramipril. The intra-day and inter-day results showed reproducibility. Conclusion: It can be concluded that the developed third-order UV derivative spectroscopic method for the simultaneous determination of metoprolol succinate and ramiprilcan be recommended for routine quantitative analysis.

Determination of Nonchaotic Behavior for Some Classes of Polynomial Jerk Equations

2020 ◽  
Vol 30 (08) ◽  
pp. 2050117
Author(s):  
Marcelo Messias ◽  
Rafael Paulino Silva
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Simple Form ◽  
Chaotic Dynamics ◽  
Third Order ◽  
Algebraic Criterion

In this work, by using an algebraic criterion presented by us in an earlier paper, we determine the conditions on the parameters in order to guarantee the nonchaotic behavior for some classes of nonlinear third-order ordinary differential equations of the form [Formula: see text] called jerk equations, where [Formula: see text] is a polynomial of degree [Formula: see text]. This kind of equation is often used in literature to study chaotic dynamics, due to its simple form and because it appears as mathematical model in several applied problems. Hence, it is an important matter to determine when it is chaotic and also nonchaotic. The results stated here, which are proved using the mentioned algebraic criterion, corroborate and extend some results already presented in literature, providing simpler proofs for the nonchaotic behavior of certain jerk equations. The algebraic criterion proved by us is quite general and can be used to study nonchaotic behavior of other types of ordinary differential equations.

scholarly journals Derivative Spectrophotometric Analysis of 4-Quinolone Antibacterials in Formulations and Spiked Biological Fluids by Their Cu(II) Complexes

2001 ◽  
Vol 84 (2) ◽  
pp. 368-375 ◽  
Author(s):  
Mohammed Rizk ◽  
Fathalla Belal ◽  
Fawiza Ibrahim ◽  
Soad Ahmed ◽  
Zeinab A Sheribah
Keyword(s):  
Aqueous Medium ◽  
Linear Correlation ◽  
Analytical Procedure ◽  
Biological Fluids ◽  
Reference Method ◽  
Spectrophotometric Analysis ◽  
Third Order ◽  
Selective Determination ◽  
Average Percentage

Abstract A derivative UV-spectrophotometric analytical procedure was developed for determination of three 4-quinolone antibacterials: norfloxacin (NFX), ciprofloxacin (CFX), and sparfloxacin (SFX). The method depends on the complexation of Cu(II) with the studied compounds in aqueous medium. A third order, measurement was applied for their quantification. A linear correlation was established between the amplitude of the peak and concentration for all the studied drugs in the range of 15–80, 35–120, and 200–700 ng/mL, with minimum detectability (S/N = 2) of 1.0, 1.3, and 5.1 ng/mL for NFX, CFX, and SFX, respectively. The method was successfully applied for accurate, sensitive, and selective determination of the studied drugs in bulk and tablets formulation with average percentage recoveries of 99.22 ± 0.55 to 100.33 ± 1.60. The results obtained were favorably compared with those of the reference method. The method was also used to determine sparfloxacin in spiked human plasma and urine. The results obtained were satisfactory, accurate, and precise.

Measurement and modelling of homogeneous axisymmetric turbulence

1998 ◽  
Vol 374 ◽  
pp. 59-90 ◽  
Author(s):  
TORBJÖRN SJÖGREN ◽  
ARNE V. JOHANSSON
Keyword(s):  
Transport Equation ◽  
Reynolds Stress ◽  
Turbulence Models ◽  
Theoretical Description ◽  
Wind Tunnel Experiments ◽  
Third Order ◽  
Point Velocity ◽  
First Time ◽  
Rapid Pressure

A new method for determining the slow and rapid pressure-strain rate terms directly from wind-tunnel experiments has been developed with the aid of a newly developed theoretical description of the kinematics of homogeneous axisymmetric turbulence. Both the straining and the return-to-isotropy process of homogeneous axisymmetric turbulence are studied with the aim of improving Reynolds stress closures. Direct experimental determination of the different terms in the transport equation for the Reynolds stress tensor plays a major role in the validation and development of turbulence models. For the first time it is shown that the pressure{strain correlation can be determined with good accuracy without balancing it out from the Reynolds stress transport equation (and without measuring the pressure). Instead it is determined through evaluation of integrals containing second- and third-order two-point velocity correlations. All the terms in the Reynolds stress equations are measured directly and balance is achieved.

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