Effect of precipitation procedure and detection technique on particle size distribution of CaCO3

The deposition of inorganic salts (“scales”) such as calcium carbonate is an important flow assurance problem during crude oil production. The knowledge of the features of the precipitated solids, mainly the particle size and morphology, is crucial to understand the nature of the solids and to avoid or reduce the effect of their deposition. For instance, the use of additives is one of the most usual procedures to mitigate this problem. Additives interact with scale-forming substances either by increasing the induction time, or by inhibiting crystal growth, changing the morphology of solids.     

Uniform-scale chromaticity diagram by logarithmic transformations

Summary Von Kires invariant chromatic-response functions are derived by a proper angular hypothesis related to the opponent chromatic processes.     

An Application of Calculus on Measure Chains to Fourier Theory and Heisenberg's Uncertainty Principle

We present "one-dimensional" Fourier theory on commutative groups T hH , 0 h h < X , 0< H h X within the framework of the so-called calculus on measure chains (or time scales). Depending on certain values of the graininess h and length H of the group the four classical types of Fourier transform are covered: Fourier integral ( T 0 X = R ), Fourier series ( T 1 X = Z ), Fourier analysis of periodic functions ( T 0,2 ~ = S 1 (0) unit circle) and discrete Fourier transform ( T 1 N = Z N ). We will present Fourier theory on these groups in a unified manner. This also allows to closely track the roles of the graininess h and length H of the group--especially for h M 0 and H M X . In the final part of the paper, we investigate the solution of a fundamental equation on T hH , which can be considered as a generalization of the Gauss function. It finally leads to a version of the Heisenberg uncertainty principle, which extends the classical one, valid for T 0 X = R , to the case T hH , where either h >0 or H < X .     

Stability analysis using multiple scales homotopy approach of coupled cylindrical interfaces under the influence of periodic electrostatic fields

The influence of axial periodic electric fields on streaming flows through three coaxial infinitely vertical cylinders is considered. The three fluid layers are assumed to be incompressible, dielectric, viscous and saturated through porous media. To relax the mathematical manipulation of the problem, the viscous potential theory is considered. Through the current work, the stability analysis of the coupled Mathieu equations is developed in the analogy of the multiple scales homotopy technique. Away from the symmetric and anti-symmetric modes, the present study investigates a general case of the surface waves deflections. To overcome the lengthy of the algebraic calculations, the matrices concept is utilized. The stability analysis reveals the resonance as well as non-resonance cases. A set of graphs are depicted to indicate some resonance cases for a chosen sample through a dimensionless system. Therefore, the influence of some physical parameters on the stability picture is indicated. In addition, the perturbed solutions of the governed Mathieu equations are graphed.     

An equivalence theorem for some integral conditions with general measures related to Hardy's inequality

It is proved that, besides the usual Muckenhoupt condition, there exist four different scales of conditions for characterizing the Hardy type inequality with general measures for the case 1<p?q<∞. In fact, an even more general equivalence theorem of independent interest is proved and discussed.     

Dynamically Stable Solitons in Optical Fibers

The existence of a dynamically stable soliton in optical fibers is established by virtue of the multiple-scale perturbation technique applied in a new way to the perturbed nonlinear Schrodinger's equation. We show that, by introducing a proper definition of the phase of the soliton, one can obtain the corrections to the pulse where the standard soliton perturbation approach fails.     

Nonlinear size-dependent longitudinal vibration of carbon nanotubes embedded in an elastic medium

In this paper, we study the longitudinal linear and nonlinear free vibration response of a single walled carbon nanotube (CNT) embedded in an elastic medium subjected to different boundary conditions. This formulation is based on a large deformation analysis in which the linear and nonlinear von Kármán strains and their gradient are included in the expression of the strain energy and the velocity and its gradient are taken into account in the expression of the kinetic energy. Therefore, static and kinetic length scales associated with both energies are introduced to model size effects. The governing motion equation along with the boundary conditions are derived using Hamilton's principle. Closed-form solutions for the linear free vibration problem of the embedded CNT rod are first obtained. Then, the nonlinear free vibration response is investigated for various values of length scales using the method of multiple scales.     

Metamerism

Summary Any heterochromatic stimulus can be matched by colour stimuli of different spectral composition. We give an equation which defines the whole set of colour stimuli of equal colour appearance and their spectral composition. Moreover, we define the group of transformations which alter the spectral composition of the stimuli and leave invariant the colour appearances.

---

Riassunto Ogni stimolo eterocromatico di colore può essere uguagliato da una somma di stimoli con differenti composizioni spettrali. Si propone un’equazione che definisce l’intero insieme degli stimoli di uguale cromaticità e differente composizione spettrale. Inoltre si definisce un gruppo di trasformazioni che modificano la composizione spettrale degli stimoli e lasciano invariata la cromaticità.

---

Резюме Любое гетерохроматическое возбуждение может быть представлено с помощью цветнях возбуждений различного спектрального состава. Мы приводим уравнение, которое определяет полную систему цветных возбуждений и их спектральных состав. Кроме того, мы определяем преобразований, которые изменяют спектральный состав возбуждений, но оставляют инвариантным цветные признаки.

     

An equivalence theorem for some integral conditions with general measures related to Hardy's inequality II

Scales of equivalent weight characterizations for the Hardy type inequality with general measures are proved. The conditions are valid in the case of indices 0<q<p<∞, p>1. We also include a reduction theorem for transferring a three-measure Hardy inequality to the case with two measures.