Quantitative NIR Raman analysis in liquid mixtures

The capability to obtain quantitative information of a simple way from Raman spectra is a subject of considerable interest. In this work, this is demonstrated for mixtures of ethanol with water and rhodamine-6G (R-6G) with methanol, which were analyzed directly in glass vessel. The Raman intensities and a simple mathematical model have been used and applied for the analysis of liquid samples. It is starting point to generate a general expression, from the experimental spectra, as the sum of the particular expression for each pure compound allow us to obtain an expression for the mixtures which can be used for determining concentrations, from the Raman spectrum, of the mixture.     

The Social Climbing Game

The structure of societies depends, to some extent, on the incentives of the individuals they are composed of. We study a stylized model of this interplay, that suggests that the more individuals aim at climbing the social hierarchy, the more society’s hierarchy gets strong. Such a dependence is sharp, in the sense that a persistent hierarchical order emerges abruptly when the preference for social status gets larger than a threshold. This phase transition has its origin in the fact that the presence of a well defined hierarchy allows agents to climb it, thus reinforcing it, whereas in a “disordered” society it is harder for agents to find out whom they should connect to in order to become more central. Interestingly, a social order emerges when agents strive harder to climb society and it results in a state of reduced social mobility, as a consequence of ergodicity breaking, where climbing is more difficult.     

Application of a He3Ne infrared laser source for detection of geometrical dimensions of cracks and scratches on finished surfaces of metals

In this study, the authors addressed a new method of measurement for microscratches and cracks on finished metallic surfaces. The technology proposed here can be used in aviation, automobile, machine-tools, bearings, electrical and thermal devices (detection of electrical and thermal contact resistance), and many other industrial fields where finished surfaces have to be inspected for quality before use. The technology is based on the application of He3Ne laser optics. This measurement method allows for the inspection of geometrical parameters such as depth and width of scratches and cracks and consists of a low-energy He3Ne red laser beam (wavelength 633 nm) with a cross-section of 0.48 mm, beam expander with special designed slit, multi-axis stage with sample holder and CCD (charge-coupled device) visual detection system. Using experimental data, a mathematical algorithm was created in order to calculate the depths and widths of the scratches and cracks where the method of center of gravity (centroid) of the imaged area was used. The results showed a good correlation between the experimental and calculated values of the dimensions of the scratches. Future work will deal with the determination of the geometrical dimensions of microcracks.     

A phase-field model for quasi-incompressible solid–liquid transitions

According to a unified thermodynamic scheme, we derive the general kinetic equation ruling the phase-field evolution in a binary quasi-incompressible mixture for both transition and separation phenomena. When diffusion effects are negligible in comparison with source and production terms, a solid–liquid phase transition induced by temperature and pressure variations is obtained. In particular, we recover the explicit expression of the liquid–pressure curve separating the solid from the liquid stability regions in the pressure–temperature plane. Consistently with physical evidence, its slope is positive (negative) for substances which compress (expand) during the freezing process.     

Preconditioned iterative regularization in Banach spaces

Regularization methods for inverse problems formulated in Hilbert spaces usually give rise to over-smoothness, which does not allow to obtain a good contrast and localization of the edges in the context of image restoration. On the other hand, regularization methods recently introduced in Banach spaces allow in general to obtain better localization and restoration of the discontinuities or localized impulsive signals in imaging applications. We present here an expository survey of the topic focused on the iterative Landweber method. In addition, preconditioning techniques previously proposed for Hilbert spaces are extended to the Banach setting and numerically tested.     

On the Null Cone for Quiver Representations Under Reflection Functors

Let d be a prehomogeneous dimension vector for a connected quiver Q with the property that c ^? d has a negative entry for some ? ∈ ? where c is the Coxeter transformation corresponding to an admissible numbering of the vertices Q ₀ of Q. Denote by rep(Q, d) the variety of d-dimensional representations of Q and by Sl(d) the product of the special linear groups at all vertices Q ₀. We show how to find the irreducible components of the null cone of the algebraic quotient rep(Q, d)//Sl(d).     

High Frequency Resolvent Estimates for Perturbations by Large Long-range Magnetic Potentials and Applications to Dispersive Estimates

We prove optimal high-frequency resolvent estimates for self-adjoint operators of the form ${G=\left(i\nabla+b(x)\right)^2+V(x)}$ on ${L^2({\bf R}^n), n\ge 3}$ , where the magnetic potential b(x) and the electric potential V(x) are long-range and large. As an application, we prove dispersive estimates for the wave group ${{\rm e}^{it\sqrt{G}}}$ in the case n = 3 for potentials b(x), V(x) = O(|x|^?2-δ ) for ${|x|\gg 1}$ , where δ > 0.     

Shift-invariant approximations of structured shift-variant blurring matrices

In this paper we analyze in a general and pure algebraic way imaging systems characterized by shift-variant integral kernels which hide some intrinsic shift-invariance, related to an appropriate coordinate change; we call as structured shift-variant these kinds of imaging systems. In this respect, we propose an algorithm for finding a coordinate transformation which allows a structured shift-variant PSF to become explicitly shift-invariant. The usage of the computed coordinate transformation will highly reduce the numerical complexity of the imaging system, providing a real time deblurring in some real applications. Some preliminary numerical results show the effectiveness of the proposal.