Vibration control of a transversely excited cantilever beam with tip mass

The problem of controlling the vibration of a transversely excited cantilever beam with tip mass is analyzed within the framework of the Euler–Bernoulli beam theory. A sinusoidally varying transverse excitation is applied at the left end of the cantilever beam, while a payload is attached to the free end of the beam. An active control of the transverse vibration based on cubic velocity is studied. Here, cubic velocity feedback law is proposed as a devise to suppress the vibration of the system subjected to primary and subharmonic resonance conditions. Method of multiple scales as one of the perturbation technique is used to reduce the second-order temporal equation into a set of two first-order differential equations that govern the time variation of the amplitude and phase of the response. Then the stability and bifurcation of the system is investigated. Frequency–response curves are obtained numerically for primary and subharmonic resonance conditions for different values of controller gain. The numerical results portrayed that a significant amount of vibration reduction can be obtained actively by using a suitable value of controller gain. The response obtained using method of multiple scales is compared with those obtained by numerically solving the temporal equation of motion and are found to be in good agreement. Numerical simulation for amplitude is also obtained by integrating the equation of motion in the frequency range between 1 and 3. The developed results can be extensively used to suppress the vibration of a transversely excited cantilever beam with tip mass or similar systems actively.     

Role of epidermis in the optics and thermal physics of human skin

Some engineering approaches to the problems of optics and thermophysics of biological tissues have been developed. The light fields both within and beyond biological medium have been studied. The role of the epidermis in the formation of these fields is revealed. It is shown that in the general case epidermis cannot be considered as a spectral filter that only absorbs and does not scatter light. A convenient approximation of the fluence rate in a two-layer (epidermis and dermis) tissue is proposed, which is the sum of two exponential functions of depth in the epidermis. This approximation made it possible to obtain an analytical solution to the problem of heating biological tissues by an external narrow light beam. It is found that epidermis only slightly affects the temperature fields under blue light irradiation. However, when an external source of red light is used, the epidermis works as a heater and can increase several times the dermis temperature in comparison with a single-layer tissue. The reasons for these heating features are discussed. Examples of corresponding calculations are given.     

Light reflection spectra as a diagnostic tool for the structural and biophysical parameters of skin

The calculation scheme and the diagnostic algorithm for diagnosing the structural and biophysical parameters of skin from the spectrum of reflected radiation are constructed. The sought parameters are determined from the solution of the spectroscopic problem under conditions of multiple scattering. The method presented is based on the previously proposed model of the spectral properties of a tissue and on the engineering approaches to the solution of the transfer equation. The sought parameters are the volume concentrations of melanin and capillaries, the thickness of epidermis, the average diameter of capillaries, and the degree of blood oxygenation. In order to optimize the algorithm with respect to wavelength and to elaborate the experimental diagnostic scheme, the sensitivity of the reflection spectrum to the sought parameters is studied. The procedure of their successive restoration is proposed.     

β-Alkoxycarbonyl Alkyl Tin Chelates 2. Dithizonates – Preparation and Spectroscopic Studies

Dithizone forms stable complexes with β-alkoxycarbonyl ethyl tin chlorides (the so called “Estertins” – a unique class of PVC stabilizer). Reduction of Lewis acidity of the resulting organotin chloride can improve the efficiency of a stabilizer and therefore the β-alkoxycarbonyl ethyl tin dithizonates are likely to show PVC stabilization property. A number of β-alkoxycarbonyl ethyl tin dithizonates of the types R₂SnL₂, R₂SnLX, and RSnL₂X where R = CH₃OCOCH₂CH₂–, C₄H₉OCOCH₂CH₂–, and CH₃OCOCH(CH₃)CH₂–; X = Cl, SCN and L = Dithizone (i. e. 1,5-diphenyl thiocarbazone) and one complex (CH₃OCOCH₂CH₂)₂SnL′Cl where L′ = Diphenylcarbazone have been prepared and characterized by elemental analysis, electronic, IR and PMR spectral data. Possible structural features of the isolated complexes have also been discussed. Preliminary evaluation of the complex (CH₃OCOCH₂CH₂)₂Sn(HDz)₂ as a PVC stabilizer has also been reported.     

Possible allosteric interactions of monoindazole-substituted P2 cyclic urea analogues with wild-type and mutant HIV-1 protease

Our ongoing efforts to understand the difference in the binding pattern of HIV-1 protease inhibitor (HIVPI) with the wild-type and mutant HIV-1 protease (HIVPR) and to provide mechanistic insight are continued further. We report here the results of a recent quantitative structure-activity relationship (QSAR) study on monoindazole-substituted P2 analogues of cyclic urea HIVPIs. The QSAR models revealed an inverted parabolic relationship between biological activity and calculated molar refractivity (CMR). That is, biological activity first decreases with increase in CMR and at a certain minimum point (inversion point) it suddenly changes and increases with further increase in CMR. CMR is a measure of volume-dependent-polarizability and is an indication of the polar interactions between ligand and receptor. The results seem to be best rationalized by larger molecules inducing a change in a receptor unit that allows for a new mode of interaction. Similar QSAR models were also observed for the biological activity of these molecules tested against a panel of mutant viruses including mutant strains with single amino acid substitution (I84V), double amino acid substitutions (I84V/V82F), and multiple amino acid changes corresponding to mutations observed in clinical isolates of patients treated with Ritonavir((R)). Interestingly the inversion points for these mutant strains were found larger than for wild-type. The subtle but significant difference in the inversion point indicates change in the shape and size of the binding pocket. Earlier QSAR studies have shown that the correlation of biological activity with an inverted parabola is an indicative of the 'allosteric interaction' of the ligands with the receptor. This report presents a detail analysis of these observations.     

Approximation Algorithms for Dispersion Problems

Given a collection of weighted sets, each containing at most k elements drawn from a finite base set, the k-set packing problem is to find a maximum weight sub-collection of disjoint sets. A greedy algorithm for this problem approximates it to within a factor of k, and a natural local search has been shown to approximate it to within a factor of roughly k − 1. However, neither paradigm can yield approximations that improve on this.We present an approximation algorithm for the weighted k-set packing problem that combines the two paradigms by starting with an initial greedy solution and then repeatedly choosing the best possible local improvement. The algorithm has a performance ratio of 2(k + 1)/3, which we show is asymptotically tight. This is the first asymptotic improvement over the straightforward ratio of k.     

Quantification of piperine in different varieties of Piper nigrum by a validated high-performance thin-layer chromatography‒densitometry method

JPC – Journal of Planar Chromatography – Modern TLC - Piperine is the most important alkaloid molecule present in Piper nigrum. In this study, a simple, rapid, quantitative...     

Depth distributions of light action spectra for skin chromophores

Light action spectra over wavelengths of 300–1000 nm are calculated for components of the human cutaneous covering: melanin, basal (bloodless) tissue, and blood oxy- and deoxyhemoglobin. The transformation of the spectra with depth in biological tissue results from two factors. The first is the wavelength dependence of the absorption coefficient corresponding to a particular skin chromophore and the second is the spectral selectivity of the radiation flux in biological tissue. This factor is related to the optical properties of all chromophores. A significant change is found to take place in the spectral distribution of absorbed radiant power with increasing depth. The action spectrum of light for the molecular oxygen contained in all components of biological tissue is also studied in the 625–645 nm range. The spectra are found to change with both the volume fraction of blood vessels and the degree of oxygenation of the blood. These results are useful for analyzing processes associated with optical absorption that are possible mechanisms for the interaction of light with biological tissues: photodissociation of oxyhemoglobin and the light-oxygen effect.     

Absorption spectra and light penetration depth of normal and pathologically altered human skin

A three-layered skin model (stratum corneum, epidermis, and dermis) and engineering formulas for radiative transfer theory are used to study absorption spectra and light penetration depths of normal and pathologically altered skin. The formulas include small-angle and asymptotic approximations and a layer-addition method. These characteristics are calculated for wavelengths used for low-intensity laser therapy. We examined several pathologies such as vitiligo, edema, erythematosus lupus, and subcutaneous wound, for which the bulk concentrations of melanin and blood vessels or tissue structure (for subcutaneous wound) change compared with normal skin. The penetration depth spectrum is very similar to the inverted blood absorption spectrum. In other words, the depth is minimal at blood absorption maxima. The calculated absorption spectra enable the power and irradiation wavelength providing the required light effect to be selected. Relationships between the penetration depth and the diffuse reflectance coefficient of skin (unambiguously expressed through the absorption coefficient) are analyzed at different wavelengths. This makes it possible to find relationships between the light fields inside and outside the tissue. __________ Translated from Zhurnal Prikladnoi Spektroskopii Vol. 74, No. 3, pp. 387–394, May–June, 2007.     

Estimate of the Contribution of Localized Light Absorption by Blood Vessels to the Optical Properties of Biological tissue

A simple analytical procedure of considering localized light absorption by blood vessels and its effect on the absorption characteristics of multicomponent biological tissue is proposed. The final results are presented in the form of a single integral of elementary functions. A comparison of the estimates obtained with data in the literature shows their good agreement. The limiting cases of random and ordered arrangement of vessels are considered. It was shown that, in the blue spectral range, the absorption coefficient of biological tissues can reach saturation when it ceases to be dependent on the optical characteristics of blood and is determined only by the diameter of vessels and their volume concentration. The depth of light penetration into tissue and the reflection coefficient of tissue are estimated for both a localized and a homogeneously distributed absorber. Possible biomedical applications of the results obtained are illustrated.