Non-contact optical fibre phased array generation of ultrasound for non-destructive evaluation of materials and processes

The use of non-contact laser techniques for the generation of ultrasound has extended the limits of the application of traditional ultrasonic techniques. This paper focusses on the use of one such non-contact laser technique, known as ‘optical fibre array’, to generate shear and surface waves. The shear wave experimental directivity pattern results are presented and compared with the theoretical results of a single source and an array source. The experimental directivity results for the surface wave are also presented, and compared with the theoretical results. The data show that the array enhances signal generation in the forward direction for both shear and surface waves. The array gain is also discussed. The receiver for the directivity measurements was a contact piezoelectric transducer.     

Generalized Nonlinear Variational-Like Inequalities

This study investigates how to dynamically allocate resources with a given budget for advertising through Web portals using keyword-activated banner ads on the Internet. Identifying the factors that affect the potential number of banner ad clickthroughs in each portal, we show that the process of budget allocation between the two types of portals (generic vs specialized) that leads to the largest banner clicksthrough in the long run is an optimal control problem. Using techniques of dynamic programming, we find analytical solutions for the optimal budgeting decisions. Our analysis shows that an advertisers optimal portal budgeting depends nonlinearly on the number of visitors who type the same trigger keyword and the average clicksthrough rates, as well as on the advertiser and ad effectiveness. Further, we find that the maximal number of banner clickthroughs from both portals, at time t, depends on the remaining budget until the end of the planning period. The analytical results have useful managerial insight. One of the interesting features of our solution shows that, while a large visitor base may favor the generic portal, other parameters may affect it unfavorably: e.g., lower clickthrough rates of keyword banners from a more heterogeneous audience. Using a specificaction that is consistent with empirical observations, we show that, in the long run, an advertiser must always spend more ad money at the specialized portal.     

A Critical Review on Pulsed Electric Field: A Novel Technology for the Extraction of Phytoconstituents

Different parts of a plant (seeds, fruits, flower, leaves, stem, and roots) contain numerous biologically active compounds called “phytoconstituents” that consist of phenolics, minerals, amino acids, and vitamins. The conventional techniques applied to extract these phytoconstituents have several drawbacks including poor performance, low yields, more solvent use, long processing time, and thermally degrading by-products. In contrast, modern and advanced extraction nonthermal technologies such as pulsed electric field (PEF) assist in easier and efficient identification, characterization, and analysis of bioactive ingredients. Other advantages of PEF include cost-efficacy, less time, and solvent consumption with improved yields. This review covers the applications of PEF to obtain bioactive components, essential oils, proteins, pectin, and other important materials from various parts of the plant. Numerous studies compiled in the current evaluation concluded PEF as the best solution to extract phytoconstituents used in the food and pharmaceutical industries. PEF-assisted extraction leads to a higher yield, utilizes less solvents and energy, and it saves a lot of time compared to traditional extraction methods. PEF extraction design should be safe and efficient enough to prevent the degradation of phytoconstituents and oils.     

Common fixed point theorems for weakly compatible quasi contraction mappings

Summary Recently, Pathak [13] has made an extension of the notion of compatibility to weak compatibility, and extended the coincidence theorem for compatible mappings in Kaneko and Sessa [11] to weakly compatible mappings [13]. In the present paper, we define a new class of weakly compatible mappings (Definition 4) and prove some common fixed point theorems for these mappings, which satisfy Condition (2) below. Although our main theorem is formulated for weakly compatible mappings, its corresponding formulation for commutative mappings is also a new result, thus presenting a generalization of some theorems of Fisher, Das and Naik, Khan and Kubiaczyk, Reich, Ćirić and Rhoades and Watson.     

Modified Ishikawa Iteration Process for Nonlinear Lipschitz Generalized Strongly Pseudo-Contractive Operators in Arbitrary Banach Spaces

In this paper, we modify the Ishikawa iteration process and show that such process, associated with a nonlinear Lipschitzian generalized strongly pseudo-contractive operator with a fixed point in a (not necessarily uniformly smooth) Banach space, converges strongly to the unique fixed point of this operator.     

Existence and iterative approximations of solutions for mixed quasi-variational-like inequalities in Banach spaces

In this paper, we introduce and investigate a new class of mixed quasi-variational-like inequalities in reflexive Banach spaces. By applying a minimax inequality due to Ding–Tan and a lemma due to Chang, we establish some existence and uniqueness results of solution for the mixed quasi-variational-like inequality. Next, by using a KKM theorem due to Fan and an auxiliary principle technique due to Cohen, we suggest two iterative algorithms and study the convergence criteria of iterative sequences generated by the iterative algorithms. Our results extend, improve and unify several known results in the literature.     

Alkylation of [Pt2(μ-S)2(PPh3)4] with boronic acid derivatives

The reactivity of the metalloligand [Pt₂(μ-S)₂(PPh₃)₄] with the boron-functionalized alkylating agents BrCH₂(C₆H₄)B(OR)₂ (R = H or C(CH₃)₂) was investigated by electrospray ionization mass spectrometry (ESI-MS) in real time using pressurized sample infusion (PSI). The macroscopic reaction of [Pt₂(μ-S)₂(PPh₃)₄] with one mole equivalent of alkylating agents BrCH₂(C₆H₄)B{OC(CH₃)₂}₂ and BrCH₂(C₆H₄)B(OH)₂ gave the dinuclear monocationic μ-sulfide thiolate complexes [Pt₂(μ-S){μ-SCH₂(C₆H₄)B{OC(CH₃)₂}₂}(PPh₃)₄]⁺ and [Pt₂(μ-S){μ-S⁺CH₂(C₆H₄)B(OH)(O^?)}(PPh₃)₄]. The products were isolated as the [PF₆]^? salt and zwitterion, respectively, and fully characterized by ESI-MS, IR, ¹H and ³¹P NMR spectroscopy, and single-crystal X-ray structure determinations.     

Hyperbolic heat equations in laser generated ultrasound models

The generation of ultrasound by pulsed lasers is a thermoelastic process, and in the literature on general thermoelasticity there are presently three different forms of the heat equation in popular use, the classical, Lord-Schulman (LS), and Green-Lindsay (GL) heat equations. The question may thus arise as to which heat equation should be used to model laser generated ultrasound. The purpose of this work is to summarize the current rationale for using these different heat equations, in order to provide a basis for choosing one of the forms. A review of the classical, LS and GL theories is given, and the potential advantages of hyperbolic heat flow theories in laser ultrasonics are discussed. A numerical example is given that clearly shows the small time differences these theories predict, and also points out potential problems with using hyperbolic heat equations on small time scales.     

On the convergence of the Ishikawa iterates associated with a pair of multi-valued mappings

Let X be a normed linear space and let S and T be multi-valued mappings of X into a family of closed, not necessarily compact subsets of X. In this paper some results on the convergence of the Ishikawa iterates associated with a pair S, T which satisfy the condition (8) below, are obtained. This revised version was published online in June 2006 with corrections to the Cover Date.