Embedded diagonally implicit Runge–Kutta–Nystrom 4(3) pair for solving special second-order IVPs

In this paper, third-order 3-stage diagonally implicit Runge–Kutta–Nystrom method embedded in fourth-order 4-stage for solving special second-order initial value problems is constructed. The method has the property of minimized local truncation error as well as the last row of the coefficient matrix is equal to the vector output. The stability of the method is investigated and a standard set of test problems are tested upon and comparisons on the numerical results are made when the same set of test problems are reduced to first-order system and solved using existing Runge–Kutta method. The results clearly shown the advantage and the efficiency of the new method.     

Effect of Deborah number and phase difference on peristaltic transport of a third-order fluid in an asymmetric channel

The effect of a third-order fluid on the peristaltic transport in an asymmetric channel is studied. The wavelength of the peristaltic waves is assumed to be large compared to the varying channel width, whereas the wave amplitudes need not be small compared to the varying channel width. The channel asymmetry is produced by choosing the peristaltic wave train on the walls to have different amplitudes and phase. The flow is investigated in a wave frame of reference moving with velocity of the wave. The effects of Deborah number, phase difference, varying channel width and wave amplitudes on the pumping characteristics, streamline pattern and trapping phenomena are investigated. It is observed that the trapping regions increase as the channel becomes more and more symmetric and the trapped bolus volume decreases for increasing Deborah number, phase difference and varying channel width whereas it increases for increasing flow rate and wave amplitudes. Furthermore, the obtained results could also have applications to a range of peristaltic flows for a variety of non-Newtonian fluids such as aqueous solutions of high-molecular weight polyethylene oxide and polyacrylamide.     

The deoxygenation kinetics of new oxovanadium(IV) complexes

Summary The deoxygenation reaction kinetics of some monomeric, dimeric and polymeric oxovanadium(IV) complexes with SOCl₂ have been studied by the stopped-flow technique in DMF. The reaction is bimolecular and obeys second-order kinetics; first-order in both SOCl₂ and complex. The polymeric halogeno product decays with time, but at a rate much slower compared to the rate of its formation. The correlation observed between the structure of these complexes and their reactivities is discussed.     

Some remarks on the Jensen-Hadamard inequalities and applications

We provide some inequalities and integral inequalities connected to the Jensen-Hadamard inequalities for convex functions. In particular, we give some refinements to these inequalities. Some natural applications and further extensions are given.

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Sunto Forniamo alcune diseguaglianze e diseguaglianze integrali connesse alle dise-gueglianze di Jensen-Hadamard per funzioni convesse. In particolare, diamo qualche miglioramento di queste diseguaglianze. Alcune applicazioni naturali ed ulteriori estensioni sono date.

     

Estimating market shares in each market segment using the information entropy concept

Sales data of a certain product for the various competitors are usually available at the aggregate level. However these data give no clue to the heterogeneities in the sales pattern across different market segments. Heterogeneities are caused by different purchasing behavior in each market segment; as a purchaser in a segment will be attracted to the attributes of the product most important to that segment. This concept can be formalized via a simple attraction model that utilizes an elasticity measure for each quality or price attribute [G.S. Carpenter, L.G. Cooper, D.M. Hanssens, D.F. Midgley, Modeling asymmetric competition, Marketing Science 7 (4) (1998) 393–412]. Assessment of these elasticities is not difficult since customer response – in each market segment – to perception of quality and price is tracked by most firms [J. Ross, D. Georgoff, A survey of productive and quality issues in manufacturing. The state of the industry, Industrial Management 3 (5) (1991) 22–25]. This paper attempts to formulate a generic framework based on the information entropy concept that utilizes such an attraction model to estimate competitors’ sales in each market segment.     

UV protection filters by dielectric multilayer thin films on Glass BK-7 and Infrasil 301

The increasing use of Ultraviolet (UV) light in medicine, industrial environments, for cosmetic use, and even in consumer products necessitates that greater attention be paid to the potential hazards of this type of electromagnetic radiation. To avoid any adverse effects of exposure to this type of radiation, four suitable protection filters were produced to block three UV bands (UVA, UVB, and UVC). The design structure of the required dielectric multilayer filters was done by optical thin film technology using the absorbing property of UV radiation for the substrates and dielectric materials. The computer analyses of the multilayer filter formulas were prepared using Macleod Software for the production processes. The deposition technique was achieved on optical substrates (Glass BK-7 and Infrasil 301) by dielectric material combinations including Titanium dioxide (Ti₂O₃), Hafnium dioxide (HfO₂), and Lima (mixture of oxides SiO₂/Al₂O₃); deposition being achieved using an electron beam gun. The output results of the theoretical and experimental transmittance values for spectral band from 200 nm to 800 nm were discussed in four processes. To analyze the suitability for use in ‘real world’ applications, the test pieces were subjected to the durability tests (adhesion, abrasion resistance, and humidity) according to Military Standard MIL-C-675C and MIL-C-48497A.     

Integrability of det▽u and Evolutionary Wente''s Problem Associated to Heat Operator

In this note, the authors resolve an evolutionary Wente's problem associated to heat equation, where the special integrability of det▽u for u ∈ H1(R2,R2) is used.     

Intraspinal endodermal cyst: ultrastructural study of abnormal cilia.

Abnormal cilia were demonstrated in the lining epithelial cells of three cases of intraspinal endodermal (bronchogenic) cyst. The changes comprised a wide spectrum of ultrastructural abnormalities, including (a). cilia with abnormal axonemal microtubules, (b). swollen cilia, (c). compound cilia with or without excessive ciliary matrix, (d). naked cilia without limiting membrane, and (e). intracytoplasmic cilia and aggregates of microtubules. Of these, compound cilia and swollen cilia were most common. Cilia with dynein arm deficiency were not observed. Ciliary abnormalities found in the present study were very similar to those described in the bronchial epithelium of various diseases. The present findings suggest that the lining epithelium of intraspinal endodermal cyst shares similar ciliogenesis and susceptibility to abnormal ciliary formation as that of the bronchial epithelium.     

A short and efficient synthesis of 2′-deoxybenzo- and pyridoimidazole C-nucleosides

A short route to a series of 2′-deoxy-C-nucleosides featuring substituted nucleobases has been developed. The key step is the formation of the cyclized products following Mukaiyama's type amide coupling and a simple dehydration, starting from readily accessible synthons. The epimerization of the C1′-stereogenic center was avoided under mild and controlled conditions.