General KKM Theorem with Applications to Minimax and Variational Inequalities

In this paper, a general version of the KKM theorem is derived by using the concept of generalized KKM mappings introduced by Chang and Zhang. By employing our general KKM theorem, we obtain a general minimax inequality which contains several existing ones as special cases. As applications of our general minimax inequality, we derive an existence result for saddle-point problems under general setting. We also establish several existence results for generalized variation inequalities and generalized quasi-variational inequalities.     

On Nondifferentiable and Nonconvex Vector Optimization Problems

In this paper, we prove the equivalence among the Minty vector variational-like inequality, Stampacchia vector variational-like inequality, and a nondifferentiable and nonconvex vector optimization problem. By using a fixed-point theorem, we establish also an existence theorem for generalized weakly efficient solutions to the vector optimization problem for nondifferentiable and nonconvex functions.     

Minimum Cost Compromise Mixed Allocation

When more than one (say p) characteristics in multivariate stratified population are defined on each unit of the population, the individual optimum allocations may differ widely and can not be used practically. Moreover, there may be a situation such that no standard allocation is advisable to all the strata, for one reason or another. In such a situation, Clark and Steel (J R Stat Soc, Ser D Stat 49(2):197–207, 2000) suggested that different allocations may be used for different groups of strata having some common characteristics for double sampling in stratification. Later on, Ahsan et al. (Aligarh J Stat 25:87–97, 2005) used the same concept in univariate stratified sampling. They minimized the variance of the stratified sample mean for a fixed cost to obtain an allocation and called this allocation “mixed allocation”. In the present paper, a “compromise mixed allocation” is worked out for the fixed precisions of the estimates of the p-population means of a multivariate stratified population. A numerical example is also presented.     

A comprehensive study on the oscillation frequency of spherical fullerenes in carbon nanotubes under different system parameters

Amongst possible new nanomechanical devices created based on carbon nanostructures, high-frequency nanoscale oscillators, or the so-called gigahertz oscillators have attracted much attention. In this paper, the oscillatory behavior of spherical fullerenes inside carbon nanotubes is thoroughly investigated. To this end, the continuum approximation together with Lennard-Jones potential is used to evaluate the van der Waals potential energy and interaction force. The equation of motion is directly solved based on the actual force distribution between the two nanostructures, without any simplifying assumption. A semi-analytical expression is obtained for the oscillation frequency into which the effect of initial conditions is incorporated. Thereafter, this newly derived expression is utilized in order to present a comprehensive study on the effects of different system variables such as geometrical parameters and initial conditions on the oscillation frequency. Based upon these studies, some new features of such oscillations have been revealed.     

Iterative algorithms for systems of extended regularized nonconvex variational inequalities and fixed point problems

This paper points out some fatal errors in the equivalent formulations used in Noor 2011 [Noor MA. Projection iterative methods for solving some systems of general nonconvex variational inequalities. Applied Analysis. 2011;90:777–786] and consequently in Noor 2009 [Noor MA. System of nonconvex variational inequalities. Journal of Advanced Research Optimization. 2009;1:1–10], Noor 2010 [Noor MA, Noor KI. New system of general nonconvex variational inequalities. Applied Mathematics E-Notes. 2010;10:76–85] and Wen 2010 [Wen DJ. Projection methods for a generalized system of nonconvex variational inequalities with different nonlinear operators. Nonlinear Analysis. 2010;73:2292–2297]. Since these equivalent formulations are the main tools to suggest iterative algorithms and to establish the convergence results, the algorithms and results in the aforementioned articles are not valid. It is shown by given some examples. To overcome with the problems in these papers, we consider a new system of extended regularized nonconvex variational inequalities, and establish the existence and uniqueness result for a solution of the aforesaid system. We suggest and analyse a new projection iterative algorithm to compute the unique solution of the system of extended regularized nonconvex variational inequalities which is also a fixed point of a nearly uniformly Lipschitzian mapping. Furthermore, the convergence analysis of the proposed iterative algorithm under some suitable conditions is studied. As a consequence, we point out that one can derive the correct version of the algorithms and results presented in the above mentioned papers.     

Predictor–Corrector Methods for General Regularized Nonconvex Variational Inequalities

This paper is devoted to the study of a new class of nonconvex variational inequalities, named general regularized nonconvex variational inequalities. By using the auxiliary principle technique, a new modified predictor–corrector iterative algorithm for solving general regularized nonconvex variational inequalities is suggested and analyzed. The convergence of the iterative algorithm is established under the partially relaxed monotonicity assumption. As a consequence, the algorithm and results presented in the paper overcome incorrect algorithms and results existing in the literature.     

Label-Free Electrochemical Sensor Based on Manganese Doped Titanium Dioxide Nanoparticles for Myoglobin Detection: Biomarker for Acute Myocardial Infarction

A label free electrochemical sensor based on pure titanium oxide and manganese (Mn)-doped titanium oxide (TiO₂) nanoparticles are fabricated and characterized for the sensitive detection of myoglobin (Mb) levels to analyze the cardiovascular infarction. Pristine and Mn-doped TiO₂ nanoparticles were synthesized via the sol-gel method and characterized in order to understand their structure, morphologies, composition and optical properties. The structural properties revealed that the pure- and doped-TiO₂ nanoparticles possess different TiO₂ planes. FTIR studies confirm the formation of metal oxide nanoparticles by exhibiting a well-defined peak in the range of 600–650 cm⁻¹. The values of the optical band gap, estimated from UV-Vis spectroscopy, are decreased for the Mn-doped TiO₂ nanoparticles. UV-Vis spectra in the presence of myoglobin (Mb) indicated interaction between the TiO₂ nanoparticles and myoglobin. The SPE electrodes were then fabricated by printing powder film over the working electrode and tested for label-free electrochemical detection of myoglobin (Mb) in the concentration range of 0–15 nM Mb. The fabricated electrochemical sensor exhibited a high sensitivity of 100.40 μA-cm^−2/nM with a lowest detection limit of 0.013 nM (0.22 ng/mL) and a response time of ≤10 ms for sample S3. An interference study with cyt-c and Human Serum Albumin (HSA) of the sensors show the selective response towards Mb in 1:1 mixture.     

Optical absorption spectroscopic studies on holmium(III) complexes with beta-diketone and heterocyclic amines: the environment effect on 4f-4f hypersensitive transitions

The optical absorption spectra of [Ho(acac)(3)(H(2)O)(2)].H(2)O, [Ho(acac)(3)phen] and [Ho(acac)(3)bpy] (where acac is the anion of acetylacetone; phen is 1,10-phenanthroline and bpy is 2,2'-bipyridyl) complexes in the visible region, in a series of non-aqueous solvents (methanol, ethanol, isopropanol, chloroform, acetonitrile and pyridine.) have been analyzed. The largest intensity variation was observed in the (5)G(6)<--(5)I(8) (centered at 450 nm), and (5)G(5), (3)H(5), (3)H(6)<--(5)I(8) (centered at 360 nm) transition regions. The band shape and oscillator strength of the hypersensitive transitions display pronounced changes as compared to Ho(3+) aqua-ion. The band shapes of the hypersensitive transitions show remarkable changes on passing from aqueous solution to various non-aqueous solutions which is the result of change in the environment about the Ho(III) ion in the various solutions and suggests coordination of solvent molecule(s), in some cases. The results clearly show that among the solvents studied pyridine is the most effective in promoting the 4f-4f spectral intensity. It has been inferred from this study that 2,2'-bipyridyl is a stronger ligand for heavier lanthanides. A comparative account of hypersensitivity in the present complexes with those of other adducts of Ho(beta-diketoenolate)(3) with heterocyclic amines is discussed. The TGA analyses showed that the phen complex is thermally more stable over its bpy analogue.     

Relaxed extragradient iterative methods for variational inequalities

In this paper, we suggest and analyze some new relaxed extragradient iterative methods for finding a common element of the solution set of a variational inequality, the solution set of a general system of variational inequalities and the set of fixed points of a strictly pseudo-contractive mapping defined on a real Hilbert space. Strong convergence of the proposed methods under some mild conditions is established.