Partial order relations on family of sets and scalarizations for set optimization

In this study, some new order relations on family of sets are introduced by using Minkowski difference. The relations between these orders and the ordering cone of the vector space are obtained. It is shown that depending on the corresponding cone, these order relations are partial orders on the family of nonempty bounded sets. Some relationships between these order relations and upper and lower set less order relations are investigated. Also, two scalarizing functions are introduced in order to replace set optimization problems with respect to these partial order relations with scalar optimization problems. Moreover, necessary and sufficient optimality conditions are presented.     

Primes in tuples II

We prove that

$ \mathop{ \lim \inf}\limits_{n \rightarrow \infty} \frac{p_{n+1}-p_{n}}{\sqrt{\log p_{n}} \left(\log \log p_{n}\right)^{2}}< \infty, $

where p _n denotes the nth prime. Since on average p _n+1?p _n is asymptotically log _n , this shows that we can always find pairs of primes much closer together than the average. We actually prove a more general result concerning the set of values taken on by the differences p?p′ between primes which includes the small gap result above.

     

A critical analysis of N. Bohr's reply to the EPR argument

N. Bohr's counter-argument to EPR assumes that the complementarity principle imposes a limitation on the types of predictions permissible in quantum theory, similar to the limitation imposed on the types of measurements by the Heisenberg uncertainty relation. Since this assumption has no quantum-theoretical justification, the EPR argument cannot be refuted on the basis of the complementarity principle.     

Entropy generation in parallel plate microchannels

In this study the entropy generation in microchannels in microdevices induced by the transient laminar forced convection in the combined entrance region between two parallel plates has been investigated numerically. The study considers the microscales in the region of Kn < 0.001. The effects of aspect ratio, Reynolds number, Prandtl number, Brinkman number, and the motion of the lower plate on the entropy generation during the simultaneously developing flow in a parallel-plates channel are investigated. The obtained results addressing all cases are thoroughly in good agreement with the expectations that the entropy generation has its highest value at channel with the smallest aspect ratio at counter motion of the lower plate with the highest Re, Pr and Br/Ω values considered in the problem. An erratum to this article can be found at     

Transient temperature and thermally induced stress distributions in a partly-circumferentially heated cylindrical workpiece

This paper presents the numerical solutions of the transient temperature and thermally induced stress distributions in a partly-circumferentially heated cylindrical hollow workpiece (steel) with conjugate heat transfer. Outer surface of the workpiece is heated partly-circumferentially heat flux as its remainder outer surface is circumferentially cooled with fluid (water). Three phenomena have been considered as; (1) conduction inside the cylinder, (2) convection from the cylinder surface to the surrounding fluid, and (3) thermal stress produced by high temperature gradient inside the cylinder. The governing flow and energy equations have been solved numerically by using a control volume approach. The PHOENICS 3.2 and HEATING7 computer codes have been used for the numerical evaluation. The transient calculations have been performed individually for four fluid inlet velocities, u_i = 0.005, 0.01, 0.015 and 0.020 m/s, until the system attains steady-state. The results of this study clearly demonstrate that the temperature contours in the low inlet velocity cases are more near to a symmetric case with respect to the y = 0 plane than that in the high inlet velocity cases, and the increment of the inlet velocity exponentially reduces the temperatures and thermally induced stresses in the workpiece. The effective thermal stress differences occurring in the workpiece can be significantly reduced by the high fluid inlet velocity.     

Immobilization of CoII-(N,N′-bis(salicylidene)-2-aminobenzylamine) on Poly(pyrrole-co-o-anisidine)/Chitosan Composite Films: Application to Electrocatalytic Oxidation of Catechol

In this study, poly (pyrrole-co-o-anisidine)/chitosan composite (Cs) films were prepared by cyclic voltammetry technique on platinum electrode using different pyrrole and o-anisidine mole ratios. Immobilization process was accomplished in Co^II-(N,N′-bis(salicylidene)-2-aminobenzylamine)(CoL) dissolved 0.15 M acetonitrile-LiClO₄ solution by cyclic voltammetry technique at 0.2–2.0 V potential range. Three electrode methods were applied in all electrochemical studies. After immobilization process, the characterizations of the electro catalytic surfaces (Cs−CoL−Pt) were carried out by cyclic voltammetry and SEM images. The SEM images clearly indicated that the [CoL] complex is immobilized onto composite films. The electrocatalytic activity of the modified electrodes on the catechol was investigated using buffer solutions of different pH values. The results of catalytic studies revealed that, pH=10 buffer solution was the optimal solution and 1 : 1 Cs−CoL−Pt electrode was the best electrode for catechol oxidation. In square wave voltammetry measurements using this electrode, two linear working ranges were determined. The linear response ranges for catechol determination were found as 3.0 μM–6.0 μM and 16 μM–80 μM for the first and the second linear working ranges, respectively, with 1.1 μM detection limit.     

Spin-flop and spin-Peierls transition in doped CuGeO3

Ni⁺⁺ ions doped inorganic CuGeO₃ sample has been studied by using electron spin resonance (ESR) technique in the temperature range of 3–300 K. The ESR spectrum of Cu⁺⁺ ion has been observed to be strongly temperature dependent for inorganic spin-Peierls (SP) Cu_0.96Ni_0.04GeO₃ samples. The ESR line width and ESR amplitude exponentially vanishes below a critical temperature, T_sp = 14 K. The one-dimensional (1D) antiferromagnetic (AF) spin chain formed of Cu⁺⁺ is broken by Ni⁺⁺ (spin-1) ion, giving uncoupled spins at the end of the chains that give extra contribution to the spectra at lower temperature and stabilizes a Néel state. The g-factor is much smaller than the expected value for isolated Cu⁺⁺ and Ni⁺⁺ ions and is much more anisotropic than for undoped samples [O. Yalçın, B. Aktaş, J. Magn. Magn. Mater. 258/259 (2003) 137 (reference therein)]. It is shown that the ground state of dimerized spins is singlet. The spin-flop (SF) phenomenon is obtained from AF state mixed condition and then ferromagnetic (FM) state. The spin-flop field slightly increases when increasing temperature in the temperature range 100–300 K. The SF transition is showed almost AF order for Cu_0.96Ni_0.04GeO₃.     

Comparison effects of different doping on spin-Peierls transition in CuGeO(3)

The comparison between non-magnetic spin-Peierls (SP) and magnetic Néel ground states have been investigated in CuGeO₃ doped with Zn²⁺, Ni²⁺ and Mn²⁺ ions by using the electron spin resonance (ESR) techniques in the temperature range of 3–300 K. It was concluded that the one-dimensional (1D) antiferromagnetic (AF) spin chain formed of spin-1/2 (Cu²⁺) ions is broken by spin-0 (Zn²⁺), spin-1 (Ni²⁺), and spin-5/2 (Mn²⁺) ions, giving uncoupled spins at the end of the chains that give extra contribution to the spectra at lower temperature. An almost linearly dependence of frequency of resonance field has been showed for X-, K- and Q-band spectra. By the analysis of resonance field–frequency relations, the effects of the internal field is refined and thus the spectroscopic g-factor and internal field were calculated to be g = 1.9386 and H_i = 148 G, respectively.     

Novel fluorene/fluorenone DNA and RNA binders as efficient non-toxic ds-RNA selective fluorescent probes

A series of structurally similar 1-substitued heteroaryl fluorene derivatives were prepared in a simple single step reaction, oxidized to fluorenones and then both, fluorenes and fluorenones, were methylated to enhance the solubility and increase the affinity to DNA/RNA. Interactions of both, fluorene and fluorenone analogues with various ds-DNA, ds-RNA revealed strong ds-DNA/RNA binding, and various thermal stabilization effects. Most intriguingly, some fluorene derivatives showed opposite fluorescence change (increase for ds-RNA and decrease for ds-DNA), which was not previously reported for any fluorene analogue. CD experiments along with other methods support ds-DNA minor groove binding and major groove ds-RNA binding. All compounds showed negligible interaction with G-quadruplex DNA. Very low cell cytotoxicity of studied compounds combined with very efficient cellular uptake makes these fluorescent dyes safe for laboratory applications. Moreover, especially compounds which show opposite fluorescence response to ds-DNA and ds-RNA, are promising lead compounds for further studies aimed toward ds-RNA-specific fluorescence markers.     

Low pressure chromatographic separation of inorganic arsenic species using solid phase extraction cartridges

Routine water analysis of arsenic species requires simple, inexpensive, rapid and sensitive methods. To this end, we have developed two methods, which are based on the use of inexpensive solid phase extraction (SPE) cartridges as low pressure chromatographic columns for separation and hydride generation atomic absorption spectrometry (HGAAS) and hydride generation atomic fluorescence spectrometry (HGAFS) for detection of arsenic. Both anion exchange and reverse phase cartridges were successfully used to separate arsenite [As(III)] and arsenate [As(V)]. The composition, concentration, and pH of eluting buffers and the effect of flow rate were systematically investigated. Speciation of inorganic As(III) and As(V) were achieved within 1.5 min, with detection limits of 0.2 and 0.4 ng/ml, respectively. Both isocratic and step gradient elution techniques were suitable for the baseline resolution of As(III) and As(V) using anion exchange cartridges. Application of the methods to the speciation of As(III) and As(V) in untreated water, tap water, and bottled water samples were demonstrated. Results from the speciation of arsenic in a standard reference material water sample using these methods were in good agreement with the certified value and with inter-laboratory comparison results obtained using HPLC separation and inductively coupled plasma mass spectrometric detection (HPLC-ICPMS).