A STUDY OF A FULLY COUPLED TWO-PARAMETER SYSTEM OF SEQUENTIAL FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS WITH NONLOCAL INTEGRO-MULTIPOINT BOUNDARY CONDITIONS

In this article, we discuss the existence and uniqueness of solutions for a coupled two-parameter system of sequential fractional integro-differential equations supplemented with nonlocal integro-multipoint boundary conditions. The standard tools of the fixed-point theory are employed to obtain the main results. We emphasize that our results are not only new in the given configuration, but also correspond to several new special cases for specific values of the parameters involved in the problem at hand.     

On the importance of zero-point effects in molecular level classical simulations of water

We discuss the fundamental difficulties involved in comparing energetic results obtained via classical simulations of bulk water with the observed values. Emphasis is placed on the difference between quantum and classical dynamics, and correction techniques, which can be used to emulate quantum effects in a classical system, are investigated. We present molecular dynamics simulation results for liquid water using the ‘Thole-type’ all atom polarizable water model, which has previously been shown to give reasonable results for both ice Ih and small water clusters. We employ expressions for the density of states power spectrum in the liquid in either atomic or rigid-body coordinates that are appropriate for rigid molecule simulations. It is demonstrated that the atomic power spectra can be written as a linear combination of the center of mass and rotational power spectra via the use of the ‘coupling matrix’ of linear coefficients. This approach allows us to introduce the concept of ‘fractional degrees of freedom’ (DOF) for nuclei in rigid molecule simulation. Within this framework, it is illustrated that in a rigid water molecule the oxygen and hydrogen atoms have 2.82 and 1.59 DOF, respectively (for the TIP4P geometry). Within our suggested approach, we finally demonstrate that Debye–Waller factors can be obtained from the coupling matrix and show that quantum corrections to the structure can be accounted for by raising the temperature of the system in a classical simulation by approximately 50°, a result consistent with previous suggestions.     

Differential evolution for sequencing and scheduling optimization

This paper presents a stochastic method based on the differential evolution (DE) algorithm to address a wide range of sequencing and scheduling optimization problems. DE is a simple yet effective adaptive scheme developed for global optimization over continuous spaces. In spite of its simplicity and effectiveness the application of DE on combinatorial optimization problems with discrete decision variables is still unusual. A novel solution encoding mechanism is introduced for handling discrete variables in the context of DE and its performance is evaluated over a plethora of public benchmarks problems for three well-known NP-hard scheduling problems. Extended comparisons with the well-known random-keys encoding scheme showed a substantially higher performance for the proposed. Furthermore, a simple slight modification in the acceptance rule of the original DE algorithm is introduced resulting to a more robust optimizer over discrete spaces than the original DE.     

Synthesis, structural characterization, and biological studies of six- and five-coordinate organotin(IV) complexes with the thioamides 2-mercaptobenzothiazole, 5-chloro-2-mercaptobenzothiazole, and 2-mercaptobenzoxazole

Organotin(IV) complexes with the formulas [(C6H5)3Sn(mbzt)] (1), [(C6H5)3Sn(cmbzt)] (3), and [(C6H5)2Sn(cmbzt)2] (4) (Hmbzt = 2-mercaptobenzothiazole and Hcmbzt = 5-chloro-2-mercaptobenzothiazole) have been synthesized and characterized by elemental analysis; FT-IR, Raman, 1H, 13C, and 119Sn NMR, and M?ssbauer spectroscopic techniques; and X-ray crystallography at various temperatures. The crystal structures of complexes 1, 3, and 4 were determined by X-ray diffraction at room temperature [295(1) or 293(2) K]. The complexes [(C6H5)3Sn(mbzo)] (2) and [(n-C4H9)2Sn(cmbzt)2] (5) (Hmbzo = 2-mercaptobenzoxazole) were synthesized by new improved methods, and their structures were determined at low temperature [100(1) K] and compared to those solved at room temperature. Comparison with {(CH3)2Sn(cmbzt)2]} (6), already reported, was also attempted. The influence of temperature on the geometry of the complexes is discussed. In the cases of complexes 1-3, three carbon atoms from phenyl groups and one sulfur atom and one nitrogen atom from thione ligands form a tetrahedrally distorted trigonal-bipyramidal geometry around the five-coordinate tin(IV) ion. In complexes 4-6, two carbon atoms from aryl groups and two sulfur atoms and two nitrogen atoms from thione ligands form a distorted tetrahedral geometry, tending toward octahedral, around the six-coordinate tin(IV) ions, with trans-C2, cis-N2, and cis-S2 configurations. Although the C-Sn and S-Sn bond distances are found to be constant in compounds 1-6, their N-Sn bond lengths vary significantly (from 2.635 to 3.078 A), with the longer distances found in the cases of five-coordinate complexes 1-3.     

Infrared spectrum of NH4+(H2O): evidence for mode specific fragmentation

The gas phase infrared spectrum (3250-3810 cm-1) of the singly hydrated ammonium ion, NH4+(H2O), has been recorded by action spectroscopy of mass selected and isolated ions. The four bands obtained are assigned to N-H stretching modes and to O-H stretching modes. The N-H stretching modes observed are blueshifted with respect to the corresponding modes of the free NH4+ ion, whereas a redshift is observed with respect to the modes of the free NH3 molecule. The O-H stretching modes observed are redshifted when compared to the free H2O molecule. The asymmetric stretching modes give rise to rotationally resolved perpendicular transitions. The K-type equidistant rotational spacings of 11.1(2) cm-1 (NH4+) and 29(3) cm-1 (H2O) deviate systematically from the corresponding values of the free molecules, a fact which is rationalized in terms of a symmetric top analysis. The relative band intensities recorded compare favorably with predictions of high level ab initio calculations, except on the nu3(H2O) band for which the observed value is about 20 times weaker than the calculated one. The nu3(H2O)/nu1(H2O) intensity ratios from other published action spectra in other cationic complexes vary such that the nu3(H2O) intensities become smaller the stronger the complexes are bound. The recorded ratios vary, in particular, among the data collected from action spectra that were recorded with and without rare gas tagging. The calculated anharmonic coupling constants in NH4+(H2O) further suggest that the coupling of the nu3(H2O) and nu1(H2O) modes to other cluster modes indeed varies by orders of magnitude. These findings together render a picture of a mode specific fragmentation dynamic that modulates band intensities in action spectra with respect to absorption spectra. Additional high level electronic structure calculations at the coupled-cluster singles and doubles with a perturbative treatment of triple excitations [CCSD(T)] level of theory with large basis sets allow for the determination of an accurate binding energy and enthalpy of the NH4+(H2O) cluster. The authors' extrapolated values at the CCSD(T) complete basis set limit are De [NH4+-(H2O)]=-85.40(+/-0.24) kJ/mol and DeltaH(298 K) [NH4+-(H2O)]=-78.3(+/-0.3) kJ/mol (CC2), in which double standard deviations are indicated in parentheses.     

Interaction of Fe(III) with herbicide-carboxylato ligands – Di-, tri- and tetra-nuclear compounds: Structure and magnetic behavior

The iron complexes with the phenoxyalkanoic acids 3,4-D, 2,3-D and 2,4,5-T in the presence or not of a nitrogen donor heterocyclic ligand, phen, were prepared and characterized. Interaction of Fe(III) with phenoxyalkanoic acids and phen leads to dinuclear neutral complexes while the absence of phen favours trinuclear cationic or tetranuclear neutral forms. The crystal structure of hexakis(2,3-dichlorophenoxyacetato)tris(methanol)oxotri-iron(III) chloride–methanol(1/3), [Fe₃O(2,3-D)₆(MeOH)₃]Cl · 3MeOH (2), and tetrakis(dimethyl-sulfoxide)octakis(2,4,5-trichlorophenoxyacetato)dioxotetra-iron(III) methanol(1/2)–water(1/1)–dimethylsulfoxide(1/0.8), {[Fe₄O₂(2,4,5-T)₈(dmso)₄] · 2MeOH · H₂O · 0.8dmso} (3), have been determined and refined by least-squares methods using three-dimensional Mo Kα data.     

TE Waves in Arbitrary Periodic Slow-wave Structures with Rectangular Grooves

The dispersion characteristics of the transverse electric modes in a waveguide with circular cross-section and periodic rectangular surface corrugations with smoothed edges are examined by the space harmonic method. The whole structure is divided into two regions, one in the propagation area and one inside the grooves. In the first region, the Floquet theorem is applied and the field distribution is expressed as a summation of spatial Bloch components, while an appropriate Fourier expansion of standing waves is used inside the grooves. Applying the appropriate interface conditions, an infinite system of equations is obtained, which is solved numerically by truncation. Numerical results are presented for several cases to check the convergence and the accuracy of the method, as well as its dependence on the corrugation profile. This formalism could be easily expanded to include all kind of waves that can in principle propagate in such slow-wave structures.     

Multiple image watermarking applied to health information management.

Information technology advances have brought forth new challenges in healthcare information management, due to the vast amount of medical data that needs to be efficiently stored, retrieved, and distributed, and the increased security threats that explicitly have to be addressed. The paper discusses the perspectives of digital watermarking in a range of medical data management and distribution issues, and proposes a complementary and/or alternative tool that simultaneously addresses medical data protection, archiving, and retrieval, as well as source and data authentication. The scheme imperceptibly embeds in medical images multiple watermarks conveying patient's personal and examination data, keywords for information retrieval, the physician's digital signature for authentication, and a reference message for data integrity control. Experimental results indicate the efficiency and transparency of the scheme, which conforms to the strict requirements that apply to regions of diagnostic significance.     

Partial backlogging inventory lot-size models for deteriorating items with fluctuating demand under inflation

In this paper, the traditional inventory lot-size model is extended to allow not only for general partial backlogging rate but also for inflation. The assumptions of equal cycle length and constant shortage length imposed in the model developed by Moon et al. [Moon, I., Giri, B.C., Ko, B., 2005. Economic order quantity models for ameliorating/deteriorating items under inflation and time discounting, European Journal of Operational Research 162(3), 773–785] are also relaxed. For any given number of replenishment cycles the existence of a unique optimal replenishment schedule is proved and further the convexity of the total cost function of the inventory system in the number of replenishments is established. The theoretical results here amend those in Yang et al. [Yang, H.L., Teng, J.T., Chern, M.S., 2001. Deterministic inventory lot-size models under inflation with shortages and deterioration for fluctuating demand, Naval Research Logistics 48(2), 144–158] and provide the solution to those two counterexamples by Skouri and Papachristos [Skouri, K., Papachristos, S., 2002. Note on “deterministic inventory lot-size models under inflation with shortages and deterioration for fluctuating demand” by Yang et al. Naval Research Logistics 49(5), 527–529.]. Finally we propose an algorithm to find the solution, and obtain some managerial results by using sensitivity analyses.