Flow invariance for solutions to nonlinear nonautonomous partial differential delay equations

We investigate the problem of existence and flow invariance of mild solutions to nonautonomous partial differential delay equations , t?s, us=φ, where B(t) is a family of nonlinear multivalued, α-accretive operators with D(B(t)) possibly depending on t, and the operators F(t,.) being defined—and Lipschitz continuous—possibly only on “thin” subsets of the initial history space E. The results are applied to population dynamics models. We also study the asymptotic behavior of solutions to this equation. Our analysis will be based on the evolution operator associated to the equation in the initial history space E.     

Near-pole polar diagram of objects and duality

The polar diagram of a set of points in a plane and its extracted dual EDPD were recently introduced for static and dynamic cases. In this paper, the near-pole polar diagram NPPD for a set of points is presented. This new diagram can be considered as a generalization of the polar diagram and has applications in several communication systems and robotics problems. After reviewing the NPPD of points, we solve the problem for a set of line segments and simple polygons in optimal time Θ(n log n), where n is the number of line segments or polygon vertices. We introduce duality for the NPPD of points and identify some applications.     

On integral Cayley sum graphs

Let S be a subset of a finite abelian group G. The Cayley sum graph Cay⁺(G, S) of G with respect to S is a graph whose vertex set is G and two vertices g and h are joined by an edge if and only if g + h ∈ S. We call a finite abelian group G a Cayley sum integral group if for every subset S of G, Cay⁺(G, S) is integral i.e., all eigenvalues of its adjacency matrix are integers. In this paper, we prove that all Cayley sum integral groups are represented by Z₃ and Zn₂ ⁿ, n ≥ 1, where Z_k is the group of integers modulo k. Also, we classify simple connected cubic integral Cayley sum graphs.     

Experimental Evaluation of the Influence of the Seawater Characteristics on Spatial and Temporal Variations of the Sound Speed in the Southern Abyssal,Intermediate and Shelf Zones of the Caspian Sea

Acoustical Physics - The results of the evaluation on the spatial and temporal changes of the underwater sound speed in the southern abyssal zone of the Caspian Sea are investigated. Experimental...     

Sonochemical Synthesis and Characterization of the Copper(II) Nanocomplex: DNA- and BSA-Binding,Cell Imaging,and Cytotoxicity Against the Human Carcinoma Cell Lines

The focus of the present work is the preparation of new metal-based nanodrug to overcome limitations of chemotherapy such as poor water solubility of most common chemotherapeutic drugs. The copper(II) complex of 1,2,4-triazine derivatives, [Cu(dppt)₂(H₂O)₂]²⁺ (dppt is 5,6-diphenyl- 3- (2-pyridyl)-1,2,4-triazine), has been synthesized at nano-size by sonochemical method and characterized by FTIR, zetasizer, and scanning electron microscopy (SEM). The interaction of the complex and nanocomplex with fish sperm DNA (FS–DNA) and BSA have been investigated under physiological conditions by a series of experimental methods. The results have indicated that the complex binds to FS–DNA by two biding modes, viz., electrostatic and intercalates into the base pairs of DNA. The competitive study with ethidium bromide (EB) shows that the complex and nanocomplex competes for the DNA–binding sites with EB. Protein binding studies show that the complex and nanocomplex could bind with BSA. The results of synchronous fluorescence of BSA show that additions of the complex affect the microenvironment of both tyrosine and tryptophan residues during the binding process. The in vitro cytotoxicity of the complex (solution in DMSO) and nanocomplex (colloid in H₂O) against the human carcinoma cell lines (MCF-7 and A-549) was evaluated by MTT assay. The results of in vitro cytotoxicity indicate that the complex and nanocomplex have excellent cytotoxicity activity against MCF-7 and A-549. Results of the microscopic analyses of the cancer cells confirm the results of the cytotoxicity.     

<Emphasis Type="SmallCaps">l</Emphasis>-Cysteine-functionalized magnetic nanoparticles (LCMNP): as a magnetic reusable organocatalyst for one-pot synthesis of 9-(1<Emphasis Type="Italic">H</Emphasis>-indol-3-yl) xanthen-4-(9<Emphasis Type="Italic">H</Emphasis>)-ones

l-Cysteine-functionalized magnetic nanoparticles (LCMNP) were introduced as an efficient and magnetically separable organocatalyst for the synthesis of 9-(1H-indol-3-yl) xanthen-4-(9H)-one derivatives. This class of compounds was synthesized via a one-pot three-component coupling reaction of 2-hydroxybenzaldehyde, dimedone, and indole in the presence of catalytic amount of LCMNP under mild and green conditions. High yields, short reaction time, easy workup, using environmental friendly conditions, and magnetic reusable catalyst are the advantages of this synthetic methodology. The LCMNP catalyst was reusable in this reaction at least for 6 times without significant decreasing in its catalytic activity.     

Removal of Arsenic (III) from natural contaminated water using magnetic nanocomposite: kinetics and isotherm studies

The application of newly synthesized Fe₃O₄/TiO₂–SiO₂ that is modified with zinc (FTSZ) as a sorbent, for the removal of arsenic from contaminated water has been investigated in the present study. SEM, FTIR, XRD, BET, Zeta potential sizer (ξ) analyses are used to determine the sorbent characterization. The effect of the operational parameters such as initial pH, initial concentration, and the contact time were studied. In addition, the equilibrium behavior of FTSZ in As(III) removal was investigated in the temperature range of 20–40 °C. The results showed that the equilibrium data were fitted well with Langmuir than Freundlich isotherm model. The maximum monolayer adsorption capacity estimated by Langmuir isotherm was 24.010 mg g^?1. Thermodynamic parameters, ?H°, ?S° and ?G° were also calculated from graphical interpretation of the experimental data. Standard heats of sorption (?H°) were found to be endothermic and ?S° values were calculated to be positive for the sorption of As(III) onto the adsorbent.     

Complete order amenability of the Fourier algebra

We define complete order amenability and first complete order cohomology groups for quantized Banach ordered algebras and show that the vanishing of the latter is equivalent to the operator amenability for the Fourier algebra.