C n -almost automorphic solutions for partial neutral functional differential equations

In this work, we study the existence of C ⁿ -almost periodic solutions and C ⁿ -almost automorphic solutions (n?≥?1), for partial neutral functional differential equations. We prove that the existence of a bounded integral solution on ?⁺ implies the existence of C ⁿ -almost periodic and C ⁿ -almost automorphic strict solutions. When the exponential dichotomy holds for the homogeneous linear equation, we show the uniqueness of C ⁿ -almost periodic and C ⁿ -almost automorphic strict solutions.     

AF-Domains and Their Generalizations

In this article, we are concerned with the study of the dimension theory of tensor products of algebras over a field k. We introduce and investigate the notion of generalized AF-domain (GAF-domain for short) and prove that any k-algebra A such that the polynomial ring in one variable A[X] is an AF-domain is in fact a GAF-domain, in particular any AF-domain is a GAF-domain. Moreover, we compute the Krull dimension of A? _k B for any k-algebra A such that A[X] is an AF-domain and any k-algebra B generalizing the main theorem of Wadsworth in [16 Wadsworth , A. R. ( 1979 ). The Krull dimension of tensor products of commutative algebras over a field . J. London Math. Soc. 19 : 391 – 401 .[Crossref], [Web of Science ®] , [Google Scholar]].     

A new method for solving Pareto eigenvalue complementarity problems

In this paper, we introduce a new method, called the Lattice Projection Method (LPM), for solving eigenvalue complementarity problems. The original problem is reformulated to find the roots of a nonsmooth function. A semismooth Newton type method is then applied to approximate the eigenvalues and eigenvectors of the complementarity problems. The LPM is compared to SNM_min and SNM_FB, two methods widely discussed in the literature for solving nonlinear complementarity problems, by using the performance profiles as a comparing tool (Dolan, Moré in Math. Program. 91:201–213, 2002). The performance measures, used to analyze the three solvers on a set of matrices mostly taken from the Matrix Market (Boisvert et al. in The quality of numerical software: assessment and enhancement, pp. 125–137, 1997), are computing time, number of iterations, number of failures and maximum number of solutions found by each solver. The numerical experiments highlight the efficiency of the LPM and show that it is a promising method for solving eigenvalue complementarity problems. Finally, Pareto bi-eigenvalue complementarity problems were solved numerically as an application to confirm the efficiency of our method.     

Global stability and a non-standard finite difference scheme for a diffusion driven HBV model with capsids

A diffusion driven model for hepatitis B virus (HBV) infection, taking into account the spatial mobility of both the HBV and the HBV DNA-containing capsids is presented. The global stability for the continuous model is discussed in terms of the basic reproduction number. The analysis is further carried out on a discretized version of the model. Since the standard finite difference (SFD) approximation could potentially lead to numerical instability, it has to be restricted or eliminated through dynamic consistency. The latter is accomplished by using a non-standard finite difference (NSFD) scheme and the global stability properties of the discretized model are studied. The results are numerically illustrated for the dynamics and stability of the various populations in addition to demonstrating the advantages of the usage of NSFD method over the SFD scheme.     

Interactions of gamma rays with undoped and Mn-doped sodium phosphate glasses

Ultraviolet and visible spectroscopic measurements were used to investigate prepared undoped and Mn-doped sodium phosphate glasses before and after successive gamma irradiation. The effects of both glass composition and MnO₂ content on the generation of radiation-induced defects were investigated. Undoped sodium phosphate glass shows strong UV absorption, which is attributed to the presence of trace iron impurities present in the raw materials. Mn-doped glasses reveal an additional visible broad band centered at about 500 nm due to Mn³⁺, which has recently been related to the ⁵E_g →⁵T_2g transition. The radiation-induced bands are correlated with the generation of liberated electron–hole pairs during the process of gamma irradiation and the possibility of photochemical reactions especially with trace iron impurities and manganese ions. The intensity and the position of the induced bands are observed to depend on the type and composition of glass, concentration of the dopant and also on the irradiation dose. Manganese ions when present in relatively higher content have been found to show a shielding behavior towards the effects of progressive gamma irradiation causing a retardation of the growth of the induced defects. Infrared and Raman spectra of the undoped and Mn-doped glasses were measured to investigate the structural phosphate groups present and the effect of MnO₂ on the network structure. An ESR investigation was carried out to confirm the state of manganese ions in the prepared sodium phosphate glasses.     

Role of non-lamellar-forming lipid in promotion of liposomal fusion

Membrane fusion is an important process in a wide range of cellular and sub-cellular activities. It is evident that during the intermediate stages of fusion some transitory non-bilayer configurations must appear within the lipid moiety. Using fluorescence techniques, we have studied here the process of aggregation and fusion of liposomes made of lipids, namely 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) and 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC). When mixed together, the complete fusion between these two liposomes took around 44 h as both DPPC and DMPC favour lamellar configuration. When the mixture was incubated at 42°C the fusion process was completed after 23 h. But, when 1,2-dipalmitoyl-sn-glycero-3-phosphoethanolamine (DPPE) was added in the liposomal matrix the time for fusion was reduced to 21 h for mixture without incubation and 17 h when the mixture was incubated. This indicates that DPPE having a tendency to assume non-lamellar conformation, promoted destabilisation of the lamellar conformation within the liposome which facilitated the fusion between two apposing bilayers.     

Semi-Analytical Simulation of Titanium-Indiffused Lithium Niobate–Integrated Optic Directional Couplers Consisting of Curved Waveguides

Integrated optic directional couplers consisting of curved waveguides are simulated analytically by solving the Riccati equation. The coupling coefficient between the curved waveguides with a parabolically varying gap and the condition of total power transfer between the waveguides are derived. In order to compute the overall coupling coefficient and hence the power distribution along the waveguides for Ti:LiNbO ₃ curved waveguide directional couplers, the coupling coefficient for straight waveguide couplers is computed for different gaps using the effective-index-based matrix method (EIMM). Finally, the power distribution in the curved waveguides along the length is computed. The method is mostly analytical except the effective-index method and is computationally simple.     

A general nonlocal nonlinear model for buckling of nanobeams

This study presents a unified model for the nonlocal response of nanobeams in buckling and postbuckling states. The formulation is suitable for the classical Euler–Bernoulli, first-order Timoshenko, and higher-order shear deformation beam theories. The small-scale effect is modeled according to the nonlocal elasticity theory of Eringen. The equations of equilibrium are obtained using the principle of virtual work. The stress resultants are developed taking into account the nonlocal effect. Analytical solutions for the critical buckling load and the amplitude of the static nonlinear response in the postbuckling state are obtained. It is found out that as the nonlocal parameter increases, the critical buckling load reduces and the amplitude of buckling increases. Numerical results showing variation of the critical buckling load and the amplitude of buckling with the nonlocal parameter and the length-to-height ratio for simply supported and clamped–clamped nanobeams are presented.     

Interactions of Nile Blue with Micelles, Reverse Micelles and a Genomic DNA

In this contribution we report studies on the nature of binding of a small ligand/drug Nile blue (NB) with sodium dodecyl sulfate (SDS) micelles, bis-(2-ethylehexyl) sulfosuccinate (AOT)/isooctane reverse micelles (RM) and a genomic DNA extracted from Salmon sperm. With detailed steady state and picosecond resolved optical spectroscopic techniques, we examined the fluorescence quenching of the ligand upon complexation with the SDS monomers and DNA. Polarization analyzed picosecond-resolved fluorescence measurements reveal geometrical restriction on the probe in SDS micelles, AOT-RM and DNA. Steady state and time resolved studies on the probe in nanocages of AOT RM with various degrees of hydration (w₀) reveal the existence of NB as two distinct species namely, neutral and cationic. This study confirms that the emission of NB in aqueous micelles and DNA solution is due to the cationic form of the drug. Our experiments clearly identified non-specific electrostatic and intercalative modes of interaction of the probe with the DNA at lower and higher DNA concentrations respectively. The nature of binding of NB in presence of the DNA and SDS micelles reveals that the binding affinity of the probe is higher with the micelles than with the DNA. The complex rigidity of NB with DNA and its fluorescence quenching with DNA elucidate a strong recognition mechanism between NB and DNA.