New predictor-corrector approach for nonlinear fractional differential equations: error analysis and stability

In this paper, the predictor-corrector approach is used to propose two algorithms for the numerical solution of linear and non-linear fractional differential equations (FDE). The fractional order derivative is taken to be in the sense of Caputo and its properties are used to transform FDE into a Volterra-type integral equation. Simpson''s 3/8 rule is used to develop new numerical schemes to obtain the approximate solution of the integral equation associated with the given FDE. The error and stability analysis for the two methods are presented. The proposed methods are compared with the ones available in the literature. Numerical simulation is performed to demonstrate the validity and applicability of both the proposed techniques. As an application, the problem of dynamics of the new fractional order non-linear chaotic system introduced by Bhalekar and Daftardar-Gejji is investigated by means of the obtained numerical algorithms.     

Dynamics of a hepatitis B model with saturated incidence

In this article, we present a hepatitis B epidemic model with saturated incidence. The dynamic behaviors of the deterministic and stochastic system are studied. To this end, we first establish the local and global stability conditions of the equilibrium of the deterministic model. Second, by constructing suitable stochastic Lyapunov functions, the sufficient conditions for the existence of ergodic stationary distribution as well as extinction of hepatitis B are obtained.     

Existence of approximate solutions of the forced Duffing equation with discontinuous type integral boundary conditions

We develop a generalized quasilinearization technique to obtain a sequence of approximate solutions converging monotonically and quadratically to the unique solution of the forced Duffing equation with discontinuous type integral boundary conditions.     

Commutative zeropotent semigroups with few invariant congruences

Commutative semigroups satisfying the equation 2x + y = 2x and having only two G-invariant congruences for an automorphism group G are considered. Some classes of these semigroups are characterized and some other examples are constructed. The first author was supported by the Grant Agency of Czech Republic, grant no. 201/01/D047. This work is a part of the research project MSM 0021620839 financed by MŠMT     

Gas-phase basicities of the isomeric dihydroxybenzoic acids and gas-phase acidities of their radical cations

The thermochemical acid/base properties of the six dihydroxybenzoic acids (x,y-DHB) as prototypical matrices used in matrix-assisted laser desorption/ionization (MALDI) have been investigated. The ground-state gas-phase basicities (GB) of the six DHB isomers and the gas-phase acidities (deltaG acid) of the corresponding radical cations ([x,y-DHB]*+) have been determined by Fourier-transform ion cyclotron resonance mass spectrometry employing the thermokinetic method. The gas-phase basicities vary from 814 kJ mol-1 for the least basic isomer, 3,5-DHB, to 831 kJ mol-1 for the most basic isomer, 2,4-DHB. The obtained gas-phase acidities of the corresponding radical cations vary from 815 kJ mol-1 for the most acidic species, 3,4-DHB, to 858 kJ mol-1 for the least acidic one, 2,5-DHB. The results indicate that ground-state proton transfer from the matrix radical cations to the analyte may play a role in the ionization process of MALDI, whereas proton transfer from protonated matrix molecules can be excluded.     

On the complexation kinetics for metallization of organic layers: palladium onto a pyridine-terminated araliphatic thiol film

Palladium nanoparticles have been deposited electrochemically onto self-assembled monolayers (SAMs) of 4-(4-(4-pyridyl)phenyl)phenylmethanethiol. A pronounced correlation between the kinetics of the complexation between pyridine nitrogens and Pd cations and the sample potential has been observed. The amount of the Pd deposit significantly increases by adjusting the sample potential during the complexation step to values below the point of zero charge. The size of the spherical shaped Pd nanoparticles varies within a certain limit according to the amount of Pd(2+) ions initially coordinated on top of the SAM. The metallic state of these particles was confirmed by X-ray photoelectron spectroscopy and infrared reflection-absorption spectroscopy. Moreover, CO adsorption on the clean Pd deposit revealed further information about the crystallographic orientation of the nanoparticles.     

Antioxidant potential in callus culture of Artemisia amygdalina Decne

This study was conducted to analyse the free radical scavenging potential of callus obtained from nodal segments and leaf explants of Artemisia amygdalina Decne. The explants were inoculated on MS medium augmented with various concentrations of BAP, Kn, NAA and 2,4-D for callus induction. In this study, 12.42?g of callus developed from the leaf explant on MS (NAA 10?+?BAP 7.5?μM) and 8.81?g of callus developed from nodal explant on NAA 2?μM+BAP 2?μM. Callus raised from both explants on all treatments seemed non-regenerative but BAP 2?μM produced 7.33 shoots and BAP 15?μM produced callus and 5 shoots per nodal segment. Callus was analysed for antioxidant activity via DPPH, riboflavin photoxidation and DNA damage assays. Methanol and aqueous extracts show more scavenging in DPPH, deoxyribose assay and in contrast, petroleum ether and ethyl acetate extracts show higher activity in riboflavin photoxidation assay. Tocopherol, ascorbic acid and BHT were used as controls.     

Electrochemically deposited Pd islands on an organic surface: the presence of Coulomb blockade in STM I(V) curves at room temperature

Palladium islands with a thickness of a few monolayers were deposited on top of a self-assembled monolayer (SAM) fabricated from 4-mercaptopyridine. In the I(V) curves obtained using the scanning tunneling microscope (STM) clearly the signature of Coulomb blockade is observed, explicitly demonstrating that these islands are coupled to the underlying gold substrate only via a tunneling barrier; this spectroscopic feature also allows to distinguish the palladium islands from similar morphological features present on the gold substrate prior to palladium deposition.     

A multifunctional micro-fluidic system for dielectrophoretic concentration coupled with immuno-capture of low numbers of Listeria monocytogenes

In this study, we demonstrated a micro-fluidic system with multiple functions, including concentration of bacteria using dielectrophoresis (DEP) and selective capture using antibody recognition, resulting in a high capture efficiency of bacterial cells. The device consisted of an array of oxide covered interdigitated electrodes on a flat silicon substrate and a approximately 16 microm high and approximately 260 microm wide micro-channel within a PDMS cover. For selective capture of Listeria monocytogenes from the samples, the channel surface was functionalized with a biotinylated BSA-streptavidin-biotinylated monoclonal antibody sandwich structure. Positive DEP (at 20 V(pp) and 1 MHz) was used to concentrate bacterial cells from the fluid flow. DEP could collect approximately 90% of the cells in a continuous flow at a flow rate of 0.2 microl min(-1) into the micro-channel with concentration factors between 10(2)-10(3), in sample volumes of 5-20 microl. A high flow rate of 0.6 microl min(-1) reduced the DEP capture efficiency to approximately 65%. Positive DEP attracts cells to the edges of the electrodes where the field gradient is the highest. Cells concentrated by DEP were captured by the antibodies immobilized on the channel surface with efficiencies of 18 to 27% with bacterial cell numbers ranging from 10(1) to 10(3) cells. It was found that DEP operation in our experiments did not cause any irreversible damage to bacterial cells in terms of cell viability. In addition, increased antigen expression (antigens to C11E9 monoclonal antibody) on cell membranes was observed following the exposure to DEP.