Strongly almost (<Emphasis Type="Italic">ω, λ, q</Emphasis>)-summable sequences

The purpose of this paper is to introduce the spaces of sequences that are strongly almost (ω, λ, q)-summable with respect to a modulus function. We give some relations related to these sequence spaces. It is also shown that if a sequence is strongly (ω, λ, q)-summable with respect to a modulus function, then it is S(λ _q )-statistically convergent.     

One-Parameter Homothetic Motion in the Hyperbolic Plane and Euler-Savary Formula

In [10] one-parameter planar motion was first introduced and the relations between absolute, relative, sliding velocities (and accelerations) in the Euclidean plane \mathbb E²{{\mathbb E}^2} were obtained. Moreover, the relations between the complex velocities of one-parameter motion in the complex plane were provided by [10]. One-parameter planar homothetic motion was defined in the complex plane, [9]. In this paper, analogous to homothetic motion in the complex plane given by [9], one-parameter planar homothetic motion is defined in the hyperbolic plane. Some characteristic properties about the velocity vectors, the acceleration vectors and the pole curves are given. Moreover, in the case of homothetic scale h identically equal to 1, the results given in [15] are obtained as a special case. In addition, three hyperbolic planes, of which two are moving and the other one is fixed, are taken into consideration and a canonical relative system for one-parameter planar hyperbolic homothetic motion is defined. Euler-Savary formula, which gives the relationship between the curvatures of trajectory curves, is obtained with the help of this relative system.     

Comparison of polyphenol extractions from olive pomace and solid fraction of olive mill waste water

The solid fraction of olive mill waste water (OMWW) was separated from OMWW and then the solutes in the solid fraction of OMWW were extracted with ethanol. The detection of polyphenols in the ethanol extract showed the presence of polyphenols in the solid fraction of OMWW. Effects of solvent-to-solid ratio, extraction and agitation time on the extraction of polyphenols from the solid fraction of OMWW were examined and the maximum amount of polyphenol was extracted from the solid fraction of OMWW with a solvent-to-solid ratio of 15 at 70?min of extraction and 10?min of agitation time. Percent yields and purities of the polyphenols extracted from solid fraction of OMWW were higher than those of the polyphenols extracted from olive pomace with ethanol at 70?min of extraction and 10?min of agitation time with solvent-to-solid ratio of 15.     

Stochastic resonance in hybrid scale-free neuronal networks

We study the phenomenon of stochastic resonance in a system of coupled neurons that are globally excited by a weak periodic input signal. We make the realistic assumption that the chemical and electrical synapses interact in the same neuronal network, hence constituting a hybrid network. By considering a hybrid coupling scheme embedded in the scale-free topology, we show that the electrical synapses are more efficient than chemical synapses in promoting the best correlation between the weak input signal and the response of the system. We also demonstrate that the average degree of neurons within the hybrid scale-free network significantly influences the optimal amount of noise for the occurrence of stochastic resonance, indicating that there also exists an optimal topology for the amplification of the response to the weak input signal. Lastly, we verify that the presented results are robust to variations of the system size.     

Centralizers of Involutions in Locally Finite Groups

The present article deals with locally finite groups G having an involution φ such that C _G (φ) is an SF-group. It is shown that G possesses a normal subgroup B which is a central product of finitely many groups isomorphic to PSL(2, K _i ) or SL(2, K _i ) for some infinite locally finite fields K _i of odd characteristic, such that [G, φ]′/B and G/[G, φ] are both SF-groups.     

Global Well-Posedness for the Generalized Large-Scale Semigeostrophic Equations

We prove existence and uniqueness of global classical solutions to the generalized large-scale semigeostrophic equations with periodic boundary conditions. This family of Hamiltonian balance models for rapidly rotating shallow water includes the L ₁ model derived by R. Salmon in 1985 and its 2006 generalization by the second author. The results are, under the physical restriction that the initial potential vorticity is positive, as strong as those available for the Euler equations of ideal fluid flow in two dimensions. Moreover, we identify a special case in which the velocity field is two derivatives smoother in Sobolev space as compared to the general case. Our results are based on careful estimates which show that, although the potential vorticity inversion is nonlinear, bounds on the potential vorticity inversion operator remain linear in derivatives of the potential vorticity. This permits the adaptation of an argument based on elliptic L ^p theory, proposed by Yudovich in 1963 for proving existence and uniqueness of weak solutions for the two-dimensional Euler equations, to our particular nonlinear situation.     

Optical helicity and Hertz vectors

We study the conserved quantity associated with the dual symmetry of the Maxwell equations, called the optical helicity, by means of transverse Hertz vectors. In the presence of charges, its evolution yields the integral of $\mathit{E}?\mathit{B}$ which is the anomaly term for chiral fermions. We also discuss the helicity change in condensed matter systems where topological magnetoelectric effect emerges. An alternative expression of the optical helicity is also found. Lastly, a dual symmetric Hertz Lagrangian is constructed and its conserved charge is derived.     

Effects of the network structure and coupling strength on the noise-induced response delay of a neuronal network

The Hodgkin-Huxley (H-H) neuron model driven by stimuli just above threshold shows a noise-induced response delay with respect to time to the first spike for a certain range of noise strengths, an effect called “noise delayed decay” (NDD). We study the response time of a network of coupled H-H neurons, and investigate how the NDD can be affected by the connection topology of the network and the coupling strength. We show that the NDD effect exists for weak and intermediate coupling strengths, whereas it disappears for strong coupling strength regardless of the connection topology. We also show that although the network structure has very little effect on the NDD for a weak coupling strength, the network structure plays a key role for an intermediate coupling strength by decreasing the NDD effect with the increasing number of random shortcuts, and thus provides an additional operating regime, that is absent in the regular network, in which the neurons may also exploit a spike time code.     

Microwave Assisted Synthesis of Chitosan Nanoparticles

Chitosan nanoparticles (CHN) were prepared based on ionotropic gelation between low moleculer weight chitosan and sodium tripolyphosphate (TPP) under microwave irradiation. Particle size, zeta potential, and FT-IR techniques were used for characterization of CHN. The influence of reaction time on the nanoparticle size distribution was investigated, and the results showed that the microwave irradiation method evidently decreases the reaction times and particle size over the conventional method. It was determined by the results of the zeta potential measurements that synthesized CHN under microwave irradiation clearly exhibits more homogeneous and stable dispersion.     

Synthesis of chiral crown ethers and complexation with chiral protonated amine compounds: X-ray crystal and nuclear magnetic resonance studies of perchlorate salt of chiral benzo-monoaza-15-crown-5 and chiral monoaza-15-crown-5

The X-ray crystal structure of IX, perchlorate salt of R-(?-2-ethyl-N-benzyl-4,7,19,13-tetraoxa-8,9-benzo-1-azacyclopentadec-8-ene has been determined. In the molecule, the protonated nitrogen atom participates in two N-H?O hydrogen bonds. The unusually high proton affinity of aza crown ether leads to the formation of diastreomer instead of complex formation with chiral R-(+)-1-phenyl ethyl ammonium perchlorate and S-(?)-1-phenyl ethyl ammonium perchlorate. The complex ability of host ethers was evaluated in terms of structural modification.