Suppression of Chaos and Phase Locking in Two Coupled Nonidentical Neurons under Periodic Input

Dynamical behaviour of two coupled neurons with at least one of them being chaotic is presented. Bifurcation diagrams and Lyapunov exponents are calculated to diagnose the dynamical behaviour of the coupled neurons with the increasing coupling strength. It is found that when the coupling strength increases, a chaotic neuron can be controlled by the coupling between neurons. At the same time, phase locking is studied by the maxima of the differences of instantaneous phases and average frequencies between two coupled neurons, and the inherent connection of phase locking and the suppression of chaos is formulated. It is observed that the onset of phase locking is closely related to the suppression of chaos. Finally, a way for suppression of chaos in two coupled nonidentical neurons under periodic input is suggested.     

The Hochschild class of the Chern character for semifinite spectral triples

We provide a proof of Connes’ formula for a representative of the Hochschild class of the Chern character for (p,∞)-summable spectral triples. Our proof is valid for all semifinite von Neumann algebras, and all integral p?1. We employ the minimum possible hypotheses on the spectral triples.     

Optical studies of pulsed-laser fragmentation of biliary calculi

The fragmentation of gallstones and kidney stones using pulsed visible laser radiation has recently been demonstrated; however, the fragmentation mechanism is not well understood. The temporal and spectral characteristics of the bright flash of light accompanying fragmentation of gallstones were studied using 0.8 and 360-s-long, 690-nm-wavelength, dye-laser pulses. Time-resolved visible emission spectra show a broad continuum upon which line spectra are superimposed. The continuum emission is due to free-free and free-bound electron transitions indicative of a plasma and the line spectra are due to neutral and ionized calcium. Initiation of this plasma is fluence rather than intensity dependent. A model is proposed in which laser energy is coupled to the plasma, which then impulsively expands, generating intense acoustic transients which fracture the stone.     

Evidence of a phase transition of RbHCO3 from high-resolution solid-state 13C and 87Rb NMR by comparison with KHCO3

A variable-temperature high-resolution 13C and 87Rb solid-state NMR study of powder rubidium hydrogencarbonate, RbHCO3, is presented for the first time. At ambient temperature, RbHCO3 is formed by centrosymmetric dimers linked by hydrogen bonds, but almost no information is available on this compound concerning proton disorder and the low-temperature phase. However, potassium hydrogencarbonate, KHCO3, which has an isomorphic structure for the high temperature phase, was well studied: it undergoes a non-ferroic, non-ferroelectric phase transition at Tc = 318 K between two monoclinic structures. The protons are disordered in an asymmetric double-well potential in the low-temperature phase, and the double-well potential becomes symmetric in the high-temperature phase. By comparison with recent solid-state NMR experimental results on KHCO3, we show that RbHCO3 undergoes a phase transition at Tc approximately 245 K, and give evidence that the proton dynamic disorder in both compounds is very similar.     

On bounds for the range of ordered variates II

Letx ₁, ,x _n be real numbers with8721.gif" alt="sum" align="MIDDLE" BORDER="0"> ₁ ⁿ x _j =0, |x ₁ ||x ₂ ||x _n |, and 8721.gif" alt="sum" align="MIDDLE" BORDER="0"> ₁ ⁿ f(|x _i |)=A>0, wheref is a continuous, strictly increasing function on [0, 8734.gif" alt="infin" align="MIDDLE" BORDER="0">) withf(0)=0. Using a generalized Chebycheff inequality (or directly) it is easy to see that an upper bound for |x _m | isf ^–1 (A/(n–m+1)). If (n–m+1) is even, this bound is best possible, but not otherwise. Best upper bounds are obtained in case (n–m+1) is odd provided either (i)f is strictly convex on [0, 8734.gif" alt="infin" align="MIDDLE" BORDER="0">), or (ii)f is strictly concave on [0, 8734.gif" alt="infin" align="MIDDLE" BORDER="0">). Explicit best bounds are given as examples of (i) and (ii), namely the casesf(x)=x ^p forp>1 and 0<p<1 respectively.     

Existence for evolutionary problems with linear growth by stability methods

We establish that solutions to the Cauchy–Dirichlet problem

${?}_{t}u?\mathrm{div}(D_{\xi }f(x,Du))=0$

for functionals $f:\mathrm{\Omega }\times {\mathbb{R}}^{N\times n}\to [0,\infty )$ of linear growth can be obtained as limits of solutions to flows with p-growth in the limit $p\downarrow 1$. The result can be interpreted on the one hand as a stability result. On the other hand it provides an existence result for general flows with linear growth.     

Nonlinear obstacle problems with double phase in the borderline case

In this paper we study a double phase problem with an irregular obstacle. The energy functional under consideration is characterized by the fact that both ellipticity and growth switch between a type of polynomial and a type of logarithm, which can be regarded as a borderline case of the double phase functional with $(p,q)$-growth. We obtain an optimal global Calderón–Zygmund type estimate for the obstacle problem with double phase in the borderline case.     

Synthesis and cytotoxicity of novel cholesterol–cobalt bis(dicarbollide) conjugates

The novel conjugates of cholesterol with cobalt – bis(dicarbollide) were synthesized by the ring-opening reactions of the cyclic oxonium derivatives of [3,3′-Co(C₂B₉H₁₁)₂]^– with the OH group of cholesterol 2-hydroxyethyl ether. The compounds obtained were tested for toxicity to glioblastoma U-87 MG cells and human embryo fibroblasts FECH-15 cells     

Multifractal detrended fluctuation analysis of derivative and spot markets

We investigate the multifractal properties of price increments in the cases of derivative and spot markets. Through the multifractal detrended fluctuation analysis, we estimate the generalized Hurst and the Renyi exponents for price fluctuations. By deriving the singularity spectrum from the above exponents, we quantify the multifractality of a financial time series and compare the multifractal properties of two different markets. The different behavior of each agent-group in transactions is also discussed. In order to identify the nature of the underlying multifractality, we apply the method of surrogate data to both sets of financial data. It is shown that multifractality due to a fat-tailed distribution is significant.