On a family of models of cell division cycle

The aim of this work is to generalize and study a model of cell division cycle proposed recently by Zheng et al. [Zheng Z, Zhou T, Zhang S. Dynamical behavior in the modeling of cell division cycle. Chaos, Solitons & Fractals 2000;11:2371–8]. Here we study the qualitative properties of a general family to which the above model belongs. The global asymptotic stability (GAS) of the unique equilibrium point E (idest of the arrest of cell cycling) is investigated and some conditions are given. Hopf’s bifurcation is showed to happen. In the second part of the work, the theorems given in the first part are used to analyze the GAS of E and improved conditions are given. Theorem on uniqueness of limit cycle in Lienard’s systems are used to show that, for some combination of parameters, the model has GAS limit cycles.     

Construction of recurrent bivariate fractal interpolation surfaces and computation of their box-counting dimension

Recurrent bivariate fractal interpolation surfaces (RBFISs) generalise the notion of affine fractal interpolation surfaces (FISs) in that the iterated system of transformations used to construct such a surface is non-affine. The resulting limit surface is therefore no longer self-affine nor self-similar. Exact values for the box-counting dimension of the RBFISs are obtained. Finally, a methodology to approximate any natural surface using RBFISs is outlined.     

Loss of alignment gain in the πh 9/2[541 1/2−] ⊗ (νi 13/2)2 band in 167Tm and neighbouring odd-Z N = 98 nuclei

Theπh_9/2[541 1/2^?] band in ¹⁶⁷Tm has been studied through the ¹²⁴Sn(⁴⁸Ca, p4n)¹⁶⁷Tm reaction at E _beam = 210 MeV. The favoured signature of the πh_9/2[541 1/2^?] band is observed to spin 61/2h?. A remarkable small gain in aligned angular momentum at the AB-band crossing has been found. The crossing frequency and the gain in aligned angular momentum for ¹⁶⁷Tm are compared with data for the N = 98 isotones of Lu, Ta and Re, and contrasted with Cranked Shell Model predictions, based on frequency diabatic configurations. Large deviations are found for the gain in aligned angular momentum.     

Quantum nondemolition measurements on two-level atomic systems and temporal Bell inequalities

The evolution of a two-level system subjected to stimulated transitions which is undergoing a sequence of measurements of the level occupation probability is evaluated. Its time correlation function is compared to the one obtained through the pure Schr?dinger evolution. Systems of this kind have been recently proposed for testing the quantum mechanical predictions against those of macrorealistic theories, by means of temporal Bell inequalities. The classical requirement of noninvasivity, needed to define correlation functions in the realistic case, finds a quantum counterpart in the quantum nondemolition condition. The consequences on the observability of quantum mechanically predicted violations to temporal Bell inequalities are drawn and compared to the already dealt case of the rf-SQUID dynamics. Received: 28 March 1996 / Revised version: 13 August 1996     

On the graded identities ofM 1,1(E)

We determine theS _n ×S _m -cocharacterX _n,m of the algebraM _1,1(E) and prove that theT ₂-ideal of its graded identities is generated by the polynomialsy ₁ y ₂−y ₂ y ₁ andz ₁ z ₂ z ₃+z ₃ z ₂ z ₁.     

Synthesis of 8,9-dihydrodipyrazolo[3,4-b:4′,3′-f][1,5]diazocin-10(1H)-one. A new ring system

8,9-Dihydrodipyrazolo[3,4-b:4′,3′-f][1,5]diazocin-10(1H)-ones 7 were prepared by cyclization of 1-ethyl-N,3-dimethyl-4-acetamido-N-(1-R₁-3-R₂-1H-pyrazol-5-yl)-1H-pyrazole-5-carboxamides 6 by a Bischler-Napieralski cyclization. A complete assignment of the chemical shifts to the carbon atoms of compound 7 was performed by different nmr experiments, such as DEPT and XHDEPT for one? bond C? H correlations and COLOC experiments for long-range C-H correlations.     

Solution and Solid‐State Studies on the Halide Binding Affinity of Perfluorophenyl‐Armed Uranyl–Salophen Receptors Enhanced by Anion–π Interactions

The enhancement of the binding between halide anions and a Lewis acidic uranyl–salophen receptor has been achieved by the introduction of pendant electron‐deficient arene units into the receptor skeleton. The association and the occurrence of the elusive anion–π interaction with halide anions (as tetrabutylammonium salts) have been demonstrated in solution and in the solid state, providing unambiguous evidence on the interplay of the concerted interactions responsible for the anion binding.     

Asymptotics of Two-boundary First-exit-time Densities for Gauss-Markov Processes

Methodology and Computing in Applied Probability - The problem of escape times from a region confined by two time-dependent boundaries is considered for a class of Gauss-Markov processes....     

The Norton–Simon hypothesis and the onset of non-genetic resistance to chemotherapy induced by stochastic fluctuations

By studying a simple but realistic biophysical model of tumor growth in the presence of a constant continuous chemotherapy, we show that if an extended Norton–Simon hypothesis holds, the system may have multiple equilibria. Thus, the stochastic bounded fluctuations that affect both the tumor carrying capacity and/or the drug pharmacodynamics (and/or the drug pharmacokinetics) may cause the transition from a small equilibrium to a far larger one, not compatible with the life of the host. In particular, we mainly investigated the effects of fluctuations that involve parameters nonlinearly affecting the deterministic model. We propose to frame the above phenomena as a new and non-genetic kind of resistance to chemotherapy.     

2,7-dimethyl-3,8-dinitrodipyrazolo[1,5-a:1',5'-d]pyrazine-4,9-dione: a new labelling reagent for liquid chromatographic analysis of amino acids

Linear alkylbenzenes (LABs) are discharged into the environment as sub-products of linear alkylbenzenesulfonate (LAS) detergent. Their association with LAS is attributed to the incomplete sulfonation of the LABs in detergent manufacturing resulting in products having LAB. Recently there has been widespread interest in their use as markers of sewage effluent in the aquatic environment. Although LABs may be potentially useful in assessing the distribution and degradation of domestic wastewater, studies about it are still limited probably due to the analytical difficulties.In this article, a new analytical method for the determination of LABs in detergents using gas chromatography coupled to mass spectrometry (GC-MS) in combination with solid phase microextraction (SPME) is proposed. This alternative sample preparation technology presents several advantages, since it is solvent free, fast, uses the whole sample for analysis, requires only small amounts of sample and the fibers for the extraction procedure are reusable. A factorial experimental design was utilized to obtain the optimum values for the main operational parameters in the analysis of LABs in detergents using direct SPME in the pre-concentration step.