Political and economic rationality leads to velcro bifurcation

In this paper political and economic rationality is modelled regarding an economic problem with a four-dimensional dynamical system taking into consideration the information about the problem spread among the people who support the political alternatives. Under special parameter conditions velcro bifurcation occurs, which destabilizes the equilibrium points when information is going to spread. The last stable equilibrium point is related to the economically rational equilibrium point.     

Bifurcations in a predator-prey model with memory and diffusion II: Turing bifurcation

Research partially supported by the Hungarian National Foundation for Scientific Research, grant numbers 1186, 1994.     

A simple proof of Sanov’s theorem*

A simple self-contained proof of Sanov's theorem in τ-topology is given, well suited for a first course on large deviations. *This work was supported by the Hungarian National Foundation for Scientific Research under Grant T046376     

Characterisations of function spaces of generalised smoothness

We investigate function spaces of generalised smoothness of Besov and Triebel–Lizorkin type. Equivalent quasi-norms in terms of maximal functions and local means are given. An atomic decomposition theorem for this type of spaces is proved. Mathematics Subject Classification (2000) 46E35     

Multiple recurrence and nilsequences

Aiming at a simultaneous extension of Khintchine(X,X,m,T)(X,\mathcal{X},\mu,T) and a set A ? XA\in\mathcal{X} of positive measure, the set of integers n such that A T^2nA T^knA)(A)^k+1-\mu(A{\cap} T^{n}A{\cap} T^{2n}A{\cap} \ldots{\cap} T^{kn}A)>\mu(A)^{k+1}-\epsilon is syndetic. The size of this set, surprisingly enough, depends on the length (k+1) of the arithmetic progression under consideration. In an ergodic system, for k=2 and k=3, this set is syndetic, while for kòf(x)f(Tⁿx)f(T²ⁿx)? f(T^knx)  dm(x)\int{f(x)f(T^{n}x)f(T^{2n}x){\ldots} f(T^{kn}x) \,d\mu(x)} , where k and n are positive integers and f is a bounded measurable function. We also derive combinatorial consequences of these results, for example showing that for a set of integers E with upper Banach density d^*(E)>0 and for all {n ? \mathbbZ\colon d^*(E?(E+n)?(E+2n)?(E+3n)) > d^*(E)⁴-e}\big\{n\in\mathbb{Z}{\colon} d^*\big(E\cap(E+n)\cap(E+2n)\cap(E+3n)\big) > d^*(E)^4-\epsilon\big\}     

Mimicking catalase and catecholase enzymes by copper(II)-containing complexes

An imidazolate-bridged copper(II)-zinc(II) complex (Cu(II)-diethylenetriamino-μ-imidazolato-Zn(II)-tris(2-aminoethyl)amine perchlorate (denoted as “Cu,Zn complex”) and a simple copper(II) complex (Cu(II)-tris(2-aminoethyl) amine chloride (“Cu-tren”) were prepared and immobilised on silica gel (by hydrogen or covalent bonds) and montmorillonite (by ion exchange). The immobilised substances were characterised by FT-IR spectroscopy and their thermal characteristics were also studied. The obtained materials were tested in two probe reactions: catalytic oxidation of 3,5-di-tert-butyl catechol (DTBC) (catecholase activity) and the decomposition of hydrogen peroxide (catalase activity). It was found that the catecholase activity of the Cu,Zn complex increased considerably upon immobilization on silica gel via hydrogen bonds and intercalation by ion exchange among the layers of montmorillonite. The imidazolate-bridged copper(II)-zinc(II) complex and its immobilised versions were inactive in hydrogen peroxide decomposition. The Cu(II)-tris(2-aminoethyl)amine chloride complex displayed good catalase activity; however, immobilisation could not improve it.     

X-ray investigation of the role of the mixed emulsifier in the structure formation in o/w creams

The aim of this research work was to clarify the role of the mixed emulsifier in the structure formation and water binding mode in the case of o/w creams prepared with different surfactants. The swelling behavior of mixed emulsifiers was examined by means of direct investigation methods such as transmission electron microscopy (TEM) and X-ray diffraction. The detailed structure image of the creams was created with the help of the latter. The influence of the structure of the hydrophilic gel phase, and the structural changes during storage were studied with rheological methods. On the basis of the results, it can be stated that the investigated creams had different structures from those mentioned in the literature: surfactant did not create a mixed bilayer with the structure to furnish fatty amphiphile; instead, micelles were formed. These results correlated well with the results of the rheological tests.     

Study of fragmentation pattern and adsorption of 9-O-(triphenylsilyl)-10,11-dihydrocinchonidine on platinum by hydrogen/deuterium exchange using electrospray ionization ion-trap tandem mass spectrometry

We have studied the adsorption on a platinum (Pt) catalyst of two compounds utilizable as a chiral basic catalyst and a chiral modifier, dihydrocinchonidine (DHCD), and a new cinchona alkaloid derivative containing a bulky group, the Ph3SiO-DHCD molecule. The method of choice was the detection by electrospray ionization (ESI) ion-trap tandem mass spectrometry (MS/MS) of hydrogen/deuterium (H/D) exchange at room temperature, in tetrahydrofuran, at a D2 pressure of 1 bar. Based on the ESI-MS/MS spectrum of the new compound, we propose a mechanism for the formation of the silatropylium cation containing a Si-O bond. From the fragmentation pattern of Ph3SiO-DHCD it was confirmed that ESI-ion-trap MS/MS can be used to study the adsorption processes of complicated carbon compounds by investigating their H/D exchange reactions. In the case of Ph3SiO-DHCD, the results demonstrate that H/D exchange takes place mainly on the quinoline skeleton. However, the strong pi-bonded adsorption of the quinoline skeleton parallel with the imaginary plane of Pt is not preferred because the bulky Ph3Si group inhibits the multiple pi-bonded adsorption of the Ph3SiO-DHCD. Because of this hindrance the molecule was adsorbed tilted via the nonbonding electron pair of the N atom and C2' atom of the quinoline skeleton; consequently, mainly alkaloid-d1 and alkaloid-d2 are formed.     

Synthesis and characterization of Cu,Ni and Zn binding capability of some amino- and imidazole hydroxamic acids: Effects of substitution of side chain amino-N for imidazole-N or hydroxamic-N-H for -N-CH3 on metal complexation

Solution equilibrium studies on Cu(II)-, Ni(II)- and Zn(II)-N-Me-β-Alaninehydroxamic acid (N-Me-β-Alaha), -N-Me-α-alaninehydroxamic acid (N-Me-α-Alaha), -Imidazole-4-carbohydroxamic acid (Im-4-Cha), -N-Me-imidazole-4-carbohydroxamic acid (N-Me-Im-4-Cha) and -Imidazole-4-acetohydroxamic acid (Im-4-Aha) systems have been performed by pH-potentiometry, UV–Vis spectrophotometry, EPR, CD, ESI-MS and ¹H NMR methods. According to the results: (i) the amino-N atoms are more basic in N-Me-α-Alaha and N-Me-β-Alaha than the hydroxamate function, but the trend is just the opposite between the imidazole-N(3) and hydroxamate. (ii) The metal ion anchor is always the hydroxamate part in the amino acid derivatives, while it is always the imidazole-N(3) in the studied imidazolehydroxamic acids. (iii) The three studied N-Me derivatives do not form metallacrowns. Only hydroxamate type chelate is formed with N-Me-β-Alaha, but with N-Me-α-Alaha a new type of coordination mode (via amino-N and hydroxamate-O) also exists. N-Me-Im-4-Cha also forms a dinuclear complex, [M₂L₃], with Cu(II) and Ni(II) (but not with Zn(II)). In this complex, one of the three ligands might bridge the two metal ions (five-membered hydroxamate-(O,O) plus five-membered (N_im, O_carb) bridging bis-chelating mode), while each of the additional two ligands binds to one metal. (iv) The two studied N–H derivatives, having dissociable proton on the hydroxamic-N, are able to form metallacrown species. A pentanuclear complex, [M₅L₄H₋₄], is exclusively formed above pH 4 between Cu(II) and Im-4-Aha. Interestingly, this 12-metallacrown-4 type complex, although together with various mononuclear binding isomers, appears also with Ni(II) and Zn(II). Unfortunately, the complexes of Im-4-Cha are not soluble in water at physiological pH at all.