Ionok kölcsönhatásai biológiailag aktív molekulákkal és szigetelő nano-strukturákkal = Interactions of Ions with Biologically Active Molecules and Nano Structures

Az ionterelés jelenségét elsőként mutattuk ki Al2O3 anyagú nanokapillárisokon az ATOMKI ECR ionforrásánál. Egyszerű modelleket állítottunk fel a jelenség értelmezésére. Két dimenzióban tanulmányoztuk a kilépő ionok szögeloszlását és jelentős UV foton kibocsátást figyeltünk meg a kapillárisokból az ion - felület kölcsönhatások eredményeképpen. Kb. 55 mikron hosszú és 10 mikron átmérőjű kapillárisokat állítottunk elő PMMA műanyagból, de ionterelést ilyen kis átmérő-hossz aránynál nem lehetett kimutatni. Külföldi együttműködésben vizsgáltuk PET polimer anyagú kapillárisokon az iontereléshez vezető feltöltődés dinamikáját és kimutattuk az időlegesen kialakuló feltöltött szigetek jelenlétét a kapillárisok belsejében. Vizsgáltuk biológiai szempontból fontos, kis molekulák ionbombázás hatására történő széttöredeződését, nagy és kis ütközési energiákon itthon és francia együttműködésben. Megmértük a különböző molekulatöredékek szög- és energiaeloszlását. Kis energiákon anizotrópiák jelentek meg, melyek a lövedék ion utóhatásainak valamint direkt mag-mag ütközéseknek tulajdoníthatók. Az aszimmetrikus vízmolekula esetében ezektől eltérő típusú anizotrópia is megjelent, orientációs effektusokra utalva a széttöredeződést előidéző elektron befogási folyamatokban. A hasonló szerkezetű H2S molekula esetén nem találtunk ilyen típusú anizotrópiát. A széttöredeződés módja minden vizsgált molekulánál erősen függött a lövedékion töltésétől, elméletileg egyelőre nem tisztázott okokból. | We observed the ion guiding phenomena in Al2O3 capillaries for the first time at the ECR ion source in ATOMKI. We developed simple models in order to explain the phenomena. The angular distribution of the transmitted ions was studied in two dimensions. Significant UV emission was observed as a result of ion-surface interactions. Nanocapillaries with a length of 55 micron and a diameter of ~10 micron were produced of PMMA polymer. At this aspect ratio ion guiding was not found. We studied the charging-up dynamics of PET polymer capillaries within an international collaboration. Evidence for temporary, charged patches developing in the capillaries has been found. We studied ion impact induced fragmentation of small molecules of biological relevance at low and high impact energies at our institute and in French collaboration. The energy and angular distributions of the different molecule fragments were measured. Anisotropies have been found at low energies due to post collision and binary encounter effects. Another type of anisotropy was found for the asymmetric H2O molecule indicating the presence of orientation effects in the electron capture processes that lead to fragmentation. For H2S with a similar structure, such anisotropy was not found. The way of fragmentation strongly depends on the projectile charge for all the investigated molecules. This is not fully understood theoretically

Coloring Cantor sets and resolvability of pseudocompact spaces

Let us denote by $\Phi(\lambda,\mu)$ the statement that $\mathbb{B}(\lambda) = D(\lambda)^\omega$, i.e. the Baire space of weight $\lambda$, has a coloring with $\mu$ colors such that every homeomorphic copy of the Cantor set $\mathbb{C}$ in $\mathbb{B}(\lambda)$ picks up all the $\mu$ colors. We call a space $X\,$ {\em $\pi$-regular} if it is Hausdorff and for every non-empty open set $U$ in $X$ there is a non-empty open set $V$ such that $\overline{V} \subset U$. We recall that a space $X$ is called {\em feebly compact} if every locally finite collection of open sets in $X$ is finite. A Tychonov space is pseudocompact iff it is feebly compact. The main result of this paper is the following. Theorem. Let $X$ be a crowded feebly compact $\pi$-regular space and $\mu$ be a fixed (finite or infinite) cardinal. If $\Phi(\lambda,\mu)$ holds for all $\lambda < \widehat{c}(X)$ then $X$ is $\mu$-resolvable, i.e. contains $\mu$ pairwise disjoint dense subsets. (Here $\widehat{c}(X)$ is the smallest cardinal $\kappa$ such that $X$ does not contain $\kappa$ many pairwise disjoint open sets.) This significantly improves earlier results of van Mill , resp. Ortiz-Castillo and Tomita.Comment: 8 page

Pinning Down versus Density

The pinning down number ${pd}(X)$ of a topological space $X$ is the smallest cardinal $\kappa$ such that for any neighborhood assignment $U:X\to \tau_X$ there is a set $A\in [X]^\kappa$ with $A\cap U(x)\ne\emptyset$ for all $x\in X$. Clearly, c$(X) \le {pd}(X) \le {d}(X)$. Here we prove that the following statements are equivalent: (1) $2^\kappa<\kappa^{+\omega}$ for each cardinal $\kappa$; (2) ${d}(X)={pd}(X)$ for each Hausdorff space $X$; (3) ${d}(X)={pd}(X)$ for each 0-dimensional Hausdorff space $X$. This answers two questions of Banakh and Ravsky. The dispersion character $\Delta(X)$ of a space $X$ is the smallest cardinality of a non-empty open subset of $X$. We also show that if ${pd}(X)<{d}(X)$ then $X$ has an open subspace $Y$ with ${pd}(Y)<{d}(Y)$ and $|Y| = \Delta(Y)$, moreover the following three statements are equiconsistent: (i) There is a singular cardinal $\lambda$ with $pp(\lambda)>\lambda^+$, i.e. Shelah's Strong Hypothesis fails; (ii) there is a 0-dimensional Hausdorff space $X$ such that $|X|=\Delta(X)$ is a regular cardinal and ${pd}(X)<{d}(X)$; (iii) there is a topological space $X$ such that $|X|=\Delta(X)$ is a regular cardinal and ${pd}(X)<{d}(X)$. We also prove that $\bullet$ ${d}(X)={pd}(X)$ for any locally compact Hausdorff space $X$; $\bullet$ for every Hausdorff space $X$ we have $|X|\le 2^{2^{{pd}(X)}}$ and ${pd}(X)<{d}(X)$ implies $\Delta(X)< 2^{2^{{pd}(X)}}$; $\bullet$ for every regular space $X$ we have $\min\{\Delta(X),\, w(X)\}\le 2^{{pd}(X)}\,$ and ${d}(X)<2^{{pd}(X)},\,$ moreover ${pd}(X)<{d}(X)$ implies $\,\Delta(X)< {2^{{pd}(X)}}$

Anti-Urysohn spaces

All spaces are assumed to be infinite Hausdorff spaces. We call a space "anti-Urysohn" $($AU in short$)$ iff any two non-emty regular closed sets in it intersect. We prove that $\bullet$ for every infinite cardinal ${\kappa}$ there is a space of size ${\kappa}$ in which fewer than $cf({\kappa})$ many non-empty regular closed sets always intersect; $\bullet$ there is a locally countable AU space of size $\kappa$ iff $\omega \le \kappa \le 2^{\mathfrak c}$. A space with at least two non-isolated points is called "strongly anti-Urysohn" $($SAU in short$)$ iff any two infinite closed sets in it intersect. We prove that $\bullet$ if $X$ is any SAU space then $\mathfrak s\le |X|\le 2^{2^{\mathfrak c}}$; $\bullet$ if $\mathfrak r=\mathfrak c$ then there is a separable, crowded, locally countable, SAU space of cardinality $\mathfrak c$; \item if $\lambda > \omega$ Cohen reals are added to any ground model then in the extension there are SAU spaces of size $\kappa$ for all $\kappa \in [\omega_1,\lambda]$; $\bullet$ if GCH holds and $\kappa \le\lambda$ are uncountable regular cardinals then in some CCC generic extension we have $\mathfrak s={\kappa}$, $\,\mathfrak c={\lambda}$, and for every cardinal ${\mu}\in [\mathfrak s, \mathfrak c]$ there is an SAU space of cardinality ${\mu}$. The questions if SAU spaces exist in ZFC or if SAU spaces of cardinality $> \mathfrak c$ can exist remain open