On Witten multiple zeta-functions associated with semisimple Lie algebras IV

In our previous work, we established the theory of multi-variable Witten zeta-functions, which are called the zeta-functions of root systems. We have already considered the cases of types $A_2$, $A_3$, $B_2$, $B_3$ and $C_3$. In this paper, we consider the case of $G_2$-type. We define certain analogues of Bernoulli polynomials of $G_2$-type and study the generating functions of them to determine the coefficients of Witten's volume formulas of $G_2$-type. Next we consider the meromorphic continuation of the zeta-function of $G_2$-type and determine its possible singularities. Finally, by using our previous method, we give explicit functional relations for them which include Witten's volume formulas.Comment: 22 pag

Crater formation by fast ions: comparison of experiment with Molecular Dynamics simulations

An incident fast ion in the electronic stopping regime produces a track of excitations which can lead to particle ejection and cratering. Molecular Dynamics simulations of the evolution of the deposited energy were used to study the resulting crater morphology as a function of the excitation density in a cylindrical track for large angle of incidence with respect to the surface normal. Surprisingly, the overall behavior is shown to be similar to that seen in the experimental data for crater formation in polymers. However, the simulations give greater insight into the cratering process. The threshold for crater formation occurs when the excitation density approaches the cohesive energy density, and a crater rim is formed at about six times that energy density. The crater length scales roughly as the square root of the electronic stopping power, and the crater width and depth seem to saturate for the largest energy densities considered here. The number of ejected particles, the sputtering yield, is shown to be much smaller than simple estimates based on crater size unless the full crater morphology is considered. Therefore, crater size can not easily be used to estimate the sputtering yield.Comment: LaTeX, 7 pages, 5 EPS figures. For related figures/movies, see: http://dirac.ms.virginia.edu/~emb3t/craters/craters.html New version uploaded 5/16/01, with minor text changes + new figure

Creation of multiple nanodots by single ions

In the challenging search for tools that are able to modify surfaces on the nanometer scale, heavy ions with energies of several 10 MeV are becoming more and more attractive. In contrast to slow ions where nuclear stopping is important and the energy is dissipated into a large volume in the crystal, in the high energy regime the stopping is due to electronic excitations only. Because of the extremely local (< 1 nm) energy deposition with densities of up to 10E19 W/cm^2, nanoscaled hillocks can be created under normal incidence. Usually, each nanodot is due to the impact of a single ion and the dots are randomly distributed. We demonstrate that multiple periodically spaced dots separated by a few 10 nanometers can be created by a single ion if the sample is irradiated under grazing angles of incidence. By varying this angle the number of dots can be controlled.Comment: 12 pages, 6 figure

Parametric Polyhedra with at least kk Lattice Points: Their Semigroup Structure and the k-Frobenius Problem

Given an integral $d \times n$ matrix $A$, the well-studied affine semigroup \mbox{ Sg} (A)=\{ b : Ax=b, \ x \in {\mathbb Z}^n, x \geq 0\} can be stratified by the number of lattice points inside the parametric polyhedra $P_A(b)=\{x: Ax=b, x\geq0\}$. Such families of parametric polyhedra appear in many areas of combinatorics, convex geometry, algebra and number theory. The key themes of this paper are: (1) A structure theory that characterizes precisely the subset \mbox{ Sg}_{\geq k}(A) of all vectors b \in \mbox{ Sg}(A) such that $P_A(b) \cap {\mathbb Z}^n$ has at least $k$ solutions. We demonstrate that this set is finitely generated, it is a union of translated copies of a semigroup which can be computed explicitly via Hilbert bases computations. Related results can be derived for those right-hand-side vectors $b$ for which $P_A(b) \cap {\mathbb Z}^n$ has exactly $k$ solutions or fewer than $k$ solutions. (2) A computational complexity theory. We show that, when $n$, $k$ are fixed natural numbers, one can compute in polynomial time an encoding of \mbox{ Sg}_{\geq k}(A) as a multivariate generating function, using a short sum of rational functions. As a consequence, one can identify all right-hand-side vectors of bounded norm that have at least $k$ solutions. (3) Applications and computation for the $k$-Frobenius numbers. Using Generating functions we prove that for fixed $n,k$ the $k$-Frobenius number can be computed in polynomial time. This generalizes a well-known result for $k=1$ by R. Kannan. Using some adaptation of dynamic programming we show some practical computations of $k$-Frobenius numbers and their relatives

Kindlin-3 maintains marginal zone B cells but confines follicular B cell activation and differentiation

Integrin-mediated interactions between hematopoietic cells and their microenvironment are important for the development and function of immune cells. Here, the role of the integrin adaptor Kindlin-3 in B cell homeostasis is studied. Comparing the individual steps of B cell development in B cell-specific Kindlin-3 or alpha4 integrin knockout mice, we found in both conditions a phenotype of reduced late immature, mature, and recirculating B cells in the bone marrow. In the spleen, constitutive B cell-specific Kindlin-3 knockout caused a loss of marginal zone B cells and an unexpected expansion of follicular B cells. Alpha4 integrin deficiency did not induce this phenotype. In Kindlin-3 knockout B cells VLA-4 as well as LFA-1-mediated adhesion was abrogated, and short-term homing of these cells in vivo was redirected to the spleen. Upon inducible Kindlin-3 knockout, marginal zone B cells were lost due to defective retention within 2 weeks, while follicular B cell numbers were unaltered. Kindlin-3 deficient follicular B cells displayed higher IgD, CD40, CD44, CXCR5, and EBI2 levels, and elevated PI3K signaling upon CXCR5 stimulation. They also showed transcriptional signatures of spontaneous follicular B cell activation. This activation manifested in scattered germinal centers in situ, early plasmablasts differentiation, and signs of IgG class switch

Mapping Hidden Potential Identity Elements by Computing the Average Discriminating Power of Individual tRNA Positions

The recently published discrete mathematical method, extended consensus partition (ECP), identifies nucleotide types at each position that are strictly absent from a given sequence set, while occur in other sets. These are defined as discriminating elements (DEs). In this study using the ECP approach, we mapped potential hidden identity elements that discriminate the 20 different tRNA identities. We filtered the tDNA data set for the obligatory presence of well-established tRNA features, and then separately for each identity set, the presence of already experimentally identified strictly present identity elements. The analysis was performed on the three kingdoms of life. We determined the number of DE, e.g. the number of sets discriminated by the given position, for each tRNA position of each tRNA identity set. Then, from the positional DE numbers obtained from the 380 pairwise comparisons of the 20 identity sets, we calculated the average excluding value (AEV) for each tRNA position. The AEV provides a measure on the overall discriminating power of each position. Using a statistical analysis, we show that positional AEVs correlate with the number of already identified identity elements. Positions having high AEV but lacking published identity elements predict hitherto undiscovered tRNA identity elements

Antifascism, the 1956 Revolution and the politics of communist autobiographies in Hungary 1944-2000

This is a postprint of an article whose final and definitive form has been published in Europe-Asia Studies © 2006 University of Glasgow; Europe-Asia Studies is available online at http://www.informaworld.com.Using oral history, this contribution explores the reshaping of individuals' public and private autobiographies in response to different political environments. In particular, it analyses the testimony of those who were communists in Hungary between 1945 and 1956, examining how their experiences of fascism, party membership, the 1956 Revolution and the collapse of communism led them in each case to refashion their life stories. Moreover, it considers how their biographies played varying functions at different points in their lives: to express identification with communism, to articulate resistance and to communicate ambition before 1956; to protect themselves from the state after 1956; and to rehabilitate themselves morally in a society which stigmatised them after 1989.I didn't use this word 'liberation' (felszabadulás), because in 1956 my life really changed. Everybody's lives went through a great change, but mine especially. … I wasn't disgusted with myself that I had called the arrival of the Red Army in 1945 a liberation, but [after 1956] I didn't use it anymore

Efficient Performance of Electrostatic Spray-Deposited TiO2 Blocking Layers in Dye-Sensitized Solar Cells after Swift Heavy Ion Beam Irradiation

A compact TiO2 layer (~1.1 μm) prepared by electrostatic spray deposition (ESD) and swift heavy ion beam (SHI) irradiation using oxygen ions onto a fluorinated tin oxide (FTO) conducting substrate showed enhancement of photovoltaic performance in dye-sensitized solar cells (DSSCs). The short circuit current density (Jsc = 12.2 mA cm-2) of DSSCs was found to increase significantly when an ESD technique was applied for fabrication of the TiO2 blocking layer, compared to a conventional spin-coated layer (Jsc = 8.9 mA cm-2). When SHI irradiation of oxygen ions of fluence 1 × 1013 ions/cm2 was carried out on the ESD TiO2, it was found that the energy conversion efficiency improved mainly due to the increase in open circuit voltage of DSSCs. This increased energy conversion efficiency seems to be associated with improved electronic energy transfer by increasing the densification of the blocking layer and improving the adhesion between the blocking layer and the FTO substrate. The adhesion results from instantaneous local melting of the TiO2 particles. An increase in the electron transport from the blocking layer may also retard the electron recombination process due to the oxidized species present in the electrolyte. These findings from novel treatments using ESD and SHI irradiation techniques may provide a new tool to improve the photovoltaic performance of DSSCs

Robust water repellent ZnO nanorod array by Swift Heavy Ion Irradiation: Effect of Electronic Excitation Induced Local Chemical State Modification

Tailoring the surface properties by varying the chemistry and roughness could be of interest for self-cleaning applications. We demonstrate the transformation of hydrophobic ZnO Nano rod (NR) array into superhydrophobic nature by changing the local chemical state and without altering the surface roughness by swift heavy ion (SHI) irradiation. The aligned ZnO NR arrays were irradiated using 150 MeV Ag ions with different fluences from 5E10 to 3E12 ions/cm2. The observed static water contact angles of ZnO NRs samples were 103° ± 3°, 152° ± 4°,161° ± 3°, 164° ± 2°, 167° ± 2°,154 ± 3° and 151° ± 2° for the pristine, ion fluencies of 1E11, 3E11, 5E11, 7E11, 1E12 and 3E12 ions cm−2, respectively. The change in local surface chemistry via formation of surface oxygen related defects due to electronic excitations induced by ion irradiation determine the water dewetting properties. It is found that surface oxygen related defects could be tuned by varying the fluence of the SHIs. Durability tests show that the SHI induced surface oxygen-deficient ZnO NRs have the stable superhydrophobic behavior for more than a year

Recrystallization of amorphous nano-tracks and uniform layers generated by swift-ion-beam irradiation in lithium niobate.

The thermal annealing of amorphous tracks of nanometer-size diameter generated in lithium niobate (LiNbO3) by Bromine ions at 45 MeV, i.e., in the electronic stopping regime, has been investigated by RBS/C spectrometry in the temperature range from 250°C to 350°C. Relatively low fluences have been used (<1012 cm−2) to produce isolated tracks. However, the possible effect of track overlapping has been investigated by varying the fluence between 3×1011 cm−2 and 1012 cm−2. The annealing process follows a two-step kinetics. In a first stage (I) the track radius decreases linearly with the annealing time. It obeys an Arrhenius-type dependence on annealing temperature with activation energy around 1.5 eV. The second stage (II) operates after the track radius has decreased down to around 2.5 nm and shows a much lower radial velocity. The data for stage I appear consistent with a solid-phase epitaxial process that yields a constant recrystallization rate at the amorphous-crystalline boundary. HRTEM has been used to monitor the existence and the size of the annealed isolated tracks in the second stage. On the other hand, the thermal annealing of homogeneous (buried) amorphous layers has been investigated within the same temperature range, on samples irradiated with Fluorine at 20 MeV and fluences of ∼1014 cm−2. Optical techniques are very suitable for this case and have been used to monitor the recrystallization of the layers. The annealing process induces a displacement of the crystalline-amorphous boundary that is also linear with annealing time, and the recrystallization rates are consistent with those measured for tracks. The comparison of these data with those previously obtained for the heavily damaged (amorphous) layers produced by elastic nuclear collisions is summarily discussed