Unconstrained multilayer switchbox routing

Consider the gradually more and more complexproblems of single row routing, channel routing and switchbox routing on the one hand, and the gradually less and less restrictivemodels (1-layer, Manhattan, unconstrained 2-layer, multilayer) on the other hand. The single row routing problems can always be solved in the Manhattan model, and the channel routing problem can always be solved in the unconstrained 2-layer model, in fact, both in linear time. In this paper, we show that the switchbox routing problem is solvable in the multilayer model, also in linear time.Supported in part by the Office of Naval Research (Grants N0001492J1375 and N0001492J4083) and by the Air Force Office of Scientific Research (Grants 89-0512B and F49620-93-1-0041).Research partially supported by the Hungarian National Foundation for Scientific Research (Grant No. OTKA 2118, 2505), and by the EC Cooperative Action IC 1000, Algorithms for Future Technologies (ALTEC).     

Inversion of the Short-Time Fourier Transform Using Riemannian Sums

The inversion formula for the short-time Fourier transform is usually considered in the weak sense, or only for specific combinations of window functions and function spaces such as L₂ and modulation spaces. In the present note the Riemannian sums of the inverse short-time Fourier transform are investigated. Under some conditions on the window functions we prove that the Riemannian sums converge to f in the modulation spaces and inWiener amalgam norms, hence also in the L_p sense.     

Delayed nonlinear cournot and bertrand dynamics with product differentiation

Dynamic duopolies will be examined with product differentiation and isoelastic price functions. We will first prove that under realistic conditions the equilibrium is always locally asymptotically stable. The stability can however be lost if the firms use delayed information in forming their best responses. Stability conditions are derived in special cases, and simulation results illustrate the complexity of the dynamism of the systems. Both price and quantity adjusting models are discussed.     

Structural variability of endotoxins from R-type isogenic mutants of Shigella sonnei

The structural variations in the rough-type endotoxins [lipopolysaccharides (LPSs)] of Shigella sonnei mutant strains (S. sonnei phase II-4303, R41, 562H and 4350) were investigated by Matrix-assisted laser desorption/ionization time-of-flight mass spectrometry (MALDI-TOF-MS) and tandem MS. A series of S. sonnei mutants had previously been the subject of analytical studies on the biosynthesis of heptose components in the core oligosaccharide region of LPSs. This study gives a complete overview on the structures of the full core and lipid A of S. sonnei mutant strains by MS. We found that the LPSs of the isogenic rough mutants were formed in a step-like manner containing 0:1:2:3 heptose in the deep core region of 4350, 562H, R41 and 4303, respectively, and the longest LPS from the mutant S. sonnei 4303 contained also five hexoses. The structural variations in the lipid A moiety and in the oligosaccharide part of the intact LPS were followed by MALDI-TOF-MS/MS. For the dissolution and the ionization of the samples, 2,5-dihydroxybenzoic acid in citric acid solution was applied as matrix. The detailed evaluation of the mass spectra indicates heterogeneity in the lipid part due to the differences in the phosphate and fatty acid composition.     

Exploring and characterizing the folding processes of Lys- and Arg-containing Ala-based peptides: a molecular dynamics study

In this study, molecular dynamics simulations were carried out on Lys- and Arg-containing Ala-based peptides (i.e. Ace-(AAAAK)(n)A-NH(2) and Ace-(AAAAR)(n)A-NH(2), where n=1-4), in order to explore and characterize their folding processes. For the oligopeptides, the evolution of α-helical structure with regard to the whole conformation, as well as to each residue was investigated, and the helix-forming propensities were characterized. On the basis of the helicity curves, representing the alteration of average helicity as a function of time, the typical time values describing the folding processes and subprocesses were identified. In the case of each peptide, the evolution and role of helix-stabilizing, non-local and side-chain-to-backbone H-bonds were examined. The appearing i←i+4 H-bonds pointed out the role of these interactions in the stabilization of α-helical conformations, while the occurring i←i+3 H-bonds indicated the presence of β-turn or 3(10)-helical structures. Studying the formation and role of non-local and side-chain-to-backbone H-bonds led to the observation that these types of interactions produced an effect on the evolution of helical conformations, as well as on the folding processes.     

Binding of alkaloids into the S1 specificity pocket of α-chymotrypsin: evidence from induced circular dichroism spectra

Non-covalent binding of planar aromatic molecules into the S1 specificity pocket of the serine protease α-chymotrypsin (αCHT) can be detected by measuring induced circular dichroism (CD) spectroscopic signals. Utilizing this phenomenon, αCHT association of proflavine (PRF), the well known serine protease inhibitor has been investigated together with plant-derived compounds including isoquinoline, pyridocarbazole and indoloquinoline alkaloids, of which αCHT binding has never been reported. Non-degenerate exciton coupling between π-π* transitions of the ligand molecules and two tryptophan residues (Trp172 and Trp215) near to the binding site is proposed to be responsible for the induced CD activity. The association constants calculated from CD titration data indicated strong αCHT association of sanguninarine, ellipticine, desmethyl-isocryptolepine and isoneocryptolepine (K(a) ≈ 10(5) M(-1)) while berberine, coptisine and chelerythrine bind to the enzyme with lower, PRF-like affinity (K(a) ≈ 10(4) M(-1)). PRF-trypsin and ellipticine-trypsin binding interactions have also been demonstrated. The binding of the alkaloids into the S1 pocket of αCHT has been confirmed by CD competition experiments. Molecular docking calculations showed the inclusion of PRF as well as the alkaloid molecules in the S1 cavity where they are stabilized by hydrophobic and H-bonding interactions. These novel nonpeptidic scaffolds can be used for developing selective inhibitors of serine proteases having chymotrypsin-like folds. Furthermore, the results provide a novel, CD spectroscopic based approach for probing the ligand binding of αCHT and related proteases.     

? 1-Summability of d-Dimensional Fourier Transforms

A general summability method of more-dimensional Fourier transforms is given with the help of a continuous function θ. Under some weak conditions on θ we show that the maximal operator of the ℓ ₁–θ-means of a tempered distribution is bounded from H _p (ℝ ^d ) to L _p (ℝ ^d ) for all d/(d+α)<p≤∞ and, consequently, is of weak type (1,1), where 0<α≤1 depends only on θ. As a consequence we obtain a generalization of the one-dimensional summability result due to Lebesgue, more exactly, the ℓ ₁–θ-means of a function f∈L ₁(ℝ ^d ) converge a.e. to f. Moreover, we prove that the ℓ ₁–θ-means are uniformly bounded on the spaces H _p (ℝ ^d ), and so they converge in norm (d/(d+α)<p<∞). Similar results are shown for conjugate functions. Some special cases of the ℓ ₁–θ-summation are considered, such as the Weierstrass, Picar, Bessel, Fejér, de La Vallée-Poussin, Rogosinski, and Riesz summations.     

Absolute convergence of double Walsh?CFourier series and related results

We consider the double Walsh orthonormal system $$\{w_m(x)w_n(y):\, m,n \in \mathbb{N}\}$$ on the unit square $\mathbb{I}^{2}$ , where {w _m (x)} is the ordinary Walsh system on the unit interval $\mathbb{I}:=[0,1)$ in the Paley enumeration. Our aim is to give sufficient conditions for the absolute convergence of the double Walsh?CFourier series of a function $f \in L^{p}(\mathbb{I}^{2})$ for some 1<p?Q2. More generally, we give best possible sufficient conditions for the finiteness of the double series $$\sum_{m=1}^{\infty}\ \sum_{n=1}^{\infty} a_{mn} {|\hat{f}(m,n)|}^r,$$ where {a _mn } is a given double sequence of nonnegative real numbers satisfying a mild assumption and 0<r<2. These sufficient conditions are formulated in terms of (either global or local) dyadic moduli of continuity of?f.     

Triangular Ces??ro summability of two dimensional Fourier series

It is proved that the maximal operator of the triangular Ces??ro means of a two-dimensional Fourier series is bounded from the periodic Hardy space $H_{p}(\mathbb{T}^{2})$ to $L_{p}(\mathbb{T}^{2})$ for all 2/(2+??)<p?Q?? and, consequently, is of weak type (1,1). As a consequence we obtain that the triangular Ces??ro means of a function $f \in L_{1}(\mathbb{T}^{2})$ converge a.e. to?f.