Oligonucleotide Analogues with Integrated Bases and Backbone. Part 14

The self‐complementary tetrameric propargyl triols 8, 14, 18 , and 21 were synthesized to investigate the duplex formation of self‐complementary, ethynylene‐linked UUAA, AAUU, UAUA, and AUAU analogues with integrated bases and backbone (ONIBs). The linear synthesis is based on repetitive Sonogashira couplings and C‐desilylations (34–72% yield), starting from the monomeric propargyl alcohols 9 and 15 and the iodinated nucleosides 3, 7, 11 , and 13 . Strongly persistent intramolecular H‐bonds from the propargylic OH groups to N(3) of the adenosine units prevent the gg‐type orientation of the ethynyl groups at C(5′). As such, an orientation is required for the formation of cyclic duplexes, this H‐bond prevents the formation of duplexes connected by all four base pairs. However, the central units of the UAUA and AAUU analogues 18 and 14 associate in CDCl₃/(D₆)DMSO 10 : 1 to form a cyclic duplex characterized by reverse Hoogsteen base pairing. The UUAA tetramer 8 forms a cyclic UU homoduplex, while the AUAU tetramer 21 forms only linear associates. Duplex formation of the O‐silylated UUAA and AAUU tetramers is no longer prevented. The self‐complementary UUAA tetramer 22 forms Watson–Crick‐ and Hoogsteen‐type base‐paired cyclic duplexes more readily than the sequence‐isomeric AAUU tetramer 23 , further illustrating the sequence selectivity of duplex formation.     

Analysis and parametric sensitivity of the behavior of overshoots in the concentration of a charged adsorbate in the adsorbed phase of charged adsorbent particles: practical implications for separations of charged solutes

In this work, an analysis of the parametric sensitivity of the overshoot in the concentration of the adsorbate in the adsorbed phase, which occurs under certain conditions during an ion-exchange adsorption process, is presented and used to suggest practical implications of the concentration overshoot phenomenon on operational policies and configurations of chromatographic columns and finite bath adsorption systems. The results presented in this work demonstrate and explain how the development of an overshoot in the concentration of the adsorbate in the adsorbed phase could be enhanced or suppressed by (i) varying the diffusion coefficient, D3, of the adsorbate relative to the diffusion coefficients, D1 and D2, of the cations and anions, respectively, of the background/buffer electrolyte, (ii) altering the initial surface charge density, delta0, of the charged adsorbent particles, (iii) varying the Debye length, lambda, and (iv) changing the initial concentration, Cd3(0), of the adsorbate in the bulk liquid of the finite bath. The influence of the pH and ionic strength, Iinfinity, of the liquid solution on the development of an overshoot in the concentration of the adsorbate in the adsorbed phase is also presented and discussed through the relationships of these parameters to delta0 and lambda, respectively. Furthermore, a detailed explanation of the effects of each parameter on the interplay between the diffusive and electrophoretic molar fluxes, as well as on the structure and functioning of the electrical double layer, which are responsible for the concentration overshoot phenomenon, is presented.     

The embedding theorem in limiting cases and its applications in singular perturbation

In 1980, Brézis^[6], using the technique of dividing the total space into two parts, proved the embedding theorem of limiting case which is very important in applications. In 1982, Ding Xiaqi improved the proof given in [6], by using of the technique of dividing the total space into three parts. In this paper, using the technique of dividing the total space into three parts, the author proves uniformly the results obtained by Ding^[3,4], and gives an embedding theorem of limiting case including (Lemma 2.2). And he also gives two kinds of examples, applying the embedding theorems (limiting case and non-limiting case) and the interpolation theorems. These examples are the singular perturbation problems in the sense of Lions^[1] (for the definition of singular perturbation, see [1], Introduction). But the singular solutionU _e converges uniformly to the limit solution (degenerate)U, ase0.     

On the maximum modulus of complete trigonometric sums

LetQ _k (p) be a set consisting of all polynomials of degreek with integral coefficientsf(x)=a _k x ^k +...+a ₁ x, wherep×a _k . For givenk andp any polynomialf _k,p (x)εQ _k (p) satisfying ‖S(p, f _k,p )‖=sup ‖S(p, f)‖fεQ(p) is called a maximum modular polynomial inQ _k (p), where $$S(p,f) = \sum\limits_{x = 0}^{p - 1} {e^{2\pi if(x)/p} } $$ Moreover, we definec(k, p)=‖S(p, f _k.p (x))‖. The main results are the following theorems.

1. For k=p?1 and p≥3 we have $$c(k,p) = \sqrt {p^2 - 4(p - 1)\sin ^2 \frac{\pi }{p}} $$ Besides, we may take \(f_{k,p} (x) = \prod\limits_{r = 0}^{p - 2} {(x - r)} \)
2. For k=p?s, 2≤s≤(p+1)/2 and p≥5, we have $$c(k,p) \leqslant p - 4(s - 1)\sin ^2 \frac{\pi }{p}$$ .

In Theorems 3 and 4, an interesting connextion between the present question and the famous problem of Prouhet and Tarry is given, some conditions under which the sign of equality in Theorem 2 holds are given and a method used to construct a maximum modular polynomial inQ _k (p) is also given.     

Equivalence of functional-differential equations of neutral type and abstract Cauchy problems

Equivalence of functional-differential equations of neutral type to well-posed abstract Cauchy problems in the state spaces ⁿ }L ^p ,L ^p resp.C is investigated. The assumptions allow non-atomic difference operators.This work was supported by the Fonds zur Förderung der wissenschaftlichen Forschung (Austria) under Grant No. P4534.Work done by this author was done during a stay at the University of Graz from October 1981 till April 1984.