Evaluating and monitoring the packing behavior of process-scale chromatography columns

The packing characteristics of process-scale chromatography columns were evaluated using the responses to conductivity-based pulse and step inputs derived from tracer experiments and in-process transitions (i.e. column equilibration and regeneration steps). Characteristics of the measured residence time distributions (RTDs) were quantified by statistical moments and using the equations derived from the Gaussian model. The first and second moments calculated from in-process step transitions for multiple runs were in good agreement with those moments calculated from the pulse-input experiments conducted immediately after column packing. This indicates that most of the time the bed behavior at the time of packing is consistent with that at the time of operation. Due to the significant resistance to protein mass transfer inside the particles, estimated plate heights for protein solutes are expected to be much greater than those observed from the experiments using saltbased tracers. Thus, the column efficiency derived from salt-based experiments can be a useful measure of packing consistency rather than a significant parameter influencing the outcome of protein separations.     

Synthesis, Spectral and Structural Study of N-[1-(N,N,N′,N′-Tetramethylphosphoramidoyl)- 1H-Benzimidazol-2-yl]-Propionimidic Ethyl Ether

The preparation of N-[1-(N,N,N,N-tetramethylphosphoramidoyl)-1H-benzimidazol-2-yl]-proponimidic ethyl ester 2 has been achieved by the reaction of N-(1H-benzimidazol-2-yl)-proponimidic acid ethyl ester 1 with N,N,N,N-tetramethylchlorophosphoramide. The structure of compound 2 has been determined by X-ray diffraction. The results of (¹H, ¹³C, ³¹P) NMR, IR, EI-MS spectral data are consistent with those obtained from the X-ray diffraction. The compound crystallizes in the triclinic system, following the EsZ conformation. In the crystal, there are two weak C3–H3s1 and C15–H15sO1 intermolecular hydrogen bonds.     

A simple proof of a curious congruence by Zhao

The author gives a simple proof of the following curious congruence for odd prime 3$"> which was established by Jianqiang Zhao:

0}}}\frac{1}{ijk}\equiv -2B_{p-3}(\text{mod} p).\end{displaymath}">

     

On the Linear Complexity and Multidimensional Distribution of Congruential Generators over Elliptic Curves

We show that the elliptic curve analogue of the linear congruential generator produces sequences with high linear complexity and good multidimensional distribution.communicated by: A. MenezesAMS Classification: 11T23, 14H52, 65C10     

Purely periodic -expansions with Pisot unit base

Let 1$"> be a Pisot unit. A family of sets defined by a -numeration system has been extensively studied as an atomic surface or Rauzy fractal. For the purpose of constructing a Markov partition, a domain constructed by an atomic surface has appeared in several papers. In this paper we show that the domain completely characterizes the set of purely periodic -expansions.

     

Class groups of imaginary function fields: The inert case

Let be a finite field and a transcendental element over . An imaginary function field is defined to be a function field such that the prime at infinity is inert or totally ramified. For the totally imaginary case, in a recent paper the second author constructed infinitely many function fields of any fixed degree over in which the prime at infinity is totally ramified and with ideal class numbers divisible by any given positive integer greater than 1. In this paper, we complete the imaginary case by proving the corresponding result for function fields in which the prime at infinity is inert. Specifically, we show that for relatively prime integers and , there are infinitely many function fields of fixed degree such that the class group of contains a subgroup isomorphic to and the prime at infinity is inert.

     

Wecken property for roots

We show that maps from a compact space into a topological manifold which have geometric Nielsen root number zero satisfy the Wecken property, i.e., such that .

     

Symmetrically approximately continuous functions, consistent density theorems, and Fubini type inequalities

Using the continuum hypothesis, Sierpinski constructed a nonmeasurable function such that is countable for every Clearly, such a function is symmetrically approximately continuous everywhere.

Here we to show that Sierpinski's example cannot be constructed in ZFC. Moreover, we show it is consistent with ZFC that if a function is symmetrically approximately continuous almost everywhere, then it is measurable.

     

Prime Producing Quadratic Polynomials and Class Number One or Two

Let d≡ 5 mod 8 be a positive square-free integer and let h(d) be the class number of the real quadratic field ℚ(√d). Let p be a divisor of d = pq and let . Assume that is prime or equal to 1 for all integers x with 0≤x<W. Under the assumption that the Riemann hypothesis is true, we prove that if , then h(d) < 2. Furthermore we show that h(d)< 2 implies d < 4245. In the case when there exists at least one split prime less than W, we prove the following results without any assumptions on the Riemann hypothesis. If then h< 2 or h = 4. If , then h≤ 2, h = 4 or h = 2^t−2, where t is the number of primes dividing d. In the case when h = 2^t−2 we have , where φ = 2 or 4. 2000 Mathematics Subject Classification: Primary–11R29     

Generalized Zeta Regularizations,Quantum Class Number Formulas,and Appell's <Emphasis Type="Italic">O</Emphasis>-Functions

We introduce a generalized notion of the zeta regularization. As applications we show the quantum analogue of the Lerch formula and of the Dirichlet class number formulas. We also give some further examples related to Appell's O-functions. 2000 Mathematics Subject Classification: Primary—11M36 Work in part supported by Grant-in Aid for Scientific Research (B) No. 11440010, and by Grant-in Aid for Exploratory Research No. 13874004, Japan Society for the Promotion of Science.