Distance-dependent fluorescence quenching ofN-acetyl-l-tryptophanamide by acrylamide

We examined the time-dependent intensity decays ofN-acetyl-l-tryptophanamide (NATA) when collisionally quenched by acrylamide in propylene glycol over a range of temperatures. The intensity decays of NATA became increasingly heterogeneous in the presence of acrylamide. The NATA intensity decays were not consistent with the Collins-Kimball radiation boundary condition (RBC) model for quenching. The steady-state Stern-Volmer plots show significant upward curvature, and quenching of NATA by acrylamide was observed even in vitrified propylene glycol, where translational diffusion cannot occur during the lifetime of the excited state. These frequencydomain and steady-state data indicate a through-space quenching interaction between NATA and acrylamide, and the results are consistent with a rate constant for quenching that depends exponentially on the fluorophore-quencher separation distance. The exponential distance-dependent rate of quenching also explains the upward curvature of the Stern-Volmer plot, and the steady-state data aid in determining the interaction distance between NATA and acrylamide. These results suggest that the distance-dependent quenching rates need to be considered in the interpretation of acrylamide quenching of proteins.     

Biological production of ethanol from coal synthesis gas

The anaerobic bacteriaClostridium ljungdahlii produces ethanol and acetate from CO, CO₂, and H₂ in synthesis gas. Early studies with the bacterium showed that relatively high concentrations of ethanol could be produced by lowering the fermentation pH and eliminating yeast extract from the medium in favor of a defined medium. This article presents the results from a medium development study based on the aerobic bacteriumEscherichia coli. The results of continuous-reactor studies in a continuously stirred tank reactor (CSTR) with and without cell recycle are shown to demonstrate the utility of this improved medium.     

Hermite interpolation with trigonometric polynomials

Interpolation methods of Hermite type in translation invariant spaces of trigonometric polynomials for any position of interpolation points and any number of derivatives are constructed. For the case of an odd number of interpolation conditions-periodic trigonometric polynomials of minimum order are chosen as interpolation functions while for the case of an even number of interpolation conditions-antiperiodic trigonometric polynomials of minimum order are appropriate.     

The coefficients of the Laurent series expansions of real analytic functions

Letf be a real analytic function of a real variable such that 0 is an isolated (possibly essential) singularity off. In the existing literature the coefficients of the Laurent series expansion off around 0 are obtained by applying Cauchy's integral formula to the analytic continuation off on the complex plane. Here by means of a conformal mapping we derive a formula which determines the Laurent coefficients off solely in terms of the values off and the derivatives off at a real point of analyticity off. Using a more complicated mapping, we similarly determine the coefficients of the Laurent expansion off around 0 where now 0 is a singularity off which is not necessarily isolated.     

Functional connectedness and Darboux property of multivalued functions

To 80^th birthday of Paul Erds     

Mortality of iterated Gallai graphs

For a finite or infinite graphG, theGallai graph (G) ofG is defined as the graph whose vertex set is the edge setE(G) ofG; two distinct edges ofG are adjacent in (G) if they are incident but do not span a triangle inG. For any positive integert, thetth iterated Gallai graph ^t (G) ofG is defined by ( ^t–1(G)), where ⁰(G):=G. A graph is said to beGallai-mortal if some of its iterated Gallai graphs finally equals the empty graph. In this paper we characterize Gallai-mortal graphs in several ways.     

Cyclic actions on some Klein bottle bundles over S1

Leth be a cyclic action of periodn onM, whereM is eitherS ¹×K, K is the Klein bottle or on , the twisted Klein bottle bundle overS ¹, such that there is a fiberingq:MS ¹ with fiber a Klein bottleK or a torusT with respect to which the action is fiber preserving. We classify all such actions and show that they might be distinguished by their fixed points or by their orbit spaces.     

Der Richtungsabstand

In the study of chemical structural phenomena, the idea of mixedness appears to provide most valuable information if this notion is understood as a quantity that counts for a natural distinction between more or less mixed situations. The search for such a concept was initiated by the need of a corresponding valuation of chemical molecules that differ in the type-composition of a system of varying molecular parts at given molecular skeleton sites. In other words, an order relation for the partitions of a finite set was sought that explains the extent of mixing in a canonical way. This and related questions led to the concepts of themixing character andmixing distance. Success in applying these concepts to further chemical and physical problems, to graph theory, to representation theory of the symmetric group, and to probability theory confirmed the hope that there is a common background in some basic mathematics that allows a systematic treatment.The expected concept summarizing the above-mentioned experience is called thedirection distance and the mathematics concerned is linear geometry with a normspecific metric or structural analysis of normed vector spaces, respectively. Direction distance is defined as a map that represents the total metric information on any pair of directions (= pair of half-lines with a common vertex or a corresponding figure in normed vector spaces). Generally, that metrical figure changes when the half-lines are interchanged. As a consequence thereof, Hilbert's congruence axioms do not permit a metric criterion for the congruence of angles except in particular cases. The metric figures of direction pairs, however, may be classified according to metric congruence, and the normspecific metric induces an order in the set of congruence classes. This order, as a rule, is partial; it proves to be total if and only if the vector spaces are (pre-) Hilbert spaces (Lemma 8). A thorough comparison of the direction distance with the conventional distance deepens the understanding of the novel concept and justifies the terminology. The results are summarized in a number of lemmata. Furthermore, so-calledd-complete systems of order-homomorphic functional (so-calledd-functionals) establish an alternative formulation of the direction distance order. If and only if the order is total,d-complete systems can be represented by singled-functionals. Consequently, the case that normed vector spaces are (pre-) Hilbert spaces is pinpointed by the fact that the negative scalar product is already ad-complete system. These particular circumstances allow a metric congruence relation for angles.Another family of normed vector spaces is traced out by the conditions under which the direction distance takes the part of the mixing distance. Roughly speaking, a subset of vectors may be viewed as representing mixtures if it has two properties. First, with any two vectors of this subset all positive linear combinations are vectors of it as well. Second, the length of these vectors is an additive property. Correspondingly, the definition of the mentioned family, the family of so-calledmc-spaces, is based on the concepts of ameasure cone (Def. 5 and Def. 5) and an associated class ofmc- (= measure cone)norms being responsible for length additivity ofpositive vectors (= vectors of the measure cone) (Def. 6). Such norms provide congruence classes for positive vectors and positive direction pairs marked by the propertieslength andmixing distance, respectively. These congruence classes do not depend on the choice of the particularmc-norm within the class associated with a given measure cone, however, the mixing distance does. The consistency of the stipulated mathematical instrumentarium becomes apparent with Theorem 1 stating: The mixing distanceorder doesnot depend on the choice of a particular norm within the measure cone specific class; this order, together with the stipulated length of positive vectors, are properties necessary and sufficient for fixing the measure cone specific class ofmc-norms.Decreasing (or constant) mixing distance was found to describe a characteristic change in the relation between two probability distributions on a given set of classical events, a change in fact necessary and sufficient for the existence of alinear stochastic operator that maps a given pair of distributions into another given pair. This physically notable statement was originally proved for the space ofL ¹-functions on a compact -interval, it was expected to keep its validity for probability distributions in the range of classical physics and, as a consequence of that, for measures of any type. Theorem 2 presents the said statement in terms ofmc-endomorphisms ofmc-spaces; after an extension of the original proof to a more general family ofL ¹-spaces another method presented in a separate paper confirms Theorem 2 for bounded additive set functions and, accordingly, secures the expected range of validity. The discussion below is without reference to the validity range and primarily devoted to geometrical consequences without detailed speculations about physical applications.A few remarks on applications, however, illustrate the physical relevance of the mixing distance and its specialization, theq-character, in the particular context of Theorem 2. With reference to measure cones with such physical interpretations as statistical systems,mc-endomorphisms effect changes that can be described by linear stochastic operators and result physically either from an approach to some equilibrium state or from an adoption to a time-dependent influence on the system from outside. Theorem 2 provides a necessary and sufficient criterion for such changes. The discussion may concern phenomena of irreversible thermodynamics as well as evolving systems under the influence of a surrounding world summarized asorganization phenomena. Entropies and relative entropies of the Renyi-type ared-functionais which do not establishd-complete systems. The validity of Theorem 2 does not encompass the nonclassical case; the reason for it is of high physical interest. The full range of validity and its connection with symmetry arguments seems a promising mathematical problem in the sense of Klein'sErlanger Programm. From the point of mathematical history, the Hardy-Littlewood-Polya theorem should be quoted as a very special case of Theorem 2.

     

Homomorphisms to oriented cycles

We discuss the existence of homomorphisms to oriented cycles and give, for a special class of cyclesC, a characterization of those digraphs that admit, a homomorphism toC. Our result can be used to prove the multiplicativity of a certain class of oriented cycles, (and thus complete the characterization of multiplicative oriented cycles), as well as to prove the membership of the corresponding decision problem in the classNPcoNP. We also mention a conjecture on the existence of homomorphisms to arbitrary oriented cycles.     

On depth first search strees inm-out digraphs

We consider depth first search (DFS for short) trees in a class of random digraphs: am-out model. Let _i be thei ^th vertex encountered by DFS andL(i, m, n) be the height of _i in the corresponding DFS tree. We show that ifi/n asn, then there exists a constanta(,m), to be defined later, such thatL(i, m, n)/n converges in probability toa(,m) asn. We also obtain results concerning the number of vertices and the number of leaves in a DFS tree.