Homotopy of spaces of diffeomorphisms of some three-dimensional manifolds

The goal of the paper is to calculate the homotopy type of the space of diffeomorphisms for most orientable three-dimensional manifolds with finite fundamental group containing the Klein bottle. The fundamental group of such a manifold Q has the form <a, b ¦abab ^–1=1,a ^mb²ⁿ=1>. As m and n one can have any relatively prime natural numbers; these numbers m, n determine the manifold Q up to diffeomorphism. Let K be a Klein bottle lying in Q and let P be a closed tubular neighborhood in Q of this Klein bottle K. We denote by Diff_o(Q) the connected component of the space of diffeomorphisms QQ containing id Q, and by E₀(K, Q) the connected component of the space of imbeddings KQ containing the inclusion KQ; analogously we define E₀(K, P). The main results of the paper are the following two theorems. THEOREM 1. If m, n1, then the space Diff_o(Q) is homotopy equivalent with a circle. THEOREM 2. If m, n1, then the inclusion E₀(K, P) E₀(K, Q) is a homotopy equivalence. With the help of familiar results on spaces of diffeomorphisms of irreducible manifolds which are sufficiently large, Theorem 1 reduces without difficulty to Theorem 2. The main difficulty is the proof of Theorem 2. This proof develops a technique of Hatcher and the author which deals with spaces of PL-homeomorphisms and diffeomorphisms of irreducible manifolds which are sufficiently large. In the paper we use a different structure definition of the class of manifolds considered. It is easy to verify that these definitions are equivalent.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 122, pp. 72–103, 1982.     

Band structure of even and ions of odd polyenes

The analysis of experimental data for singlet transitions (E _n) of even polyenes (I), cations (II) and anions (III) of odd polyenes show that for infinite chains E (I)/E (II)=E (I)/E (III) = 2:1. It is shown that the energy gap is equal for the three systems. In cases (II) and (III) there is a level (NBMO) in the gap which is vacant in (II) and occupied in (III). That is why the first optical transition in (II) and (III) depends on the semiwidth of the gap.     

Rational approximations of real numbers

For anyx ∈ r put $$c(x) = \overline {\mathop {\lim }\limits_{t \to \infty } } \mathop {\min }\limits_{(p,q\mathop {) \in Z}\limits_{q \leqslant t} \times N} t\left| {qx - p} \right|.$$ . Let [x₀; x₁,..., x_n, ...] be an expansion of x into a continued fraction and let \(M = \{ x \in J,\overline {\mathop {\lim }\limits_{n \to \infty } } x_n< \infty \}\) .Forx∈M put D(x)=c(x)/(1?c(x)). The structure of the set \(\mathfrak{D} = \{ D(x),x \in M\}\) is studied. It is shown that $$\mathfrak{D} \cap (3 + \sqrt 3 ,(5 + 3\sqrt 3 )/2) = \{ D(x^{(n,3} )\} _{n = 0}^\infty \nearrow (5 + 3\sqrt 3 )/2,$$ where \(x^{(n,3)} = [\overline {3;(1,2)_n ,1} ].\) This yields for \(\mu = \inf \{ z,\mathfrak{D} \supset (z, + \infty )\}\) (“origin of the ray”) the following lower bound: μ?(5+3√3)/2=5.0n>(5 + 3/3)/2=5.098.... Suppose a∈n. Put \(M(a) = \{ x \in M,\overline {\mathop {\lim }\limits_{n \to \infty } } x_n = a\}\) , \(\mathfrak{D}(a) = \{ D(x),x \in M(a)\}\) . The smallest limit point of \(\mathfrak{D}(a)(a \geqslant 2)\) is found. The structure of (a) is studied completely up to the smallest limit point and elucidated to the right of it.     

Single-molecule nanopore sensing of actin dynamics and drug binding

Actin is a key protein in the dynamic processes within the eukaryotic cell. To date, methods exploring the molecular state of actin are limited to insights gained from structural approaches, providing a snapshot of protein folding, or methods that require chemical modifications compromising actin monomer thermostability. Nanopore sensing permits label-free investigation of native proteins and is ideally suited to study proteins such as actin that require specialised buffers and cofactors. Using nanopores, we determined the state of actin at the macromolecular level (filamentous or globular) and in its monomeric form bound to inhibitors. We revealed urea-dependent and voltage-dependent transitional states and observed the unfolding process within which sub-populations of transient actin oligomers are visible. We detected, in real-time, filament-growth, and drug-binding at the single-molecule level demonstrating the promise of nanopore sensing for in-depth understanding of protein folding landscapes and for drug discovery.

Nanopipettes were used for real-time investigation into actin dynamics and drug binding at single-molecule resolution, showing promise for a better understanding of the mechanism of protein–protein interactions and drug discovery.     

A novel blue fluorescent chemosensor for metal cations and protons,based on 1,8‐naphthalimide and its copolymer with styrene

A new blue emitting 2‐allyl‐6‐(2‐dimethylaminoethyloxy)‐benzo[de]isoquinoline‐1,3‐dione, bearing an allylic group has been designed and synthesized. Bulk radical copolymerization has been carried out in order to prepare a fluorescent copolymer, based on styrene. The main photophysical characteristics of the monomeric and polymeric fluorophores have been investigated both in the absence and presence of metal cations and protons. It has been found that the monomeric naphthalimide can be used as a sensor for protons and Zn²⁺, Ni²⁺, Ce³⁺, Cu²⁺, Co²⁺, Ag⁺ cations. The polymeric fluorophore has been shown to be a selective chemosensor for Cu²⁺ cations. Copyright © 2006 John Wiley & Sons, Ltd.     

Potentiometric titration of sorbed hydrogen on palladium carrier catalysts

A method of determination of adsorbed and absorbed hydrogen on palladium catalysts with carbon carriers is suggested and verified. The method allows H_ad and H_ab to be determined with an accuracy of about 10% using catalysts containing at least 5% Pd.

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- . . . 10% , , - , 5% Pd.

     

Reactions of 4-Aryl-2-hydrazino-3-nitro-6-R-quinolines with HNO2

The reaction of 4-aryl-2-hydrazino-3-nitro-6-R-quinolines with NaNO₂ in AcOH gives the corresponding tetrazolo[1,5-a]quinolines. In contrast to tetrazolo[1,5-c]pyrimidines they cannot be converted to 6-R-4-phenyl[1,2,5]oxadiazolo[3,4-b]quinoline-3-oxides by heating in THF, toluene, or AcOH. Total energy quantum-chemical calculations using the MINDO/3 and MNDO methods show that [1,2,5]oxadiazolo[3,4-b]quinoline-3-oxides are significantly higher in energy (230-280 kcal/mol) than the mentioned tetrazolo[1,5-a]quinolines and hence their formation is unlikely.     

Kinetic model ofCO oxidation on nonuniform surface analyzed regardingCOads spillover, 2. homotopic method. Effect ofm1 surface portion

The homotopic method has been used to analyze the kinetic model of three-stageCO oxidation on two nonuniform surface patches conjugated byCO ₂ spillover. Diagrams of steady states depending on the portion of surface patchm ₁ at various temperatures and pressure ratiosP(O ₂)/P(CO) have been constructed. The ratios of different type patches corresponding to the maximum overall reaction rate have been found.     

New approaches to the synthesis of functionally substituted pyrido[3′,2′:4,5]thieno[3,2-b]pyridines and the structure of the products obtained

Substituted pyrido,[3',2':4,5]thieno[3,2-b]pyndines were obtained by the reaction of 3-amino-2-benzoylthieno [2,3-b]pyridines with malononitrile and the reaction of 3-cyanopyridine-2(IH)-thiones with 2-aryl-3-bromo-I,I-dicyanopropene. 2-Amino-4-(4-bromophenyl)-7, 9-dimethyl-3-cyanopyrido [3',2':4,5]thieno[3, 2-b]-pyridine was used for the synthesis of a derivative of pyrido[3",2":4', 5']thieno[2',3':5,6]pyrido[2,3-d]-pyrimidine. The structure of these compounds was confirmed by spectral data and x-ray diffraction structural analysis.Deceased.     

Excitation decay pathways of Lhca proteins: a time-resolved fluorescence study

Light-harvesting complex I (LHCI), which serves as a peripheral antenna for photosystem I (PSI) in green plants, consists mainly of four polypeptides, Lhca1-4. We report room temperature emission properties of individual reconstituted monomeric Lhca proteins (Lhca1, -2, -3, and -4) and dimeric Lhca1/4, performed by steady-state and time-resolved fluorescence techniques. The emission quantum yields of the samples are approximately 0.12, 0.085, 0.081, 0.041, and 0.063 for Lhca1, -2, -3, -4, and the -1/4 dimer, respectively, which is considerably lower than the value of 0.22 found for light-harvesting complex II (LHCII), the main peripheral antenna complex of photosystem II in green plants. The decay components of LHCI proteins can be divided in two categories: Lhca1 and Lhca3 have decay times of 1.1-1.6 ns and 3.3-3.6 ns, and Lhca2 and Lhca4 have decay times of 0.7-0.9 ns and 3.1-3.2 ns. These categories seem to correlate with the pigment composition of the samples. All decay times are faster than that observed previously for LHCII. When the absolute emission yields and the lifetimes of the Lhca samples are combined, the overall emission properties of the individual Lhca proteins are expressed in terms of their emitting dipole moment strength. In the samples without extreme red states, that is, Lhca1 and Lhca2, the emitting dipole moment has a value close to unity (relative to monomeric chlorophyll in acetone), which is similar to that for LHCII, whereas, in the samples with the red-most state (F-730), that is, Lhca3, -4, and the -1/4 dimer, the emitting dipole moment has a value less than unity (0.6-0.8), which can be explained by mixing the red-most (exciton) state with a dark charge-transfer state, as suggested in previous PSI red pigment studies. In addition, we find a lifetime component of approximately 50-150 ps in all red-pigment-containing samples, which cannot be due to "slow" energy transfer, but is instead assigned to an unrelaxed state of the pigment-protein, which, on this time-scale, is converted into the final emitting state.