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Synthesis of New Porphyrin-Fullerene Dyads Capable of Forming Charge-Separated States on a Microsecond Lifetime Scale

2014
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Chemistry - A European Journal
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A series of covalently linked axially symmetric porphyrin-fullerene dyads with a rigid pyrrolo[3,4-c]pyrrolic linker enabling a fixed and orthogonal arrangement of the chromophores has been synthesized and studied by means of transient absorption spectroscopy and cyclic voltammetry. The lifetime of the charge-separated state has been found to depend on the substituents on the porphyrin core, reach-ing up to 4 ms for a species with meso-(p-MeOC 6 H 4 ) substituents. The ground and excited

doi:10.1002/chem.201404435
pmid:25382590
fatcat:qpm37rfainalvoqixayp2lelty
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... nic states of model compounds have been calculated at the DFT and TD-DFT B3LYP(6-31G(d)) levels of theory and analyzed with regard to the effect of the substituent on the stabilization of the charge-separated state in the porphyrin-fullerene ensemble with a view to explaining the observed dependence. [a] Dr. Scheme 1. Retrosynthetic disconnection of the target porphyrin-fullerenes 1 a-d.##
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The direct algorithm for solving of the graph isomorphism problem
[article]

2005
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arXiv
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pre-print

FAIZULLIN,

arXiv:math/0502251v4
fatcat:5pkr7vaewjbedliwfxpjsnq47q
*ALEXANDER*V.*PROLUBNIKOV*The sets R(A 4 ) and R(B 4 ) are already simple before 5-th iteration. ... FAIZULLIN,*ALEXANDER*V.*PROLUBNIKOV*Let machine numbers mantissas length is equals to the number of graph vertices (n = 6). ...##
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An estimation of the greedy algorithm's accuracy for a set cover problem instance
[article]

2019
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arXiv
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pre-print

Considering the set cover problem, by modifying the approach that gives a logarithmic approximation guarantee for the greedy algorithm, we obtain an estimation of the greedy algorithm's accuracy for a particular input. We compare the presented estimation to another estimations of this type. We give such examples of the set cover problem instances that the presented estimation sagnificantly improves over linear programming relaxation based estimation.

arXiv:1811.04037v3
fatcat:4jdwe6yi6ncvhm65cgrglcaabi
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The interval greedy algorithm for discrete optimization problems with interval objective function
[article]

2020
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arXiv
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pre-print

We consider a wide class of the discrete optimization problems with interval objective function. We give a generalization of the greedy algorithm for the problems. Using the algorithm, we obtain the set of all possible greedy solutions and the set of all possible values of the objective function for the solutions. For a given probability distribution on intervals of objective function' coefficients, we compute probabilities of the solutions, compute expected values of the objective function for

arXiv:2003.01937v3
fatcat:fwr4qqlvvvhaxjdnsrmb5k4vka
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... them and other probabilistic characteristics of the problem.##
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Reduction of the graph isomorphism problem to equality checking of n-variables polynomials and the algorithms that use the reduction
[article]

2016
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arXiv
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pre-print

The graph isomorphism problem is considered. We assign modified characteristic polynomials for graphs and reduce the graph isomorphism problem to the following one. It is required to find out, is there such an enumeration of the graphs vertices that the polynomials of the graphs are equal. We present algorithms for the graph isomorphism problem that use the reduction. We prove the propositions that justify the possibility of a numerical realization of the algorithms for the general case of the

arXiv:1512.03139v4
fatcat:u5yt673vejf2ph5h2cqqcxdbzy
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... raph isomorphism problem. The algorithms perform equality checking of graphs modified n-variables characteristic polynomials. We show that probability of obtaining a wrong solution of the graph isomorphism problem using recursive modification of the algorithm is negligible if the algorithm parameter is sufficiently large. In the course of its implementation, the algorithm checks the equality of the graphs modified characteristic polynomials in predefined points. For n-vertices graph, the polynomial has 2^n coefficients so its value in some point cannot be evaluated directly for large enough n. We show that we may check the equality of the polynomials in predefined points without direct evaluation of the polynomials values in these points. We prove that, for the graphs on n vertices, it is required O(n^4) elementary machine operations and it is requred machine numbers with mantissa's length O(n^2) to check equality of the graphs polynomials values in predefined points. In general, it needs an exponential time to solve the GI instance using the presented approach, but in practice, it is efficient even for compuationally hard instances of the graph isomorphism problem.##
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On the representativeness of approximate solutions of discrete optimization problems with interval cost function
[article]

2022

We consider discrete optimization problems with interval uncertainty of cost function coefficients. The interval uncertainty models the measurements errors. A possible optimal solution is a solution that is optimal for some possible values of the coefficients. The probability of a possible solution is a probability of obtaining such coefficients that the solution is optimal. Similarly we define the notion of a possible approximate solution and its probability. We consider a possible solution

doi:10.48550/arxiv.2201.00182
fatcat:4z7lpzrznzgblft7336eagumti
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... epresentative if its probability less than some boundary value. The mean (optimal or approximate) solution is a solution that we obtain for mean values of interval coefficients. We show that the share of instances of a discrete optimization problem with unrepresentative mean approximate solution may be large enough for rather small values of errors.##
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Page 2287 of Mathematical Reviews Vol. , Issue Index
[page]

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Mathematical Reviews
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., 2004a:68116

*Prolubnikov*, A. V. An estimate for the approximate solution of the covering problem by Chvatal’s algorithm. (Russian. ... (English summary) 2004i:90089 Schwartz,*Alexander*see Kaibel, Volker, 2004e:05125 Schwoon, Stefan Determinization and complementation of Streett automata. ...##
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Page 684 of Mathematical Reviews Vol. , Issue Index
[page]

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Mathematical Reviews
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(

*Alexander*N. Petrov) 2004j:83008 83C05 (83C40) Fairlie, David B. Extra dimensions and non-linear equations. ... (with*Prolubnikov*, A. V.) A heuristic algorithm for decrypting a double permutation cipher. (Russian. English summary) Mathematical structures and modeling, No. 9 (Russian), 62-69, Omsk. Gos. ...