Mixing of electronic states in molybdenum complexes involved in nitrogen activation

The mechanism for nitrogen activation by molybdenum complexes is a complicated one, involving as it does the coupling of a quartet molybdenum reactant with a singlet nitrogen molecule, passing via a series of quartet and doublet encounter complexes to a triplet intermediate, with the subsequent spin crossing to the singlet surface which then leads via a singlet transition state to the final pair of singlet products. We have investigated in detail a variety of levels of theory to describe the crossing of these electronic surfaces and have calculated both lower-bound and actual minimum energy crossing points for the key spin inversion processes.     

Computed Potential Energy Surfaces and Minimum Energy Pathways for Chemical Reactions

Computed potential energy surfaces are often required for computation of such observables as rate constants as a function of temperature, product branching ratios, and other detailed properties. We have found that computation of the stationary points/reaction pathways using CASSCF/derivative methods, followed by use of the internally contracted CI method with the Dunning correlation consistent basis sets to obtain accurate energetics, gives useful results for a number of chemically important systems. Applications to complex reactions leading to NO_x and soot formation in hydrocarbon combustion are discussed.     

Data loci in algebraic optimization

We consider parametric optimization problems from an algebraic viewpoint. The idea is to find all of the critical points of an objective function thereby determining a global optimum. For generic parameters (data) in the objective function the number of critical points remains constant. This number is known as the algebraic degree of an optimization problem. In this article, we go further by considering the inverse problem of finding parameters of the objective function so it gives rise to critical points exhibiting a special structure. For example if the critical point is in the singular locus, has some symmetry, or satisfies some other algebraic property. Our main result is a theorem describing such parameters.     

Extragradient and extrapolation methods with generalized Bregman distances for saddle point problems

In this paper, we introduce two Bregman-type algorithmic frameworks to generalize the extragradient and extrapolation methods. With the help of relative Lipschitzness and the Bregman distance tool, the iteration properties of the proposed frameworks are analyzed. As applied to smooth convex-concave saddle point problems, our theory rediscovers the main results in Mokhtari et al. (2020) [14] for wider frameworks under weaker assumptions via a conceptually different approach.     

一类联图的距离谱半径以及盖理论（英文）

令X=(n₁,n₂,…,n_t),Y=(m₁,m₂,…,m_t)是两个t维递减序列.如果对所有的j,1≤j≤t,都有∑_i=1~j、n_i≥∑_i=1~j m_i以及∑_i=1~t n_i=∑_i=1~t m_i,则称X可盖Y,记作X■Y.如果X≠Y,则记作X■Y.本文考虑联图G(n₁,n₂,…,n_t;a)=(K_n1∪_n2∪…∪K_nt)∨K_a的谱半径,这里n₁+n₂+…+n_t+a=n,(n₁,n     

Lower semicontinuous solutions of the Bellman equation for the minimum time problem

The minimum time problem associated with a nonlinear control system is considered, and the unicity of the lower semicontinuous solution of the corresponding Bellman equation is investigated. A main tool in our approach is the Kruzkov transformation that enables us to work on ⁿ –{0}, where {0} is the target set, instead of the unknown reachable set.This research was carried out while the first author was visiting the Department of Mathematics, University of Genova, Genova, Italy.     

Minimum cost multiflows in undirected networks

LetN = (G, T, c, a) be a network, whereG is an undirected graph,T is a distinguished subset of its vertices (calledterminals), and each edgee ofG has nonnegative integer-valuedcapacity c(e) andcost a(e). Theminimum cost maximum multi(commodity)flow problem (*) studied in this paper is to find ac-admissible multiflowf inG such that: (i)f is allowed to contain partial flows connecting any pairs of terminals, (ii) the total value off is as large as possible, and (iii) the total cost off is as small as possible, subject to (ii). This generalizes, on one hand, the undirected version of the classical minimum cost maximum flow problem (when |T| = 2), and, on the other hand, the problem of finding a maximum fractional packing ofT-paths (whena 0). Lovász and Cherkassky independently proved that the latter has a half-integral optimal solution.A pseudo-polynomial algorithm for solving (*) has been developed earlier and, as its consequence, the theorem on the existence of a half-integral optimal solution for (*) was obtained. In the present paper we give a direct, shorter, proof of this theorem. Then we prove the existence of a half-integral optimal solution for the dual problem. Finally, we show that half-integral optimal primal and dual solutions can be designed by a combinatorial strongly polynomial algorithm, provided that some optimal dual solution is known (the latter can be found, in strongly polynomial time, by use of a version of the ellipsoid method).This work was partially supported by Chaire municipale, Mairie de Grenoble, France.     

Distance distributions and dynamics of a zinc finger peptide from fluorescence resonance energy transfer measurements

Time-resolved fluorescence resonance energy transfer (FRET) measurements were used to measure distance distributions and intramolecular dynamics (site-to-site diffusion) of a 28-residue single-domain zinc finger peptide in the absence and presence of zinc ion. Energy transfer was measured between TRP₁₄ and a N-terminal DNS group. As expected, the TRP-to-DNS distance distribution for zinc-bound peptide is shorter and narrower (R _av=11.2 Å,hw=2.8 Å) than the metal-free peptide (R _av=20.1 Å,hw=14.5 Å). The degree of mutual donor-to-acceptor diffusion (D) was also determined for these distributions. For zinc-bound peptide there is no detectible diffusion (D0.2 Ų/ns), whereas for metal-free peptide a considerable amount of motion is occurring between the donor and the acceptor (D=12 Ų/ns). These results indicate that the zinc-bound peptide folds into a unique, well-defined conformation, whereas the metal-free conformation is flexible and rapidly changing. The absence of detectible mutual site-to-site diffusion between the donor and the acceptor in the metal-bound zinc finger peptide indicates that intramolecular motion is essentially frozen out, on the FRET time scale, as a consequence of zinc coordination.Dedicated to the memory of Barbara D. Wells.     

Thermal analysis and X-ray studies of chiral ferroelectric liquid crystalline materials and their binary mixtures

Summary Thermal properties of a homologous series of ferroelectric liquid crystals S-(-)-[4-(2-n-alkoxy-propionyloxy)]biphenyl-4'-[n-alkoxy-(3,5-dimethyl)]benzoate have been investigated by polarizing optical microscopy and differential scanning calorimetry. The mesophases were identified and confirmed by X-ray too. Three binary mixtures were prepared from the individual homologues. In one of the mixtures (Mix1), the ferroelectric SmC* phase has broadened and became enantiotropic. This mesophase remained monotropic in the other two mixtures (Mix2, Mix3). The chiral nematic N* phase did not appear in Mix1, but remained monotropic for the other two mixtures. Two molecular parameters, the layer spacing and the average intermolecular distance have been calculated from the X-ray results for the homologues and their mixtures. An intercalated tail-to-tail packing of molecules was found both in the single compounds and their mixtures resulting in the layer spacing about half of the molecular length of the single compounds.     

Properties of the skeleton of aggregates grown on a Cayley tree

We discuss and analyze a family of trees grown on a Cayley tree, that allows for a variable exponent in the expression for the mass as a function of chemical distance, M(l)l ^dl . For the suggested model, the corresponding exponent for the mass of the skeleton,d _l ^s , can be expressed in terms ofd _l asd _l ^s = 1,d _l d _l ^c = 2;d _l ^s = d _l –1,d ₁ d _l ^c = 2, which implies that the tree is finitely ramified ford _l 2 and infinitely ramified whend _l 2. Our results are derived using a recursion relation that takes advantage of the one-dimensional nature of the problem. We also present results for the diffusion exponents and probability of return to the origin of a random walk on these trees.