The Transition Towards Immortality: Non-linear Autocatalytic Growth of Citations to Scientific Papers

We discuss microscopic mechanisms of complex network growth, with the special emphasis of how these mechanisms can be evaluated from the measurements on real networks. As an example we consider the network of citations to scientific papers. Contrary to common belief that its growth is determined by the linear preferential attachment, our microscopic measurements show that it is driven by the nonlinear autocatalytic growth. This invalidates the scale-free hypothesis for the citation network. The nonlinearity is responsible for a dramatic dynamical phase transition: while the citation lifetime of majority of papers is 6–10 years, the highly-cited papers have practically infinite lifetime.     

Search for a mixed quark-hadron phase of QCD matter at the JINR nuclotron

Physics aspects of a JINR project to reach the planned 5 A GeV energy for the Au and U beams and to increase the bombarding energy up to 10 AGeV are discussed. The project aims to search for a possible formation of a strongly interacting mixed quark-hadron phase. The relevant problems are exemplified. The need for scanning heavy-ion interactions in bombarding energy, collision centrality, and isospin asymmetry is emphasized. The text was submitted by the authors in English.     

A Possibilistic Approach of the Max-Product Bernstein Kind Operators

By analogy with the probabilistic approach of the classical Bernstein polynomials, in this paper firstly we give the proof for the uniform convergence of the nonlinear max-product Bernstein operator by using the theory of possibility. This new approach, which interprets the max-product Bernstein operator as a possibilistic expectation of a particular fuzzy variable having a possibilistic Bernoulli distribution, does not only offer a good justification for the max-product Bernstein operator, but also allows to extend the method to other discrete max-product Bernstein type operators.     

Catalytic and Atom‐Economic C −C Bond Formation: Alkyl Tantalum Ureates for Hydroaminoalkylation

Atom‐economic and regioselective C ?C bond formation has been achieved by rapid C?H alkylation of unprotected secondary arylamines with unactivated alkenes. The combination of Ta(CH₂SiMe₃)₃Cl₂, and a ureate N,O‐chelating‐ligand salt gives catalytic systems prepared in situ that can realize high yields of β‐alkylated aniline derivatives from either terminal or internal alkene substrates. These new catalyst systems realize C?H alkylation in as little as one hour and for the first time a 1:1 stoichiometry of alkene and amine substrates results in high yielding syntheses of isolated amine products by simple filtration and concentration.     

Solvation of phenylglycine- and leucine-derived chiral stationary phases: molecular dynamics simulation study

A theoretical study of the solvation of ( R)- N-(3,5-dinitrobenzoyl)phenylglycine- and ( R)- N-(3,5-dinitrobenzoyl)leucine-derived chiral stationary phases (CSPs) is presented. Semiflexible models of the chiral selectors are prepared from B3LYP/6-311G** calculations, and these are used in the molecular dynamics simulations of the corresponding interface. The chiral interface is examined for four solvents: 100% hexane, 90:10 hexane:2-propanol, 80:20 hexane:2-propanol, and 100% 2-propanol. Despite the similarities between phenylglycine and leucine, the interfaces are distinct both in terms of the selector orientations at the surface and in the number of hydrogen bonds formed with 2-propanol. We also find that an increase in alcohol concentration alters the preferred orientations of the selectors.     

Amalgamated free products of weakly rigid factors and calculation of their symmetry groups

We consider amalgamated free product II₁ factors M = M _1*B M _2*B … and use “deformation/rigidity” and “intertwining” techniques to prove that any relatively rigid von Neumann subalgebra Q ⊂ M can be unitarily conjugated into one of the M _i ’s. We apply this to the case where the M _i ’s are w-rigid II₁ factors, with B equal to either C, to a Cartan subalgebra A in M _i , or to a regular hyperfinite II₁ subfactor R in M _i , to obtain the following type of unique decomposition results, àla Bass–Serre: If M = (N _1 * CN_2*C …) ^t , for some t > 0 and some other similar inclusions of algebras C ⊂ N _i then, after a permutation of indices, (B ⊂ M _i ) is inner conjugate to (C ⊂ N _i ) ^t , for all i. Taking B = C and , with {t _i } _i⩾1 = S a given countable subgroup of R ₊ ^*, we obtain continuously many non-stably isomorphic factors M with fundamental group equal to S. For B = A, we obtain a new class of factors M with unique Cartan subalgebra decomposition, with a large subclass satisfying and Out(M) abelian and calculable. Taking B = R, we get examples of factors with , Out(M) = K, for any given separable compact abelian group K.     

Approximation of Analytic Functions with an Arbitrary Order by Generalized Baskakov–Faber Operators in Compact Sets

By using a sequence \(\lambda _{n}>0\), \(n\in \mathbb {N}\) with the property that \(\lambda _{n}\rightarrow 0\) as fast we want, in this paper we obtain the approximation order \(O(\lambda _{n})\) for a generalized Baskakov–Faber operator attached to analytic functions of exponential growth in a continuum \(G\subset \mathbb {C}\). Several concrete examples of continuums G are given for which this operator can explicitly be constructed.     

A unique decomposition result for HT factors with torsion free core

We prove that II₁ factors M have a unique (up to unitary conjugacy) cross-product type decomposition around “core subfactors” N⊂M satisfying the property HT of [S. Popa, On a class of type II₁ factors with Betti numbers invariants, Ann. of Math. (2) 163 (2006) 809-899] and a certain “torsion freeness” condition. In particular, this shows that isomorphism of factors of the form Lαi(Z²)?Fni, i=1,2, for Fni⊂SL(2,Z) free groups of rank ni and αj=e2πitj, tj∉Q, implies n₁=n₂.