Approximation of nonsmooth solutions of linear ill-posed problems

In the multidimensional case, for the Tikhonov regularization, two new families of stabilizers containing the norms of the Lipschitz spaces and the norms of the Sobolev spaces with fractional derivatives are suggested. Theorems of convergence of Tikhonov regularized approximate solutions and their discrete approximations are proved. Detailed step-by-step investigation of the solving algorithm is performed by the example of an integral Fredholm equation of the first kind.     

Similar quartz crystallographic textures in rocks of continental earth’s crust (by neutron diffraction data): II. Quartz textures in monophase rocks

The types of quartz textures found in a large collection of multiphase rocks from different regions of the earth are analyzed. Crystallographic textures of granulite, amphibolite, slate, and gneiss samples are measured, classified, and compared with the similar textures of monomineral rocks.     

Can multivalency be expressed kinetically? The answer is yes

Inspired by the concept of multivalency and in pursuit of ever more intricate artificial molecular machines, we investigated the strict self-assembly of a triply threaded two-component superbundle, starting from a tritopic receptor in which three benzo[24]crown-8 macrorings are fused onto a triphenylene core and a trifurcated trication wherein three bipyridinium units are linked 1,3,5 to a central benzenoid core. The result of the investigation was quite unexpected and surprising. It transpired that the rapid formation of a doubly threaded two-component complex was followed by an extremely slow conversion (a week at 253 K in CD3COCD3 to reach equilibrium) of this kinetically controlled product into a thermodynamically controlled one, namely a triply threaded two-component superbundle. This intriguing observation begs the question: are there instances in nature where multivalency is expressed as a kinetically controlled process, prior to an equilibrium state being reached, and if so, what are the biological implications, if any?     

Projections on Lp-spaces of polyanalytic functions

The fundamental result: for an arbitrary bounded, simply connected domain in , the subspace L_n,m ^p() of the space L^p(, ) ( is the plane Lebesgue measure, p 1), consisting of the (m, n)-analytic functions in , is complemented in LP(, ) (a function f is said to be (m, n)-analytic if (^m+n/¯Z^mZⁿ)f=0 in ). Consequently, by virtue of a theorem of J. Lindenstrauss and A. Pelczyski, the space L_n,m ^P() is linearly homeomorphic to lP. In particular, for m=n=1 we obtain that the space of all harmonic L^P-functions in is complemented in L^P(, ). This result has been known earlier only for smooth domains.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 190, pp. 15–33, 1991.     

Analytical characteristics of combined gas chromatographic systems: Packed precolumn-open tubular column

The peculiarities of the flow splitting technique for sample injection into a capillary column have been discussed. A comparative investigation of reproducibility of the analytical results obtained for two gas chromatographic systems using flow splitting [1) sample injector-packed predolumn-splitter-open tubular capillary column and (2) sample injector-splitter-open tubular capillary column] has been carried out. It was experimentally shown that the first system ensures considerably better reproducibility for the results concerning the composition of the analyzed mixtures. Other advantages of the first system are also discussed.     

Reaction of 1-bromovinyl and 1-bromo-2-phenylvinyl sulfones with some CH acids

Benzyl, methyl, and phenyl α-bromovinyl sulfones reacted with malononitrile and dimethyl malonate sodium enolates in THF to give sulfonyl-substituted cyclopropanes. Reactions of the same sulfones with methyl acetoacetate sodium enolate afforded the corresponding sulfonyl-substituted cyclopropanes as mixtures of cis and trans isomers with a small impurity of 5-sulfonyl-4,5-dihydrofuran derivative. Phenyl and p-tolyl 1-bromo-2-phenylvinyl sulfones reacted with methyl acetoacetate sodium salt to produce a mixture of trans-isomeric 5-sulfonyl-4,5-dihydrofuran and Michael adduct of the CH acid with activated acetylene generated by concurrent 1,2-dehydrobromination of the initial α-bromovinyl sulfone.     

Verification of the postulate of isotropy during variable-rate deformation

Thin-wall tubular specimens of high-density polyethylene were tested along deformation trajectories following two broken-line segments. The results verify the postulate that isotropy prevails when the deformation rate changes by two orders of magnitude within a single test.     

Hadroproduction of direct <Emphasis Type="Italic">J/ψ</Emphasis> and <Emphasis Type="Italic">ψ</Emphasis>′ mesons in the fragmentation of gluons and <Emphasis Type="Italic">c</Emphasis> quarks at high energies

The transverse-momentum spectra of direct J/ψ and ψ′ mesons in pp interactions at the Tevatron collider energy of \(\sqrt s = 1.8\) TeV are calculated on the basis of nonrelativistic QCD, the fragmentation model, the k_T-factorization approach, and the standard parton model. The contribution of gluon fragmentation is shown to exceed the contribution of c-quark fragmentation both within the parton model and within the k_T-factorization approach. Experimental data of the CDF Collaboration agree with the assumption that gluon fragmentation plays a dominant role in the \(Q\bar Q[^3 S_1 ,8]\) octet state, with the nonperturbative matrix element taking approximately equal values in the parton model and in the k_T-factorization approach.