Homological invariants of modules over contracting endomorphisms

It is proved that when R is a local ring of positive characteristic, \({\phi\colon R{\to} R}\) is its Frobenius endomorphism, and some non-zero finite R-module has finite flat dimension or finite injective dimension for the R-module structure induced through \({\phi}\) , then R is regular. This broad generalization of Kunz’s characterization of regularity in positive characteristic is deduced from a theorem concerning a local ring R with residue field of k of arbitrary characteristic: If \({\phi}\) is a contracting endomorphism of R, then the Betti numbers and the Bass numbers over \({\phi}\) of any non-zero finitely generated R-module grow at the same rate, on an exponential scale, as the Betti numbers of k over R.     

Application of nonsmooth transformations to analyze a vibroimpact duffing system

The forced vibrations of an impact Duffing oscillator with one degree of freedom are studied using Zhuravlev's nonsmooth transformation and the multiple-scales method. Detailed consideration is given to the forced vibrations in the domain of resonance family. The stability and bifurcations of periodic vibrations are analyzed Translated from Prikladnaya Mekhanika, Vol. 44, No. 10, pp. 114–121, October 2008.     

Theoretical study of the toroidal forms of carbon and related endohedral complexes with lithium

The atomic and electron structures of toroidal carbon molecules (C₂₄₀ and two C₁₂₀ isomers) and related endohedral complexes with lithium (Li₂@C_n and Li₄@C_n) were theoretically studied using both nonempirical (3–21G basis set) and semiempirical (MNDO) calculation schemes. For the metal-containing compounds, the behavior of lithium atoms embedded into internal cavities of the carbon framework was studied using methods of molecular dynamics. It is demonstrated that the structure of electron levels of metal-containing carbon complexes exhibits an embedded state in the forbidden band, which appears due to the presence of electrons accepted from metal atoms. The position of this embedded state and the bandgap width depend both on the initial carbon structure and on the amount of metal atoms incorporated.     

Interaction of elastic system with snap-through vibration absorber

Interaction of essentially non-linear vibration absorber (snap-through truss) with primary 1DOF linear oscillator is investigated. The study covers both free and forced (external excitation applied to the linear oscillator) responses of the system. The analysis is performed by complexification-averaging technique, describing a slow variation of amplitudes of principal harmonic components. Periodic and quasiperiodic oscillations are revealed and investigated. It turns out that for realistic parameters of the system vast majority of the responses, including those suitable for the vibration absorption, is quasiperiodic. The results are verified by means of a direct numeric simulation.     

Underestimating the width of the bandgap in the electronic spectra of La2CuO4

It is shown that the width of the bandgap determined by the simultaneous analysis of the experimental photoelectron and inverse photoemission spectra of the surface of La₂CuO₄ using a common energy scale is underestimated by 1 eV. The electronic and satellite structures of the spectra of La₂CuO₄ are calculated on the basis of the multiband p-d model and the sudden perturbation approximation. It is shown that shakedown processes shift the one-electron contour of the final two-hole configuration of the photoelectron spectrum 1 eV down the energy scale and shift the contour of the final d ¹⁰ configuration of the inverse photoemission spectrum downward by 2 eV; these shifts cause the energy splitting between the filled and empty bands to be underestimated. Fiz. Tverd. Tela (St. Petersburg) 39, 449–451 (March 1997)     

Finite generation of Hochschild homology algebras

We prove converses of the Hochschild-Kostant-Rosenberg Theorem, in particular: If a commutative algebra S is flat and essentially of finite type over a noetherian ring , and the Hochschild homology HH _* (S|) is a finitely generated S-algebra for shuffle products, then S is smooth over . Oblatum 27-V-1999 & 27-IX-1999 / Published online: 24 January 2000     

Reduction of derived Hochschild functors over commutative algebras and schemes

We study functors underlying derived Hochschild cohomology, also called Shukla cohomology, of a commutative algebra S essentially of finite type and of finite flat dimension over a commutative noetherian ring K. We construct a complex of S-modules D, and natural reduction isomorphisms for all complexes of S-modules N and all complexes M of finite flat dimension over K whose homology H(M) is finitely generated over S; such isomorphisms determine D up to derived isomorphism. Using Grothendieck duality theory we establish analogous isomorphisms for any essentially finite-type flat map of noetherian schemes, with f^!OY in place of D.