Synthesis and reactions of β-lactones

In contrast to -propiolactone and diketene, -trichloromethyl--propiolactone generally reacts with -amino heterocyclic nitrogen compounds to give amides of 3-hydroxy-4,4,4-trichlorobutyric acid (with the participation of the exocyclic and endocyclic nitrogen atoms of the reagents) rather than condensed heterocycles (pyrimidine derivatives). The reasons for the difference in the reactivities of the indicated -lactones are discussed.See [1] for communication XIV.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 2, pp. 260–265, February, 1972.     

Accurate calculation of functional determinants

A dependence of the functional determinant of the operator from the family D() satisfying the condition D()=fD()+D()f on the parameter m² of infrared regularization is found in the regularization method using a generalized function.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 27–32, June, 1988.     

The effect of silicon-substrate orientation on the local piezoelectric characteristics of LiNbO<Subscript>3</Subscript> films

The domain structure of lithium-niobate thin films grown on Si(111) and Si(100) substrates coated with a native oxide layer with a thickness of no less than 2 nm is investigated by X-ray diffraction, scanning electron microscopy and piezoresponse force microscopy. The films are synthesized by the rf magnetron sputtering of a single-crystal lithium-niobate target. A high degree of grain orientation in the polycrystalline films is demonstrated. The piezoelectric coefficients d _zz of the lithium-niobate films on Si(111) and Si(100) substrates are calculated from the measured dependences of the amplitude of the piezoresponse signal on the ac voltage applied between the cantilever tip and the substrate. Piezoelectric hysteresis loops are obtained in the remanent piezoelectric response regime     

A new look at the John–Nirenberg and John–Strömberg theorems for BMO

We develop some techniques for studying various versions of the function space BMO. Special cases of one of our results give alternative proofs of the celebrated John–Nirenberg inequality and of related inequalities due to John and to Wik. Our approach enables us to pose a simply formulated “geometric” question, for which an affirmative answer would lead to a version of the John–Nirenberg inequality with dimension free constants.     

Structural,ferroelectric and magnetic properties of Bi0.85Sm0.15FeO3 perovskite

Room temperature crystal structure, ferroelectric and magnetic properties of polycrystalline Bi_0.85Sm_0.15FeO₃ samples were investigated. X‐ray diffraction study shows that the compound possesses a dominant PbZrO₃‐like orthorhombic structure with √2a ×2√2a ×2a superlattice (a is the parameter of the cubic perovskite subcell). In contrast to piezoresponse force microscopy data demonstrating some features characteristic of ferroelectrics, polarization vs. electric field measurements reveal the behavior expected for nonpolar materials. Investigation of magnetic properties confirms that 15% samarium substitution suppresses the spin modulation typical of BiFeO₃ and induces the appearance of spontaneous magnetization. (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Local approximations and intrinsic characterization of spaces of smooth functions on regular subsets of ℝn

We give an intrinsic characterization of the restrictions of Sobolev (?ⁿ ), Triebel–Lizorkin (?ⁿ ) and Besov (?ⁿ ) spaces to regular subsets of ?ⁿ via sharp maximal functions and local approximations. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A Note on the Thermomechanics of Curvature Flows in IR3 and on Surfaces in IR3

Equations for the evolution of curves in IR³ and on surfaces in IR³ are derived from a configurational force balance, a mechanical version of the second law, and suitable constitutive assumptions. Both the isotropic and anisotropic cases are considered.Sommario.In questo lavoro si derivano le equazioni di evoluzione per curve in IR³ e su superfici di IR³, utilizzando un bilancio di forze configurazionali, una versione meccanica del secondo principio e opportune ipotesi costitutive. Sono trattati sia il caso isotropo che anisotropo.     

Configurational Forces and the Dynamics of Planar Cracks in Three-Dimensional Bodies

This paper develops a three-dimensional framework for the evolution of planar cracks, concentrating on the derivation of balances and constitutive equations that describe the motion of the crack tip. The theory is based on the notion of configurational forces in conjunction with a mechanical version of the second law. This revised version was published online in August 2006 with corrections to the Cover Date.     

Relativistic spinning particle in a gravitational field with torsion

A model of a relativistic spinning particle in a gravitational field with a flat metric and a constant torsion is analyzed within the framework of classical mechanics. The Lagrange equations allow an exact integration.Tomsk State Pedagogical Institute. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 50–54, November, 1993.