Vol. 45 No. 3 (226) (2011)

In this paper the notion of quasi-hard determinative formulas is introduced and the proof complexities of such formulas are investigated. For some class of quasi-hard determinative formulas the same order lower and upper bounds for the length of proofs are obtained in several proof systems, basing on disjunctive normal forms (conjunctive normal forms).

In this paper the concept of $q$-bilattice is studied. Interlaced $q$-bilattices are characterized by the pair of congruencies.

In the paper a formula for the chord length distribution function of a lens is obtained. In the special case of a regular lens the table of values of the chord length distribution function is given.

The paper considers a factorization problem of a matrix-function, obtained from a circulant by a right and left multiplication by diagonal rational matrixfunctions. Formulas for partial indices are obtained by means of ranks of a finite number of explicit type matrices. A factorization construction of this matrixfunction based on factorization of finite number of functions is given as well.

The problem of optimal stabilizatioin of a double pendulum, when its suspension center moved in the horizontal direction according to the given law, has been treated. The problem was reduced to the case of a linear nonuniform system that was solved in the event when the first and the second pendulums had equal masses and lengths. An optimal Lyapunov function and an optimal control action have been constructed.

The paper is devoted to the logic programming with negation and with built-in predicates. General logic programs (logic programs with negation) and general goals (goals with negation) are considered. Modification of SLDNF-resolution for built-in predicates is introduced. The soundness of modified SLDNF-resolution is proved. SLDNF-resolution used in real systems (practical SLDNF-resolution) is considered and the soundness of practical SLDNF-resolution is proved.

A single-layer flat-coil-oscillator activated by a low power backward tunnel diode has been elaborated and created. As an inductance in a pick-up circuit of the oscillator, such a flat coil served as a “magnetic-field” probe in such a measuring instrument. The created oscillator was activated both without and with an external capacitance C₀ in its resonant circuit, i.e. the flat-coil oscillator might be also activated with its own (internal) capacitance C_c. Investigation of “probe-forma-tive” capabilities of this research instrument with such an unusual coil (versus C₀) showed that with a reduction of the value of this capacitance the feeling (probing) field of such a probe exponentially becomes longer, i.e. these probes become more far-ranging with decreasing C₀. The revealed property of “magnetic-field” probes would permit an essential widening of capabilities of flat-coil-based probe microscopes. It may also permit to enhance the efficiency of searching and detec-tion of the nodal structure, arising at an unusual phase transition from the “uni-form” to “non-uniform” superconductivity, predicted independently by Fulde and Ferrell, and Larkin and Ovchinnikov.

The thermal denaturation profiles of Calf Thymus DNA in the presence of binuclear compounds of bivalent platinum (cis-[{Pt(NH₃)₂Cl}₂Pyr]Cl₂) were studied by absorption spectrophotometry and differential adiabatic scanning microcalorimetry. A comparison with an active antitumor drug cis-diamminedichloroplatinum (cis-DDP) was made. Experimental data witness that small concentrations (r<0.3) of binuclear platinum compound stabilized the structure of Calf Thymus DNA stronger than cis-DDP. Both the complexes tend to refold the denaturated DNA. It is rather interesting that in case of 10^-6 M concentration of binuclear platinum compound (r=0.03) the denaturated DNA is refolded by 77.62%, whereas under the same condition cis-DDP leads to 49.01% refolding of denaturated DNA. Such a high percent of renaturation was probably the result of interstrand cross-links formation.

The dispersion relation of a novel semiconductor-gap-dielectric waveguide in terahertz range are investigated. It is shown that InAs–SiO₂–Si structure supports strongly confined guided mode with а sizes ~0.0016 λ × 0.02 λ at 1 THz.

We have proved, that if $n\geq1003$ is an arbitrary odd number and $\phi$ is a splitting automorphism of period $n$ of group $B(m,n)$ that has a prime order, then $\phi$ is inner automorphism.