Modeling the influence of mineral content and porosity on ultrasound parameters in bone by using synthetic phantoms

Model composite media – 10×15×80 mm³ bone tissue phantoms based on an epoxy resin with fillers—were made to study the influence of porosity and mineral content on ultrasound velocity and attenuation. The pores were simulated by 1 mm³ particles of a soft rubber, while the mineral content was imitated by a mineral residue of natural bone obtained by burning and grinding. The porosity and mineral content were varied in the range of 0–70% by volume with a step of 10%. The velocity, attenuation, and prevalent frequency of ultrasound were measured by the pulse transition method, using transducers with nominal frequencies 0.1, 0.2, 0.5, and 1.0 MHz. It was experimentally found that the ultrasound velocity decreased nearly exponentially with growth in porosity, while the velocity dispersion was negligible at frequencies >0.2 MHz; the ultrasound attenuation increased linearly with growth in porosity and strongly depended on the frequency; the velocity increased nonlinearly with growth in mineral content above 40%; the attenuation did not exhibit a distinct dependence on the mineral content; the porosity provoked a shift in the prevalent frequency of transducers, tending to the common value of 0.2 MHz, while the mineral content did not excite similar changes. The complex measurement of velocity, frequency-dependent attenvation, and prevenlent frequency of ultrasound is proposed in ultrasonic diagnostics of bone for more precise determination of the influence of the porosity and the degree of mineralization on the bone condition.Published in Mekhanika Kompozitnykh Materialov, Vol. 35, No. 2, pp. 211–220, March–April, 1999.     

A characterization of Gaussian measures on locally compact Abelian groups

Let and be independent random variables having equal variance. In order that + and – be independent, it is necessary and sufficient that and have normal distributions. This result of Bernshtein [1] is carried over in [7] to the case when and take values in a locally compact Abelian group. In the present note, a characterization of Gaussian measures on locally compact Abelian groups is given in which in place of + and –, functions of and are considered which satisfy the associativity equation.Translated from Matematicheskie Zametki, Vol. 22, No. 5, pp. 759–762, November, 1977.     

Elastic properties of certain polymer matrices at low temperatures

A study is made of the viscoelastic behavior of the polyimide DFO and polybenzoxasol (PBZ) at low temperatures. Pulsed ultrasound is used to measure ultrasonic velocity in polymers at the frequency f=5 MHz within the temperature interval 4.2–240 K. Data obtained from acoustic measurements is used to calculate the dynamic elastic modulus, shear modulus, compressive bulk modulus, Poisson's ratio, and certain thermophysical characteristics (Debye temperature, specific heat, coefficient of linear expansion, Grünheisen parameter). It is established that the investigated polymers have low dynamic moduli at 4.2 K. Their values change by 18–20% within the temperature range 4.2–240 K. The polymers also have a large free volume at the temperature of liquid helium. The results show that polyimide DFO and PBZ have good service properties at low temperatures.Paper presented at the IX International Conference on the Mechanics of Composite Materials, Riga, October, 1995.Moscow State Academy of Automotive and Tractor Engineering, Russia. Translated from Mekhanika Kompozitmykh Materialov, No. 4, pp. 454–459, July–August, 1996.     

On the extension principle in internal set theory

Moscow. Translated fromSibirski Matematicheski Zhurnal, Vol. 33, No. 6, pp. 66–78, November–December, 1992.     

Parametric oscillations of solutions to the telegraph equation with moderately small diffusion

Moscow. Translated fromSibirski Matematicheski Zhurnal, Vol. 33, No. 6, pp. 79–86, November–December, 1992.     

Nondestructive Evaluation of Graphite-Epoxy Composites by the Laser Ultrasonic Method

A laser ultrasonic method for nondestructive evaluation of the structure of composite materials is proposed. Specimens of graphite-epoxy composites with compaction-type defects and air cavities are investigated. The method is based on the laser thermooptical generation of wide-band acoustic pulses - optoacoustic (OA) signals - in the material investigated. The acoustic pulses backscattered by structural ingomogeneities and defects are registered by a wide-band piezotransducer, which makes it possible to detect acoustic pulses in the frequency range from 0.1 to 30 MHz. Since the generation and detection of acoustic pulses takes place on the front surface of the specimen, this method allows us to carry out nondestructive evaluation with one-sided access to the object under study. The spectral and correlation analyses of backscattered OA signals are used for mathematical processing of the experimental data. The method developed makes it possible to determine the type of defects and the depth of their location.     

On a method of studying multipoint boundary value problems

Moscow. Translated fromSibirski Matematicheski Zhurnal, Vol. 33, No. 6, pp. 87–93, November–December, 1992.     

Applied theories of the plasticity of porous, “unequally strong,” and anisotropic media. 2. Basic results

Conclusions We obtained practically convenient modifications of the theory of flow and TSEPD [3] for porous and anisotropic media with different strength. These qualities are taken into account with the aid of the respective stress and strain intensities. The fundamental hypotheses are confirmed by verification in known experiments with polymer and composite materials. As an example we examined elastoplastic tension of an anisotropic specimen and the limit state of an internally loaded disk, both made of materials with the mentioned qualities.Communication 1, see [2].Translated from Mekhanika Kompozitnykh Materialov, No. 3, pp. 426–432, May–June, 1986.     

Nondestructive Evaluation of One-Dimensional Periodic Structures by Transmission of Laser-Excited Wide-Band Acoustic Pulses

The propagation of ultrasound in a one-dimensional model and actual periodic structures (PSs) is studied experimentally by the method of optoacoustic spectroscopy based on the laser thermooptical excitation and wide-band piezodetection of short acoustic pulses. It is shown that the ultrasound transmission spectrum of a PS has stop and pass bands, and the greater the number of layers in the PSs, the deeper the stop bands. The case where the thickness, density, and ultrasound velocity of one or several layers in the PS are modified is studied in detail. In this case, a narrow local maximum of ultrasound transmission appears in the stop band, whose location depends considerably on the position of the defective layer in the PS. The experimental data obtained coincide well with the theoretical calculation. The nondestructive evaluation of actual PSs consisting of two epoxy-glued identical aluminum plates is carried out by the optoacoustic method. Such materials are widely used in aircraft industry. It is shown that the ultrasound transmission spectrum for these materials depends considerably on the thickness of the epoxy-glue layer.     

Nonresonant acoustic absorption of Ising magnet

Zubarev's nonequilibrium statistical operator method is used to construct a theory of the nonresonant acoustic absorption of the linear Ising magnet, the basic Hamiltonian of which is of the two-particle kind and is treated without approximations. The frequency dependence of the absorption is determined and found to differ analytically from the well-known Debye curve _D () but for reasonable values of the physical parameters gives an envelope that agrees qualitatively with _D ().Kazan Physicotechnical Institute, Russian Academy of Sciences; Moscow Institute of Instrument Manufacture. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 98, No. 1, pp. 149–159, January, 1994.     

Thermodynamic stability of crystalline polymers in the transition region

The type of phase transition can be determined from the temperature dependence of the coefficient (–P/av)_s and the stability determinant D. We have calculated these quantities for polyethylene from data on the speed of ultrasound, density, and the specific heat C_p.Krupskaya Moscow Regional Pedagogical Institute. Translated from Mekhanika Polimerov, No. 4, pp. 724–726, July–August, 1971.     

Methods and results in the theory of univalent functions

This paper is the original version of the author's survey, published in an abridged form in the Mathematical Encyclopedia (N. A. Lebedev, Univalent function, in: Mathematical Encyclopedia, Vol. 3, Moscow (1982), pp. 1163–1168).This paper of N. A. Lebedev, which opens the present collection, represents a more developed preliminary version of N. A. Lebedev's survey paper Univalent functions, published in Mathematical Encyclopedia. The paper is published with only insignificant modifications. By italic letters we have denoted the titles of the sections in the Mathematical Encyclopedia, directly related to this survey paper — Editors' remark.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 125, pp. 5–21, 1983.     

Comultiplication inABCD algebra and scalar products of bethe wave functions

The representation of scalar products of Bethe wave functions in terms of dual fields, proved by A. G. Izergin and V. E. Korepin in 1987, plays an important role in the theory of completely integrable models. The proof in [A. G. Izergin, Dokl. Akad. Nauk SSSR,297, No. 2, 331 (1987)] and [V. E. Korepin, Commun. Math. Phys.,113, 177–190 (1978)] is based on the explicit expression for the senior coefficient, which was guessed in the Izergin paper and then proved to satisfy some recurrent relations, which determine it unambiguously. In this paper we present an alternative proof based on direct computation. It uses the operation of comultiplication in the ABCD-algebra.The Moscow State University, Moscow, Russia; Published in Teoreticheskaya i Matematicheskaya Fizika, Vol. 100, No. 1, pp. 113–118, July, 1994.     

The (-1/2λϕ2) model of quantum field theory

The model of a scalar field with interaction potential exp (-1/2²) ind-dimensional spacetime (d2) is considered. It is shown that the Green's functions of the model are the same as the Green's functions of the free field.Physicotechnical Institute, Moscow. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 91, No. 3, pp. 411–417, June, 1992.     

Nonclassical analogs of solitons in quantum field theory

The possible existence of quantum copies of classical soliton solutions that cannot exist if the effective Planck constant of the theory tends to zero is discussed. In the framework of the standard expansion in , such nonclassical solitons have energy of orderO() and thus occupy an intermediate position between purely classical configurations and second-quantized degrees of freedom. Analytic calculations are made for the profile functions, masses, and stability of such configurations in the ⁴ kink model.Physics Faculty, Moscow State University. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 94, No. 1, pp. 52–65, January, 1993.     

Some more general bounds on the residual term of the Lagrange interpolation formula

Error bounds are derived for the Lagrange interpolation formula and for the k-th derivative of the residual term of this formula in terms of the Lipschitz constant of the n-th derivative for the case with (n+1) nodes and also for the case when the functions satisfy a special condition: G x, y, z [a, b]: ¦ (x)(z–y) +(y)(x–z)+(z)(y–x)¦G¦(x–y)(y–z)(z–x)¦.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 73, pp. 27–32, 1992.     

Rubber life over a broad interval of stresses and aggressive medium concentrations

A generalized dependence of rubber life on stress and the concentration of the aggressive medium is proposed for a broad interval of variation of stresses and concentrations. The known expressions for the life in air and aggressive media as functions of stress (at large values of ) and concentration at constant stress are obtained as special cases. At zero concentration the proposed relation goes over into Zhurkov's equation with =(). The proposed equation and the graphic construction can be used, in particular, for determining rubber life in air at low stresses, i.e., under conditions similar to those encountered in service.The experiments were performed by N. L. Novikova.Scientific-Research Institute of the Rubber Industry, Moscow. Translated from Mekhanika Polimerov, Vol. 4, No. 6, pp. 1020–1025, November–December, 1968.     

Temperature-frequency reduction of the dynamic functions of black-filled rubbers in the nonlinear region

The possibility of using temperature-frequency reduction of the dynamic functions of black-filled rubbers in the nonlinear region is demonstrated and an additional applicability criterion — similar slopes of the isotherms of the amplitude dependences of the dynamic functions — is formulated. In the case of heavily filled rubbers it may be necessary to determine the constants of the Williams-Landel-Ferry equation and the reference temperature T_S from the experimental data — they may not coincide with the universal values. Master curves of the dynamic functions are obtained for a series of shock-absorbing rubbers at a shear strain amplitude =0.01.A. V. Topchiev Institute of Petrochemical Synthesis, Academy of Sciences of the USSR, Moscow. Scientific-Research Institute of the Rubber Industry, Moscow. Translated from Mekhanika Polimerov, No. 4, pp. 751–754, July–August, 1973.     

On the quotient ring by diagonal invariants

For a finite Coxeter group, W, and its reflection representation , we find the character and Hilbert series for a quotient ring of [^*] by an ideal containing the W–invariant polynomials without constant term. This confirms conjectures of Haiman.