混合Bitsadze-Lavrentév-Tricomi边值问题

It is well known that F. G. Tricomi (1923) is the originator of the theoryof boundary value problems for mixed type equations by establishing the Thicomi equation: y·u_xx+u_yy=0 which is hyperbolic for y < 0, elliptic for y=0. and parabolic for y= 0 and then applied it in the theory of transonic flows.Then A.V.Bitsadze together with M. A . Lavrent′ev (1950) established the Bitsadze Lavre nt′ev equation: sgn( y ) ·u_xx+u_yy=0 where sgn(y) = 1 for y > 0, = -1 for y<0, 0 for y=0 with the discontinuous coefficient sgn( y ) of u_xx, while in the case of Tricomi equation the corre sponding coefficient y is continuous. In this paper we establish the mixed Bitsadze Lavrent′ev Tricomi equation. Lu=K(y)·u_xx+sgn(x) ·u_yy+r(x,y)·u=f(x,y), where the coefficient K=K(y) of u_xx is increasing continuous and coefficient M=sgn(x) of u_yy discontinuous, r=r(x,y) is once continuously differentiable, f=f(x,y) continuous. Finally we prove the uniqueness of quasi regular solutions and observe that these new results can bbe applied in fluid dynamics.     

Stress-Strain State in the Zone of Load Transfer in a Composite Specimen under Uniaxial Tension

The stress-strain state in the zone of load transfer in a uniaxially stretched specimen made of a unidirectional epoxy carbon-fiber-reinforced plastic (CFRP) is investigated. A parametric analysis of the influence of geometric and mechanical characteristics of the specimen on its stress-strain state is performed by means of finite-element modeling. The parameters allowing us to significantly reduce the dangerous concentration of transverse and tangential stresses are revealed. The mechanical tensile characteristics of a high-strength pultruded unidirectional CFRP are determined experimentally, and the size effect of its strength is estimated.     

Isometric Isomorphisms Between Banach Algebras Related to a Certain Class of Clifford Topological Semigroups

In the present paper it is shown that if S₁ and S₂ are two Clifford topological semigroups satisfying certain conditions and T is an isometric isomorphism of LUC(S₁*) onto LUC(S₂*), then T maps S₁ topologically isomorphically onto S₂. Furthermore, T maps M ^l _n(S₁) (M(S₁), respectively) isometrically isomorphically onto M ^l _n(S₂) (M(S₂), respectively). Indeed, we have obtained a generalization of a well-known result of Ghahramani, Lau and Losert for locally compact groups to a more general setting of Clifford topological semigroups.     

An electron spin resonance study of radical decay in γ-ray irradiated pepper by thermal treatments

Applied Magnetic Resonance - We examined by electron spin resonance (ESR) spectroscopy the thermal decay of radicals as induced by γ-irradiation on pepper. Upon irradiation, the satellite...     

K X-ray production cross sections for 40-180 keV protons

Considering the importance of the X-ray production cross sections for the determination of the element concentrations in a given material, we have measured them experimentally for Al Si, Sc, Ti, V, Fe, Co, Ni and Cu bombarded by protons with energies ranging from 40 to 180 keV. This revised version was published online in July 2006 with corrections to the Cover Date.     

Polariton gap solitary waves in semiconductor microcavities

We study nonlinear dynamics of optical pulse propagation in the spectral region inside the polariton gap. It is shown that the Kerr nonlinearity can lead to formation of solitary waves in this region of frequencies.     

Dynamics and spectra of excited states of water-micellar suspensions of single-walled carbon nanotubes

The dynamics of the photoinduced differential absorption and excited-state bleaching spectra of single-walled carbon nanotubes suspended in a micellar solution were studied in the spectral range from 40 to 1000 nm within a time interval from 70 fs to 150 ps under excitation by 50-fs pulses with photon energies 2 and 4 eV. The bleaching and absorption bands were observed in the spectra; the positions of the bleaching peaks were independent of the photon energy of the exciting femtosecond pulse in the range 2–4 eV. It was established that, for delay times shorter than 1 ps, the shape of the differential spectrum of excited nanotubes coincided with the shape of the second derivative of the absorption spectrum of unexcited nanotubes in the frequency range of exciting pulse above 18000 cm^?1 (the range of absorption bands of metallic nanotubes). In the frequency range below 16000 cm^?1 (the range of absorption peaks of semiconducting nanotubes), the bleaching peaks in the differential spectrum of excited nanotubes undergo a high-frequency shift of 200–300 cm^?1 with respect to the second-derivative spectrum of unexcited nanotubes. The excited-state relaxation rate constants were measured. They are well approximated by the exponential dependences and depend on the probe-pulse wavelength. An assumption was made about the nature of the observed spectra of excited nanotubes and about the excitation relaxation.     

Measurement of apex angle of the prism using total internal reflection

Total internal reflection technique is examined critically for the measurement of apex angle of the prism. Recognition of the critical boundary completely specifies the apex angle ‘A’ of the prism by keeping constant the ratio of refractive index of sample fluid (n₁=1.4) to that of glass (n₂=1.7). Recording of observations in the laboratory is dependent upon whether the apex angle ‘A’ of prism is greater than or less than or equal to critical angle ‘r_c’. The minimum value of error function ‘χ’ in the proximity of Abbe angle explain the choice of Abbe type instruments and shown invariant by relating positive ‘₊’ and the negative angle of emergence ‘₋’. Using ray-tracing technique, an expression for the length of the critical boundary ‘l’ is derived and is shown as a measure of the apex angle ‘A’ of the prism.

The choice of the realistic grazing condition leads us to two turning points for which error function ‘χ’ is minimal and yields appropriate option of the measurement of apex angle ‘A’ of the prism. It is further shown that the small error ‘ζ’ crept in the apex angle ‘A’ of the prism can lead to a significant error in the design of Pulfrich type instruments.

Experimental measurements are in-line with the predictions made.