Ultrasound diagnosis of psoriatic arthritis in children

Chebysheva, S.N.; Geppe, N. A.; Meleshkina, А.V.; Жолобова, Елена; Shevchenko, T.Ya.; Leontyeva, A.A.; Aleksanyan, K.

doi:10.26442/2413-8460_2016.1.84-86

Cited by 1 publication

(4 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As it became clear to us recently, the polynomials (4.7) coincide, up to some factor depending on z = cos(θ/N) with Chebyshev polynomials of 2-d kind, discovered in the middle of 19-th century [17,18,19]. The connection of characteristic polynomials J 2 N [cos(θ/N)] with Chebyshev polynomials of 2-d kind (CKZ-polynomials) will be described in next section.…”

Section: Quadratic Form In Angular Deviations Characteristic Polynommentioning

confidence: 99%

“…Table. Characteristic polynomials J 2 N (x) presented in [5,6] and Chebyshev polynomials of 2-d kind U N −1 given in literature [17,18,19]. x = cos(θ/N).…”

Section: Connection With Chebyshev Polynomials Of 2-d Kindmentioning

confidence: 99%

“…The recurrent relations for the characteristic polynomials in polar angles deviations have been obtained in [6] and are reproduced in present paper. The connection of these polynomials with Chebyshev polynomials of 2-d kind, known in mathematics since middle of 19-th century [17,18,19] and used in approximation theory, has been established. It is an example of interest when physics arguments have led to some results in mathematics.…”

Section: Introductionmentioning

confidence: 99%

“…According to[19], the Chebyshev polynomials of 2-d kind have been considered first by his pupils A.Korkin and E.Zolotarev and were named in honor of their teacher. Therefore, it is correct to name these polynomials Chebyshev-Korkin-Zolotarev, or CKZ-polynomials.…”

mentioning

confidence: 99%

See 3 more Smart Citations

Mathematical aspects of the nuclear glory phenomenon: from backward focusing to Chebyshev polynomials

Kopeliovich

2017

J. Phys.: Conf. Ser.

View full text Add to dashboard Cite

The angular dependence of the cumulative particles production off nuclei near the kinematical boundary for multistep process is defined by characteristic polynomials in angular variables, describing spatial momenta of the particles in intermediate and final states. Physical argumentation, exploring the small phase space method, leads to the appearance of equations for these polynomials in cos(θ/N ), where θ is the polar angle of the momentum of final (cumulative) particle, the integer N being the multiplicity of the process (the number of interactions). It is shown explicitly how these equations aappear, and the recurrent relations between polynomials with different N are obtained. Factorization properties of characteristic polynomials found previously, are extended, and their connection with known in mathematics Chebyshev polynomials of 2-d kind is established. As a result, differential cross section of the cumulative particle production has characteristic behaviour dσ ∼ 1/ √ π − θ near the strictly backward direction (θ = π, the backward focusing effect). Such behaviour takes place for any multiplicity of the interaction, beginning with n = 3, elastic or inelastic (with resonance excitations in intermediate states), and can be called the nuclear glory phenomenon, or 'Buddha's light' of cumulative particles. *

show abstract

Section: Quadratic Form In Angular Deviations Characteristic Polynommentioning

confidence: 99%

“…Table. Characteristic polynomials J 2 N (x) presented in [5,6] and Chebyshev polynomials of 2-d kind U N −1 given in literature [17,18,19]. x = cos(θ/N).…”

Section: Connection With Chebyshev Polynomials Of 2-d Kindmentioning

confidence: 99%