Polynomial regression models with errors in variables are considered. A goodness-of-fit test is constructed, which is based on an adjusted least-squares estimator and modifies the test introduced by Zhu et al. for a linear ...

We consider the difference equation with continuous argument x(t+2)−2λx(t+1)+λ²x(t)=f(t,x(t)), where λ > 0, t ∈ [0, ∞), and f: [0, ∞) × R → R. Conditions for the existence and uniqueness of continuous asymptotically ...

Let f be an entire function of finite type with respect to finite order ρ in Cⁿ and let E be a subset of an open cone in a certain n-dimensional subspace R²ⁿ ( = Cⁿ) (the smaller ρ , the sparser E ). We assume that this ...

For any nonlinear regression function, it is shown that the orthogonal regression procedure delivers an inconsistent estimator. A new technical approach to the proof of inconsistency based on the implicit-function theorem ...

We show that a soluble group satisfying the minimal condition for its normal subgroups is co-hopfian and that a torsion-free finitely generated soluble group of finite rank is hopfian. The latter property is a consequence ...

Long-range order is proved to exist for lattice linear oscillator systems with ferromagnetic potential energy containing a term with strong nearest-neighbor (n-n) quadratic pair potential. A contour bound and a generalized ...

Yu. Mel’nik showed that the Leont’ev coefficients Κ f (λ) in the Dirichlet series 2n/(n+1)<p>2 of a function f ∈E p (D), 1 < p < ∞, are the Fourier coefficients of some function F ∈L p , ([0, 2π]) and that the first ...

It is well known that if Г is a geodesic line of the tangent (sphere) bundle with Sasaki metric of a locally symmetric Riemannian manifold, then all geodesic curvatures of the projected curve λ=π₁₄₆₃₋₀₁ Г are constant. In ...

The stochastic dynamics for point particles that corresponds to the Boltzmann equation with arbitrary differential scattering cross section is constructed. We derive the stochastic Boltzmann hierarchy the solutions of which ...

В області, що є декартовим добутком відрізка і прямої, вивчається двоточкова гранична задача для диференціальних рівнянь з частинними похідними. Встановлено умови асимптотичної коректності задачі у класі обмежених ...