Strong consistency of least squares estimates in multiple regression II

The strong consistency of least squares estimates in multiple regression models is established under minimal assumptions on the design and weak dependence and moment restrictions on the errors.     

Central limit theorem and weak law of large numbers with rates for martingales in Banach spaces

This paper is concerned with large-$\text{O}$ error estimates concerning convergence in distribution as well as norm convergence for Banach space-valued martingale difference sequences. Indeed, two general limit theorems equipped with rates of convergence for such difference sequences are established. Applications of these lead to the central limit theorem and the weak law of large numbers with rates for Banach space-valued martingales.     

Asymptotic stability in perturbed delay difference systems

Consider the delay difference system

     

On the periodic nature of the solutions of the reciprocal difference equation with maximum

We prove that every positive solution of the third order difference equation

     

Absorption Spectra of Gasolines in the Region 1090–1220 nm

The difference absorption spectra of different grades of gasoline (A-76, AI-92, and AI-95) with octane numbers lying within 76–85 have been investigated experimentally in comparison with hydrocarbons: isooctane, benzene, and n-heptane. The spectra obtained contain absorption bands of the CH₃, CH₂, and CH groups and supposedly of the olefin double bond. The possibility of determining the octane number of an unknown grade of gasoline by using the absorption of a measured difference spectrum at one selected wavelength is shown.     

Calculation of Families of Stationary Filtration Convection Regimes in a Narrow Container

A plane Darcy filtration convection problem for rectangular containers elongated in the vertical direction is considered. By the spectraldifference method, which preserved cosymmetry of the initial problem, evolution of families of stationary regimes from the onset of instability on the primary family till the collision of the families is studied.     

Oscillations of nonlinear partial difference systems

This paper studies the following two-dimensional nonlinear partial difference systems

     

Existence for nonoscillatory solutions of higher-order nonlinear neutral difference equations

In this paper, we consider the following forced higher-order nonlinear neutral difference equation

     

Looking for Difference Sets in Groups with Dihedral Images

We prove four theorems about groups with a dihedral (or cyclic) image containing a difference set. For the first two, suppose G, a group of order 2p with p an odd prime, contains a nontrivial (v, k, ) difference set D with order n = k – prime to p and self-conjugate modulo p. If G has an image of order p, then 0 2a + 2 for a unique choice of = ±1, and for a = (k – )/2p. If G has an image of order 2p, then and ( – 1)/( – 1). There are further constraints on n, a and . We give examples in which these theorems imply no difference set can exist in a group of a specified order, including filling in some entries in Smith's extension to nonabelian groups of Lander's tables. A similar theorem covers the case when p|n. Finally, we show that if G contains a nontrivial (v, k, ) difference set D and has a dihedral image D _2m with either (n, m) = 1 or m = p ^t for p an odd prime dividing n, then one of the C ₂ intersection numbers of D is divisible by m. Again, this gives some non-existence results.