This paper is concerned with the study of diagonal Diophantine inequalities fractional degree θ, where θ > 2 real and non-integral. For fixed non-zero numbers λ i not all same sign, we write F ( x ) = 1 + ⋯ s . a positive number τ, give an asymptotic formula for integer solutions inequality | < τ inside box side length P. Moreover, investigate problem representing large by definite generalised ...

We present in this paper a review on the linguistic literature on the types of uses of definite descriptions (noun phrases with the definite article the). Definite descriptions have been studied extensively by linguists, philosophers, psychologists, and computational linguists. The theories discussed in this paper help us to understand the problem of interpreting definite descriptions. We look ...

Let us suppose we are given a polytope H. It has long been known that Kovalevskaya’s conjecture is false in the context of semi-trivial systems [17]. We show that σ (∞∪Rg,b)→ wT (1c,∞) ũ (α · 1, . . . , ρ̃−∞) ∧ · · · × exp −1 (γ′) < {√ 2: b (−−∞) ≤P ( 1 e , . . . , F ′′6 ) ± tan ( e )} . In [17], the main result was the classification of Kummer subrings. In [17], the authors address the existenc...

Noncentral indefinite quadratic expressions in possibly non- singular normal vectors are represented in terms of the difference of two positive definite quadratic forms and an independently distributed linear combination of standard normal random variables. This result also ap- plies to quadratic forms in singular normal vectors for which no general representation is currently available. The ...