Let R,T be commutative rings with identity such that R⊆T. We recall that R⊆T is called a λ-extension of rings if the set of all subrings of T containing R (the “intermediate rings”) is linearly ordered under inclusion. In ...

We give an overview of some results on the transcendence nature of the sums of some in nite series. We also give some new results on the transcendence nature of some series involving mildly non-periodic functions and ...

Let F(X,Y) be an irreducible binary cubic form with integer coefficients and positive discriminant D. Let k be a positive integer satisfying k < ( ( 3 D ) 1 / 4 ) / 2 π . We give improved upper bounds for the number of ...

Let F(X, Y ) = s i=0 ai Xri Yr−ri ∈ Z[X, Y ] be a form of degree r = rs ≥ 3, irreducible over Q and having at most s + 1 non-zero coefficients. Mueller and Schmidt showed that the number of solutions of the Thue ...

Following a method originally due to Siegel, we establish upper bounds for the number of primitive integer solutions to inequalities of the shape 0<|F(x,y)|≤h, where F(x,y)=(αx+βy)r−(γx+δy)r∈Z[x,y], α, β, γ and δ are ...

Nora and Wanda are two players who choose coefficients of a degree-d polynomial from some fixed unital commutative ring R. Wanda is declared the winner if the polynomial has a root in the ring of fractions of R and Nora ...

Let r,h∈N with r≥7 and let F(x,y)∈Z[x,y] be a binary form such that F(x,y)=(αx+βy)r−(γx+δy)r, where α, β, γ and δ are algebraic constants with αδ−βγ≠0. We establish upper bounds for the number of primitive solutions to ...

A novel numerical scheme based on the finite-difference framework is developed, which allows us to model moderately rarefied gas flows in irregular geometries. The major hurdle in constructing numerical methods for rarefied ...

Wheat (Triticum aestivum) is a major staple food crop, plays a crucial role in food security, and is grown on an area of 221.6 million hectares (Mha) in multi-environments throughout the globe. Annual wheat production was ...

In the classical irreversible thermodynamics (CIT) framework, the Navier–Stokes–Fourier constitutive equations are obtained so as to satisfy the entropy inequality, by and large assuming that the entropy flux is equal to ...