On two-parametric family of quartic Thue equations
We show that for all integers and there are no non-trivial solutions of Thue equationsatisfying the additional condition .
On two-point configurations in a random set.
On two-primary algebraic K-theory of quadratic number rings with focus on K₂
On type numbers of split orders of definite quaternion algebras.
On Uniform Distribution of Double Sequences.
On uniform distribution of sequences
On uniform lower bound of the Galois images associated to elliptic curves
Let be a prime and let be a number field. Let be the Galois representation given by the Galois action on the -adic Tate module of an elliptic curve over . Serre showed that the image of is open if has no complex multiplication. For an elliptic curve over whose -invariant does not appear in an exceptional finite set (which is non-explicit however), we give an explicit uniform lower bound of the size of the image of .
On unit equations and decompsable form equations.
On unit equations with rational coefficients
On unit fractions with denominators in short intervals
On unit solutions of the equation xyz = x+y+z in the ring of integers of a quadratic field
On unit solutions of the equation xyz=x+y+z in a number field with unit group of rank 1
On unitary representations of Jacobi groups.
On units and fundamental units.
On universal binary Hermitian forms.
On universal forms in finite fields
On unlikely intersections of complex varieties with tori
On Unramified Galois Extensions Over Maximum Abelian Extensions of Algebraic Number Fields.
On upper triangular nonnegative matrices
We first investigate factorizations of elements of the semigroup of upper triangular matrices with nonnegative entries and nonzero determinant, provide a formula for , and, given , also provide formulas for , and . As a consequence, open problem 2 and problem 4 presented in N. Baeth et al. (2011), are partly answered. Secondly, we study the semigroup of upper triangular matrices with only positive integral entries, compute some invariants of such semigroup, and also partly answer open Problem...
On useful schema in survival analysis after heart attack
Recent model of lifetime after a heart attack involves some integer coefficients. Our goal is to get these coefficients in simple way and transparent form. To this aim we construct a schema according to a rule which combines the ideas used in the Pascal triangle and the generalized Fibonacci and Lucas numbers