The Cauchy problem for one-dimensional flow of a compressible viscous heat-conducting micropolar fluid is considered. It is assumed that the fluid is thermodynamically perfect and polytropic. A corresponding initial-boundary value problem has a unique strong solution on ]0, 1[×]0, T [, for each T > 0. By using this result we construct a sequence of approximate solutions which converges to a sol...

The crease set of an event horizon or a Cauchy horizon is an important object which determines qualitative properties of the horizon. In particular, it determines the possible topologies of the spatial sections of the horizon. By Fermat’s principle in geometric optics, we relate the crease set and the Maxwell set of a smooth function in the context of singularity theory. We thereby give a class...

Continued fractions in R have a single definition and algorithms for approximating them are well known. There also exists a well known result which states that √ m, m ∈ Q, always has a periodic continued fraction representation. In Qp, the field of p-adics, however, there are competing and non-equivalent definitions of continued fractions and no single algorithm exists which always produces a p...

The purpose of this paper is to prove that every sequence of closed approximable measures defined on the Borelfield of a normal topological space with values in an abelian topological group is Cauchy convergent for all Borel sets if it is Cauchy convergent for all regular open sets. In particular every sequence of measures on the Borel-field of a perfectly normal topological space which is Cauc...

3. Since Lp and Lr are subspaces of CX , their intersection is a vector space. It is clear that ‖ · ‖ is a norm (this follows directly from the fact that ‖ · ‖p and ‖ · ‖r are norms). Let 〈fn〉n=1 be a Cauchy sequence in Lp ∩ Lr. Since ‖fm − fn‖p ≤ ‖fm − fn‖ and ‖fm − fn‖r ≤ ‖fm − fn‖ for all m,n ∈ N, it is clear that 〈fn〉n=1 is a Cauchy sequence in both Lp and Lr. Let gp ∈ Lp and gr ∈ Lr be the...

‎Let $X,Y$ be normed spaces with $L(X,Y)$ the space of continuous‎ ‎linear operators from $X$ into $Y$‎. ‎If ${T_{j}}$ is a sequence in $L(X,Y)$,‎ ‎the (bounded) multiplier space for the series $sum T_{j}$ is defined to be‎ [ ‎M^{infty}(sum T_{j})={{x_{j}}in l^{infty}(X):sum_{j=1}^{infty}%‎ ‎T_{j}x_{j}text{ }converges}‎ ‎]‎ ‎and the summing operator $S:M^{infty}(sum T_{j})rightarrow Y$ associat...

*Correspondence: [email protected]; [email protected] 1Department of Mathematics, Maltepe University, Marmara Eğİtİm Köyü, TR 34857, Maltepe, İstanbul, Turkey Full list of author information is available at the end of the article Abstract An ideal I is a family of subsets of positive integersN which is closed under taking finite unions and subsets of its elements. A sequence (xn) of real...

We extract verified algorithms for exact real number computation from constructive proofs. To this end we use a coinductive representation of reals as streams binary signed digits. The main objective paper is the formalisation proof that numbers are closed with respect to limits. All proofs theorem and first application implemented in Minlog system extracted terms further translated into Haskel...

It is proved that a Banach space contains a subspace isomorphic to l(1) if (and only if) it has a bounded sequence with no weak-Cauchy subsequence. The proof yields that a sequence of subsets of a given set has a subsequence that is either convergent or Boolean independent.