Two-scale convergence is an important tool in homogenization theory. The contribution deals with its alternative definition based on two-scale mapping and transform. It removes the problems with choice of the space of admissible test functions and simplifies the proofs.

Let $(K,v)$ be a valued field and let $(K^h,v^h)$ the henselization determined by choice of an extension $v$ to algebraic closure $K$. Consider embedding $v(K^*)\hookrightarrow\Lambda$ value group into divisible ordered abelian group. $T(K,\Lambda)$, $T(K^h,\Lambda)$ trees formed all $\Lambda$-valued extensions $v$, $v^h$ polynomial rings $K[x]$, $K^h[x]$, respectively. We show that natural res...

The Effectiveness of the first-order resolution calculus is impaired when lifting it to higher-order logic. The main reason for that is the semi-decidability and infinitary nature of higher-order unification problems, which requires the integration of unification within the calculus and results in a non-effective search for refutations. We present a modification of the constrained resolution ca...

We generated a lambda gt11 Neurospora crassa cDNA library and screened the library for the cytoplasmic leucyl-tRNA synthetase (cyto LeuRS) clones using cyto LeuRS specific antibody. Two clones, lambda NCLRSC1 and lambda NCLRSC2, were obtained which have inserts of approximately 2 kbp and approximately 1.3 kbp, and which overlap by about 0.6 kbp. The following lines of evidence indicate that lam...

The gene TOP2 encoding yeast topoisomerase II has been cloned by immunological screening of a yeast genomic library constructed in the phage lambda expression vector, lambda gt11. The ends of the message encoded by the cloned DNA fragment were delimited by the Berk and Sharp procedure (S1 nuclease mapping) for the 5' end and mapping of the polyA tail portion of a cDNA fragment for the 3' end. T...

The existence of admissible vectors for a locally compact group is closely related to the group's profile. In the compact groups, according to Peter-weyl theorem, every irreducible representation has admissible vector. In this paper, the conditions under which the inverse of this case is being investigated has been investigated. Conditions such as views that are admissible and stable will get c...

We compare the Pontryagin duals of fine Selmer groups two congruent $p$-adic Galois representations over admissible pro-$p$, Lie extensions $K_\infty$ number fields $K$. prove that in several natural settings $\pi$-primary submodules are pseudo-isomorphic Iwasawa algebra; if coranks not equal, then we can still inequalities between $\mu$-invariants. In special case a $\mathbb{Z}_p$-extension $K...

In this note, we define the concepts of admissible relation and admissible partition for an arbitrary BL-general fuzzy automaton.In particular, a connection between the admissible partition and the quotient BL-general fuzzy automaton is presented.It is shown that if we use the maximal admissible partition, then we obtain a quotient BL-general fuzzy automaton and this quotient is minimal. Finall...

For a given weighted mean $\mathscr{M}$ defined on subinterval of $\mathbb{R}_+$ and sequence weights $\lambda=(\lambda_n)_{n=1}^\infty$ we define Hardy constant $\mathscr H(\lambda)$ as the smallest extended real number such that $$ \sum_{n=1}^\infty \lambda_n \mathscr{M}\big((x_1,\dots,x_n),(\lambda_1,\dots,\lambda_n)\big) \le \mathscr H(\lambda) \cdot x_n \text{ for all }x \in \ell^1(\lambda...