In reductive proof search, proofs are naturally generalized by solutions, comprising all possibly infinite structures generated locally correct, bottom-up application of inference rules. We propose an extension the Curry-Howard paradigm representation, from to solutions: represent solutions terms a dedicated lambda-calculus. This new, comprehensive approach search is exemplified with sequent ca...

In the study of fixed points of an operator it is useful to consider a more general concept, namely coupled fixed point. Edit In this paper, by using notion partial metric, we introduce a metric space $S$-Hausdorff on the set of all close and bounded subset of $X$. Then the fixed point results of multivalued continuous and surjective mappings are presented. Furthermore, we give a positive resul...

The energy levels of light hypernuclei are experimentally accessible observables that contain valuable information about the interaction between hyperons and nucleons. In this work we study strangeness $S = -1$ systems $^{3,4}_\Lambda$H $^{4,5}_\Lambda$He using ab initio no-core shell model (NCSM) with realistic interactions obtained from chiral effective field theory ($\chi$EFT). particular, q...

To probe Pol zeta functions in vivo via its error signature, here we report the properties of Saccharomyces cerevisiae Pol zeta in which phenyalanine was substituted for the conserved Leu-979 in the catalytic (Rev3) subunit. We show that purified L979F Pol zeta is 30% as active as wild-type Pol zeta when replicating undamaged DNA. L979F Pol zeta shares with wild-type Pol zeta the ability to per...

Notice that the Riemann Zeta function is simply ζ(s, 1) = ζ(s). In the next section we provide a new family of distributions, the Zeta family, which is based on the Hurwitz Zeta function, and provide its characteristic function. We also show that the well known generalized gamma family of distributions is a special case of the proposed family. (Notice that the exponential power family of distri...

The concept of partial metric which is a generalized metric space was introduced by Matthews 1 in 1994, inwhich the distance between two identical elements needs not be zero. The existence of fixed point for contraction-type mappings on such spaces was considered by many authors 1–12 . A modified version of a Banach contraction mapping principle, more suitable to solve certain problems arising ...

Let $Z(t)=\chi ^{-1/2}(1/2+it)\zeta (1/2+it)=e^{i\theta (t)}\zeta (1/2+it)$ be Hardy’s function and $g(n)$ the $n$th Gram point defined by $\theta (g(n))=\pi n$. Titchmarsh proved that $$ \sum _{n \leq N} Z(g(2n)) =2N+O(N^{3/4}\log ^{3/4}N) \

In the piece of this note, we mention various Suzuki-type fuzzy contractive inequalities in 1-Z-complete metric-like spaces for uniqueness and existence a fixed point prove few theorems, which are appropriate generalizations some latest famed results literature. Mainly, generalize Θ-contraction terms also ϓ-contractive mapping view Suzuki-type. For new group functions, acceptable conditions for...