In this paper, we first consider (po-)torsion free and principally weakly (po-)flat $S$-posets, specifically  we discuss when (po-)torsion freeness implies principal weak (po-)flatness. Furthermore, we give a counterexample to show that Theorem 3.22 of Shi is incorrect. Thereby we present a correct version of this theorem. Finally, we characterize pomonoids over which all cyclic $S$-posets are ...

in the present paper, measure differential equations involving the distributional henstock-kurzweil integral are investigated. theorems on the existence and structure of the set of solutions are established by using schauder$^prime s$ fixed point theorem and vidossich theorem. two examples of the main results paper are presented. the new results are generalizations of some previous results in t...


 a variant of fixed point theorem is proved in the setting of s-metric spaces

comnode classification within membrane residue curves (m-rcms) currently hinges on lyapunov’s theorem and therefore the computation of mathematically complex eigenvalues. this paper presents an alternative criterion for the classification of nodes within m-rcms based on the total membrane flux at node compositions. this paper demonstrates that for a system exhibiting simple permeation behaviour...

in this paper we study the notions of cogenerator and subdirectlyirreducible in the category of s-poset. first we give somenecessary and sufficient conditions for a cogenerator $s$-posets.then we see that under some conditions, regular injectivityimplies generator and cogenerator. recalling birkhoff'srepresentation theorem for algebra, we study subdirectlyirreducible s-posets and give this theo...

let x ,..., xn 1 be a random sample from a distribution with sample mean x and samplevariance s 2. in this paper we consider certain very general properties of the so-called “z-scores”x x s i n i ( − )/ : = 1,...., . a representation theorem is then given for z-scores obtained from an underlyingnormal population, together with a theorem for their limiting distribution as the sample size tends t...

 A variant of fixed point theorem is proved in the setting of S-metric spaces

In this article, we have proved the Darboux's theorem. This theorem is important to prove the Riemann integrability. We can replace an upper bound and a lower bound of a function which is the definition of Riemann integration with convergence of sequence by Darboux's theorem. We adopt the following rules: x, y are real numbers, i, j, k are natural numbers, and p, q are finite sequences of eleme...

In modern form, Hilbert’s Theorem 90 tells us that Rǫ∗(Gm) = 0, where ǫ : Xét → Xzar is the canonical map between the étale site and the Zariski site of a scheme X. I construct examples showing that the corresponding statement for algebraic spaces does not hold.

The articles [4], [3], [5], [2], and [1] provide the notation and terminology for this paper. For simplicity we follow the rules: a, x, y will be arbitrary, B, D, N , X, Y will denote sets, R, S, T will denote relations, F will denote a function, and W will denote a relation. We now state several propositions: (1) x ∈ fieldR if and only if there exists y such that 〈x, y〉 ∈ R or 〈y, x〉 ∈ R. (2) ...