In recent work, Schweber [7] introduces a framework for reverse mathematics in a third order setting and investigates several natural principles of transfinite recursion. The main result of that paper is a proof, using the method of forcing, that in the context of two-person perfect information games with moves in R, open determinacy (Σ1 -DET) is not implied by clopen determinacy (∆ R 1 -DET). ...

Background: Atherosclerosis is a chronic inflammatory disease affecting large and medium arteries. CD4+ T cells are known to play a role in the progression of the disease. CD4+CD25+Foxp3+ natural Treg (nTreg) cells seem to have a protective role in the disease and their reduction in acute coronary syndrome is recently shown. Objective: To investigate the frequency of nTreg subsets in the pe...

A Π1 class P is called thin if, given a subclass P ′ of P there is a clopen C with P ′ = P ∩C. Cholak, Coles, Downey and Herrmann [7] proved that a Π1 class P is thin if and only if its lattice of subclasses forms a Boolean algebra. Those authors also proved that if this boolean algebra is the free Boolean algebra, then all such think classes are automorphic in the lattice of Π1 classes under i...

Recently, we accelerated ordered subsets (OS) methods for low-dose X-ray CT image reconstruction using momentum techniques, particularly focusing on Nesterov’s momentum method. This paper develops an “optimized” momentum method that is faster than Nesterov’s method. Drori and Teboulle’s original version requires substantial memory space and computation time per iteration. Therefore, we design a...

In response to cytokine signalling and other factors, CD4-positive T lymphocytes differentiate into distinct populations that are characterized by the production of certain cytokines and are controlled by different master transcription factors. The spectrum of such populations, which was initially limited to Th1 and Th2 subsets, is currently broadened to include Th17 and Treg subsets, as well a...

background: although the pathogenesis of diabetes type 1 (t1d) is not fully elucidated. different clusters of lymphocytes such as cd4+ and cd8+ t cells are involved in it. moreover, the mechanism of how stem-cell therapy results in significant therapeutic outcomes in diabetes remains obscure. in the current study, we aimed to analyze lymphocyte subsets in patients with t1d before and after trea...

The purpose of this paper is to study matrix hemiring $S_{2}$ via fuzzy subsets and fuzzy $h$-ideals.

‎A topological space is called submaximal if each of its dense subsets is open and is called nodec if each of its nowhere dense ea subsets is closed‎. ‎Here‎, ‎we study a variety of spaces some of which have already been studied in $C(X)$‎. ‎Among them are‎, ‎most importantly‎, ‎quasi $P$-spaces and pointwise quasi $P$-spaces‎. ‎We obtain some new useful topological characterizations of quasi $...

The main purpose of this paper is to introduce several concepts of the metric-like spaces. For instance, we define concepts such as equal-like points, cluster points and completely separate points. Furthermore, this paper is an attempt to present compatibility definitions for the distance between a point and a subset of a metric-like space and also for the distance between two subsets of a metr...

Measurement results contain different kinds of uncertainty. Besides systematic errors andrandom errors individual measurement results are also subject to another type of uncertainty,so-called emph{fuzziness}. It turns out that special fuzzy subsets of the set of real numbers $RR$are useful to model fuzziness of measurement results. These fuzzy subsets $x^*$ are called emph{fuzzy numbers}. The m...