Hypergroups are generalizations of groups. If this binary operation is taken to be multivalued, then we arrive at a hypergroup. The motivation for generalization of the notion of group resulted naturally from various problems in non-commutative algebra, another motivation for such an investigation came from geometry. In various branches of mathematics we encounter important examples of topologi...

BACKGROUND AND PURPOSE Quantitative CBF usage as a biomarker for cognitive impairment and disease progression in MS is potentially a powerful tool for longitudinal patient monitoring. Dynamic susceptibility contrast perfusion with bookend T1-calibration (bookend technique) and pseudocontinuous arterial spin-labeling have recently been used for CBF quantification in relapsing-remitting MS. The n...

In this paper, we extend the notion of semi-hypergroups (resp. hypergroups) to neutro-semihypergroups neutro-hypergroups). We investigate property anti-semihypergroups anti-hypergroups). also give a new alternative neutro-hyperoperations anti-hyperoperations), neutro-hyperoperation-sophications anti-hypersophications). Moreover, show that these concepts are different from classical by several e...

A new signal-to-noise ratio (SNR) efficient method is introduced for the mapping of vascular territories based on pseudocontinuous arterial spin labeling (ASL). A pseudocontinuous tagging pulse train is modified using additional transverse gradient pulses and phase cycling to place some arteries in a tag condition, while others passing through the same tagging plane are in a control condition. ...

A new technique for the imaging of flow territories of individual extra- and intracranial arteries is presented. The method is based on balanced pseudocontinuous arterial spin labeling but employs additional time-varying gradients in between the radiofrequency pulses of the long labeling train. The direction of the additional gradient vector is perpendicular to the selected artery and its azimu...

BACKGROUND AND PURPOSE Three-dimensional pseudocontinuous arterial spin labeling with multiple postlabeling delays has been used to assess cerebral blood flow (CBF). We used this modality to estimate antegrade and collateral flow in patients with unilateral middle cerebral artery stenosis. METHODS Consecutive patients with unilateral middle cerebral artery 50% to 99% stenosis at 2 centers und...

Krasner hyperrings are a generalization of rings. Indeed, in hyperring the addition is hyperoperation, while multiplication an ordinary operation. On other hand, rough set theory near theory. Now, this paper we interested combining these concepts. We study and investigate notion on nearness approximation space. Also, define subhyperring, hyperideal, homomorphism prove some results present sever...

A neutrosophic hyperstructure is an algebraic structure generated by a given hyperstructure H and an indeterminacy factor I under the hyperoperation(s) of H. The objective of this paper is to study canonical hypergroups and hyperrings in which addition and multiplication are hyperoperations in a neutrosophic environment. Some basic properties of neutrosophic canonical hypergroups and neutrosoph...

PURPOSE To compare quantitative cerebral blood flow (CBF) values in patients with Alzheimer disease (AD), patients with mild cognitive impairment (MCI), and subjects with subjective complaints by using a whole-brain three-dimensional (3D) pseudocontinuous arterial spin-labeling (ASL) technique at 3.0 T. MATERIALS AND METHODS The local institutional review board approved the study. All subject...

BACKGROUND AND PURPOSE Previous studies showed conflicting results concerning the value of CBF maps obtained from arterial spin-labeling MR imaging in grading gliomas. This study was performed to investigate the effectiveness of CBF maps derived from 3D pseudocontinuous arterial spin-labeling in preoperatively assessing the grade, cellular proliferation, and prognosis of gliomas. MATERIALS AN...