In this paper, we aresupposed to introduce the definitions of n-fold commutative, andimplicative hyper K-ideals. These definitions are thegeneralizations of the definitions of commutative, andimplicative hyper K-ideals, respectively, which have been definedin [12]. Then we obtain some related results. In particular wedetermine the relationships between n-fold implicative hyperK-ideal and n-fol...

Maternal hypothyroidism during pregnancy impairs brain function in human and rat offspring, but little is known regarding the influence of maternal hyperthyroidism on neurodevelopment. We have previously shown that the expression of neuronal and glial differentiation markers in fetal brain is compromised in hypothyroid rat dam pregnancies and have now therefore extended this investigation to hy...

we present some connections between the max-min general fuzzy automaton theory and the hyper structure theory. first, we introduce a hyper bck-algebra induced by a max-min general fuzzy automaton. then, we study the properties of this hyper bck-algebra. particularly, some theorems and results for hyper bck-algebra are proved. for example, it is shown that this structure consists of different ty...

Background. Transcranial sonography (TCS) has emerged as a potential diagnostic tool for Parkinson's disease. Recent research has suggested that abnormal echogenicity of substantia nigra, raphe nuclei and third ventricle is associated with increased risk of depression among these patients. We sought to reproduce these findings in an ongoing larger study of patients with parkinsonian syndromes. ...

An improved M.I.T. bag model with hyper central interaction is used to calculate the charge radius for proton containing u and d quarks. We present a theoretical approach to the internal structure of three-body hyper central interacting quarks in a proton, in which we take proton as a bag. We discuss a few of results obtained using a six-dimension potential, which is attractive for small separa...

Alopecia areata (AA) is a common dermatological disease characterized by patchy areas of nonscarring alopecia. Sometimes, differentiating patchy AA from trichotillomania (TTM) can be difficult. We report a case of AA mimicking TTM.

It is easy to see that for any pair of matrices A ∈ Rn×k and B ∈ Rk×n, Tr(AB) = Tr(BA). The matrix dot product is defined analogous to the vector dot product. For matrices A,B ∈ Rk×n, A •B := k ∑ i=1 n ∑ j=1 A(i, j)B(i, j). It is easy to see that A •B = Tr(AB). Lemma 3.1. For any symmetric matrix A with eigenvalues λ1, . . . , λn, Tr(A) = n ∑ i=1 λi. Proof. Let x1, . . . , xn be orthonormal eig...

Introduction: The transtheoretical model of behaviour change (TTM) is often used to understand and predict changes in health related behaviour, for example exercise behaviour and eating behaviour. Fitness professionals like personal trainers typically service and support clients in improving multiple types of health-related behaviour. Research on the population of European fitness professionals...