background :many studies have reported the increase in strength of the untrained contralateral limb after unilateral training. the aim of this study was to compare the cross education effect in the young and elderly persons.   methods : in this quasi-experimental and pre-post study, 12 young people aged 28.25 ±3.11 years and 12 elderly persons (aged 73.08 ± 5.3 years) participated. the subjects...

in this paper we classify fuzzy subgroups of the dihedral group $d_{pqrs}$  for distinct primes  $p$, $q$, $r$ and $s$. this follows similar work we have done on distinct fuzzy subgroups of some dihedral groups.we present formulae for the number of (i) distinct maximal chains of subgroups, (ii) distinct fuzzy subgroups and (iii) non-isomorphic classes of fuzzy subgroups under our chosen equival...

we derive the formulas of the maximal andminimal ranks of four real matrices $x_{1},x_{2},x_{3}$ and $x_{4}$in common solution $x=x_{1}+x_{2}i+x_{3}j+x_{4}k$ to quaternionmatrix equations $a_{1}x=c_{1},xb_{2}=c_{2},a_{3}xb_{3}=c_{3}$. asapplications, we establish necessary and sufficient conditions forthe existence of the common real and complex solutions to the matrixequations. we give the exp...

In recent times there has been some interest in studying partial latin squares which have no completions or precisely one completion, and which are critical with respect to this property. Such squares are called, respectively, premature partial latin squares and critical sets. There has also been interest in related maximal partial latin squares. This paper will explore the connection between t...

Let H be a closed half-space of n-dimensional Euclidean space. Suppose S is a unit sphere in H that touches the supporting hyperplane of H . The one-sided kissing number B(n) is the maximal number of unit nonoverlapping spheres in H that can touch S. Clearly, B(2) = 4. It was proved that B(3) = 9. Recently, K. Bezdek proved that B(4) = 18 or 19, and conjectured that B(4) = 18. We present a proo...

Let S be a finite set of words such that Fact(S) 6= Σ. We deal with the problem of finding bounds on the minimal length of words in Σ \ Fact(S) in terms of the maximal length of words in S.

Let (X, d, μ) be a metric measure space. For ∅ 6= R ⊆ (0,∞) consider the Hardy-Littlewood maximal operator MRf(x) def = sup r∈R 1 μ(B(x, r)) ∫

We propose an approach via Frobenius manifolds to the study (began in [BCK2]) of the relation between rational Gromov-Witten invariants of nonabelian quotients X//G and those of the corresponding “abelianized” quotients X//T, for T a maximal torus in G. The ensuing conjecture expresses the Gromov-Witten potential of X//G in terms of the potential of X//T. We prove this conjecture when the nonab...

Let G be a connected complex semi-simple group, B ⊂ G a Borel subgroup, and T ⊂ B a maximal torus. We construct a class of smooth T stable subvarieties inside the flag variety G/B, each of which is an embedding of a product of projective lines.

We prove that in the presence of a maximal giant graviton state in N = 4 SYM, the states dual to open strings attached to the giant graviton give rise to an PSU(2, 2|4) open spin chain model with integrable boundary conditions in the SO(6) sector of the spin chain to one loop order.