The original aim of this paper is to construct a graph associated to a vector space. By inspiration of the classical definition for the Cayley graph related to a group we define Cayley graph of a vector space. The vector space Cayley graph ${rm Cay(mathcal{V},S)}$ is a graph with the vertex set the whole vectors of the vector space $mathcal{V}$ and two vectors $v_1,v_2$ join by an edge whenever...

toxoplasmosis is a common and widespread infection in humans and many other species of warm–blooded animals. toxoplasma gondii-derived heat shock protein 70 (hsp70) may play an important role in the virulence of toxoplasma gondii (t. gondii). in the present study, t. gondii hsp70 was amplified by polymerase chain reaction (pcr) from the dna of the t. gondiitachyzoite rh strain through the use o...

Let V be an n-dimensional vector space over the finite field Fq, and [Vk] denote family of all k-dimensional subspaces V. The families F1⊆[Vk1],F2⊆[Vk2],…,Fr⊆[Vkr] are said to r-cross t-intersecting if dim⁡(F1∩F2∩⋯∩Fr)≥t for Fi∈Fi,1≤i≤r. F1, F2,…,Fr non-trivial dim⁡(∩1≤i≤r∩F∈FiF)<t. In this paper, we first determine structure with maximum product their sizes. As a consequence, partially prove o...

Consider y" (t) + A (t)y (t) + 0, y is a real n-dimensinal vector and A(t) is a real nxn matrix, continuous on some interval. Some positivity properties of solutions and conjugate points of y"(t) + A(t)y (t) = 0 appeared in literature. We prove similar results for focal points

has the unit circle as its graph, but these equations do not represent the same curve— because the circle is traced out in different ways on the graphs. Be sure you see the distinction between the vector-valued function and the real-valued functions and All are functions of the real variable but is a vector, whereas and are real numbers for each specific value of . Vector-valued functions serve...