(g, x) → gx : G × X → X such that ex = x for every x in X and g(hx) = (gh)x for g and h in G and x in X (here e denotes the neutral element of G). It is easily seen that for each g in G the map x → gx is a homeomorphism of X whose inverse is the map x → g−1x . If x belongs to X and U is a subset of G, then U x = {gx : g ∈ U}. The action of G on X is transitive if Gx = X for every x in X . It is...

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T h i s p a p e r p r e s e n t s a n e w t e x t u r e a n a l y s i s m e t h o d i n c o r p o r a t i n g w i t h t h e p r o p e r t i e s o f b o t h t h e g ray l eve l c o o c c u r r e n c e m a t r i x ( G L C M ) a n d t e x t u r e s p e c t r u m (TS) m e t h o d s . T h e c o o c c u r r e n c e f ea tu res e x t r a c t e d f r o m t h e c r o s s d i a g o n a l t e x t u r e m ...

Let G = (V,E) be an undirected graph without loops and multiple edges [1], V (G) and E(G) be the sets of vertices and edges of G, respectively. The degree of a vertex x ∈ V (G) is denoted by dG(x), the maximum degree of a vertex of G-by ∆(G), and the chromatic index [2] of G-by χ(G). A graph is regular, if all its vertices have the same degree. If α is a proper edge colouring of the graph G [3]...

In the G protein-coupled receptor rhodopsin, the conserved NPxxY(x)(5,6)F motif connects the transmembrane helix VII and the cytoplasmic helix 8. The less geometrically constrained retinal analogue 9-demethyl-retinal prevents efficient transformation of rhodopsin to signaling metarhodopsin (Meta) II after retinal photoisomerization. Here, we demonstrate that Ala replacement mutations within the...

where p > , φp(x) = |x|p–x for x =  and φp() = , c ∈ Cn(R,R) and c(t + T) ≡ c(t), f is a continuous function defined in R and periodic in t with f (t, ·) = f (t + T , ·) and f (t, ) = , g(t,x) = g(x) + g(t,x), where g : R × (, +∞) → R is an L-Carathéodory function, g(t, ·) = g(t + T , ·), g ∈ C((,∞);R) has a singularity at x = , e : R→ R is a continuous periodic function with ...

For a vertex x in a connected graph G = (V (G), E(G)) of order p ≥ 3, a set S ⊆ V (G) is an x-geodominating set of G if each vertex v ∈ V (G) lies on an x-y geodesic for some element y in S. The minimum cardinality of an x-geodominating set of G is defined as the x-geodomination number of G, denoted by gx(G). An x-geodominating set of cardinality gx(G) is called a gx-set of G. For an edge e = x...

Fix integers r, k, g with r > k > 0 and g ≥ 2. Let X be an integral projective curve with g := pa(X) and E a rank r torsion free sheaf on X which is a flat limit of a family of locally free sheaves on X. Here we prove the existence of a rank k subsheaf A of E such that r(deg(A)) ≥ k(deg(E)) − k(r − k)g. We show that for every g ≥ 9 there is an integral projective curve X,X not Gorenstein, and a...