We claim that monomorphisms in Sets and Groups are the usual injective maps and homomorphisms. First, suppose that f : A → B is a set injection and that fg = gh. Then for all c ∈ C, we have f(g(c)) = f(h(c)) implies g(c) = h(c) by injectivitiy. Hence g = h. Conversely, suppose f : A → B is not an injection. Then let f(a) = f(a′) for some a 6= a′ ∈ A. Then let g(c) = a and h(c) = a′ for all c ∈ ...

Introduction One of the fundamental properties of typical AIS is its monomorphism. The C-shaped scoliosis is a “pure” 3D deformation, while S-shaped form consists of two 3D curves, etc. Mathematical modeling has shown a steady sequence of forming units of 3D deformation. Real clinical manifestations in the initial period of development of typical AIS are identical to changes, predicted by mathe...

Sexual selection, more so than natural selection, is posited as the major cause of sex differences. Here I show ecological correlations between solar radiation levels and sexual dimorphism in body color of a Hawaiian damselfly. Megalagrion calliphya exhibits sexual monomorphism at high elevations, where both sexes are red in color; sexual dimorphism at low elevations, where females are green; a...

We prove induced Ramsey theorems in which the monochromatic induced subgraph satisfies that all members of a prescribed set of its partial isomorphisms extend to automorphisms of the colored graph (without requirement of preservation of colors). We consider vertex and edge colorings, and extensions of partial isomorphisms in the set of all partial isomorphisms between singletons as considered b...

We answer two open questions posed by Cameron and Nesetril concerning homomorphismhomogeneous graphs. In particular we show, by giving a characterization of these graphs, that extendability to monomorphism or to homomorphism leads to the same class of graphs when defining homomorphism-homogeneity. Further we show that there are homomorphism-homogeneous graphs that do not contain the Rado graph ...

All organisms with sexual reproduction undergo a process of mating, which essentially involves the encounter of two individuals belonging to different sexes. During mate search, both sexes should mutually optimize their encounters, thus raising a question of how they achieve this. Here, we show that a population with sexually dimorphic movement patterns achieves the highest individual mating su...

Although the vast majority of higher animals are fixed for one chiral morph or another, the cause for this directionality is known in only a few cases. In snails, for example, rare individuals of the opposite coil are unable to mate with individuals of normal coil, so directionality is maintained by frequency-dependent selection. The snail subgenus Amphidromus presents an unexplained exception,...

UNLABELLED PREMISE OF THE STUDY Tung tree, Vernicia fordii, is native to China. Little has been done on genetics and breeding at the molecular level in this species, let alone utilizing microsatellite (simple sequence repeat [SSR]) markers. Therefore, a set of SSR molecular markers was developed for studies on molecular genetics and breeding in tung tree. • METHODS AND RESULTS We designed ...

Summary This is the first part of a two-part article formalizing existence and uniqueness algebraic closures using Mizar system [1], [2]. Our proof follows Artin’s classical one as presented by Lang in [3]. In this we prove that for given field F there exists extension E such every non-constant polynomial p ∈ [ X ] has root . applies Kronecker’s construction to each \F simultaneously. To do so ...