It is known that for every nonorientable surface there are infinitely many (large) snarks that can be polyhedrally embedded on that surface. We take a dual approach to the embedding of snarks on the Klein bottle, and investigate edge-colorings of 6-chromatic triangulations of the Klein bottle. In the process, we discover the smallest snarks that can be polyhedrally embedded on the Klein bottle....

We consider the nonlinear stability of the Kaluza-Klein monopole viewed as the static solution of the five-dimensional vacuum Einstein equations. Using both numerical and analytical methods, we give evidence that the Kaluza-Klein monopole is asymptotically stable within the cohomogeneity-two biaxial Bianchi type-IX ansatz recently introduced by Bizoń, Chmaj, and Schmidt. We also show that for s...

The standard Klein bottle coefficient in the construction of open descendants is shown to equal the Frobenius-Schur indicator of a conformal field theory. Other consistent Klein bottle projections are shown to correspond to simple currents. These observations enable us to generalize the standard open string construction from C-diagonal parent theories to include non-standard Klein bottles. Usin...

A Klein polyhedron is defined as the convex hull of nonzero lattice points inside an orthant of R n. It generalizes the concept of continued fraction. In this paper facets and edge stars of vertices of a Klein polyhedron are considered as multidimensional analogs of partial quotients and quantitative characteristics of these " partial quotients " , so called determinants, are defined. It is pro...

effects of formulation parameters on the fractional release profile of diclofenac sodium from matrices having the manufacturing formulation ingredients are studied. as a content of cetyl alcohol (rate controlling agent) in the matrix increases, the fractional release decreases. the fractional release increases either by increasing sucrose content outside the granule or by decreasing sucrose con...

A Klein polyhedron is defined as the convex hull of nonzero lattice points inside an orthant of R. It generalizes the concept of continued fraction. In this paper facets and edge stars of vertices of a Klein polyhedron are considered as multidimensional analogs of partial quotients and quantitative characteristics of these “partial quotients”, so called determinants, are defined. It is proved t...

We propose that cold dark matter is made of Kaluza-Klein particles and explore avenues for its detection. The lightest Kaluza-Klein state is an excellent dark matter candidate if standard model particles propagate in extra dimensions and Kaluza-Klein parity is conserved. We consider Kaluza-Klein gauge bosons. In sharp contrast to the case of supersymmetric dark matter, these annihilate to hard ...

Complex classical Cayley-Klein categories A(j), B(j), C(j) and D(j) are constructed by the method of categorical extension of the complex classical Cayley-Klein groups SL(2n; j;C), SO(2n + 1; j;C), Sp(2n; j;C) and SO(2n; j;C), respectively. The explicit construction of the irreducible representations of the complex classical Cayley-Klein categories is received. Completeness of lists of the irre...