In this article we research the structure of d-convex simple graphs in order to extend the already known classes of graphs of this type. We do this using some new operations and new graphs. We introduce the notion of M-prime graphs and split all d-convex simple graphs into M-prime graphs using the M operation. After that we describe all M-prime graphs we know. Mathematics subject classification...

We obtain computational hardness results for f-vectors of polytopes by exhibiting reductions the problems DIVISOR and SEMI-PRIME TESTABILITY to on polytopes. Further, we show that corresponding simplicial are polytime solvable. The situation where prove this difference (conditioned standard conjectures density primes $$P \ne NP $$ ) is when dimension d tends infinity number facets linear in d.

We present the design and performance of TANSPEC, a medium-resolution $0.55-2.5~\mu$m cryogenic spectrometer imager, now in operation at 3.6-m Devasthal Optical Telescope (DOT), Nainital, India. The TANSPEC provides three modes which include, photometry with broad- narrow-band filters, spectroscopy short slits 20$^{\prime \prime}$ length different widths (from 0.5$^{\prime to 4.0$^{\prime \prim...

In this paper, we present a characterization of a semi-multiplicative analogue of planar functions over finite fields. When the field is a prime field, these functions are equivalent to a variant of a doubly-periodic Costas array and so we call these functions Costas. We prove an equivalent conjecture of Golomb and Moreno that any Costas polynomial over a prime field is a monomial. Moreover, we...