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In the present paper we consider the problem of the existence of pre-semigeodesic coordinates on manifolds with affine connection. We proved that pre-semigeodesic coordinates exist in the case when the components of the affine connection are twice differentiable functions.

Possible existence of a molecular-type heavy-flavored strange pentaquark is considered. No narrow state of such a type is shown to exist.

The Energetic X-ray Timing Survey Telescope (EXIST) mission concept is under study as the Black Hole Finder Probe (BHFP), one of the three Einstein Probe missions in the Beyond Einstein Program in the current NASA Strategic Plan. EXIST would conduct an all-sky imaging hard X-ray ($\sim$10-600 keV) survey with unprecedented sensitivity: about 5 $\times 10^{-13}$ cgs over any factor of 2 bandwidth, or comparable to that achieved at soft X-rays in the ROSAT survey. The proposed angular resolution of 5arcmin, temporal resolution of 10microsec, energy resolution of 1-4 keV over the broad band, and duty cycle of 0.2-0.5 for continuous coverage of any source provide an unprecedented phase space for timing and spectral studies of black holes --from stellar to supermassive, as well as neutron stars and accreting white dwarfs. The large sky coverage allows intrinsically rare events to be studied. One particularly exciting example is the possible detection of tidal disruption of stars near quiescent AGN. Super flares from SGRs could be detected out to the Virgo cluster. The large duty cycle and all sky monitor nature of the mission will enable QPOs from luminous AGN and BH X-ray binaries to b

We investigate the question if quantum algorithms exist that compute the maximum of a set of conjugated elements of a given number field in quantum polynomial time. We will relate the existence of these algorithms for a certain family of number fields to an open conjecture from elementary number theory.

Despite the obvious utility of the concept, it has often been argued that time does not exist. I take the opposite perspective: let's imagine that time does exist, and the universe is described by a quantum state obeying ordinary time-dependent quantum mechanics. Reconciling this simple picture with the known facts about our universe turns out to be a non-trivial task, but by taking it seriously we can infer deep facts about the fundamental nature of reality. The arrow of time finds a plausible explanation in a "Heraclitean universe," described by a quantum state eternally evolving in an infinite-dimensional Hilbert space.

Let S be a cyclic n-ary sequence. We say that S is a {\it universal cycle} ((n,k)-Ucycle) for k-subsets of [n] if every such subset appears exactly once contiguously in S, and is a Ucycle packing if every such subset appears at most once. Few examples of Ucycles are known to exist, so the relaxation to packings merits investigation. A family {S_n} of (n,k)-Ucycle packings for fixed k is a near-Ucycle if the length of S_n is $(1-o(1))\binom{n}{k}$. In this paper we prove that near-(n,k)-Ucycles exist for all k.

We construct a family of unital non-associative algebras $\{T_α\vert~ 2<α\in\mathbb R\}$ such that $\underline{exp}(T_α)=2$, whereas $α\le\overline{exp}(T_α)\leα+1$. In particular, it follows that ordinary PI-exponent of codimension growth of algebra $T_α$ does not exist for any $α> 2$. This is the first example of a unital algebra whose PI-exponent does not exist.

We identify infinite classes of potentials for which the Coleman instantons do not exist. For these potentials, the decay of a false vacuum must be described by the new instantons introduced in [7,8].

For any Anosov diffeomorphims on a closed odd dimensional manifold, there exists no invariant contact structure.

We prove that nine-dimensional exceptional quotient singularities exist.