This paper discusses lower bounds for proof length, especially as measured by number of steps (inferences). We give the first publicly known proof of Gödel’s claim that there is superrecursive (in fact, unbounded) proof speedup of (i + 1)-st order arithmetic over i-th order arithmetic, where arithmetic is formalized in Hilbert-style calculi with + and · as function symbols or with the language ...

We prove algebraic analogues of the facts that a curve on a surface with self-intersection number zero is homotopic to a cover of a simple closed curve, and that two simple closed curves on a surface with intersection number zero can be isotoped to be disjoint. In [15] and [16], analogues of the classical JSJ-decompositions of Haken manifolds were described using the notion of isotopic disjoint...

In this paper we give some necessary and sufficient conditions for which each Banach lattice  is    space and we study some properties of b-weakly compact operators from a Banach lattice  into a Banach space . We show that every weakly compact operator from a Banach lattice  into a Banach space  is b-weakly compact and give a counterexample which shows that the inverse is not true but we prove ...

the bft approach is used to formulate the electronic states in graphene through a non-commutative space in the presence of a constant magnetic field b for the first time. in this regard, we introduce a second class of constrained system, which is not gauge symmetric but by applying bft method and extending phase space, the second class constraints  converts  to the first class constraints so th...

pseudo ricci symmetric real hypersurfaces of a complex projective space are classified and it is proved that there are no pseudo ricci symmetric real hypersurfaces of the complex projective space cpn for which the vector field ξ from the almost contact metric structure (φ, ξ, η, g) is a principal curvature vector field.

The original aim of this paper is to construct a graph associated to a vector space. By inspiration of the classical definition for the Cayley graph related to a group we define Cayley graph of a vector space. The vector space Cayley graph ${rm Cay(mathcal{V},S)}$ is a graph with the vertex set the whole vectors of the vector space $mathcal{V}$ and two vectors $v_1,v_2$ join by an edge whenever...

the present article is extracted from a multi-dimensional research around “space”, how architecture instructors interpret it and how this interpretation can influence their instruction. to fulfill this end, special attention has been paid to different spatial patterns of architecture besides a thorough study of opinions stated on the subject by different patterns. following a lexical investigat...

We survey recent work of Burghelea, Malta and both authors on the topology of critical sets of nonlinear ordinary differential operators. For a generic nonlinearity f , the critical set of the first order nonlinear operator F1(u)(t) = u (t) + f(u(t)) acting on the Sobolev space H1 p of periodic functions is either empty or ambient diffeomorphic to a hyperplane. For the second order operator F2(...

We construct quantum deformation of Poincaré group using as a starting point SU(2, 2) conformal group and twistor-like definition of the Minkowski space. We obtain quantum deformation of SU(2, 2) as a real form of multi-parametric GL(4, C) q ij ,r. It is shown that Poincaré subgroup exists for special nonstandard one-parametric deformation only, the deformation parameter r being equal to unity....

A transition of focus from state space to frames of reference and their transformations is argued as being the appropriate setup for ensuring the covariance of physical laws. Such an approach can not only simplify and clarify aspects of General Relativity, but can possibly help in the development of a Grand Unified Theory as well. " Physics may be not only too important, but also too deep, in o...