The primary goal of this paper is to investigate the geometry p-adic eigencurve at a point f corresponding weight one cuspidal CM theta series θψ irregular prime number p. We show that belongs exactly three or four irreducible components and study their intersection multiplicities. In particular, we introduce an anti-cyclotomic L-invariant L-(ψ-) congruence ideal component Θψ has simple zero if...

In this paper, we prove that every automorphism of the first homology group of a closed, connected, nonorientable surface which preserves the associated Z2-valued intersection pairing is induced by a diffeomorphism of this surface. 0. Introduction It is well known that the diffeomorphisms on a closed, connected, orientable surface of genus g, Mg, induce the full group of automorphisms of H1(Mg,...

THIS report presents a graphic expression of the accident-volume relation at divided highway intersections. The expression was produced by averaging the past accident experience at 150 intersections. A total of 1, 811 accidents was tabulated in developing the chart. Uses of the chart include: (1) estimating the probable number of accidents which wil l occur in a future period and (2) correcting...

We provide succinct covariant amplitude decompositions of 2-body weak hadronic decays, with which to compare data, including exclusive rates, helicity amplitudes and polarizations. For weak decays, the systematic dependence of these amplitudes on masses and quantum numbers of participating particles are determined within a factor of about two by the CKM angles and the Fermi constant so theoreti...

Let C ⊂ P be a smooth irreducible complete algebraic curve of degree d embedded in a projective 3-space over an algebraically closed field k. It is called n-regular if H(IC(n− 1)) = H(IC(n− 2)) = 0, where IC is the ideal sheaf of C. Among all this implies that the homogeneous ideal IC = ⊕ l H (IC(l)) ⊂ k[x0, x1, x2, x3] is generated in degree ≤ n ([7], Lecture 14) and C ⊂ P is (scheme-theoretic...

We study the fluctuations of self-intersection counts of random geodesic segments of length t on a compact, negatively curved surface in the limit of large t. If the initial direction vector of the geodesic is chosen according to the Liouville measure, then it is not difficult to show that the number N(t) of self-intersections by time t grows like κt2, where κ = κM is a positive constant depend...

Let X be a simplicial complex on the vertex set V . The rational Leray number L(X) of X is the minimal d such that H̃i(Y ;Q) = 0 for all induced subcomplexes Y ⊂ X and i ≥ d. Suppose V = ⋃m i=1 Vi is a partition of V such that the induced subcomplexes X[Vi] are all 0-dimensional. Let π denote the projection of X into the (m − 1)-simplex on the vertex set {1, . . . ,m} given by π(v) = i if v ∈ Vi...

An intersection is a shared space that is used by more than one approach at a time. A signalized intersection is one where the shared space is used alternatively by a fixed number of approaches for a pre defined time interval as per the phasing scheme used for the intersection. Delay and queuing process are the main characteristics of such an intersection which help in analyzing and designing t...

In this article, a number of the results relevant to the concept of sublattices of a basic crystallographic lattice are reviewed, emphasizing particularly previously unpublished work on the algebraic aspects. A three-dimensional geometric lattice L can be considered as an infinite Abelian group under addition. A sublattice S of L, which is also three-dimensional, is a subgroup of L such that th...

Let n ≥ k ≥ l ≥ 2 be integers, and let F be a family of k-element subsets of an n-element set. Suppose that l divides the size of the intersection of any two (not necessarily distinct) members inF . We prove that the size ofF is at most (⌊n/l⌋ k/l ) provided n is sufficiently large for fixed k and l.