This paper extends joint work with R. Friedman to show that the closure of the locus of intermediate Jacobians of smooth cubic threefolds, in the moduli space of principally polarized abelian varieties (ppavs) of dimension five, is an irreducible component of the locus of ppavs whose theta divisor has a point of multiplicity three or more. This paper also gives a sharp bound on the multiplicity...

In a recent work PRD 106, L021501 (2022), new geometric approach is proposed to obtain the photon sphere (circular orbit) and black hole shadow radius. this approach, spheres radius are determined using geodesic curvature Gaussian in optical geometry of spacetimes. However, calculations (2022) only restricted subclass static spherically symmetric holes with spacetime metric $g_{tt} \cdot g_{rr}...

R-trees and related structures, like R-trees and R-trees, have been used to answer queries involving topological information about objects represented by their minimum bounding rectangles (MBRs). This paper describes how the R-tree method can be used for the storage and retrieval of direction relations. Direction relations deal with order in space, as for instance, left, above, north, southeast...

We begin with establishing properties of the unit revenue function, g(·). Lemma 6. 1. g(·) is a non-negative, continuous, non-decreasing, and concave function on R+, with g(0) = 0. 2. yg(1/y) is non-decreasing and concave on R++. 3. g(y)/y is non-increasing on R+. 4. If u, v > 0, then g(u) g(v) ≥ min( u v , 1), 1 u ∫ u 0 g(v)dv ≤ g(u/2). Proof. 1. That g(·) is non-negative, continuous and non-d...

The R-Tree and variant indexes have been used for multidimensional indexing since 1984 and applied to temporal data since 1994. Despite this, there are few functional implementations of the index that can be applied directly to the temporal data. This paper explores the use of the index for temporal subsequence searches and identifies two implications that must be considered so the index can be...

We present a maximal $$L_{q}(L_{p})$$ -regularity theory with Muckenhoupt weights for the equation 0.1 $$\begin{aligned} \partial ^{\alpha }_{t}u(t,x)=a^{ij}(t,x)u_{x^{i}x^{j}}(t,x)+f(t,x),\quad t>0,x\in {\mathbb {R}}^{d}. \end{aligned}$$ Here, $$\partial }_{t}$$ is Caputo fractional derivative of order $$\alpha \in (0,2)$$ and $$a^{ij}$$ are functions (t, x). Precisely, we show that \begin{ali...

Abstract The present discussion is to study the following second order nonlinear delay dynamic equation of form: $$\begin{aligned}{}[r(\theta )(\mathcal {W}^{\Delta }(\theta ))^{\alpha }]^{\Delta } +\mathcal {P}(\theta )\mathcal {W}^{\beta }(\eta (\theta ))=0,\;\theta \in \mathbb {T}_{0}=[\theta _{0},\infty )\cap {T} \end{aligned}$$ <mml...

In order to better characterize changes in water structure induced by a hydrophobic solute the oxygen-oxygen and hydrogen-hydrogen radial distribution functions (goo(r), ghh(r)) and the hydrogen bond angle distribution function p(theta) for water molecules in the first hydration shell of the tetramethyl ammonium (TMA) cation were computed using Monte Carlo simulations. goo(r) and ghh(r) were co...