2 ∥∥∥(x∗ − x̃) + σ n z̃− δ∥∥2l2 s.t. δ ∈ C − x̃. Letting R1 and R2 denote orthogonal subspaces that contain Q1 and Q2, i.e., Q1 ⊆ R1 and Q2 ⊆ R2, and letting δ = PR1(δ), δ (2) = PR2(δ), δ̂ (1) n (C) = PR1(δ̂n(C)), δ̂ (2) n (C) = PR2(δ̂n(C)) denote the projections of δ, δ̂n(C) onto R1, R2, we can rewrite the above reformulated optimization problem as: [ δ̂ (1) n (C), δ̂ (2) n (C) ] = arg min δ∈Q1,δ∈Q2 1 2...

This paper investigates the principles ta λ,δ, weakenings of λ which allow δ many clubs at each level but require them to agree on a tail-end. First, we prove that ta λ,<ω implies λ. Then, by forcing from a model with a measurable cardinal, we show that λ,2 does not imply ta λ,δ for regular λ, and ta δ+,δ does not imply δ+,<δ. With a supercompact cardinal the former result can be extended to si...

An independent dominating set of a graph, also known as maximal set, is S pairwise non-adjacent vertices such that every vertex not in adjacent to some S. We prove for Δ=4 or Δ≥6, connected n-vertex graph maximum degree at most Δ has an size (1−Δ⌊Δ2/4⌋+Δ)(n−1)+1. In addition, we characterize all graphs having the equality and show other have (1−Δ⌊Δ2/4⌋+Δ)n.

the composition of essential oil of leaves of the male and female shrubs of juniperus chinensis l. (growing in isfahan) was analyzed by gas choromatography(gc) and gc-mass spectrometery (ms). the main constituents of leaf oil of the male shrub were: bornyl acetate (26.1%), sabinene (18.3%), trans-sabinyl acetate (11.1%), myrcene (9.2%), limonene (6.1%), elemol (5.5%), α-cadinol (2.3%), δ-cadine...

BACKGROUND Stable-isotope ratios of carbon (¹³C/¹²C, expressed as δ¹³C) and nitrogen (¹⁵N/¹⁴N, or δ¹⁵N) have been proposed as potential nutritional biomarkers to distinguish between meat, fish, and plant-based foods. OBJECTIVE The objective was to investigate dietary correlates of δ¹³C and δ¹⁵N and examine the association of these biomarkers with incident type 2 diabetes in a prospective stud...

This paper reconsiders the problem of maintaining longest paths in directed graphs, which is at the core of many scheduling applications. It presents bounded incremental algorithms for arc insertion and deletion running in time O(‖δ‖ + |δ| log |δ|) on Cyclic< 0 graphs (i.e., graphs whose cycles have strictly negative lengths), where |δ| and ‖δ‖ are measures of the change in the input and output...

Animals incorporate local δ 2 H values from available water and dietary sources during tissue synthesis, which can provide evidence of elevational movements if multiple tissues with different turnover times are examined. Here we test the applicability of using δ 2 H as an indicator of altitudinal movements by examining multiple tissues (δ 2 Hbw (body water), δ 2 Hfeather, δ 2 Hfur, and δ 2 Hcla...