We compute all irregular primes less than 163 577 856. For all of these primes we verify that the Kummer–Vandiver conjecture holds and that the λ-invariant is equal to the index of irregularity.

This paper proposes a nonparametric steganalysis method for quantization index modulation (QIM) based steganography. The proposed steganalysis method uses irregularity (or randomness) in the test-image to distinguish between the coverand the stego-image. We have shown that plain-quantization (quantization without message embedding) induces regularity in the resulting quantized-image; whereas me...

An irregularity index IR(Γ) of a graph Γ is nonnegative numeric quantity (i.e., IR(Γ)≥0) such that IR(Γ)=0 iff regular graph. In this paper, we show IRC closely correlates with the normal boiling point Tbp and standard heat formation ΔHfo lower benzenoid hydrocarbons. The correlation models fit data efficiently for both are linear. We develop further mathematical properties by calculating its e...

BACKGROUND Menstrual irregularity is a common major complaint in women of reproductive age. It is also a known marker for underlying insulin resistance. We investigated the association between menstrual irregularity and metabolic syndrome in the general population of middle-aged women in Korea. METHODS This cross-sectional study used data from the Korea National Health and Nutrition Examinati...

We have simulated the effect of sidewall roughness in photonic-crystallike structures with different vertical refractive-index contrast. We treated the scattering off a sidewall irregularity as a radiating dipole excited by the incident waveguide mode. We show that the loss that is due to this scattering is significantly larger for structures with a low refractive-index contrast (such as GaAs/A...

BACKGROUND There have been few studies examining the associations between menstrual irregularity, androgens and bone mass in population-based samples of premenopausal women. This study aimed to describe the associations between menstrual pattern, testosterone, sex hormone binding globulin (SHBG) and bone mass in a population-based sample of premenopausal women. METHODS Cross-sectional study (...

We investigate the following modification of the well known irregularity strength of graphs. Given a total weighting w of a graph G = (V,E) with elements of a set {1, 2, . . . , s}, denote wtG(v) = ∑ e3v w(e)+w(v) for each v ∈ V . The smallest s for which exists such a weighting with wtG(u) 6= wtG(v) whenever u and v are distinct vertices of G is called the total vertex irregularity strength of...

In This paper, the non-orthogonal multiple access (NOMA) schemes are compared with orthogonal (OMA) on basis of resource allocation validity uplinks. By reflecting involvement a measure each user’s data system’s total amount, we analyze main reasons why NOMA provides justice service distribution over OMA unequal channels. Moreover, Jain index is observed and proposed to quantify irregularity nu...