We prove criteria for $\mathcal{H}^k$-rectifiability of subsets $\mathbb{R}^n$ with $C^{1,\alpha}$ maps, $0<\alpha\leq 1$, in terms suitable approximate tangent paraboloids. also provide a version the case when there is not an priori plane, measuring on dyadic scales how close set to lying $k$-plane. then discuss relation similar involving Peter Jones' $\beta$ numbers, particular proving that s...

Recent work in the area of Obesity has confirmed that Obesity is a state of low grade chronic inflammation and is associated with increased levels of TumorNecrosisFactor-α, a pro-inflammatory adipocytokine, which plays a key role in the pathogenesis of Diabetes. In this study we analysed the interrelations between TumorNecrosisFactor-α with anthropometric and clinical variables. The study was c...

BACKGROUND Nuclear factor-kappa B (NF-κB) plays a role in prostate cancer and agents that suppress its activation may inhibit development or progression of this malignancy. Alpha (α)-tomatine is the major saponin present in tomato (Lycopersicon esculentum) and we have previously reported that it suppresses tumor necrosis factor-alpha (TNF-α)-induced nuclear translocation of nuclear factor-kappa...

objective: diabetes mellitus type 2 is one of the most widespread chronic metabolic diseases. in most cases, this type of diabetes is associated with alterations in levels of some inflammatory cytokines and hormones. considering anti-inflammatory properties of plant extracts rich in ascorbic acid (vitamin c) and alpha-tocopherol (vitamin e), anti-diabetic properties of these two well-known anti...

Background & Aim: Singhnad Guggulu is a traditional Ayurvedic formula for detoxifying and rejuvenating the joints. The present study was to investigate the α-amylase inhibition and antioxidant activities of aqueous extract of Singhnad Guggul (AESG). Experimental: α-Amylase inhibition assay by dinitro-salicylic acid method and antioxidant activity by ferric chelating and ferrous reducing assay....

Abstract We study the minimal gap statistic for sequences of form $\left( \alpha x_n \right)_{n = 1}^{\infty}$ where is a sequence real numbers, and its connection to additive energy 1}^{\infty}$. Inspired by recent paper Aistleitner, El-Baz Munsch we show conditionally on Lindelöf Hypothesis that if lowest possible order then almost all α, $\delta_{\min}^{\alpha} (N) \min \left\{\alpha x_m - \...

The independence number α ( G ) $\alpha (G)$ and the dissociation diss $\text{diss}(G)$ of a graph $G$ are largest orders induced subgraphs maximum degree at most 0 1, respectively. We consider possible improvements obvious inequality 2 ≥ $2\alpha (G)\ge \text{diss}(G)$ . For connected cubic graphs distinct from K 4 ${K}_{4}$ , we show 5 3 $5\alpha 3\,\text{diss}(G)$ describe rich interesting s...

Let G G be a finite group admitting coprime automorphism alttext="alpha"> α encoding="application/x-tex">\al...

Ongoing neural dynamics comprise both frequency-specific oscillations and broadband-features, such as long-range dependence (LRD). Despite both being behaviorally relevant, little is known about their potential interactions. In humans, 8-12 Hz α oscillations constitute the strongest deviation from 1/f power-law scaling, the signature of LRD. We postulated that α oscillations, believed to exert ...