Approximation bounds on maximum edge 2-coloring of dense graphs

For a graph $G$ and integer $q\geq 2$, an edge $q$-coloring of $G$ is an assignment of colors to edges of $G$, such that edges incident on a vertex span at most $q$ distinct colors. The maximum edge $q$-coloring problem seeks to maximize the number of colors in an edge $q$-coloring of a graph $G$. The problem has been studied in combinatorics in the context of {\em anti-Ramsey} numbers. Algorithmically, the problem is NP-Hard for $q\geq 2$ and assuming the unique games conjecture, it cannot be approximated in polynomial time to a factor less than $1+1/q$. The case $q=2$, is particularly relevant in practice, and has been well studied from the view point of approximation algorithms. A $2$-factor algorithm is known for general graphs, and recently a $5/3$-factor approximation bound was shown for graphs with perfect matching. The algorithm (which we refer to as the matching based algorithm) is as follows: "Find a maximum matching $M$ of $G$. Give distinct colors to the edges of $M$. Let $C_1,C_2,\ldots, C_t$ be the connected components that results when M is removed from G. To all edges of $C_i$ give the $(|M|+i)$th color." In this paper, we first show that the approximation guarantee of the matching based algorithm is $(1 + \frac {2} {\delta})$ for graphs with perfect matching and minimum degree $\delta$. For $\delta \ge 4$, this is better than the $\frac {5} {3}$ approximation guarantee proved in {AAAP}. For triangle free graphs with perfect matching, we prove that the approximation factor is $(1 + \frac {1}{\delta - 1})$, which is better than $5/3$ for $\delta \ge 3$.Comment: 11pages, 3 figure

Intra articular distal radius fractures and volar plate fixation: a prospective study

Background: Despite being one of the most common fractures encountered in patients, intra-articular distal radius fractures still pose therapeutic challenge to Orthopaedic surgeons. With the advent of locking plates, the fixation of these fractures has been made better, specifically by fixed angle volar locking plate. This study investigates the efficacy of these plates using volar approach, functional and clinical outcome, in addition to the radiological alignment.Methods: Thirty patients with closed distal radius fractures, with AO TYPE B3, B4, AND C fracture pattern, operated with distal radius plate fixation using volar approach, were included in the study during the period of August 2014 to August 2016. With a minimum follow up of six months, radiological outcome was analysed and functional outcome recorded (Gartland and Werley’s demerit scoring system).Results: With a mean age of 42 years and follow up of six months, the range of movement of the wrist was very satisfactory, and the mean grip strength was 80% of the opposite wrist. Radiological parameters were well‑maintained, and functional parameters by Gartland and Werley showed a significant improvement in most of the patients during the follow‑up period. The complication rate was less and insignificant.Conclusions: Primary volar plate fixation of intraarticular distal radius fracture provides a stable construct that helps in early mobilization, thereby better functional outcomes and minimizes chances of delayed/malunion

Surface roughness assisted growth of vertically oriented ferroelectric SbSI nanorods

We report the catalyst-free synthesis of arrays of c-axis oriented antimony sulfoiodide nanorods on anodic aluminum oxide (AAO) substrates by vapor phase deposition. The surface roughness of the AAO substrates played a decisive role in the orientation control of the SbSI nanorods produced. The as-grown SbSI nanorods were single-crystalline and ⟨001⟩ oriented, as revealed from the X-ray diffraction and transmission electron microscopy analysis. Switching spectroscopy-piezoresponse force microscopy experiments demonstrated, for the first time, the presence of switchable ferroelectricity and piezoelectricity in individual SbSI nanorods. Ferroelectric switching in the SbSI nanorods was found to occur via a 180° domain reversal, because of the preferred orientation of the nanorods along their polar c-axis

Atomic vapor deposition of bismuth titanate thin films

c-axis oriented ferroelectric bismuth titanate (Bi4Ti 3O12) thin films were grown on (001) strontium titanate (SrTiO3) substrates by an atomic vapor deposition technique. The ferroelectric properties of the thin films are greatly affected by the presence of various kinds of defects. Detailed x-ray diffraction data and transmission electron microscopy analysis demonstrated the presence of out-of-phase boundaries (OPBs). It is found that the OPB density changes appreciably with the amount of titanium injected during growth of the thin films. Piezo-responses of the thin films were measured by piezo-force microscopy. It is found that the in-plane piezoresponse is stronger than the out-of-plane response, due to the strong c-axis orientation of the films

The structural and piezoresponse properties of c-axis-oriented Aurivillius phase Bi5Ti3FeO15 thin films deposited by atomic vapor deposition

The deposition by atomic vapor deposition of highly c-axis-oriented Aurivillius phase Bi 5Ti 3FeO 15 (BTFO) thin films on (100) Si substrates is reported. Partially crystallized BTFO films with c-axis perpendicular to the substrate surface were first deposited at 610°C (8 excess Bi), and subsequently annealed at 820°C to get stoichiometric composition. After annealing, the films were highly c-axis-oriented, showing only (00l) peaks in x-ray diffraction (XRD), up to (0024). Transmission electron microscopy (TEM) confirms the BTFO film has a clear layered structure, and the bismuth oxide layer interleaves the four-block pseudoperovskite layer, indicating the n 4 Aurivillius phase structure. Piezoresponse force microscopy measurements indicate strong in-plane piezoelectric response, consistent with the c-axis layered structure, shown by XRD and TEM

NMR, Mass and DFT Studies of Ariose: A Novel Oligosaccharide from Donkey (Equus asinus) Milk

Oligosaccharides play a key role in various physiological, pathological and biological activities such as biological recognition, anti-complementary, anti-coagulant, anti-inflammatory, anti-viral, anti-bacterial, anti-tumour, anti-oxidant, lipid lowering, immunological activities, prebiotic activity and hypoglycemic activity. In our endeavour to find biologically active novel oligosaccharides, donkey milk was taken, which is a rich source of oligosaccahrides and its milk is used as anti-hypertensive, anti-oxidant and heart strengthening agent in folk medicine. For this purpose donkey milk was processed by modified method of Kobata and Ginsburg followed by Gel filtration HPLC and Column Chromatography (CC) which resulted in the isolation of one novel milk oligosaccharide namely Ariose. The structure of purified milk oligosaccharide was determined with the help of chemical degradation, chemical transformation, spectroscopic techniques like 1D-NMR (1H and 13C), 2D-NMR (COSY, TOCSY, HSQC and HMBC), Structure Reporter Group (SRG) theory and Mass spectrometry (ESI-MS). The geometry optimization of compound was done by using B3LYP method at 6-31G (d, p) basis set employing Density Functional Theory (DFT). &nbsp