An Inverse Approximation and Saturation Order for Kantorovich Exponential Sampling Series

In the present article, an inverse approximation result and saturation order for the Kantorovich exponential sampling series $I_{w}^{\chi}$ are established. First we obtain a relation between the generalized exponential sampling series $S_{w}^{\chi}$ and $I_{w}^{\chi}$ for the space of all uniformly continuous and bounded functions on $\mathbb{R}^{+}.$ Next, a Voronovskaya type theorem for the sampling series $S_{w}^{\chi}$ is proved. The saturation order for the series $I_{w}^{\chi}$ is obtained using the Voronovskaya type theorem. Further, an inverse result for $I_{w}^{\chi}$ is established for the class of log-H\"{o}lderian functions. Moreover, some examples of kernels satisfying the conditions, which are assumed in the hypotheses of the theorems, are discussed

Investigation on physical and mechanical behaviour of A356 - x wt. % SiC/Gr hybrid composites

The experiments were planned to fabricate an A356 as a matrix material with 3, 6, 9, 12 wt. % of SiC and 3 wt. % of Gr as reinforcements to cast the hybrid composites at optimal process variable conditions using squeeze casting technique. Further T6 heat treated casted samples are prepared for testing as per standard procedure to record the responses like density, porosity, hardness, ultimate tensile strength, and percentage elongation respectively. There is a gradual increment in density because of adding an optimal level of up to 9 wt. % of SiC and 3 wt. % of Gr strengthening particles available in the A356 matrix and the porosity present in the sample diminishes, which in turn increases the hardness

Comparative Evaluation of Inclusion Complex of Aceclofenac Prepared by different Techniques.

Cyclodextrins Are Cyclic Oligosaccharides Containing At Least Six D-(+)- Glucopyranose Units Attached By Α (1Æ4) Glucoside Bonds. The Three Natural Cyclodextrins, Α, Β, And Γ Differ In Their Ring Size And Solubility. They Contain 6, 7 Or 8 Glucose Units, Respectively An Inclusion Complex Of Aceclofenac With Β- Cyclodextrin Could Be Prepared Successfully By Kneading In A Molar Ratio Of 1:2 And This Was Confirmed By Phase Solubility Studies, UV Spectrophotometry, Fourier Transform Infrared Spectroscopy, Differential Scanning Calorimetry, X-Ray Diffraction, Drug Content Estimation, In Vitro Dissolution Study And Stability Studies

Dirac Hamiltonians for bosonic spectra

Dirac materials are of great interest as condensed matter realizations of the Dirac and Weyl equations. In particular, they serve as a starting point for the study of topological phases. This physics has been extensively studied in electronic systems such as graphene, Weyl- and Dirac semi-metals. In contrast, recent studies have highlighted several examples of Dirac-like cones in collective excitation spectra, viz. in phonon, magnon and triplon bands. These cannot be directly related to the Dirac or Weyl equations as they are bosonic in nature with pseudo-unitary band bases. In this article, we show that any Dirac-like equation can be smoothly deformed into a form that is applicable to bosonic bands. The resulting bosonic spectra bear a two-to-one relation to that of the parent Dirac system. Their dispersions inherit several interesting properties including conical band touching points and a gap-opening-role for `mass' terms. The relationship also extends to the band eigenvectors with the bosonic states carrying the same Berry connections as the parent fermionic states. The bosonic bands thus inherit topological character as well. If the parent fermionic system has non-trivial topology that leads to mid-gap surface states, the bosonic analogue also hosts surface states that lie within the corresponding band gap. The proposed bosonic Dirac structure appears in several known models. In materials, it is realized in Ba$_2$CuSi$_2$O$_6$Cl$_2$ and possibly in CoTiO$_3$ as well as in paramagnetic honeycomb ruthenates. Our results allow for a rigorous understanding of Dirac phononic and magnonic systems and enable concrete predictions, e.g., of surface states in magnonic topological insulators and Weyl semi-metals.Comment: 10 pages, supersedes arXiv:1802.0826

Preliminary phytochemical studies for the quantification of secondary metabolites of medicinal importance in the plant, Acalypha fruticosa Forssk

The medicinal plant, Acalypha fruticosa Forssk for the treatment of dyspepsia, stomachache, fever, jaundice, skin diseases and even as an antidote is generally distributed in different environments of tropical region in Coimbatore district of Tamil Nadu. However, its occurrence is more common in lower hills of Western Ghats and other habitats in this region where the soil is stony with low moisture. So far, there was no study on the influence of habitat conditions on the change in the content of secondary metabolites of medicinal importance in this plant. Hence to know the changes in the content of such secondary metabolites in the leaves of A. fruticosa, the present study was undertaken in three different habitats. Thin layer chromatography revealed the presence of phytochemical compounds viz., alkaloids, flavonoids and saponins in the leaves of all the three populations. Further the content of all these compounds are found to be higher in the population of dry habitats

A prospective study comparing postoperative spirometry after laparoscopic cholecystectomy and laparoscopic appendicectomy surgeries

BACKGROUND: Patients undergoing laparoscopic cholecystectomy were found to have significant post-operative pulmonary dysfunction compared with lower abdominal procedures like laparoscopic appendicectomy. This study aims to measure the extent of decrease in lung volumes and capacities by spirometry. Importance of site of surgery is determined by maintaining other parameters like anaesthesia, analgesia similar in both the groups. METHODS: Two groups were formed with 20 patients each for lap-cholecystectomy and lap-appendicectomy with comparable profile. Pre-operative spirometry done for all of them and baseline values recorded. Post-operatively spirometry was done twice 6 hrs and 24 hrs following surgery. All surgeries were done under general anaesthesia. Adequate pain relief was given to attain a VAS score of less than 40. Spirometry values were compared and analysed for statistical significance. RESULTS: Reduction in FVC, FEV1, PEFR was found to be more in cholecystectomy group during initial post-operative period and did not return to pre-op levels by 24 hrs. Where as in appendicectomy group though there was a reduction in lung volumes during initial post-operative period FVC, FEV1, PEFR values returned almost to the pre-operative levels. CONCLUSION: Anatomical site of surgery is a more important factor determining postoperative lung dysfunction than patient position, pain, anesthesia related factors