Oblong Mean Prime Labeling of Some Snake Graphs

A graph labeling is an assignment of integers to the vertices or edges or both subject to certain conditions. The graph for which every edge(uv),the labels assigned to u and v are oblong numbers and for each vertex of degree at least 2, the g c d of the labels of the incident edges is 1. Here we characterize some snake graphs for oblong mean prime labeling

Square Sum Difference Product Prime Labeling of Some Tree Graphs

Square sum difference product prime labeling of a graph is the labeling of the vertices with {0,1,2---------,p-1} and the edges with absolute difference of the sum of the squares of the labels of the incident vertices and product of the labels of the incident vertices. The greatest common incidence number of a vertex (gcin) of degree greater than one is defined as the greatest common divisor of the labels of the incident edges. If the gcin of each vertex of degree greater than one is one, then the graph admits square sum difference product prime labeling. In this paper we investigate some tree graphs for square sum difference product prime labeling

Hexagonal Difference Prime Labeling of Some Path Graphs

Hexagonal difference prime labeling of vertices of a graph is the labeling of the vertices of the graph with hexagonal numbers and the edges with absolute value of the difference of the labels of the incident vertices. The greatest common incidence number (gcin) of a vertex of degree greater than one is defined as the greatest common divisor of the labels of the incident edges. If the gcin of each vertex of degree greater than one is 1, then the graph admits hexagonal difference prime labeling.  Here we identify some path related graphs for hexagonal difference prime labeling

Kernel-based Estimation of Ageing Intensity Function: Properties and Applications

The notion of ageing plays an important role in reliability and survival analysis as it is an inherent property of all systems and products. Jiang, Ji, and Xiao (2003) proposed a new quantitative measure, known as ageing intensity (AI) function, an alternative measure to study the ageing pattern of probability models. In this paper, we propose a nonparametric estimator for ageing intensity function. Asymptotic properties of the estimator are established under suitable regularity conditions. A set of simulation studies are carried out based on various probability models to examine the performance of estimator and to establish its efficiency over the classical estimator. The usefulness of the estimator is also examined through a real data set

Agricultural Field Applications of Digital Image Processing Using an Open Source ImageJ Platform

Digital image processing is one of the potential technologies used in precision agriculture to gather information, such as seed emergence, plant health, and phenology from the digital images. Despite its potential, the rate of adoption is slow due to limited accessibility, unsuitability to specific issues, unaffordability, and high technical knowledge requirement from the clientele. Therefore, the development of open source image processing applications that are task-specific, easy-to-use, requiring fewer inputs, and rich with features will be beneficial to the users/farmers for adoption. The Fiji software, an open source free image processing ImageJ platform, was used in this application development study. A collection of four different agricultural field applications were selected to address the existing issues and develop image processing tools by applying novel approaches and simple mathematical principles. First, an automated application, using a digital image and “pixel-march” method, performed multiple radial measurements of sunflower floral components. At least 32 measurements for ray florets and eight for the disc were required statistically for accurate dimensions. Second, the color calibration of digital images addressed the light intensity variations of images using standard calibration chart and derived color calibration matrix from selected color patches. Calibration using just three-color patches: red, green, and blue was sufficient to obtain images of uniform intensity. Third, plant stand count and their spatial distribution from UAS images were determined with an accuracy of ≈96 %, through pixel-profile identification method and plant cluster segmentation. Fourth, the soybean phenological stages from the PhenoCam time-lapse imagery were analyzed and they matched with the manual visual observation. The green leaf index produced the minimum variations from its smoothed curve. The time of image capture and PhenoCam distances had significant effects on the vegetation indices analyzed. A simplified approach using kymograph was developed, which was quick and efficient for phenological observations. Based on the study, these tools can be equally applied to other scenarios, or new user-coded, user-friendly, image processing tools can be developed to address specific requirements. In conclusion, these successful results demonstrated the suitability and possibility of task-specific, open source, digital image processing tools development for agricultural field applications.United States. Agricultural Research ServiceNational Institute of Food and Agriculture (U.S.

Proline-derived organocatalysis and synergism between theory and experiments

The ability of proline and its derivatives toward catalyzing asymmetric organic reactions is highlighted. Illustration of the impact of interdisciplinary efforts between computational and experimental research is provided through a number of interesting examples. (C) 2011 John Wiley & Sons, Ltd. WIREs Comput Mol Sci 2011 1 920-931 DOI: 10.1002/wcms.3

Rational design of catalysts for asymmetric diamination reaction using transition state modeling

The stereoselective synthesis of 1,2-diamines has remained a formidable challenge. A recent palladium-catalyzed asymmetric diamination of conjugated double bonds using di-tert-butyldiaziridinone appears promising. The axially chiral binol phosphoramidite ligands are successful in offering high enantioselectivity. The density functional theory investigations revealed that the energies of the stereo-controlling transition states for the C-N bond formation depend on a number of weak non-covalent interactions such as C-H center dot center dot center dot pi, C-H center dot center dot center dot O and anagostic interactions. We envisaged that the modulation in these interactions in the transition states, through subtle changes in chiral phosphoramidite substituents, could be exploited toward steering the stereoselectivity. The effect of systematic modifications on both 3,3' positions of the binol as well as on the amido nitrogen on the stereochemical outcome is predicted. It is identified that high enantioselectivity requires a balance between the nature of the substituents on binol and amido groups. The reduced size of the amido substituents demands increased bulk on the binol whereas lowering the size on the binol demands increased bulk on the amido for higher stereoselectivity. The substituent at the alpha-position of the amido group is found to be vital and appears to be a hot spot for modifications. These insights derived from studies on the stereocontrolling transition states could help improve the catalytic efficacies in palladium-catalyzed asymmetric diamination reactions

Intramolecular nonbonding interactions in organoseleniums: quantification using a computational thermochemical approach

Intramolecular Se···O nonbonding interactions in a series of ortho-formylarylselenides (O···Se–Y, with Y = –Me, –Ph, –CN, –Cl, and –F) are quantified using density functional theory. Two methods based on the relative stabilities of various conformers are employed in evaluating the strength of intramolecular interactions. These methods, namely, cis–trans (CT) and thermodynamic cycle (TDC), depends on the energy changes associated with conformational interconversion, where the nonbonding interaction is turned on or off (respectively, in cis and trans conformer). The strength of interactions are found to be dependent on the nature of Se–Y acceptor orbitals and follows the order Me ~ Ph < CN < Cl < F. Natural Bond Orbital (NBO) analysis using DFT methods points to nO→σSe–Y* electron delocalization as the key contributing factor towards Se···O nonbonding interaction. Examination of the topological properties of the electron density with the Atoms-in-Molecule (AIM) method reveals that the electron density at the Se···O bond critical point exhibits a fairly good correlation with the nonbonding interaction energies estimated using the CT and TDC methods.© Elsevie