Some new classes of graceful diameter six trees

Here we denote a diameter six tree by (a0; a1, a2, . . . , am; b1, b2, . . . , bn; c1, c2, . . . , cr), where a0 is the center of the tree; ai, i = 1, 2, . . . , m, bj , j = 1, 2, . . . , n, and ck, k = 1, 2, . . . , r are the vertices of the tree adjacent to a0; each ai is the center of a diameter four tree, each bj is the center of a star, and each ck is a pendant vertex. Here we give graceful labelings to some new classes of diameter six trees (a0; a1, a2, . . . , am; b1, b2, . . . , bn; c1, c2, . . . , cr) in which the branches of a diameter four tree incident on a0 are of same type, i.e. either they are all odd branches or even branches. Here by a branch we mean a star, i.e. we call a star an odd branch if its center has an odd degree and an even branch if its center has an even degree.Publisher's Versio

A Class Of Diameter Six Graceful Trees

In this paper we give graceful labelings to diameter six trees( a1, a2, . . . , am; b1, b2, . . . , bn; c1, c2, . . . , csatisfying the following property: m + n is odd, degree of each neighbour of a0 is even, and the centers of the branches incident on the center ai of diameter four trees are either all odd branches or all even branches

A Class of ‘n’ Distant Graceful Trees

In this paper we show that a tree T with the following properties have graceful labeling. 1) T has a path H such that every pendant vertex of T has distance n (a fixed positive integer) from H. 2) Every vertex of T excluding one end vertex of H has even degree. Key words: Graceful labeling; n distant tree; Component moving transformation; Transfer of the first typ

Cross-stream migration of drops suspended in Poiseuille flow in the presence of an electric field

The present study focuses on the cross-stream migration of a neutrally buoyant two-dimensional drop in a Poiseuille flow in a channel under the influence of an electric field. In the absence of an electric field, the important nondimensional parameters describing this problem are the viscosity ratio (λ) between the drop fluid and the surrounding medium, the ratio of drop diameter to channel height (a∗), and the capillary number (Ca). The influence of all these parameters on drop migration is investigated. It is observed that a large drop moves slowly as compared to a smaller drop, but attains a steady shape at the center line of the channel. The increase in value of the capillary number enhances the cross-stream migration rate, while the increase in viscosity ratio reduces the tendency of the drops to move towards the channel center line. The presence of an electric field introduces additional interfacial stresses at the drop interface, which in turn alters the dynamics observed in the absence of an electric field. Extensive computations are carried out to analyze the combined effect of the electric field and the shear flow on the cross-stream migration of the drop. The computational results for a perfect dielectric indicate that the droplet migration enhances in the presence of an electric field. The permittivity ratio (S) and the electric field strength (E) play major roles in drop migration and deformation. Computations using the leaky dielectric model also show that for certain combinations of electrical properties the drop undergoes immense elongation along the direction of the electric field. The conductivity ratio (R) is again a vital parameter in such a system of fluids. It is further observed that for certain conditions the leaky dielectric drops exhibit rotation together with translation

PERFORMING PREDICTIVE DATA ANALYTICS IN DATA MINING USING VARIOUS TOOLS

Predictive Data Analytics is a branch of Data Mining. Performing Predictive Data Analytics on huge data sets will help us in quick Decision Making forecasting on the results obtained on live or sample data. Data mining, the extraction of hidden predictive information from large databases, is a powerful new technology with great potential to help companies or individuals to focus on the most important information in their data warehouses. This paper helps us in specifying how to do Predictive Data Analytics in data mining using various tools. There are various Open Source Tools which help us in performing Predictive Analytics such as R Studio, Weka, KNIME etc. This paper also lists various predictive analytic tools and specify there features and usage. A comparison also can be made or decision can be taken by the reader to use a specific tool based on the requirement. The main scope is to enhance the study of predictive data analysis and provide the necessary help in quick decision making in any of the important area. Predictive data analytics can be performed in various areas such as medical, agriculture, behavior prediction of kids, behavior of a customer in a particular business etc. In this aspect the paper elaborates on the tools available to do perform predictive data analytics and also introduce the importance of data mining. Predictive data analysis is done using variables as attributes known as predictors. This paper also includes information about Knowledge Discovery Process which is a part of Data Mining

Coalescence dynamics of a hollow droplet falling in a liquid pool

The partial coalescence dynamics of a hollow droplet in a liquid pool is numerically investigated. We study the effect of the ratio of the inner to outer radii (Rr) of the hollow droplet while maintaining a constant volume. It is observed that for small values of the radius ratio, the coalescence dynamics is similar to that of a ‘filled’ droplet, but the partial coalescence is suppressed for large values of Rr. Increasing the value of increases the distance migrated by the inner bubble in the downward direction inside the pool away from the free surface. The location of the bubble after coalescence is found to play an important role in the pinch-off process of the satellite droplet. The influence of the governing dimensionless parameters on the coalescence dynamics has also been investigated

Assessment of ecosystem services of rice farms in eastern India

Authors acknowledge the financial help provided by Ministry of Earth Sciences, Govt. of India and also thank Director General, Indian Council of Agricultural Research (ICAR) and Director, ICAR-National Rice Research Institute (NRRI) for giving all the necessary help in executing the work. The help provided by Odisha state officials in carrying out the survey work is gratefully acknowledged. This study is a part of the project entitled “Delivering food security on limited land (DEVIL; Belmont Forum / FACCE-JPI via NERC: NE/M021327/1).Peer reviewedPublisher PD

Dynamics of Hot QCD Matter -- Current Status and Developments

The discovery and characterization of hot and dense QCD matter, known as Quark Gluon Plasma (QGP), remains the most international collaborative effort and synergy between theorists and experimentalists in modern nuclear physics to date. The experimentalists around the world not only collect an unprecedented amount of data in heavy-ion collisions, at Relativistic Heavy Ion Collider (RHIC), at Brookhaven National Laboratory (BNL) in New York, USA, and the Large Hadron Collider (LHC), at CERN in Geneva, Switzerland but also analyze these data to unravel the mystery of this new phase of matter that filled a few microseconds old universe, just after the Big Bang. In the meantime, advancements in theoretical works and computing capability extend our wisdom about the hot-dense QCD matter and its dynamics through mathematical equations. The exchange of ideas between experimentalists and theoreticians is crucial for the progress of our knowledge. The motivation of this first conference named "HOT QCD Matter 2022" is to bring the community together to have a discourse on this topic. In this article, there are 36 sections discussing various topics in the field of relativistic heavy-ion collisions and related phenomena that cover a snapshot of the current experimental observations and theoretical progress. This article begins with the theoretical overview of relativistic spin-hydrodynamics in the presence of the external magnetic field, followed by the Lattice QCD results on heavy quarks in QGP, and finally, it ends with an overview of experiment results.Comment: Compilation of the contributions (148 pages) as presented in the `Hot QCD Matter 2022 conference', held from May 12 to 14, 2022, jointly organized by IIT Goa & Goa University, Goa, Indi