Riemann problem for kinematical conservation laws and geometrical features of nonlinear wavefronts

A pair of kinematical conservation laws (KCL) in a ray coordinate system (ξ,t) are the basic equations governing the evolution of a moving curve in two space dimensions. We first study elementary wave solutions and then the Riemann problem for KCL when the metric g, associated with the coordinate ξ designating different rays, is an arbitrary function of the velocity of propagation m of the moving curve. We assume that m>1 (m is appropriately normalized), for which the system of KCL becomes hyperbolic. We interpret the images of the elementary wave solutions in the (ξ,t)-plane to the (x,y)-plane as elementary shapes of the moving curve (or a nonlinear wavefront when interpreted in a physical system) and then describe their geometrical properties. Solutions of the Riemann problem with different initial data give the shapes of the nonlinear wavefront with different combinations of elementary shapes. Finally, we study all possible interactions of elementary shapes

F–Geometric Mean Graphs

In a study of traffic, the labelling problems in graph theory can be used by considering the crowd at every junction as the weights of a vertex and expected average traffic in each street as the weight of the corresponding edge. If we assume the expected traffic at each street as the arithmetic mean of the weight of the end vertices, that causes mean labelling of the graph. When we consider a geometric mean instead of arithmetic mean in a large population of a city, the rate of growth of traffic in each street will be more accurate. The geometric mean labelling of graphs have been defined in which the edge labels may be assigned by either flooring function or ceiling function. In this, the readers will get some confusion in finding the edge labels which edge is assigned by flooring function and which edge is assigned by ceiling function. To avoid this confusion, we establish the F-geometric mean labelling on graphs by considering the edge labels obtained only from the flooring function. An F-Geometric mean labelling of a graph G with q edges, is an injective function from the vertex set of G to {1, 2, 3,..., q +1} such that the edge labels obtained from the flooring function of geometric mean of the vertex labels of the end vertices of each edge, are all distinct and the set of edge labels is {1, 2, 3,..., q}. A graph is said to be an F–Geometric mean graph if it admits an F–Geometric mean labelling. In this paper, we study the F-geometric meanness of the graphs such as cycle, star graph, complete graph, comb, ladder, triangular ladder, middle graph of path, the graphs obtained from duplicating arbitrary vertex by a vertex as well as arbitrary edge by an edge in the cycle and subdivision of comb and star graph

Synthesis and solution properties of comblike polymers from octadecyl methacrylate and acrylic acid

Amphiphilic polymers consisting of a statistical distribution of octadecyl methacrylate (ODMA) and acrylic acid in respective molar ratios of 83-22 and 17-78 mol% and in a molecular-weight range of 2.35-4.70×104 gmol-1 have been synthesized. The series of polymers consisting of various mole fractions of ODMA and acrylic acid are expected to exhibit unique characteristics resembling ionomer to hydrophobically modified polyelectrolytes. The changes in the I3/I1 emission intensity ratios of pyrene, occurring in the presence of tetrahydrofuran (THF) solutions of the polymers have been taken as the main basis for inferring solution structures. The polymers are found to form random-coil to collapsed-coil/aggregated structures in THF solvent depending on the copolymer compositions. The polymer consisting of 83 mol% ODMA and 17 mol% acrylic acid behaves as an ionomer, capable of forming collapsed-coil structures at concentrations of 0.02 gml-1 and above as shown by a very high I3/I1 of 1.20 (I3/I1 of pyrene in THF is 0.85). In contrast, the poly(octadecyl methacrylate) homopolymer and the sets of copolymers consisting of a very high proportion of acrylic acid to an extent of 73 mol% and above contribute to almost negligible or very small changes in I3/I1 similar to the homopolymer, poly(octadecyl methacrylate), suggesting the formation of random-coil structures

Testing of Paraffin-based Hybrid Rocket Fuel using Gaseous Oxygen Oxidiser

A series of paraffin-based hybrid rocket fuel has been studied experimentally in a laboratory-scale motor. To enhance the regression rate of paraffin solid fuel, three types of grain configurations: Cylindrical, star, and helical grain configurations of paraffin wax have been developed and tested with gaseous oxygen. The helical fuel grain presented best performance among all the test ports. About 40.2 per cent and 20.6 per cent regression rates are increased by burning paraffin fuel with helical and star grain configuration respectively, as compared to cylindrical grain configuration at Gox=0.0191 g/mm2s. The regression rates were significantly influenced by the oxygen injection pressure varied between 344.7 kPa and 620.5 kPa. Furthermore, the experimentally obtained exponents of oxidizer mass flux for all three grain configurations have been found to be significantly different from those of the classical hybrid system. Finally, thrust-time traces for all three grain configurations were also studied. The result shown no significant increase or decrease in the amplitude of the thrust oscillations.Defence Science Journal, 2012, 62(5), pp.277-283, DOI:http://dx.doi.org/10.14429/dsj.62.234

Social Media Communication and Customer Loyalty with the Mediating Role of Social Customer Relationship in Retail Chain Stores in Sri Lanka

The main aim of this study is to investigate the impact of social media communication on customer loyalty and social customer relationship and examine the mediating role of social customer relationship between social media communication and customer loyalty. An online survey was used to gather information from followers of retail chain store Facebook pages in Sri Lanka, total of 340 respondents were invited to collect the information. The proposed model was tested using structural equation modeling, and confirmatory factor analysis was used to assess the reliability and validity. The main finding of this study is that the social media communication influences consumer loyalty and social customer relationships positively, while social customer relationships partially mediate the relationship between social media communication and customer loyalty among customers of retail chain stores in Sri Lanka. Retail chains use many marketing communication tools to attract and retain their customers, they should dedicate their effort to implement social media communication as one of the marketing communication media strategy for improved customer loyalty. Keywords:Social media communication, social customer relationship, Customer loyalty, Marketing communication strategy DOI: 10.7176/EJBM/13-14-09 Publication date:July 31st 202

Advertisements on TV or Online: Which makes customers more likely to buy? With the mediating role of length of the video

This research investigates the intricate dynamics influencing consumer behavior in the context of television (TV) advertising, online advertisements, video length, and purchase intentions. With the primary objectives of assessing the impact of TV advertising and online advertisements on consumer behavior, the study formulates and tests hypotheses related to these relationships. Utilizing a quantitative approach and the sample survey method, the study employs Structural Equation Modeling (SEM) to analyze the interrelationships between the selected variables within a sample of 400 participants in Sri Lanka. Acceptance of hypotheses H1 and H2 underscores the substantial impact of TV advertising and online advertisements on consumer behavior. Standardized regression coefficients indicate significant positive relationships between TV advertising and both consumer purchase intention and video length. Similarly, a distinct influence of online advertisements is highlighted, demonstrating a substantial positive relationship with consumer purchase intention. Examining direct paths from TV advertising and online advertisements to consumer purchase intention, with video length as a mediating variable, suggests partial mediation. These findings provide actionable insights for marketers, emphasizing the intricate relationships among advertising mediums, content characteristics, and consumer decision-making. Keywords: TV Advertisement, Online Advertisement, Length of video and Consumer purchase intention. DOI: 10.7176/JMCR/91-06 Publication date: December 30th 202

Multi-Objective Optimization in Friction Welding Process Parameters on EN353 Alloy Steel using Taguchi based GRA

Joining of similar materials by varying the input factors on a continuous drive friction welding process is done in this study. The intention is to find the optimal solution in friction welding input process parameters. Among several types of welding processes, friction welding forms good metal joints. The process factors considered for this material joining practice are Upset Time (UT), Heating Time (HT), Heating Pressure (HP), Upset Pressure (UP), chemical composition and measurements of the materials. Frictional joints provide better mechanical properties, hence it is attracted by researchers. Here, EN353 is used as the specimen, for its extensive usage in the automobile and manufacturing sectors. Axial shortening, hardness testing and the temperature during welding are evaluated, compared and optimized using Taguchi Design of Experiments (DoE) scheme using L27 orthogonal array and Grey Relational Analysis (GRA)

Size and weight reduction in Holothuria scabra processed as beche-de-mer

Growing demand for beche-de-mer in the marine export market has naturally led to considerable debate among fishery biologists in our country on the problem of irrational exploitation of the natural stock. Along the Tamil Nadu coast Holothuria scabra is fished for beche-de-mer preparation. Studies on the size at first maturity indicated that the spawning size is 201-230 mm and this size group after processing attains a reduced size of 73-80 mm. Revival of the natural stock can take place and this would help in encountering specimens beyond the size of 75 mm in length. More studies are required on the biology of Holothurians to determine precisely the period of maturity and spawning in different species in a year and it is advisable to observe a 'closed season' each year to conserve the holothurian resources