Advanced Higher Algebra Ghosh And Chakraborty Pdf Free !LINK!
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In this paper, we provide a scheme to compute the absolute free energy of a smectic-A phase via the "indirect method." The state of interest is connected through a three-step reversible path to a reference state. This state consists of a low-density layer of rods coupled to two external fields maintaining these rods close to the layer's plane and oriented preferably normal to the layer. The low-density free energy of the reference state can be computed on the basis of the relevant second virial coefficients between two rods coupled to the two external fields. We apply this technique to the Gay-Berne potential for calamitics with a parameter set leading to stable isotropic (I), nematic (N), smectic-A (SmA), and crystal (Cr) phases. We locate the I-SmA phase transition at low pressure and the sequence of phase transitions I-N-SmA along higher-pressure isobars and we establish the location of the I-N-SmA triple point. Close to this triple point, we show that the N-SmA transition is clearly first order. Our results are compared to the coexistence lines of the approximate phase diagram elucidated by de Miguel et al. [J. Chem. Phys. 121, 11183 (2004), 10.1063/1.1810472] established through the direct observation of the sequence of phase transitions occurring along isobars under heating or cooling sequences of runs. Finally, we discuss the potential of our technique in studying similar transitions observed on layered phases under confinement.
The inseparable relationship between energy production and water resources has led to the emerging energy-water nexus concept, which provides a means for integrated management and decision making of these two critical resources. However, the energy-water nexus frequently involves decision makers with different and competing management objectives. Furthermore, there is a challenge that decision makers and stakeholders might be making decisions sequentially from a higher level to a lower level, instead of at the same decision level, whereby the objective of a decision maker at a higher level should be satisfied first. In this study, a bi-level decision model is advanced to handle such decision-making situations for managing the energy-water nexus. The work represents a unique contribution to developing an integrated decision-support framework/tool to quantify and analyze the tradeoffs between the two-level energy-water nexus decision makers. Here, plans for electricity generation, fuel supply, water supply, capacity expansion of the power plants and environmental impacts are optimized to provide effective decision support. The developed decision-support framework is implemented in Julia (a high-level, high-performance dynamic programming language for technical computing) and is a part of the MADS (Model Analyses & Decision Support) framework ( ). To demonstrate the capabilities of the developed methodology, a series of analyses are performed for synthetic problems consistent with actual real-world energy-water nexus management problems.
Developing the manufacture of aspheric and freeform optical elements requires an advanced metrology method which is capable of inspecting these elements with arbitrary freeform surfaces. In this dissertation, a new surface measurement scheme is investigated for such a purpose, which is to measure the absolute surface shape of an object under test through its surface slope information obtained by photogrammetric measurement. A laser beam propagating toward the object reflects on its surface while the vectors of the incident and reflected beams are evaluated from the four spots they leave on the two parallel transparent windows in front of the object. The spots' spatial coordinates are determined by photogrammetry. With the knowledge of the incident and reflected beam vectors, the local slope information of the object surface is obtained through vector calculus and finally yields the absolute object surface profile by a reconstruction algorithm. An experimental