Effective SO Superpotential for N=1 Theory with N_f Fundamental Matter

Motivated by the duality conjecture of Dijkgraaf and Vafa between supersymmetric gauge theories and matrix models, we derive the effective superpotential of N=1 supersymmetric gauge theory with gauge group SO(N_c) and arbitrary tree level polynomial superpotential of one chiral superfield in the adjoint representation and N_f fundamental matter multiplets. For a special point in the classical vacuum where the gauge group is unbroken, we show that the effective superpotential matches with that obtained from the geometric engineering approach.Comment: LaTeX, 1+19 pages, To appear in Nucl.Phys.

Composite Representation Invariants and Unoriented Topological String Amplitudes

Sinha and Vafa \cite {sinha} had conjectured that the $SO$ Chern-Simons gauge theory on $S^3$ must be dual to the closed $A$-model topological string on the orientifold of a resolved conifold. Though the Chern-Simons free energy could be rewritten in terms of the topological string amplitudes providing evidence for the conjecture, we needed a novel idea in the context of Wilson loop observables to extract cross-cap $c=0,1,2$ topological amplitudes. Recent paper of Marino \cite{mar9} based on the work of Morton and Ryder\cite{mor} has clearly shown that the composite representation placed on the knots and links plays a crucial role to rewrite the topological string cross-cap $c=0$ amplitude. This enables extracting the unoriented cross-cap $c=2$ topological amplitude. In this paper, we have explicitly worked out the composite invariants for some framed knots and links carrying composite representations in $U(N)$ Chern-Simons theory. We have verified generalised Rudolph's theorem, which relates composite invariants to the invariants in $SO(N)$ Chern-Simons theory, and also verified Marino's conjectures on the integrality properties of the topological string amplitudes. For some framed knots and links, we have tabulated the BPS integer invariants for cross-cap $c=0$ and $c=2$ giving the open-string topological amplitude on the orientifold of the resolved conifold.Comment: 1+17 pages, condensed version of arXiv/1003.5282 to appear in Nucl. Phys.

U(N) Framed Links, Three-Manifold Invariants, and Topological Strings

Three-manifolds can be obtained through surgery of framed links in $S^3$. We study the meaning of surgery procedures in the context of topological strings. We obtain U(N) three-manifold invariants from U(N) framed link invariants in Chern-Simons theory on $S^3$. These three-manifold invariants are proportional to the trivial connection contribution to the Chern-Simons partition function on the respective three-manifolds. Using the topological string duality conjecture, we show that the large $N$ expansion of U(N) Chern-Simons free energies on three-manifolds, obtained from some class of framed links, have a closed string expansion. These expansions resemble the closed string $A$-model partition functions on Calabi-Yau manifolds with one Kahler parameter. We also determine Gopakumar-Vafa integer coefficients and Gromov-Witten rational coefficients corresponding to Chern-Simons free energies on some three-manifolds.Comment: Some clarifications added. Final version to appear in NP

Smart Surge Irrigation Using Microcontroller Based Embedded Systems and Internet of Things

Surge Irrigation is a type of furrow irrigation and one of many efficient irrigation techniques. It is one of the economical techniques and requires minimum labor for monitoring it. In surge irrigation, water is applied intermittently to a field to achieve uniform distribution of water along the furrows, which is important while irrigating, as it ensures that there is enough water near the root zone of the crop. The uneven distribution can cause a loss in crop productivity. Surge irrigation uses a surge valve, which is an electro-mechanical device that irrigates a field. The commercial surge valves available on the market are made to control only the time for the irrigation. However, their functionality is limited and requires human intervention to control and monitor the irrigation process. Therefore, monitoring the irrigation with these controllers is a big challenge. The lack of monitoring may result reduced irrigation efficiency. The purpose of this thesis is to design and develop an embedded system for surge irrigation that resolves the drawback associated with the commercial surge valves. In this thesis, a “Surge Controller” is designed, implemented, and tested on the farm. The surge controller is a microcontroller-based embedded system, which runs the real-time operating system FreeRTOS on a single core ARM Cortex M3 microcontroller for multitasking. The important feature, which makes the surge controller “Smart”, is the Internet of Things (IoT) that enables the controller to send irrigation data over the Internet to a remote station. During the Spring and Summer, 2017, the surge controller was developed and tested in the field at Rice Research and Extension Center of the University of Arkansas. Five irrigation events were run in a 20 acres soybean field. The controller was tested for the durability of the components in the environment and field conditions, performance and overall feasibility of the device to achieve successful results from an irrigation event. After the successful testing, the IoT feature was added in Fall 2017 and Spring 2018 and tested for its functionality by running a few irrigation events in the Laboratory. The surge controller worked as expected continuously without interruption

Addressing the needs of seasonal migrants in Nashik, Maharashtra

In order to identify the opportunities and options available to address the vulnerabilities of and socioeconomic needs of seasonal migrants, an intervention project was launched by the Disha Foundation, a nongovernmental organization in Nashik city, Maharashtra, India. This report intends to use the project experience as a case study to provide a blueprint for interventions for seasonal migrants to access a range of basic services in areas of destination and to exercise their rights to access available services. The report documents the array of strategies used to enable seasonal migrants to recognize their entitlement and to access available public sector health, education, and other social services. At the same time, it underscores the mediating role that the project played in sensitizing government and public sector service providers about recognizing the rights and accommodating the special circumstances of seasonal migrants in accessing public services on the one hand, and apprising seasonal migrants of their rights and mobilizing them to avail themselves of public sector services on the other. The lessons learned from the implementation of this project are valuable, and should have wider application among similarly disadvantaged mobile populations across the country

Synthesis, Characterisation and Antimicrobial Activity of Essential Fatty Acid of Semicarbazide

ABSTRACT Essential fatty acids are the polyunsaturated fatty acids .Only two fatty acids are known to be essential for human , alpha-linolenic acid (an omega-3 fatty acid ) & linoleic acid ( an omega-6 fatty acid ). Linum usitatissimum respectively. Chemical properties of linseed oil shows acid value 1.05 mg KOH/g oil. Its peroxide number is 0.98 Mev/Kg. Linum usitatissimum (Linseed) Seed oil is an excellent source of nutrition. Semicarbazones are potent intermediates for the synthesis of pharmaceutical and bioactive materials and thus, they are used extensively in thefield of medicinal chemistry Omega-3 -fatty acid semicarbazide of Linum usitatissimum (Linseed) seed oil was synthesized. The absorption spectra, infrared spectra and X-ray diffraction of essential fatty acid semicarbazide was studied. The antibacterial activity of essential fatty acid semicarbazide was studied. The bacteria was found to be more active

An Efficient Photocatalytic Degradation of Methyl Blue Dye by using Synthesised PbO Nanoparticles

We report here the synthesis of visible light sensitive PbO and Ni doped PbO nanoparticles by hydrothermal method and characterized by UV-DRS, photoluminescence spectroscopy (PL), FTIR, X-ray diffraction (XRD), SEM, EDAX and TGA. Further an efficient approach has been developed for degradation of methyl blue (MB) in aqueous medium. The photodegradation of dye was monitored as a function of dye concentration, pH and catalyst amount has been determined. The reduction in the chemical oxygen demand (COD) revealed the mineralization of dye along with colour removal