Mass Gap in U(1) Higgs-Yukawa model on a unit lattice

A non perturbative proof of the mass generation of fermions via the Higgs mechanism is given. This is done by showing exponential decay of the two point fermionic correlation function in a weakly coupled U(1) Higgs-Yukawa theory on a unit lattice in $d=4$. This decay implies that the Higgs boson, the photon and the fermion all have a non zero physical mass and the theory is said to have a mass gap.Comment: Remarks addressing fermion doubling and chiral invariance added in the introduction. References updated. Typos correcte

The Variational Problem and Background Field in Renormalization Group Method for Non-Linear Sigma Models

We study the variational problem as described by Balaban in his renormalization group method for Yang-Mills theories in $d= 3, 4$ and adapt it to a class of Non-Linear Sigma Models in $d=2$. The result of the variational problem is a minimal configuration which serves as a classical background field in the renormalization group analysis.Comment: 18 page

Embedding Cosmology and Gravity

I start with a scenario where the universe is an abstract space $\mathcal{M}$ having $d$ dimensions. There is a two dimensional surface (dark surface) embedded in it. Sigma model treats embedding as scalar fields. I take these $d$ directions to be the generators of a symmetry group SU(n) of the Lagrangian theory of embedding under Sigma model. This means embedding has n flavors. Then I introduce spontaneous symmetry breaking in the theory and define the direction along which the symmetry breaking occurs as time. Next I write down the modified Einstein's equation including the embedding. Then I discuss embedding's relation to the expansion of the universe. After that I construct an inflationary scenario with embedding as inflaton and discuss its connection to Starobinsky $R^{2}$ model. Finally, I discuss the effect of inflation on the non-commutativity of the spacetime.Comment: An inflationary scenario with embedding as inflaton is added. How one axis becomes the time axis and why the observable universe is 1+3 dimensional is also explained. Other minor changes, 16 page

Learning on stage

Theatre workshop provides a platform where children can come out of their regimented academic pattern and explore various faculties for their holistic development. Many believe that schools are not providing the right ambiance for children to grow as free and independent thinkers. They instead encourage competition, social division and make children believe that one’s success is someone’s failure. This kills spontaneity and naturalness in children and makes way for the development of a regimented mind

Conservation of Tubulin-Binding Sequences in TRPV1 throughout Evolution

Transient Receptor Potential Vanilloid sub type 1 (TRPV1), commonly known as capsaicin receptor can detect multiple stimuli ranging from noxious compounds, low pH, temperature as well as electromagnetic wave at different ranges. In addition, this receptor is involved in multiple physiological and sensory processes. Therefore, functions of TRPV1 have direct influences on adaptation and further evolution also. Availability of various eukaryotic genomic sequences in public domain facilitates us in studying the molecular evolution of TRPV1 protein and the respective conservation of certain domains, motifs and interacting regions that are functionally important. analysis reveals that the TBS-1 and TBS-2 of TRPV1 can form helical structures and may play important role in TRPV1 function.Our analysis identifies the regions of TRPV1, which are important for structure – function relationship. This analysis indicates that tubulin binding sequence-1 (TBS-1) near the TRP-box forms a potential helix and the tubulin interactions with TRPV1 via TBS-1 have evolutionary significance. This interaction may be required for the proper channel function and regulation and may also have significance in the context of Taxol®-induced neuropathy

DEVELOPMENT OF LOW-COST FILTERS FOR THE TREATMENT OF WATER POLLUTED WITH FOOD WASTE LEACHATE

This study investigates the efficacy of conventional and modified bio-sand filters as a low-cost filtering device for the treatment of groundwater contaminated with food waste leachate. Two kinds of waste materials, areca nut husk and water hyacinth stems, have been selected to alter the bio-sand filter. In conventional bio-sand filters, the ashes of these wastes are used as a filter medium. The ashes\u27 physical characteristics, such as pH, ash content, and moisture content, have been measured. In leachate polluted water and purified water, tests for total solids, acidity, alkalinity, hardness, chloride content, pH, turbidity, dissolved oxygen, biological oxygen demand, and chemical oxygen demand have been performed. According to the testing findings, the developed filters are efficient in decreasing chloride, hardness, turbidity, chemical oxygen demand, and biological oxygen demand. The same filters have also detected an increase in dissolved oxygen. According to this study, these low-cost filters might be used as a preliminary treatment system for leachate created by food waste recycling plants

Sustainable tourism development in Vietnam: a case of Hue

This study aims to further integrate sustainability into the social and cultural practices of Hue. It offers an analysis of current strategies that inform decision-making in Hue’s tourism sector and makes suggestions that could further improve the existing policies. Even though Hue is a city with great potential, it is facing a number of challenges brought on by environmental degradation and uncontrolled urbanisation. Researchers point to a number of issues that impede the social, economic, and environmental development of Hue. Attention is paid to cultural events and sustainable urban development. Findings suggest that current cultural preservation efforts offer a solid foundation for future cultural development though community participation and cultural education are needed to facilitate further growth. This descriptive study employs comprehensive literature review and the Four Sphere sustainability framework to guide data collection and analysis. Further, thematic analysis is used to interpret the various aspects of the current tourism development strategies in Hue. This holistic approach highlights how different policy decisions within Hue guide the destination's development and its ability to preserve and support its human, natural and cultural capitals