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The concepts of Neutrosophic secure edge domination number and neutrosophic total secure edge domination number in single valued neutrosophic graphs (SVNG) with strong arcs are introduced and analysed in this paper, and some of their properties are studied. The relationship between the neutrosophic secure edge dominance number and its inverse is presented. The concepts inverse neutrosophic total edge domination set and inverse neutrosophic total edge domination number are also defined. Some of these concepts' properties are investigated.

The purpose of this study is to understand one of the earliest known non-brass double-reed instrument called Nagasuram (Nadaswaram). Our ancestors while defining Tamil music grammar in parallel focused on sound engineering, which helped them to invent new musical instruments. Sangam era alone saw more than 30 percussion and wind instruments. Among them, few instruments like Veenai, Urumi and Nagasuram are worth mentioning since their design techniques were known only to a handful of families. Their performance really stands out due to their versatile and adaptable nature to all genres of music. Music instrument, like any other scientific invention goes through the same process of trial and error before getting standardized for general use. Instruments with strong adherence to scientific and acoustic principles gain prominence among the rest, as they undergo minimal structural changes. Nagasuram (Nadaswaram) is one such instrument, which was passed on to us for generations. This instrument readily complies with acoustic principles such as sound impedance, Helmholtz resonance, wave theory etc. to get the characteristic of a loudest non-brass wind instrument.

In this paper, we introduce the concept of balanced neutrosophic graphs based on density functions and investigate some of their properties. The necessary conditions for a neutrosophic graph to be a balanced neutrosophic graph are identified if graph G is a selfcomplementary, regular, complete, and strong neutrosophic graph. Some properties of complement neutrosophic graphs are presented here.

Waste water recycling may cater to the water scarcity problems which are prevailing in our daily life. The conventional studies in photocatalytic degradation of organic dyes use some specifically synthesized metal-oxide nanoparticles as photocatalyst, which may leave its traces as residue in degraded water. In this prototypical study, we have reported for the first time about light induced organic dyes degradation of methylene blue (MB), malachite green (MG) and congo red (CR) carried out using a novel photosensitizing agent, Spirulina platensis cultivated water (Spcw). The aim of the present study is to probe a simple, novel, an eco-friendly and a cost effective degradation of dyes without using any chemicals. It was observed that 15 ppm MB, 70 ppm MG and 6 ppm CR got degraded to 100% within 2, 1 and 3 h respectively. The presence of trace amount of elements such as Ca, Cu, Fe, K, Mg, Mn, Na, Mo, Co and Zn and phycobiliproteins found in the Spcw were analyzed using Fourier Transform Infra-Red (FT-IR) Spectroscopy, Inductively Coupled Plasma Optical Emission Spectroscopy (ICP-OES), Scanning Electron Microscopy - Energy Dispersive X-ray Spectroscopy (SEM–EDX), UV–vis Spectroscopy, microscopic studies and mineralization studies with TOC, TSS, BOD and COD analysis. The results obtained from various control experiments with fresh medium and dark treatment clearly confirms that the light induced organic dyes degradation occurs only in the Spcw under sunlight irradiation. The effect of pH was studied with the Spcw added dye solutions and also in the degraded water from highly acidic to basic conditions to find the optimum pH. The kinetics of the light induced organic dyes degradation follows pseudo- first order reaction and the mineralization studies of the degraded water meets the water quality standards. The reason behind the photosensitization activity is due to the presence of traces of metal ions and light absorbing phycobiliproteins released during natural cell lysis process.

In this paper, we focus on the existence of Hilfer fractional stochastic differential systems via almost sectorial operators. The main results are obtained by using the concepts and ideas from fractional calculus, multivalued maps, semigroup theory, sectorial operators, and the fixed-point technique. We start by confirming the existence of the mild solution by using Dhage’s fixed-point theorem. Finally, an example is provided to demonstrate the considered Hilferr fractional stochastic differential systems theory.

In our paper, we mainly concentrate on the existence of Hilfer fractional neutral stochastic Volterra integro-differential inclusions with almost sectorial operators. The facts related to fractional calculus, stochastic analysis theory, and the fixed point theorem for multivalued maps are used to prove the result. In addition, an illustration of the principle is provided.