In this paper, an effective method is proposed called the “Dynamic Routh’s stability Criterion (DRSC)”, which is developed using the Dynamic Pole Motion (DPM) approach (DPMA). This innovative technique extends the classical Routh’s stability criterion—traditionally limited to linear time-invariant (LTI) systems—to encompass a broader range of systems, including linear time-varying and nonlinear dynamic systems. By incorporating the behavior of pole trajectories over time, the proposed method offers a more comprehensive framework for analyzing system stability in more complex and realistic scenarios. DPM approach describes the notion of dynamic poles (DP) in a three dimensional ‘g-plane’, which is an extension to the two dimensional ‘s-plane’. The s-domain approach is based upon Laplace transform and has been used for linear time-invariant (LTI) system only. This novel g-plane framework is versatile enough to be applied to both linear and nonlinear dynamic systems. For the stability of dynamic systems, the DP must present in the left-hand side (LHS) of the g-plane. For nonlinear systems, the locations of DP are the function of system states; and these systems states are the function of initial conditions with amplitude and frequency (AnF) of input signals. Therefore, in nonlinear systems, stability is influenced not only by the initial conditions but also by the AnF of the input signals. For example, for given amplitude of the input signal, system may be unstable at low frequency; however, it may become stable at high frequency or vice-versa. These stability conditions are illustrated by several examples.

Biological active Schiff base (HPMBP) was prepared from 2,4-Diamino-6hydroxypyrimidine and 5-bromo-2-hydroxybenzaldehyde by condensation method.A series of novel Ni[II], Cu[II] Co(II), Zn(II) and Mn(II) complexes have been synthesized from Schiff base ligand (HPMBP).The structural features and physical properties of Schiff base ligand (HPMBP)and their metal complexes were explored from spectral characterization techniques such as 1 H NMR, 13 C NMR, Mass, FT-IR spectra, P-XRD and TGA.The spectral analysis data shows that the metal complexes have composition of ML(1:1) type.The P-XRD data propose monoclinic crystal system for Ni(II), Co(II), Zn(II), Mn(II) complexes and orthorombhic crystal system for Cu(II) complex.The bio-efficiency of ligand and its transition metal complexes have been tested against three gram +ve /gram -ve bacteria (Staphylococcus aureus, Pseudomonas aeruginosa and Klebsiella pneumonia) and four fungi (Penicillium chrysogenum, Trichoderma viride, Aspergillus niger and Candida albicans) in vitro to examine their microbial activity.The bioactivity data reveals that the metal complexes showed good antifungal and antibacterial activity than the Schiff base ligand (HPMBP).

Functional soup is one of the possible goods that could be turned into an immediate meal.Dried soups are essential for meeting societal standards from consumers.Food that has been dehydrated, particularly dry soup mixes, has several benefits.These include resistance to oxidative and enzymatic deterioration and the capacity to maintain flavour for extended periods of time-up to a year at ambient temperature.Because it is easy to prepare, takes little time to serve, and provides the body with the necessary energy and nutrients, functional soup may replace traditional morning fare.For dried soups to be of high quality, added additives, their useful qualities, and their ratio are important considerations.Legumes and vegetables are added to it to preserve its nutritional content.Out of these few have been evaluated for the medicines.From many plants only extract have been prepared and evaluated for their usefulness and it tested diabetes in animals.This article may act as tool to abreast with the Phytochemical, Antioxidant, Antidiabetic test for dried bean powder and Proximate Analysis for soup powder.The IC50 value for antioxidant activity and anti-diabetic activity of ethanolic bean extracted from Cyamopsis tetragonoloba was found to be 415.986g/ml, 540.137g/ml, and 389.354 g/ml respectively.The Proximate analysis which includes Carbohydrate, Protein, Lipid, Moisture content and Ash was found to be 7.42 mg/ml, 3.54 mg/ml, 0.85 mg/ml, 82%, 0.79%.The soup mix formulation in the present study reported higher antidiabetic activity as compared to those reported in the literature.

In Indian financial market, there are various kind of investing tools are present whether its short-term investment or long-term investment.It's difficult task to investors to select the appropriate investment for themselves.Each and Every investor has a different mindset when they choose a certain investment avenue for own.In differ stages, every investor expects that his/her well deserved money to put into a secure and healthier investment.This study Analyze the influence of investors income on the choice of short-term investment or long-term investment.To achieve this, 100 respondents of Delhi, were surveyed.As a result, also focus those specific factors like gender, age, awareness regarding the investment avenues, occupation etc. can influence the decision.Further, it noted that income level of investors can influences the choice of the investor's decisions.

In recent years, the proliferation of deep fake images and other manipulated media has raised significant concerns about the authenticity of digital content.The advent of Generative Adversarial Networks (GANs) has enabled the generation of highly realistic fake images, posing new challenges in image forensics and security.This paper explores the application of GANs and deep learning models for the detection of fake images.By leveraging the unique architecture of GANs-comprising a generator and a discriminator-alongside advanced deep learning techniques, we propose a robust framework capable of distinguishing between real and synthetic images with high accuracy.Our approach integrates convolutional neural networks (CNNs) for feature extraction, deep residual networks (ResNet) for complex pattern recognition, and GAN-based anomaly detection to enhance the system's ability to identify subtle manipulations.Experimental results demonstrate that the proposed model outperforms traditional methods, achieving superior detection rates on a variety of benchmark datasets.This work highlights the potential of GANs not only as a tool for image generation but also as a powerful asset in the fight against digital misinformation, providing a critical layer of defense in the detection of fake imagery.