In this paper, the delay integral equations in population growth will be described,discussed , studied and transfered this model to integro-differential equation. At last,we will solve this problem by using variational approach.

Modern agriculture is challenged by soil degradation, nutrient depletion, plant diseases, and excessive dependence on chemical fertilizers and pesticides. By examining different strains of Pantoea, the study highlights their role in promoting plant growth, improving their tolerance to stress, reducing reliance on synthetic agricultural inputs, and contributing to more sustainable and environmentally friendly agricultural practices. Using a combination of practical qualitative methods and reliable quantitative data, the research gathers extensive information on how these microbes impact various crops and key soil health indicators. The improvements in plant growth statistics and nutrient levels are often quite astonishing. The result

Modern agriculture is challenged by soil degradation, nutrient depletion, plant diseases, and excessive dependence on chemical fertilizers and pesticides. By examining different strains of Pantoea, the study highlights their role in promoting plant growth, improving their tolerance to stress, reducing reliance on synthetic agricultural inputs, and contributing to more sustainable and environmentally friendly agricultural practices. Using a combination of practical qualitative methods and reliable quantitative data, the research gathers extensive information on how these microbes impact various crops and key soil health indicators. The improvements in plant growth statistics and nutrient levels are often quite astonishing. The result

The advancements in Information and Communication Technology (ICT), within the previous decades, has significantly changed people’s transmit or store their information over the Internet or networks. So, one of the main challenges is to keep these information safe against attacks. Many researchers and institutions realized the importance and benefits of cryptography in achieving the efficiency and effectiveness of various aspects of secure communication.This work adopts a novel technique for secure data cryptosystem based on chaos theory. The proposed algorithm generate 2-Dimensional key matrix having the same dimensions of the original image that includes random numbers obtained from the 1-Dimensional logistic chaotic map for given con

Abstract

  Bivariate time series modeling and forecasting have become a promising field of applied studies in recent times. For this purpose, the Linear Autoregressive Moving Average with exogenous variable ARMAX model is the most widely used technique over the past few years in modeling and forecasting this type of data. The most important assumptions of this model are linearity and homogenous for random error variance of the appropriate model. In practice, these two assumptions are often violated, so the Generalized Autoregressive Conditional Heteroscedasticity (ARCH) and (GARCH) with exogenous varia

The objective of the study to develop an amorphous solid dispersion for poorly soluble raltegravir by hot melt extrusion (HME) technique. A novel solubility improving agent plasdone  s630 was utilized. The HME raltegravir was formulated into tablet by direct compression method. The prepared tablets were assessed for all pre and post-compression parameters. The drug- excipients interaction was examined by FTIR and DSC. All formulas displayed complying with pharmacopoeial measures. The study reveals that formula prepared by utilizing drug and plasdone S630 at 1:1.5 proportion and span 20 at concentration about 30mg (trail-6) has given highest dissolution rate than contrasted with various formulas of raltegravir.

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