The theory of probabilistic programming  may be conceived in several different ways. As a method of programming it analyses the implications of probabilistic variations in the parameter space of linear or nonlinear programming model. The generating mechanism of such probabilistic variations in the economic models may be due to incomplete information about changes in demand, pro­duction and technology, specification errors about the econometric relations presumed for different economic agents, uncertainty of various sorts and the consequences of imperfect aggregation or disaggregating of economic variables. In this Research we discuss the probabilistic programming problem when the coefficient b_i is random variable

Viruses have not previously been reported to act as chemotactic/chemoattractive agents. Rather, viruses as extracellular entities are generally viewed as non-metabolically active spore-like agents that await further infection events upon collision with appropriate host cells. That a virus might actively contribute to its fate via chemotaxis and change the behavior of an organism independent of infection is unprecedented.

Lignin has emerged as a promising asphalt binder modifier due to its sustainable and renewable nature, with the potential to improve flexible pavement performance. This study investigates the use of Soda Lignin Powder (SLP), derived from Pinus wood sawdust via alkaline treatment, as an asphalt modifier to enhance mixture durability. SLP was characterized using Fourier Transformation Infrared Spectroscopy (FTIR), X-ray Diffraction (XRD), and Scanning Electron Microscopy with Energy Dispersive X-ray Analysis (SEM/EDX), revealing significant changes in its chemical structure post-extraction. These analyses showed the presence of phenolic units, including hydroxyphenyl propane, syringyl, and guaiacyl units. The morphology of SLP was identified

We explore the transform coefficients of fractal and exploit new method to improve the compression capabilities of these schemes. In most of the standard encoder/ decoder systems the quantization/ de-quantization managed as a separate step, here we introduce new way (method) to work (managed) simultaneously. Additional compression is achieved by this method with high image quality as you will see later.

This work, deals with Kumaraswamy distribution. Kumaraswamy (1976, 1978) showed well known probability distribution functions such as the normal, beta and log-normal but in (1980) Kumaraswamy developed a more general probability density function for double bounded random processes, which is known as Kumaraswamy’s distribution. Classical maximum likelihood and Bayes methods estimator are used to estimate the unknown shape parameter (b). Reliability function are obtained using symmetric loss functions by using three types of informative priors two single priors and one double prior. In addition, a comparison is made for the performance of these estimators with respect to the numerical solution which are found using expansion method. The