In this research, some probability characteristics functions (probability density, characteristic, correlation and spectral density) are derived depending upon the smallest variance of the exact solution of supposing stochastic non-linear Fredholm integral equation of the second kind found by Adomian decomposition method (A.D.M)

Abstract:In this paper, some probability characteristics functions (moments, variances,convariance, and spectral density functions) are found depending upon the smallestvariance of the solution of some stochastic Fredholm integral equation contains as aknown function, the sine wave function

في هذا البحث نحاول تسليط الضوء على إحدى طرائق تقدير المعلمات الهيكلية لنماذج المعادلات الآنية الخطية والتي تزودنا بتقديرات متسقة تختلف أحيانا عن تلك التي نحصل عليها من أساليب الطرائق التقليدية الأخرى وفق الصيغة العامة لمقدرات K-CLASS. وهذه الطريقة تعرف بطريقة الإمكان الأعظم محدودة المعلومات "LIML" أو طريقة نسبة التباين الصغرى"LVR

There are two (non-equivalent) generalizations of Von Neuman regular rings to modules; one in the sense of Zelmanowize which is elementwise generalization, and the other in the sense of Fieldhowse. In this work, we introduced and studied the approximately regular modules, as well as many properties and characterizations are considered, also we study the relation between them by using approximately pointwise-projective modules.

The main objective and primary concern to every investor not only to achieve a greater return on his or her investments, but also to create the largest possible value of these investments the, researchers and those interested in the field of investment and financial analysis  try to develop standards  for performance      valuation      is guided through the                                     &nbsp

In this paper, Touchard polynomials (TPs) are presented for solving Linear Volterra integral equations of the second kind (LVIEs-2k) and the first kind (LVIEs-1k) besides, the singular kernel type of this equation. Illustrative examples show the efficiency of the presented method, and the approximate numerical (AN) solutions are compared with one another method in some examples. All calculations and graphs are performed by program MATLAB2018b.