In this paper, our purpose is to study the classical continuous optimal control (CCOC)  for quaternary nonlinear parabolic boundary value problems (QNLPBVPs). The existence and uniqueness theorem (EUTh) for the quaternary state vector solution (QSVS) of the weak form (WF) for the QNLPBVPs with a given quaternary classical continuous control vector (QCCCV) is stated and proved via the Galerkin Method (GM) and the first compactness theorem under suitable assumptions(ASSUMS). Furthermore, the continuity operator for the existence theorem of a QCCCV dominated by the QNLPBVPs is stated and proved under suitable conditions.

This paper introduces a non-conventional approach with multi-dimensional random sampling to solve a cocaine abuse model with statistical probability. The mean Latin hypercube finite difference (MLHFD) method is proposed for the first time via hybrid integration of the classical numerical finite difference (FD) formula with Latin hypercube sampling (LHS) technique to create a random distribution for the model parameters which are dependent on time t . The LHS technique gives advantage to MLHFD method to produce fast variation of the parameters’ values via number of multidimensional simulations (100, 1000 and 5000). The generated Latin hypercube sample which is random or non-deterministic in nature is further integrated with the FD method t

Electrical Discharge Machining (EDM) is a non-traditional cutting technique for metals removing which is relied upon the basic fact that negligible tool force is produced during the machining process. Also, electrical discharge machining is used in manufacturing very hard materials that are electrically conductive. Regarding the electrical discharge machining procedure, the most significant factor of the cutting parameter is the surface roughness (Ra). Conventional try and error method is time consuming as well as high cost. The purpose of the present research is to develop a mathematical model using response graph modeling (RGM). The impact of various parameters such as (current, pulsation on time and pulsation off time) are studied on

This paper reports experimental and computational fluid dynamics (CFD) modelling studies to investigate the effect of the swirl intensity on the heat transfer characteristics of conventional and swirl impingement air jets at a constant nozzle-to-plate distance ( L = 2 D). The experiments were performed using classical twisted tape inserts in a nozzle jet with three twist ratios ( y = 2.93, 3.91, and 4.89) and Reynolds numbers that varied from 4000 to 16000. The results indicate that the radial uniformity of Nusselt number (Nu) of swirl impingement air jets (SIJ) depended on the values of the swirl intensity and the air Reynolds number. The results also revealed that the SIJ that was fitted with an insert of y = 4.89, which correspo

The precise classification of DNA sequences is pivotal in genomics, holding significant implications for personalized medicine. The stakes are particularly high when classifying key genetic markers such as BRAC, related to breast cancer susceptibility; BRAF, associated with various malignancies; and KRAS, a recognized oncogene. Conventional machine learning techniques often necessitate intricate feature engineering and may not capture the full spectrum of sequence dependencies. To ameliorate these limitations, this study employs an adapted UNet architecture, originally designed for biomedical image segmentation, to classify DNA sequences.The attention mechanism was also tested LONG WITH u-Net architecture to precisely classify DNA sequences

Some relations of inclusion and their properties are investigated for functions of type " -valent that involves the generalized operator of Srivastava-Attiya by using the principle of strong differential subordination.

Giardiasis is an infection caused by the protozoan flagellate parasite Giardia spp. in the intestine. G duodenalis, a species complex of diverse genotypes that tend to demonstrate host specificity, is responsible for most veterinary health related infections; production animals, companion animals, and wildlife can all be infected. Abdominal pain and diarrhea, typically accompanied by steatorrhea, are the most common symptoms of Giardiasis. Cysts or antigens in feces are commonly used to diagnose the disease. Treatment regimens vary and are dependent on the indication. Control methods must include hygiene measures. Despite direct evidence of Giardia sp transmission to humans via polluted water supplies, our analysis will focus on some r