This paper generalizes and improves the results of Margenstren, by proving that the number of -practical numbers  which is defined by   has a lower bound in terms of . This bound is more sharper than Mangenstern bound when  Further general results are given for the existence of -practical numbers, by proving that the interval contains a -practical for all

This paper deals with the F-compact operator defined on probabilistic Hilbert space and gives some of its main properties.

In this paper, a new analytical method is introduced to find the general solution of linear partial differential equations. In this method, each Laplace transform (LT) and Sumudu transform (ST) is used independently along with canonical coordinates. The strength of this method is that it is easy to implement and does not require initial conditions.

This is a survey study that presents recent researches concerning factional controllers. It presents several types of fractional order controllers, which are extensions to their integer order counterparts. The fractional order PID controller has a dominant importance, so thirty-one paper are presented for this controller. The remaining types of controllers are presented according to the number of papers that handle them; they are fractional order sliding mode controller (nine papers), fuzzy fractional order sliding mode controller (five papers), fractional order lag-lead compensator (three papers), fractional order state feedback controller (three papers), fractional order fuzzy logic controller (three papers). Finally,

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

In line with the advancement of hardware technology and increasing consumer demands for new functionalities and innovations, software applications grew tremendously in term of size over the last decade. This sudden increase in size has a profound impact as far as testing is concerned. Here, more and more unwanted interactions among software systems components, hardware, and operating system are to be expected, rendering increased possibility of faults. To address this issue, many useful interaction-based testing techniques (termed t-way strategies) have been developed in the literature. As an effort to promote awareness and encourage its usage, this chapter surveys the current state-of-the-art and reviews the state-of-practices in t

In line with the advancement of hardware technology and increasing consumer demands for new functionalities and innovations, software applications grew tremendously in term of size over the last decade. This sudden increase in size has a profound impact as far as testing is concerned. Here, more and more unwanted interactions among software systems components, hardware, and operating system are to be expected, rendering increased possibility of faults. To address this issue, many useful interaction-based testing techniques (termed t-way strategies) have been developed in the literature. As an effort to promote awareness and encourage its usage, this chapter surveys the current state-of-the-art and reviews the state-of-practices in t

In this paper a modified approach have been used to find the approximate solution of ordinary delay differential equations with constant delay using the collocation method based on Bernstien polynomials.