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When attempting to express a differential equation of the first order, it is usual practice to use the equation represented by dy/dx= f(x,y). The above equation contains a function denoted by the notation embodied by f(x,y), defined on a portion of the xy-plane and dependent on two variables, x, and y, which are independent variables. The equation considered to be of the first order is the one that has just the first derivative, which is denoted by the notation dy/dx since there are no higher-order derivatives present in the equation. It is usual practice to make use of the differential equation when attempting to explain the connection that exists between a function and the derivatives of that function. Using this technique to identify functions inside a given domain in physics, chemistry, and many other fields of science is feasible. In order to do so, it is necessary to have previous knowledge about functions and the derivatives of those functions. In this article, the Emad-Sara transformation is presented as a method for identifying the general solution of complex differential equations of the first order that have constant coefficients. This transformation may be used to get the general solution of these equations. This approach, which is both practical and economical, may be used to find solutions to a wide variety of linear operator equations. These equations can range from simple to complex

Differential equations are used to represent different scientific problems are handled efficiently by integral transformations, where integral transforms represent an easy and effective tool for solving many problems in the mentioned fields. This work utilizes the integral transform of the Complex SEE integral transformation to provide an efficient solution method for the difference and differential-difference equations by benefiting from the properties of this complex transform to solve some problems related to difference and differential-difference equations. The 3D, contour and 2D surfaces, as well as the related density plot surfaces of some acquired data, are used to draw the physical aspect of the obtained findings. The proposed approach offers an efficient and rapid solution for addressing the inherent complexity of differential-difference problems with initial conditions. [ABSTRACT FROM AUTHOR]

Background: Intensive care unit‐acquired weakness (ICU‐AW) is common in critically ill patients and increases the duration of mechanical ventilation (MV) and weaning time. Early mobilization, range of motion (ROM) exercises, and neuromuscular electrical stimulation (NMES) can prevent ICU‐AW by maintaining muscle mass. However, studies highlighting the effects of combining NMES with early physical activity in ICU patients are limited. Aim: To evaluate the effect of NMES and early physical activity on ICU‐AW in mechanically ventilated patients. Study Design: A single‐blinded randomized controlled trial was conducted in Alexandria, Egypt. Patients were randomly assigned to one of four groups: NMES, ROM, combined therapy (ROM + NMES), or conventional care (control group). The Medical Research Council (MRC) scale was used to assess the ICU‐AW for the study patients over a 7‐day period. The duration of the patient's MV and ICU stays were recorded. Results: Of the 180 patients who were assessed for eligibility, 124 were randomly assigned to one of four groups: 32 patients in ROM exercises, 30 in NMES, 31 in combined therapy (ROM + NMES), and 31 in the control group. On day 7, ROM + NMES and NMES groups showed higher MRC scores than ROM and control groups (50.37 ± 2.34, 49.77 ± 2.19, 44.97 ± 3.61, and 41.10 ± 3.84, respectively). ANOVA test results indicated significant differences (p <.001) across the four groups. ICU‐AW occurred in 0% of the ROM + NMES group, 60% of the ROM group, 13% of the NMES group, and 100% of the control group (p <.001). The MV duration (in days) in the ROM + NMES group was shorter (12.80 ± 3.800) than in the ROM, NMES, or control groups (21.80 ± 4.460, 18.73 ± 4.748, and 20.70 ± 3.932, respectively). ICU‐LOS was shorter in the ROM + NMES group (17.43 ± 3.17 days) compared with the ROM group (22.53 ± 4.51 days), the NMES group (21.10 ± 5.0 days), and the control group (21.50 ± 4.42 days) with significant differences (p <.001) between the four groups. Conclusion: Daily sessions of NMES and early physical activity were well tolerated, preserved muscle strength, prevented ICU‐AW, and decreased the duration of the MV and ICU stay. Relevance to Clinical Practice: The findings of this study support the use of NMES and early physical exercises by critical care nurses as part of routine care for critically ill patients. [ABSTRACT FROM AUTHOR]

In this paper, a new type of integral transform with complex power parameters called the "Mayan transform" has been introduced. The definitions of the integral transform and its inverse are given in the classical case and the corresponding neutrosophic case. The classical analytical properties of the Mayan integral transforms are proven; the application of it to some essential functions and neutrosophic functions is introduced and proven. Also, its application to the neutrosophic derivatives (first, second, and third) then the generalization of the application on the Mayan integral transform on the neutrosophic derivatives are given. The worthiness of the introduced integral transform on the actual application is also proven by applying the integral transform in solving two problems: the response of an Undamped forced mechanical oscillator and the response of an undamped forced electrical oscillator. [ABSTRACT FROM AUTHOR]

The Sadiq-Emad-Emann (SEE) transform, also known as operational calculus, has gained significant importance as a fundamental component of the mathematical knowledge necessary for physicists, engineers, mathematicians, and other scientific professionals. This is because the SEE transform offers accessible and efficient resources for resolving several applications and challenges encountered in diverse engineering and science domains. This study aims to introduce the fundamental principles of SEE transformation and establish the validity of two statements and associated attributes. The objective of this study is to use the aforementioned qualities in order to determine the solution of difference and differential-difference equations, with neutrosophic versions of difference and differential difference equations. In addition, we are able to get very effective and expeditious precise answers. [ABSTRACT FROM AUTHOR]

1-(4-substitutesd)-2-(5-phenyl-3-(1H-pyrrol-2-yl)-4,5-dihydropyrazol-1-yl)thiazol-5-yl)-2-aryldiazene 9a-f were prepared through reactions of 5-phenyl-3-(1H-pyrrol-2-yl)-4, 5-dihydropyrazole-1-carbothioamide 5 with hydrazonoyl halides. Furthermore, thioamide 5 was utilized as starting materials for thiazolidone synthesis 10 and arylidene thiazoles 15a–c. Also pyran derivatives 12a-b, 13a-b,14a-b and thioanilide derivaives 16 were obtained from the reaction of thiazilidone 10 with arylidenemalononitrile and phenyl isothiocyanat, respectively. When possible, the structures of experimentally synthesized compounds were identified by elemental analysis, spectral analysis, and alternative synthesis routes. Some of the synthesized compounds as 9f, 10, 12b, and 16 were screened for their cytotoxicity against MCF-7 and HCT-116 cells using the MTT assay. They exhibited remarkable cytotoxic activities with promising IC50 values. Interestingly, compound 16 exhibited potent cytotoxicity against MCF-7 and HCT-116 with IC50 values of 5.05 and 3.08 μM, compared to doxorubicin with IC50 values of 7.27 and 8.92 μM, respectively show interesting biological activities as anticancer activities. Additionally, the tested compounds were nontoxic against WISH cells with higher IC50 values. Hence, these compounds may serve as potent and selective cytotoxic agents. [ABSTRACT FROM AUTHOR]

The medical sector is one of the many scientific domains that may benefit from the use of mathematical models and algorithms to carry out a variety of activities that simplify and improve their job. The models that are utilized in the majority of medical areas are ones that can be anticipated or shaped using mathematical equations. These equations inspire mathematicians to handle them and alter them in order to discover the most accurate and direct form to answer the problems they provide. It's possible that some models of cardiovascular disease have solutions that are more complicated than algebraic models. Therefore, the use of integral transformations in the process of identifying the solutions to the aforementioned equations is quite beneficial. The Emad-Falih integral transformation is used throughout this article to do an analysis of the exact solutions to both of the cardiovascular models being discussed. For the purpose of calculating solutions to ordinary differential equations, the integral transform under study is a technique that is not only practical but also trustworthy and user-friendly. [ABSTRACT FROM AUTHOR]

This paper displays how Dryden's metaphorical representations of natural elements in the Fire section of his historic poem Annus Mirabilis have foregrounded the ecocritical readings of human-environmental relationships, particularly with respect to the impact of the intriguing web of the sociopolitical facts on the London community. The paper uncovers Dryden's timid perspective on the environment as a sociopolitical entity that dominates and manipulates humans' lives, which is a typical practice of the ecocritical theory. The methodology adopted in this research is both qualitative and interpretive, as it focuses on the prevalent metaphoric representations of the ecological dilemma as uniquely used by the poet in two discrete stages: first, the ecological insights of Dryden's animation of the natural through water/fire tropes, and second, the metamorphosis of the city as an ecological outcome of the metaphoric animation. Both stages reveal that Dryden's delineation of the 1666 conflagration in Annus Mirabilis has figuratively and intellectually foregrounded the key tenets of ecocriticism. [ABSTRACT FROM AUTHOR]

2-(2-oxoindolin-3-ylidene)-N-phenylhydrazinecarbothioamide (4) was synthesized by reaction of 3-hydrazonoindolin-2-one (3) with phenyl isothiocyanate in DMF in presence of potassium hydroxide. Thus, treatment of 4 with the appropriate halo ketones, hydrazonoyl halides, and benzylidene malononitriles afforded thiazolidin-4-one, and thiadiazole derivatives. Moreover, structures of the newly synthesized compounds were elucidated as based of elemental analysis and spectral data. Also, the influence of gamma irradiation on the biological activities of the new compounds was evaluated. [ABSTRACT FROM AUTHOR]