Finite dimensional approximation to fractional stochastic integro-differential equations with non-instantaneous impulses

This manuscript proposes a class of fractional stochastic integro-differential equation (FSIDE) with non-instantaneous impulses in an arbitrary separable Hilbert space. We use a projection scheme of increasing sequence of finite dimensional subspaces and projection operators to define approximations. In order to demonstrate the existence and convergence of an approximate solution, we utilize stochastic analysis theory, fractional calculus, theory of fractional cosine family of linear operators and fixed point approach. Furthermore, we examine the convergence of Faedo-Galerkin(F-G) approximate solution to the mild solution of our given problem. Finally, a concrete example involving partial differential equation is provided to validate the main abstract results

The Influence of Student's Understanding Level of ITE Law in Social Media

According to a Global WebIndex survey, social media is the longest-running platform, averaging 2.5 hours per day. Millennials are very proficient in using internet-based technology. The research objectives of writing a thesis made by the author were: 1) To find out the understanding of Sharia faculty students related to Law Number 11 of 2008. 2) To find out the understanding of Sharia faculty students related to Law No. 19 of 2016 concerning amendments to Law No. 11 of 2008 in social media. In this research, the author uses a quantitative approach method. This is a survey research, whose emphasis lies on relational research that studies the relationship of variables, so that direct or indirect hypotheses are always questioned. In this survey, information was collected using a questionnaire with a total of 150 respondents with descriptive statistical tests, classical assumption test, and hypothesis test. The hypothesis test results show the absence of influence on students’ understanding of the ITE Law by using social media. Keywords: ITE Law, social media, understandin

Existence and Stability Results of Nonlinear Fractional Differential Equations with Nonlinear Integral Boundary Condition on Time Scales

In this paper, we establish the existence and uniqueness of the solution to a nonlinear fractional differential equation with nonlinear integral boundary conditions on time scales.We used the fixed point theorems due to Banach, Schaefer’s, nonlinear alternative of Leray Schauder’s type and Krasnoselskii’s to establish these results. In addition, we study Ulam-Hyer’s (UH) type stability result. At the end, we present two examples to show the effectiveness of the obtained analytical results

A fixed point approach for finding approximate solutions to second order non-instantaneous impulsive abstract differential equations

This paper is concerned with the approximation of solutions to a class of second order non linear abstract differential equations. The finite-dimensional approximate solutions of the given system are built with the aid of the projection operator. We investigate the connection between the approximate solution and exact solution, and the question of convergence. Moreover, we define the Faedo-Galerkin(F-G) approximations and prove the existence and convergence results. The results are obtained by using the theory of cosine functions, Banach fixed point theorem and fractional power of closed linear operators. At last, an example of abstract formulation is provided

Detection of a Moving Rigid Solid in a Perfect Fluid

In this paper, we consider a moving rigid solid immersed in a potential fluid. The fluid-solid system fills the whole two dimensional space and the fluid is assumed to be at rest at infinity. Our aim is to study the inverse problem, initially introduced in [3], that consists in recovering the position and the velocity of the solid assuming that the potential function is known at a given time. We show that this problem is in general ill-posed by providing counterexamples for which the same potential corresponds to different positions and velocities of a same solid. However, it is also possible to find solids having a specific shape, like ellipses for instance, for which the problem of detection admits a unique solution. Using complex analysis, we prove that the well-posedness of the inverse problem is equivalent to the solvability of an infinite set of nonlinear equations. This result allows us to show that when the solid enjoys some symmetry properties, it can be partially detected. Besides, for any solid, the velocity can always be recovered when both the potential function and the position are supposed to be known. Finally, we prove that by performing continuous measurements of the fluid potential over a time interval, we can always track the position of the solid.Comment: 19 pages, 14 figure

An analysis of approximate controllability for Hilfer fractional delay differential equations of Sobolev type without uniqueness

This study focused on the approximate controllability results for the Hilfer fractional delay evolution equations of the Sobolev type without uniqueness. Initially, the Lipschitz condition is derived from the hypothesis, which is represented by a measure of noncompactness, in particular, nonlinearity. We also examined the continuity of the solution map of the Sobolev type of Hilfer fractional delay evolution equation and the topological structure of the solution set. Furthermore, we prove the approximate controllability of the fractional evolution equation of the Sobolev type with delay. Finally, we provided an example to illustrate the theoretical results

VR-ZYCAP: A versatile resourse-level ICAP controller for ZYNQ SOC

This article belongs to the Special Issue Architecture and CAD for Field-Programmable Gate Arrays (FPGAs)Hybrid architectures integrating a processor with an SRAM-based FPGA fabric—for example, Xilinx ZynQ SoC—are increasingly being used as a single-chip solution in several market segments to replace multi-chip designs. These devices not only provide advantages in terms of logic density, cost and integration, but also provide run-time in-field reconfiguration capabilities. However, the current reconfiguration capabilities provided by vendor tools are limited to the module level. Therefore, incremental run-time configuration memory changes require a lengthy compilation time for off-line bitstream generation along with storage and reconfiguration time overheads with traditional vendor methodologies. In this paper, an internal configuration access port (ICAP) controller that provides a versatile fine-grain resource-level incremental reconfiguration of the programmable logic (PL) resources in ZynQ SoC is presented. The proposed controller implemented in PL, called VR-ZyCAP, can reconfigure look-up tables (LUTs) and Flip-Flops (FF). The run-time reconfiguration of FF is achieved through a reset after reconfiguration (RAR)-featured partial bitstream to avoid the unintended state corruption of other memory elements. Along with versatility, our proposed controller improves the reconfiguration time by 30 times for FFs compared to state-of-the-art works while achieving a nearly 400-fold increase in speed for LUTs when compared to vendor-supported software approaches. In addition, it achieves competitive resource utilization when compared to existing approaches.This research was funded by Spanish Ministry of Science and Innovation under the ACHILLES project, grant number PID2019-104207RB-I00 and by Taif University Researchers Supporting fund, grant number (TURSP-2020/144), Taif University, Taif, Saudi Arabia

Cohesion, Multi-faithism and the Erosion of Secular Spaces in the UK: Implications for the Human Rights of Minority Women

This article explores the erosion of secular public culture in the UK and its implications for minority women whose bodies have become the battleground for the control of community representation. It argues that struggles for equality and secularism now overlap and have taken on a sense of urgency because it is the human rights of women that are being traded in the various social contracts that are emerging between state and the religious right minority leaderships in the UK. The increasing communalisation (involving religious and community groups mobilising solely around religious identities) of South Asian populations, in particular Muslims, reflects a form of instrumentalisation of religion by the state which has severely constrained the public space available for women to mobilise around a rights?based agenda and has also significantly narrowed the choices of women of faith

Efek Neuroprotektif Fraksi Air Daun Semanggi (Marsilea crenata Presl.) secara In Vitro

Background: Estrogen deficiency can trigger several diseases, one of which is neurodegenerative. Neurodegenerative begins with neuroinflammation, which triggers the activation of microglia cells resulting in a pro-inflammatory activity. Potential and relatively safe therapy to use to overcome it is by using phytoestrogen compounds. Marsilea crenata Presl. is a plant that contains phytoestrogens. Objective: The purpose of this study was to analyze the neuroprotective effect of the water fraction of Marsilea crenata Presl. leaves which was shown by inhibition of neuroinflammation and marked by increased levels of MHC II against HMC3 microglia cells. Methods: IFN-γ is induced into HMC3 microglia cells for 24 hours to cause inflammatory conditions. Marsilea crenata Presl. leaves water fraction was given at a dose of 62,5; 125; and 250 µg / ml. Analysis of the neuroprotective effect of HMC3 microglia cells using the ICC method with the aid of the CLSM instrument. Results: The results of this study indicate that the water fraction of Marsilea crenata Presl. leaves can reduce MHC II expression at concentrations of 125 and 250 μg / ml with values ​​of 465,748 and 460,884 AU at p<0,005. Conclusion: This study concludes that the water fraction of Marsilea crenata Presl. has neuroprotective activity shown at doses of 125 and 250 μg/ml which can reduce MHC II expression in HMC3 microglia cells induced by IFN-γ. The ED50 value which has a neuroprotective effect is at a dose of 0,582 μg/ml. &nbsp

Halal dating: changing relationship attitudes and experiences among young British Muslims

Young Muslims in the UK are making space to gain greater control over their personal lives through the diction of ‘halal’ and ‘haram’ when reflecting on and negotiating personal relationships. This article explores the significance of ‘halal dating’ within the lived experiences and sexual relationships of young British Muslims. It draws upon 56 in-depth interviews conducted with young (16–30 years) British Muslims of Pakistani heritage. This research shows that, contrary to popular stereotype and widespread expectations, many young British Muslims do date, or have dated. By entertaining the idea that certain forms of dating may be halal, these young Muslims are finding and claiming agency to make relationship choices of their own