Attainability of the fractional Hardy constant with nonlocal mixed boundary conditions. Applications

The first goal of this paper is to study necessary and sufficient conditions to obtain the attainability of the \textit{fractional Hardy inequality } $$\Lambda_{N}\equiv\Lambda_{N}(\Omega):=\inf_{\{\phi\in \mathbb{E}^s(\Omega, D), \phi\neq 0\}} \dfrac{\frac{a_{d,s}}{2} \displaystyle\int_{\mathbb{R}^d} \int_{\mathbb{R}^d} \dfrac{|\phi(x)-\phi(y)|^2}{|x-y|^{d+2s}}dx dy} {\displaystyle\int_\Omega \frac{\phi^2}{|x|^{2s}}\,dx},$$ where $\Omega$ is a bounded domain of $\mathbb{R}^d$, $0<s<1$, $D\subset \mathbb{R}^d\setminus \Omega$ a nonempty open set and $$\mathbb{E}^{s}(\Omega,D)=\left\{ u \in H^s(\mathbb{R}^d):\, u=0 \text{ in } D\right\}.$$ The second aim of the paper is to study the \textit{mixed Dirichlet-Neumann boundary problem} associated to the minimization problem and related properties; precisely, to study semilinear elliptic problem for the \textit{fractional laplacian}, that is, $$P_{\lambda} \, \equiv \left\{ \begin{array}{rcll} (-\Delta)^s u &= & \lambda \dfrac{u}{|x|^{2s}} +u^p & {\text{ in }}\Omega, u & > & 0 &{\text{ in }} \Omega, \mathcal{B}_{s}u&:=&u\chi_{D}+\mathcal{N}_{s}u\chi_{N}=0 &{\text{ in }}\mathbb{R}^{d}\backslash \Omega, \\ \end{array}\right.$$ with $N$ and $D$ open sets in $\mathbb{R}^d\backslash\Omega$ such that $N \cap D=\emptyset$ and $\overline{N}\cup \overline{D}= \mathbb{R}^d \backslash\Omega$, $d>2s$, $\lambda> 0$ and $0<p\le 2_s^*-1$, $2_s^*=\frac{2d}{d-2s}$. We emphasize that the nonlinear term can be critical. The operators $(-\Delta)^s$, fractional laplacian, and $\mathcal{N}_{s}$, nonlocal Neumann condition, are defined below in (1.5) and (1.6) respectively

Network coding cooperation performance analysis in wireless network over a lossy channel, M users and a destination scenario

Network coding (NC), introduced at the turn of the century, enables nodes in a network to combine data algebraically before either sending or forwarding them. Random network coding has gained popularity over the years by combining the received packet randomly before forwarding them, resulting in a complex Jordan Gaussian Elimination (JGE) decoding process. The effectiveness of random NC is through cooperation among nodes. In this paper, we propose a simple, low-complexity cooperative protocol that exploits NC in a deterministic manner resulting in improved diversity, data rate, and less complex JGE decoding process. The proposed system is applied over a lossy wireless network. The scenario under investigation is as follows: M users must send their information to a common destination D and to exchange the information between each others, over erasure channels; typically the channels between the users and the destination are worse than the channels between users. It is possible to significantly reduce the traffic amon g users and destination, achieving significant bandwidth savings, by combining packets from different users in simple, deterministic ways without resorting to extensive header information before being forwarded to the destination and the M users. The key problem we try to address is how to efficiently combine the packets at each user while exploiting user cooperation and the probability of successfully recovering information from all users at D with k < 2M unique linear equations, accounting for the fact that the remaining packets will be lost in the network and there are two transmission stages. Simulation results show the behaviour for two and three transmission stages. Our results show that applying NC protocols in two or three stages decreases the traffic significantly, beside the fact that the proposed protocols enable the system to retrieve the lost packets rather than asking for ARQ, resulting in improved data flow, and less power consumption. In fact, in some protocols the ARQ dropped from the rate 10-1 to 10-4, because of the proposed combining algorithm that enables the nodes to generate additional unique linear equations to broadcast rather than repeating the same ones via ARQ. Moreover, the number of the transmitted packets in each cooperative stage dropped from M (M − 1) to just M packets, resulting to 2 M packets instead 2 (M2 −  1) when three stages of transmission system are used instead of one stage (two cooperative stages)

Effect of Evaporative Cooling Combined with Heat Sink on PV Module Performance

&nbsp;تم استخدام مجموعة من زعانف الاسطوانية كمنفذ حراري مع وسادة صوف خشبية رطبة لاستخدام نظام تبريد جديد لتبريد الألواح الكهروضوئية. استند نظام التبريد الحالي إلى مفهوم التبريد التبخيري والمساحة الممتدة لنقل الحرارة. أعطت النتائج تحسينات في طاقة الخارجة وكفاءة اللوحة بنحو 32.7٪ و31.5٪ على التوالي. ويعزى هذا التحسن في أداء الوحدة إلى انخفاض درجة حرارة التشغيل للخلية الشمسية. كان الانخفاض في درجة الحرارة وحدة حوالي 26.05 ٪.A pin fins array as a heat sink along with a moist wood wool pad to serve as novel cooling system to cool PV panel has been used. The present cooling system was based on the evaporative cooling concept and extended area of heat transfer. The results gave enhancements in output power and panel’s efficiency about 32.7% and 31.5% respectively.&nbsp; This improvement in the module performance was attributed to the reduction in the operation temperature of the solar cell. The reduction in module temperature was about 26.05%

Comparative study of circular and rectangular microstrip patch antennas in Wi-Fi band

The growing ubiquity of Wi-Fi has necessitated the development of small and effective antenna designs, especially microstrip patch antennas. In the Wi-Fi frequency range of 2.4 GHz to 2.4835 GHz, this paper compares the performance of circular and rectangular microstrip patch antennas. The study aims to evaluate their performance regarding radiation characteristics, gain, and bandwidth to help choose antennas for Wi-Fi applications. According to the results, the rectangular patch antenna with a rectangular slot outperforms the circular patch antenna with a rectangular slot regarding return loss, coming in at roughly -37.07 dB. Furthermore, the Voltage Standing Wave Ratio (VSWR)value of the rectangular patch antenna is 1.02, which is higher than that of the circular patch antenna, which is 1.34. The rectangular patch antenna has the most excellent radiation efficiency (64.5%) and offers the broadest bandwidth (about 115 MHz). Engineers and researchers looking to enhance antenna designs for Wi-Fi applications can learn much from this study by considering variables like radiation efficiency, bandwidth, VSWR, and return loss.</p

Comparison between rectangular and circular microstrip patch antenna arrays

In this paper, several designs of microstrip array antennas suitable for wireless communication applications are presented. This paper demonstrates several shapes of microstrip array antennas, such as rectangular and circular patch antenna arrays. Specifically, single, 2 × 1, and 4 × 1 elements of both shapes are designed and simulated by High Frequency Structural Simulator (HFSS). Moreover, this paper presents a comparison between both rectangular and triangular antenna arrays. Since the resonance frequency of these antennas is 2.4 GHz, these antennas are suitable for the ISM band and WLAN).</p

Septic coronary embolism – A case report

The embolization represents one of the most dreadful complications of infective endocarditis; however, coronary embolism is a rare entity with an incidence of 2.9%. The definite line of management is rather ambiguous in published literatures. We reported an urgent coronary revascularization with double valve replacement due to infective endocarditis with large vegetation complicated by coronary embolism and acute coronary syndrome

Harnessing the power of IoT: a survey of Internet of Things applications in greenhouse agriculture

The Internet of Things (IoT) technology is now widely used in virtually all industries, including agriculture, and is adopting IoT technology. Through their IoT technology, greenhouse agriculture has entered an era of precision farming like never before. This survey is made on the recent progress in greenhouse agriculture with IoT, and the architecture of IoT is illustrated further with its application in greenhouse agriculture. For instance, the chapter investigates various disciplines like Monitoring and Control Systems, Smart Irrigation Systems, Environmental Data Collection and Analysis, and Crop Health Monitoring. It should also be noted that the many advantages IoT brings to greenhouse farming in the way of increased yield and quality of crops, greater efficiency in the use of resources, and reductions in labor and operational costs are also taken into consideration. Not with these benefits, problems like information security and privacy, integration, and interoperability issues still exist. The last part of the discussion will be about the future vision: what changes can we expect in IoT-based greenhouse farming and what new trends are emerging. The survey offers essential lessons about the cost-effectiveness and sustainability of IoT in improving production and productivity in greenhouses.</p

Resistance of High-Volume Fly Ash Self-Compacting Concrete to Internal Sulfate Attack

This paper investigates the durability of high-volume Fly ash self-compacting concrete, HVFASCC that exposed to internal sulfate attack. At the present work, HVFASCC was produced with two Fly ash replacements: 50 and 60% by weight of Portland cement. The internal sulfate attack was simulated by adding natural gypsum (CaSO4) that contain ion (SO3-2) to fine aggregate by two weight percentages: 1 and 2%. Limestone dust was used as filler with a content of 100 kg/m3. The cementitious materials, cement and Fly ash, content was 400 kg/m3 and the water to powder ratio for the studied mixes was 0.34 by weight. To ensure the self-compact ability of the mixes, slump flow, T500, V-funnel and L-box tests were done. The Compressive, Splitting and Flexural strength Tests were extended to the age of 240 days. The results showed that there is no significant difference between 1 and 2% of SO3 content on the behavior of all mixes. The presence of limestone powder in the paste solution could have a role in stabilizing ettringite and reducing paste porosity at early ages. At later age, 240 days, the harmful effect of SO3 is diminished and that may be caused by the depletion of gypsum and the dominant product will be calcium monosulfoluminate hydrates instead of calcium sulfoaluminate hydrates

Transatrial approach for total tetralogy of Fallot TOF correction: analysis of 24 cases.

Background: Tetralogy of Fallot TOF is the most common cause of congenital cyanotic heart disease. It is the most common congenital lesion that is likely to result in survival to adulthood and encountered in adult after repair. Tetralogy of Fallot comprises around 7.5 % of all congenital heart diseases in Iraq. Objective: The aim of this study is to analyse the transatrial strategy for total correction of tetralogy of Fallot TOF. Methods: Cross-sectional study was done during the period between 2012-2014 for twenty-four patients that admitted to Ibn Al-Bitar hospital in Baghdad with amenable TOF pathology for transatrial repair. Results: Twenty-four patients, 16 were males and 8 were females. Ages ranged from 2-31 years. There was no early or late postoperative mortality in this review for follow-up period ranged from 6 – 24 months. The early and late postoperative echocardiography data in regard to pulmonary and tricuspid regurgitation and right ventricle RV function were delineated. Normal pulmonary valve (62.5%, 58.3%), mild pulmonary regurgitation (29.2%, 37.5%), moderate pulmonary regurgitation (8.3%, 4.2%). Normal tricuspid valve (75%, 70.8%), mild tricuspid regurgitation (20.8%, 20.8%), moderate tricuspid regurgitation (4.2%, 8.3%) respectively. No severe pulmonary or tricuspid regurgitation was reported. Postoperative RV function was normal in (87.5%, 83.3%), mild RV dysfunction in (8.3%, 12.5%), moderate RV dysfunction in (4.2%, 4.2%) respectively. No severe RV dysfunction was reported. The mean RVOT pressure gradient was 36.8 mmHg. This gradient decreased on follow-up echocardiography, mean 24.5 mmHg. P values were less than 0.05%. Conclusion: The transatrial approach is a feasible technique for total repair of TOF in adequate pulmonary annulus size with satisfactory late postoperative echocardiography performance. الخلفية:ان رباعية فالوت هي اكثر اسباب مرض ازرقاق الدم الولادي شيوعآ. وهو اكثر تشوهات القلب الخلقية التي تستمر في الحياة الى البلوغ، وتصادف عند البالغين بعد عمليات التصليح. ويشكل تشوه رباعية فالوت حوالي ٧.٥٪ من امراض القلب الخلقية في العراق.   الهدف:ان الهدف من هذه الدراسة هو اجراء تحليل لطريقة عبر الاذين في عملية التصليح الكامل لرباعية فالوت. الطرائق. هي دراسة مستعرضة تمت للفترة من ٢٠١٢ ولغاية ٢٠١٤. تم دراسة ٢٤ طفل ادخلوا في مستشفى ابن البيطار في بغداد، كان لديهم تشوه يسمح بالتداخل عبر الاذين. النتائج: ٢٤ حالة، ١٨ ذكور و ٨ اناث. الاعمار تتراوح من ٢ ـ٣١ سنة. لم تسجل حالة موت بدائية او متقدمة في الدراسة الحالية ولمدة متابعة ٦ الى ٢٤ شهرا. معدل وقت دوران ماكنة القلب الصناعية كان ١٢٧ دقيقة. ومعدل غلق الشريان الابهر كان ١٠٣ دقيقة. ان مشاهدات فحص الامواج الصائتة القلبية مبكرا و متأخرا بعد العملية كان كما يلي، صمام رئوي طبيعي ٦٢.٥٪ و ٥٨.٣٪ ، تهدل الصمام الرئوي البسيط ٢٩.٢٪ و ٣٧.٥٪، تهدل الصمام الرئوي المعتدل ٨.٣٪ و٤.٢٪. صمام ثلاثي طبيعي ٧٥٪ و ٧٠.٨٪، تهدل الصمام الثلاثي البسيط ٢٠.٨٪ و ٢٠.٨٪، تهدل الصمام الثلاثي المعتدل ٤.٢٪ و ٨.٣٪. لاتوجد حالة تهدل صمام رئوي او ثلاثي شديد. كانت فعالية البطين الايمن الطبيعية ٨٧.٥٪ و ٨٣.٣٪، بسيطة الاعتلال ٨.٣٪ و ١٢.٥٪ معتدلة الاعتلال٤.٢٪ و ٤.٢٪، ولم تسجل شديدة الاعتلال. ان معدل نسب فرق الضغط عبر منفذ البطين الايمن كان ٣٦.٨ ملم زئبق. ان هذا الفرق يتضائل مع امتداد الفترة الزمنية، معدل ٢٤.٥ ملم زئبق. قيم معامل p كانت اقل من  ٠.٠٥ ٪. الاستنتاج: ان طريقة عبر الاذين هي الية ممكنة في الاصلاح الكامل لرباعية فالوت بوجود حجم حلقة رئوية كافي مع اداء مرضي لفحص الامواج الصائتة القلبية المتأخر