A differential operator realisation approach for constructing Casimir operators of non-semisimple Lie algebras

We introduce a search algorithm that utilises differential operator realisations to find polynomial Casimir operators of Lie algebras. To demonstrate the algorithm, we look at two classes of examples: (1) the model filiform Lie algebras and (2) the Schr\"odinger Lie algebras. We find that an abstract form of dimensional analysis assists us in our algorithm, and greatly reduces the complexity of the problem.Comment: 22 page

Analisis Komposisi Fasa Komposit Keramik Berbasis SiO2-MgO dengan Penambahan B2O3 pada Temperatur Sinter 1150C

Komposit keramik berbasis SiO2-MgO menggunakan pasir Tanah Laut sebagai bahan baku dengan penambahan variasi B2O3 telah berhasil disintesis. Tujuan penambahan B2O3 adalah untuk meningkatkan densitas dan mereduksi porositas. Komposit dibuat dengan cara mencampurkan serbuk pasir Tanah Laut dan MgO dengan penambahan massa B2O3 sebesar 0%, 4,8%, dan 9,1% (berat) diaduk menggunakan mortar selama 30 menit. Campuran serbuk dicetak dalam bentuk pelet silinder dengan tekanan 4.500 N kemudian disinter pada temperatur 1150°C untuk membentuk komposit keramik padat. Identifikasi fasa dilakukan menggunakan X-Ray Diffractometer (XRD). Data XRD dianalisis secara kualitatif menggunakan Match!2 dan secara kuantitatif menggunakan Rietica. Hasil analisis data XRD menunjukkan bahwa pada temperatur sinter 1150°C tanpa B2O3 fasa yang ditemukan adalah kuarsa, forsterit dan enstatit. Sedangkan pada penambahan 4,8% dan 9,1% B2O3 fasa yang ditemukan kuarsa dan protoenstatit. Komposit mengalami penyusutan diameter maksimal sebesar 5.4(1)% pada 9,1% B2O3. Dari pendekatan RoM dalam analisis komposisi fasa maka nilai KET sampel-sampel komposit tersebut dapat dikategorikan sebagai kandidat seal fuel cell

On Casimir Operators of Conformal Galilei Algebras

In previous work, we introduced an algorithm that utilises differential operator realisations to find polynomial Casimir operators of Lie algebras. In this article we build on this work by applying the algorithm to several classes of finite dimensional conformal Galilei algebras with central extension. In these cases we highlight the utility of an algebra anti-automorphism, and give relevant details through key examples.Comment: 18 page

Lossy Kernelization

In this paper we propose a new framework for analyzing the performance of preprocessing algorithms. Our framework builds on the notion of kernelization from parameterized complexity. However, as opposed to the original notion of kernelization, our definitions combine well with approximation algorithms and heuristics. The key new definition is that of a polynomial size $\alpha$-approximate kernel. Loosely speaking, a polynomial size $\alpha$-approximate kernel is a polynomial time pre-processing algorithm that takes as input an instance $(I,k)$ to a parameterized problem, and outputs another instance $(I',k')$ to the same problem, such that $|I'|+k' \leq k^{O(1)}$. Additionally, for every $c \geq 1$, a $c$-approximate solution $s'$ to the pre-processed instance $(I',k')$ can be turned in polynomial time into a $(c \cdot \alpha)$-approximate solution $s$ to the original instance $(I,k)$. Our main technical contribution are $\alpha$-approximate kernels of polynomial size for three problems, namely Connected Vertex Cover, Disjoint Cycle Packing and Disjoint Factors. These problems are known not to admit any polynomial size kernels unless $NP \subseteq coNP/poly$. Our approximate kernels simultaneously beat both the lower bounds on the (normal) kernel size, and the hardness of approximation lower bounds for all three problems. On the negative side we prove that Longest Path parameterized by the length of the path and Set Cover parameterized by the universe size do not admit even an $\alpha$-approximate kernel of polynomial size, for any $\alpha \geq 1$, unless $NP \subseteq coNP/poly$. In order to prove this lower bound we need to combine in a non-trivial way the techniques used for showing kernelization lower bounds with the methods for showing hardness of approximationComment: 58 pages. Version 2 contain new results: PSAKS for Cycle Packing and approximate kernel lower bounds for Set Cover and Hitting Set parameterized by universe siz

On the Optimality of Pseudo-polynomial Algorithms for Integer Programming

In the classic Integer Programming (IP) problem, the objective is to decide whether, for a given $m \times n$ matrix $A$ and an $m$-vector $b=(b_1,\dots, b_m)$, there is a non-negative integer $n$-vector $x$ such that $Ax=b$. Solving (IP) is an important step in numerous algorithms and it is important to obtain an understanding of the precise complexity of this problem as a function of natural parameters of the input. The classic pseudo-polynomial time algorithm of Papadimitriou [J. ACM 1981] for instances of (IP) with a constant number of constraints was only recently improved upon by Eisenbrand and Weismantel [SODA 2018] and Jansen and Rohwedder [ArXiv 2018]. We continue this line of work and show that under the Exponential Time Hypothesis (ETH), the algorithm of Jansen and Rohwedder is nearly optimal. We also show that when the matrix $A$ is assumed to be non-negative, a component of Papadimitriou's original algorithm is already nearly optimal under ETH. This motivates us to pick up the line of research initiated by Cunningham and Geelen [IPCO 2007] who studied the complexity of solving (IP) with non-negative matrices in which the number of constraints may be unbounded, but the branch-width of the column-matroid corresponding to the constraint matrix is a constant. We prove a lower bound on the complexity of solving (IP) for such instances and obtain optimal results with respect to a closely related parameter, path-width. Specifically, we prove matching upper and lower bounds for (IP) when the path-width of the corresponding column-matroid is a constant.Comment: 29 pages, To appear in ESA 201

Review of the Effectiveness of Mindfulness-based Cognitive Therapy (MBCT) In Reducing Symptoms of Bulimia Nervosa

Bulimia nervosa is a serious disorder with limited intervention such as mindfulness-based cognitive therapy with relapsing bulimia nervosa for patients which is require, however, few studies focus on its use in patients with bulimia nervosa. Review and examine studies of Mindfulness-based cognitive therapy Cognitive-behavioural psychotherapy as treatment. A study by Sala et al. (2021) found that MBCT improved eating behaviours, while the results of a study by Juarascio et al. (2021) indicated that MBCT led to an improvement in symptoms for patients with bulimia nervosa .Using of mindfulness-based cognitive therapy with relapsing bulimia nervosa patients is needed. The need for Arab studies comparing the effectiveness of mindfulness-based cognitive therapy with other psychological treatments for relapsing bulimia patients

Design and Development of Techniques to Ensure Integrity in Fog Computing Based Databases

The advancement of information technology in coming years will bring significant changes to the way sensitive data is processed. But the volume of generated data is rapidly growing worldwide. Technologies such as cloud computing, fog computing, and the Internet of things (IoT) will offer business service providers and consumers opportunities to obtain effective and efficient services as well as enhance their experiences and services; increased availability and higher-quality services via real-time data processing augment the potential for technology to add value to everyday experiences. This improves human life quality and easiness. As promising as these technological innovations, they are prone to security issues such as data integrity and data consistency. However, as with any computer system, these services are not without risks. There is the possibility that systems might be infiltrated by malicious transactions and, as a result, data could be corrupted, which is a cause for concern. Once an attacker damages a set of data items, the damage can spread through the database. When valid transactions read corrupted data, they can update other data items based on the value read. Given the sensitive nature of important data and the critical need to provide real-time access for decision-making, it is vital that any damage done by a malicious transaction and spread by valid transactions must be corrected immediately and accurately. In this research, we develop three different novel models for employing fog computing technology in critical systems such as healthcare, intelligent government system and critical infrastructure systems. In the first model, we present two sub-models for using fog computing in healthcare: an architecture using fog modules with heterogeneous data, and another using fog modules with homogeneous data. We propose a unique approach for each module to assess the damage caused by malicious transactions, so that original data may be recovered and affected transactions may be identified for future investigations. In the second model, we introduced a unique model that uses fog computing in smart cities to manage utility service companies and consumer data. Then we propose a novel technique to assess damage to data caused by an attack. Thus, original data can be recovered, and a database can be returned to its consistent state as no attacking has occurred. The last model focus of designing a novel technique for an intelligent government system that uses fog computing technology to control and manage data. Unique algorithms sustaining the integrity of system data in the event of cyberattack are proposed in this segment of research. These algorithms are designed to maintain the security of systems attacked by malicious transactions or subjected to fog node data modifications. A transaction-dependency graph is implemented in this model to observe and monitor the activities of every transaction. Once an intrusion detection system detects malicious activities, the system will promptly detect all affected transactions. Then we conducted a simulation study to prove the applicability and efficacy of the proposed models. The evaluation rendered this models practicable and effective

Contemporary Issues in Current Account Operations in Pakistani IBs - Sharia Compliant Solution

Contemporary Sharia scholars have three stances about the Current Account Operations in Pakistani Islamic Banks (IBs) i.e., (i) Ijarah based contract (ii) Wadi'ah based contract, and (iii) Qard based contract. This paper is an attempt to delve into the root causes of the differences of scholars and to find the Sharia-compliant solution acceptable for all. Descriptive as well as applied approaches are used in this paper. Clearing of ambiguity on this issue may result in twofold benefits: from the public point of view, it would satisfy practising Muslims which may result in form of huge deposits in this account (ii) from IBs viewpoint the Current Account is a bonus deposit

Utilization of PVC Particles to Improve the Bending Properties of Epoxy and Unsaturated Polyester

Two sets of polymeric composites were formed. The first set included epoxy as matrix ,while the second set included unsaturated polyester (UP) as matrix. The two sets were reinforced with Polyvinyl Chloride (PVC) at  different volume fractions. Each set was formed into two groups: one was allowed to cure at room temperature and the other was post cured at 40°C for 4hr . The percent of reinforcing and the curing temperature can affect the  behavior of composites. The epoxy composites is the highest in flexural properties than unsaturated polyester composites after reinforcing with thermoplastic material (PVC) . Keywords: epoxy, unsaturated polyester, polyvinyl chloride (PVC), bending.