Symbolic Capabilities Research Articles

Adomian decomposition method for first order PDEs with unprescribed data

In this paper we like to explore the full power of Adomian decomposition method (ADM), specially its symbolic capability. We will demonstrate the standard ADM and ADM with integration factor to compute explicit closed form solutions of first order scalar partial differential equations with unprescribed initial conditions, and even with parameters. These features are those numerical methods fail to do. Our examples include linear/nonlinear, constant/variable coefficients and homogeneous/nonhomogeneous equations. The method of characteristics is also tested and compared with these two ADM methods. We conclude that ADM is excellent among all existing methods.

الخصائص الفنیة فی القصة القصیرة جدا دراسة لمجموعتی (قال کل شیء فی الظلام، کحل عینیک صار خالاً) للکاتب السعودی فهد إبراهیم البکر

الخصائص الفنية في القصة القصيرة جدا دراسة لمجموعتي (قال کل شيء في الظلام، کحل عينيک صار خالا) للکاتب السعودي فهد إبراهيم البکر أسماء بنت صالح بن مطلق العمرو تخصص البلاغة والنقد، الأقسام الأدبية، کلية العلوم والآداب، جامعة القصيم، المملکة العربية السعودية البريد الإلکتروني: Asmaomro@gmail.com ملخص البحث القصة القصيرة جدا هي لون أدبي جديد لاقى شهرة، وانتشارا کبيرا بين أوساط الکتاب والمثقفين؛ وشهدت الساحة الأدبية السعودية، والعربية نموا مضطردا لهذ اللون ؛ لذا حاول النقاد وضع الأسس الحاکمة لهذا الجنس الأدبي الجديد، و الذي نشأ کنتاج للکثير من التغيرات الحادة التي أصابت العالم بسبب ذلک التسارع التکنولوجي المحموم على کافة الأصعدة سواء أکانت سياسية أو اقتصادية أو اجتماعية أو ثقافية؛ ومن ثم تبع ذلک بالضرورة تغير في أشکال التعبير الأدبي، والأدب بوجه عام أحد أهم المکونات التي أصابها هذا التغيير، وکانت القصة القصيرة جدا أحد أبرز إفرازاته. لذا کانت هذه الدراسة للکشف عن الخصائص الفنية والجمالية في القصة السعودية القصيرة جدا، ومصادرها التي انتزعت منها، وتسليط الضوء على تقنيات القصة القصيرة جدا التي تفردت بها من ناحية استلهام التراث، الاقتصاد اللغوي/التکثيف والمفارقة وقد تم اختيار مجموعتي (قال کل شيء في الظلام، کحل عينيک صار خالا ) للکاتب السعودي فهد إبراهيم البکر– کعينة محدودة للبحث- لأنها تمثل المستوى الفني الناضج للقصة السعودية القصيرة جدا، وفهم حدودها النوعية والفنية، وقد نجح الکاتب د. فهد البکر في استخدام أساليب بلاغية وأسلوبية في الکتابة کتکثيف الصور واللحظات، والإيجاز، والتلميح، والتناص، والسخرية، الکوميديا السوداء والتي تعد أحد المکونات البلاغية للصورة القصصية القصيرة جدا بسبب طاقتها التعبيرية والإيحائية والرمزية، کما برع الکاتب في اختيار عناوين قصصه، وانتقاء مفرداته إذ جاءت هذه العناوين رمزية وموحية. The Technical Characteristics of the very Short Story, a Study of the two Collections (He Said everything in Darkness & The Blackness of your Eyes has become a Beauty Spot) by Fahd Ibrahim Al- Bakr; a Saudi Author By: Asmaa Bint Saleh Bin Mutlaq Al- Amro Majored in Rhetoric and Criticism Literary Departments College of Science and Arts Qassim University Kingdom of Saudi Arabia E-mail: Asmaomro@gmail.com Abstract The very short story is a new literary genre that has become widely popular with the communities of writers and intellectuals. Lately, the Arabic and Saudi literary scene has experienced growing development of such genre and that is why the critics have tried to lay the governing principles of this new literary genre which appeared as a result of variable changes that came over the world in consequence of the rapid technological advancement in all respects be they political, economic, social or cultural. Hence, a new change, necessarily, took place in the literary expression. In general, literature is one of the constituents that have been affected by such change. The very short story was one of the most outstanding by- products of that change. Accordingly, this research is designed to highlight the technical and poetic characteristics of the Saudi very short story, its sources and its unique style of inspiration derived from the literary heritage and the economy of language / the paradox of intensification. The two collections, (He Said everything in Darkness and The Blackness of your Eyes has become a Beauty Spot) by the Saudi author Fahd Ibrahim Al- Bakr, have been selected as a study sample in this research because they embody the mature literary example of the Saudi very short story in its artistic and technical attire. The author Dr. Fahd Al- Bakr has succeeded in utilizing rhetorical and stylistic techniques of writing as an intensification of images, moments, brevity, allusion, intertextuality, irony and dark comedy which is one of the rhetorical constituents of the narrative form of the very short story because of its expressionistic, suggestive and symbolic capabilities. Moreover, the author excelled in selecting titles for his collections as well as selecting the items of vocabulary as seen in the symbolic and suggestive titles.

Intervention by international organizations in regime complexes

This article identifies the existence of a previously unknown but important type of self-directed political behavior by International Organizations (IOs) that I term intervention. Intervention occurs when an IO secretariat acts with the intention of altering an anticipated decision at a partially-overlapping IO in a regime complex. Intervention is a distinct type of behavior by IOs that differs from either bureaucratic competition among IOs for mandates, resources and policy influence, or cooperation to achieve joint regulatory goals and enhance performance. I probe the plausibility of intervention through an analysis of three illustrative case studies in the regime complex for food security showing self-directed political actions by the secretariats of the Food and Agriculture Organization (FAO), World Food Programme (WFP) and Office of the High Commissioner for Human Rights (OHCHR) directed at altering decision-making by states at the World Trade Organization (WTO). I identify three distinct intervention strategies – mobilizing states, public shaming and invoking alternative legal frameworks – in which IOs utilize their material, ideational and symbolic capabilities to influence decision-making not within their own institutions, but at other, overlapping organizations in a regime complex over which they have no direct control.

Bridging Symbolic Computation and Economics: A Dynamic and Interactive Tool to Analyze the Price Elasticity of Supply

It is not possible to achieve the objectives and skills of a program in economics, at the secondary and undergraduate levels, without resorting to graphic illustrations. In this way, the use of educational software has been increasingly recognized as a useful tool to promote students’ motivation to deal with, and understand, new economic concepts. Current digital technology allows students to work with a large number and variety of graphics in an interactive way, complementing the theoretical results and the so often used paper and pencil calculations. The computer algebra system Mathematica is a very powerful software that allows the implementation of many interactive visual applications. Thanks to the symbolic and numerical capabilities of Mathematica, these applications allow the user to interact with the graphical and analytical information in real time. However, Mathematica is a commercially distributed application which makes it difficult for teachers and students to access. The main goal of this paper is to present a new dynamic and interactive tool, created with Mathematica and available in the Computable Document Format. This format allows anyone with a computer to use, at no cost, the PES(Linear)-Tool, even without an active Wolfram Mathematica license. The PES(Linear)-Tool can be used as an active learning tool to promote better student activity and engagement in the learning process, among students enrolled in socio-economic programs. This tool is very intuitive to use which makes it suitable for less experienced users.

Symbolic Analysis of Maude Theories with Narval

AbstractConcurrent functional languages that are endowed with symbolic reasoning capabilities such as Maude offer a high-level, elegant, and efficient approach to programming and analyzing complex, highly nondeterministic software systems. Maude’s symbolic capabilities are based on equational unification and narrowing in rewrite theories, and provide Maude with advanced logic programming capabilities such as unification modulo user-definable equational theories and symbolic reachability analysis in rewrite theories. Intricate computing problems may be effectively and naturally solved in Maude thanks to the synergy of these recently developed symbolic capabilities and classical Maude features, such as: (i) rich type structures with sorts (types), subsorts, and overloading; (ii) equational rewriting modulo various combinations of axioms such as associativity, commutativity, and identity; and (iii) classical reachability analysis in rewrite theories. However, the combination of all of these features may hinder the understanding of Maude symbolic computations for non-experienced developers. The purpose of this article is to describe how programming and analysis of Maude rewrite theories can be made easier by providing a sophisticated graphical tool called Narval that supports the fine-grained inspection of Maude symbolic computations.

Brand Related Capabilities and the Process of Integrated Marketing Communications (IMC): A Resource Based View (RBV)

Purpose – This study aims at examining the effects of the brand related capabilities on the IMC process in consumer markets of Pakistan. It will extend the acceptability of the brand orientation scale in comparison to its application in retail industry only. Design/Methodology/Approach – Both brand management and IMC related literature was thoroughly reviewed to conceptually develop the links between the individual brand related capabilities and IMC process for empirical investigation. Findings – The results of the study established significantly positive relationship between the brands related capabilities and IMC process except for the functional capability. The main contribution is conceptual theorization of distinct, value adding, symbolic and functional capabilities with the IMC process and obtaining statistically significant results for the hypothesized relationships. Originality – This study takes the position of individual capabilities in contrast to studies on aggregate effect of brand orientation on the IMC process in the context of consumer companies operating in Pakistan.

In Search of ‘What Is Africa We Want’: Some Reflections and Actions From Within Africa

It has been asserted that, the land of AFRICA is and has remained to be a very fertile ground for; all diseases, wars, fight and enmity, illiteracy, ignorance, tribalism and inequality, corruption and beggaring, people who lack foresight but only sees what is near them and still fail to know what to do. All these tragedy have put AFRICA continent on the verge of collapse as poverty has become an oldest song that has refused to be forgotten in people's minds and mouth. It has become like a VIRUS or simply incurable disease that is devastating development struggles within countries of the African continent despite adequate material and human resource available therein. There are post-independence tyrannies including betrayal of the promises for liberation. Consequently, are mounting fear of what the young generation are going to become (or what choices they will make) if they continued to be locked-in by poverty which is denying them the essential social services including skills and opportunities they need to make the most of their abilities. This article makes a compelling case for a new approach on What makes Africa in search for What is Africa we want. Key message being that-it is time for Africans to learn from its historical mistakes. The continent is made to believe that it cannot stand on its own feet and develop own countries, attract investment and do business without being tied to DEPENDENCE and DOMINANCE relationship with rich nations. As the basis for growth and development, African governments need further cultivation of strong work ethics, attitudes and social values in the minds of its people, a liberatory education curricular reforms that assume a central role in the way we define our IDENTITY rather than the inherited and adopted colonizer's system of education with its emphasis on SCHOOL LITERACY, NUMERACY and learning of foreign languages with no linking of classroom teaching to a practical world. The continent need a continuity in the demands and dictates of pro-poor, pro-people, pro-development leadership and governance stance within a framework of five interdependent but mutually supportive components which are: (i) the extractive capability, (ii) regulative capability, (iii) distributive capability, (iv) responsive capability; and (v) symbolic capability. They must take responsibility that their inability to create or build business and preserve wealth should not be somebody else's fault. It is, and remains to be their (African governments) fault due to failure in comprehending the basic fundamental rule of wealth creation, which is to keep your money within your racial group.

LPaaS as Micro-Intelligence: Enhancing IoT with Symbolic Reasoning

In the era of Big Data and IoT, successful systems have to be designed to discover, store, process, learn, analyse, and predict from a massive amount of data—in short, they have to behave intelligently. Despite the success of non-symbolic techniques such as deep learning, symbolic approaches to machine intelligence still have a role to play in order to achieve key properties such as observability, explainability, and accountability. In this paper we focus on logic programming (LP), and advocate its role as a provider of symbolic reasoning capabilities in IoT scenarios, suitably complementing non-symbolic ones. In particular, we show how its re-interpretation in terms of LPaaS (Logic Programming as a Service) can work as an enabling technology for distributed situated intelligence. A possible example of hybrid reasoning—where symbolic and non-symbolic techniques fruitfully combine to produce intelligent behaviour—is presented, demonstrating how LPaaS could work in a smart energy grid scenario.

Finite element solution of Poisson Equation over Polygonal Domains using a novel auto mesh generation technique and an explicit integration scheme for nine node linear convex quadrilateral of Lagrange family

This paper presents an explicit integration scheme to compute the stiffness matrix of a nine node linear convex quadrilateral element of Lagrange family using symbolic mathematics and discretisation of polygonal domain by such finite elements using a novel auto mesh generation technique , In finite element analysis, the boundary value problems governed by second order linear partial differential equations, the element stiffness matrices are expressed as integrals of the product of global derivatives over the linear convex quadrilateral region. These matrices can be shown to depend on the material properties and the matrix of integrals with integrands as rational functions with polynomial numerator and the linear denominator (4+ ) in the bivariates over a nine node 2-square (-1 ) with nodes at the points {(-1,-1),(1,-1),(1,1),(-1,1),(0,-1),(1,0).(0,1),(- 1,0),(0,0)} in local parametric space. In this paper, we have computed these integrals in exact forms using the symbolic mathematics capabilities of MATLAB. The proposed explicit finite element integration scheme can be applied to solve boundary value problems in continuum mechanics over convex polygonal domains. We have also developed a novel auto mesh generation technique of all nine node linear convex quadrilaterals for a polygonal domain which provides the nodal coordinates and element connectivity. We have used the explicit integration scheme and this novel auto mesh generation technique to solve the Poisson equation u ,where u is unknown physical variable and in with given Dirichlet boundary conditions over the given convex polygonal domain.

Approximate Analytical Solution of a Third-Order IVP arising in Thin Film Flows driven by Surface Tension

In this paper, we present a way of applying the so-called He's variational iteration method (VIM) to numerically solve the non linear autonomous third-order ordinary dierential equation (ODE) y''' = y^-2 obtained by considering a traveling wave solution admitted by a lubrication equation modeling a two-dimensional spreading of a thin viscous lm on a inclined slope. Approximate analytical solution is derived and compared to the results obtained from the Adomian decomposition method (ADM) proposed in [20], to the exact analytical solution[7,8], to a fth order Runge-Kutta method (DOPRI), a fourth order Runge-Kutta method (RK4), a three-stage fth order Runge-Kutta method (RKD5) developed in [18]. A very good agreement and accuracy is observed. Comparisons are obtained using symbolic capabilities of Maple 18.0 package.

Finite Element Analysis Of Linear Elastic Torsion For Regular Polygons

This paper presents an explicit finite element integration scheme to compute the stiffness matrices for linear convex quadrilaterals. Finite element formulationals express stiffness matrices as double integrals of the products of global derivatives. These integrals can be shown to depend on triple products of the geometric properties matrix and the matrix of integrals containing the rational functions with polynomial numerators and linear denominator in bivariates as integrands over a 2-square. These integrals are computed explicitely by using symbolic mathematics capabilities of MATLAB. The proposed explicit finite element integration scheme can be applied to solve boundary value problems in continuum mechanics over convex polygonal domains.We have also developed an automatic all quadrilateral mesh generation technique for convex polygonal domain which provides the nodal coordinates and element connectivity.We have demonstrated the proposed explicit integration scheme to solve the Poisson Boundary Value Problem for a linear elastic torsion of a non-circular bar with cross sections having profiles of equilateral triangle, a square and regular polygons (pentagon(5-gon)to icosagon(20gon)) which are inscribed in a circle of unit radius. Monotonic convergence from below is observed with known analytical solutions for the Prandtl stress function and torsional constant .We have shown the solutions in Tables which list both the FEM and exact solutions. The graphical solutions of contour level curves and the corresponding finite element meshes are also displayed.

A Symbolic Simulator Platform for the Static Analysis of Thin Plates

The integration of symbolic capabilities into a simulation platform devoted to the analysis of thin plates can provide a greater flexibility in the learning process as it enables to incorporate, to experiment and simulate more complex and user-defined characteristics. With the present work one has built a symbolic simulator for the study of the mechanical behavior of thin plates. These plates, with a rectangular/square basis geometric configuration, are simply supported along its four edges, and can be made from homogeneous or non-homogeneous materials. The capabilities of this platform are briefly illustrated through an illustrative case study.

Symbolic Computation Applied to the Study of the Kernel of a Singular Integral Operator with Non-Carleman Shift and Conjugation

On the Hilbert space \(\widetilde{L}_{2}(\mathbb {T})\) the singular integral operator with non-Carleman shift and conjugation \(K=P_{+}+(aI+AC)P_{-}\) is considered, where \(P_{\pm }\) are the Cauchy projectors, \(A=\sum \nolimits _{j=0}^{m}a_{j}U^{j}\), \(a,a_{j}\), \(j=\overline{1,m}\), are continuous functions on the unit circle \(\mathbb {T}\), U is the shift operator and C is the operator of complex conjugation. We show how the symbolic computation capabilities of the computer algebra system Mathematica can be used to explore the dimension of the kernel of the operator K. The analytical algorithm [ADimKer-NonCarleman] is presented; several nontrivial examples are given.

Exploring the Spectra of Some Classes of Singular Integral Operators with Symbolic Computation

Spectral theory has many applications in several main scientific research areas (structural mechanics, aeronautics, quantum mechanics, ecology, probability theory, electrical engineering, among others) and the importance of its study is globally acknowledged. In recent years, several software applications were made available to the general public with extensive capabilities of symbolic computation. These applications, known as computer algebra systems (CAS), allow to delegate to a computer all, or a significant part, of the symbolic calculations present in many mathematical algorithms. In our work we use the CAS Mathematica to implement for the first time on a computer analytical algorithms developed by us and others within the Operator Theory. The main goal of this paper is to show how the symbolic computation capabilities of Mathematica allow us to explore the spectra of several classes of singular integral operators. For the one-dimensional case, nontrivial rational examples, computed with the automated process called [ASpecPaired-Scalar], are presented. For the matrix case, nontrivial essentially bounded and rational examples, computed with the analytical algorithms [AFact], [SInt], and [ASpecPaired-Matrix], are presented. In both cases, it is possible to check, for each considered paired singular integral operator, if a complex number (chosen arbitrarily) belongs to its spectrum.

Coulomb Interaction in H<sub>2</sub> Molecule for States beyond the Ground State

The focus of our investigation is to evaluate one of the four contributing terms to the coulombic potential energy of an H2 molecule. Specifically, we are interested in the term describing the electronic interaction of the charge distribution of one of the hydrogen atoms with the proton of the second atom. Quantum mechanics provides the charge distribution; hence, the evaluation of this term is a semi-classic quantum physics issue. For states other than the ground state the charge distributions are not spherically symmetric; they are functions of the radial and the angular coordinates. For the excited states we develop exact analytic expressions conducive to the potential energies. Because of the functional complexities of the wave functions, the evaluation of the core integrals is carried out utilizing symbolic capabilities of Mathematica [1]. Plots of these energies vs. the distance between the two protons reveal global features.

Trying to make rational decisions while employing intuitive reasoning: a look at the due-diligence process using the dual-system reasoning model

The main goal of this study is to analyse the utilisation of dual-system reasoning when assessing new ventures. Particularly, the study examined whether investors activate only 'system 2' and apply rational rules during their due-diligence, or if they employ 'system 1' as well, and also use intuitive reasoning during this assessment. Interviews with venture capital managers reveal that during due-diligence investors apply both systems, simultaneously. Investors make abundant efforts to acquire data about the ventures' capabilities and its managers. They then apply actuarial models to decide whether to invest in the company or withdraw. Nonetheless, during these inspections investors also assess the company in regard to its ability to gain symbolic capabilities, which are representative signals, indicating the application of intuitive reasoning to evaluate the company. The results also indicate when there is a discrepancy between the two systems investors find it hard to ignore 'system 1'.

Automatic Inference of Specifications in the K Framework

Despite its many unquestionable benefits, formal specifications are not widely used in industrial software development. In order to reduce the time and effort required to write formal specifications, in this paper we propose a technique for automatically discovering specifications from real code. The proposed methodology relies on the symbolic execution capabilities recently provided by the K framework that we exploit to automatically infer formal specifications from programs that are written in a non-trivial fragment of C, called KernelC. Roughly speaking, our symbolic analysis of KernelC programs explains the execution of a (modifier) function by using other (observer) routines in the program. We implemented our technique in the automated tool Kindspec 2.0, which generates axioms that describe the precise input/output behavior of C routines that handle pointer-based structures (i.e., result values and state change). We describe the implementation of our system and discuss the differences w.r.t. our previous work on inferring specifications from C code.

DiracQ: A Package for Algebraic Manipulation of Non-Commuting Quantum Variables

In several problems of quantum many body physics, one is required to handle complex expressions originating in the non-commutative nature of quantum operators. Their manipulation requires precise ordering and application of simplification rules. This can be cumbersome, tedious and error prone, and often a challenge to the most expert researcher. In this paper we present a software package DiracQ to facilitate such manipulations. The package DiracQ consists of functions based upon and extending considerably the symbolic capabilities of Mathematica . With DiracQ, one can proceed with large scale algebraic manipulations of expressions containing combinations of ordinary numbers or symbols (the c-numbers) and arbitrary sets of non-commuting variables (the q-numbers) with user defined properties. The DiracQ package is user extendable and comes encoded with the algebraic properties of several standard operators in popular usage. These include Fermionic and Bosonic creation and annihilation operators, spin operators, and canonical position and momentum operators. An example book is provided with some suggestive calculations of large-scale algebraic manipulations.

Polynomials orthogonal with respect to exponential integrals

Moment-based methods and related Matlab software are provided for generating orthogonal polynomials and associated Gaussian quadrature rules having as weight function the exponential integral E? of arbitrary positive order ? supported on the positive real line or on a finite interval [0,c], c>0. By using the symbolic capabilities of Matlab, allowing for variable-precision arithmetic, the codes provided can be used to obtain as many of the recurrence coefficients for the orthogonal polynomials as desired, to any given accuracy, by choosing d-digit arithmetic with d large enough to compensate for the underlying ill-conditioning.

Exploring the spectra of some classes of paired singular integral operators: the scalar and matrix cases

The main goal of this paper is to present some results on the spectra of paired singular integral operators with essentially bounded matrix functions coefficients, defined on the unit circle. In addition, we present the spectral algorithms [ASpecPaired-Scalar] and [ASpecPaired-Matrix] which use the symbolic and numeric computation capabilities of the computer algebra system Mathematica to check, for each considered paired singular integral operator with rational coefficients, if a complex number (chosen arbitrarily) belongs to its spectrum. Some nontrivial examples computed with these algorithms are presented.