Search results for: linear transformation semi-groups

Authors: Yanisa Chaiya, Jintana Sanwong

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Let V be a vector space over a field and W a subspace of V. Let Fix(V,W) denote the set of all linear transformations on V with fix all elements in W. In this paper, we show that Fix(V,W) is a semigroup under the composition of maps and describe Green’s relations on this semigroup in terms of images, kernels and the dimensions of subspaces of the quotient space V/W where V/W = {v+W : v is an element in V} with v+W = {v+w : w is an element in W}. Let dim(U) denote the dimension of a vector space U and Vα = {vα : v is an element in V} where vα is an image of v under a linear transformation α. For any cardinal number a let a'= min{b : b > a}. We also show that the ideals of Fix(V,W) are precisely the sets. Fix(r) ={α ∊ Fix(V,W) : dim(Vα/W) < r} where 1 ≤ r ≤ a' and a = dim(V/W). Moreover, we prove that if V is a finite-dimensional vector space, then every ideal of Fix(V,W) is principle.

Keywords: Green’s relations, ideals, linear transformation semi-groups, principle ideals

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Authors: Peyman Sindareh Esfahani, Jeffery Kurt Pieper

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In this paper, the problem of robust model predictive control (MPC) for discrete-time linear systems in linear fractional transformation form with structured uncertainty and norm-bounded disturbance is investigated. The problem of minimization of the cost function for MPC design is converted to minimization of the worst case of the cost function. Then, this problem is reduced to minimization of an upper bound of the cost function subject to a terminal inequality satisfying the l₂-norm of the closed loop system. The characteristic of the linear fractional transformation system is taken into account, and by using some mathematical tools, the robust predictive controller design problem is turned into a linear matrix inequality minimization problem. Afterwards, a formulation which includes an integrator to improve the performance of the proposed robust model predictive controller in steady state condition is studied. The validity of the approaches is illustrated through a robust control benchmark problem.

Keywords: linear fractional transformation, linear matrix inequality, robust model predictive control, state feedback control

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Authors: Abhijith Asok

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This paper presents a generalized approach for the simple linear data transformation, Y=bX, through an integration of multidimensional coordinate geometry, vector space theory and polygonal geometry. The scaling is performed by adding an additional ’Dummy Dimension’ to the n-dimensional data, which helps plot two dimensional component-wise straight lines on pairs of dimensions. The end result is a set of scaled extensions of observations in any of the 2n spatial divisions, where n is the total number of applicable dimensions/dataset variables, created by shifting the n-dimensional plane along the ’Dummy Axis’. The derived scaling factor was found to be dependent on the coordinates of the common point of origin for diverging straight lines and the plane of extension, chosen on and perpendicular to the ’Dummy Axis’, respectively. This result indicates the geometrical interpretation of a linear data transformation and hence, opportunities for a more informed choice of the factor ’b’, based on a better choice of these coordinate values. The paper follows on to identify the effect of this transformation on certain popular distance metrics, wherein for many, the distance metric retained the same scaling factor as that of the features.

Keywords: data transformation, dummy dimension, linear transformation, scaling

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Authors: Manojkumar Sabanayagam

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The Riemann hypothesis is an unsolved millennium problem and the search for a solution to the Riemann hypothesis is to study the pattern of prime number distribution. The scope of this paper is to identify the solution for the critical strip and the critical line axis, which has the non-trivial zero solutions using complex plane functions. The Riemann graphical plot is constructed using a linear complex variable function (X+iY) and is applicable only when X>1. But the investigation shows that complex variable behavior has two zones. The first zone is the transformation zone, where the definition of the complex plane should be a non-linear variable which is the critical strip zone in the graph (X=0 to 1). The second zone is the transformed zone (X>1) defined using linear variables conventionally. This paper deals with the Non-linear function in the transformation zone derived using cosine and sinusoidal time lag w.r.t imaginary number ‘i’. The alternate complex variable (Cosθ+i Sinθ) is used to understand the variables in the critical strip zone. It is concluded that the non-trivial zeros present in the Real part 0.5 are because the linear function is not the correct approach in the critical strip. This paper provides the solution to Reimann's hypothesis.

Keywords: Reimann hypothesis, critical strip, complex plane, transformation zone

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Authors: Abdelati El Allaoui, Said Melliani, Lalla Saadia Chadli

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The objective of this paper is to study the existence and uniqueness of Mild solutions for a complex fuzzy evolution equation with nonlocal conditions that accommodates the notion of fuzzy sets defined by complex-valued membership functions. We first propose definition of complex fuzzy strongly continuous semigroups. We then give existence and uniqueness result relevant to the complex fuzzy evolution equation.

Keywords: Complex fuzzy evolution equations, nonlocal conditions, mild solution, complex fuzzy semigroups

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Authors: Chollawat Pookpienlert, Jintana Sanwong

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An element a of a semigroup S is called left (right) regular if there exists x in S such that a=xa² (a=a²x) and said to be intra-regular if there exist u,v in such that a=ua²v. Let T(X) be the semigroup of all full transformations on a set X under the composition of maps. For a fixed nonempty subset Y of X, let Fix(X,Y)={α ™ T(X) : yα=y for all y ™ Y}, where yα is the image of y under α. Then Fix(X,Y) is a semigroup of full transformations on X which fix all elements in Y. Here, we characterize left regular, right regular and intra-regular elements of Fix(X,Y) which characterizations are shown as follows: For α ™ Fix(X,Y), (i) α is left regular if and only if Xα\Y = Xα²\Y, (ii) α is right regular if and only if πα = πα², (iii) α is intra-regular if and only if | Xα\Y | = | Xα²\Y | such that Xα = {xα : x ™ X} and πα = {xα⁻¹ : x ™ Xα} in which xα⁻¹ = {a ™ X : aα=x}. Moreover, those regularities are equivalent if Xα\Y is a finite set. In addition, we count the number of those elements of Fix(X,Y) when X is a finite set. Finally, we determine the maximal congruence ρ on Fix(X,Y) when X is finite and Y is a nonempty proper subset of X. If we let | X \Y | = n, then we obtain that ρ = (Fixn x Fixn) ∪ (H ε x H ε) where Fixn = {α ™ Fix(X,Y) : | Xα\Y | < n} and H ε is the group of units of Fix(X,Y). Furthermore, we show that the maximal congruence is unique.

Keywords: intra-regular, left regular, maximal congruence, right regular, transformation semigroup

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Authors: Faisal Yousafzai, Murad-ul-Islam Khan, Kar Ping Shum

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We introduce the concept of partially inverse AG**-groupoids which is almost parallel to the concepts of E-inversive semigroups and E-inversive E-semigroups. Some characterization problems are provided on partially inverse AG**-groupoids. We give necessary and sufficient conditions for a partially inverse AG**-subgroupoid E to be a rectangular band. Furthermore, we determine the unitary congruence η on a partially inverse AG**-groupoid and show that each partially inverse AG**-groupoid possesses an idempotent separating congruence μ. We also study anti-separative commutative image of a locally associative AG**-groupoid. Finally, we give the concept of completely N-inverse AG**-groupoid and characterize a maximum idempotent separating congruence.

Keywords: AG**-groupoids, congruences, inverses, rectangular band

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Authors: M. Berrehail, F. Benamira

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We study the quantum motion of a particle in the presence of a time- dependent linear potential using an operator invariant that is quadratic in p and linear in q within the framework of the Lewis-Riesenfeld invariant, The special invariant operator proposed in this work is demonstrated to be an Hermitian operator which has an Airy wave packet as its Eigenfunction

Keywords: airy wave packet, ivariant, time-dependent linear potential, unitary transformation

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Authors: Ibrahim Bashir, Yahaya Y. Yusuf

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The ongoing shift towards Industry 4.0 represents a critical growth factor in the industrial enterprise, where the digital transformation of industries is increasingly seen as a crucial element for competitiveness. This transformation holds substantial potential, yet its full benefits have yet to be realized due to the fragmented approach to introducing Industry 4.0 technologies. Therefore, this pilot study aims to explore the individual and collective impact of Industry 4.0 technologies and digital transformation on organizational performance. Data were collected through a questionnaire-based survey across 51 companies in the manufacturing industry in the United Kingdom. The correlations and multiple linear regression analyses were conducted to assess the relationship and impact between the variables in the study. The results show that Industry 4.0 and digital transformation positively influence organizational performance and that Industry 4.0 technologies positively influence digital transformation. The results of this pilot study indicate that the implementation of Industry 4.0 technology is vital for increasing organizational performance; however, their roles differ largely. The differences are manifest in how the types of Industry 4.0 technologies correlate with how organizations integrate digital technologies into their operations. Hence, there is a clear indication of a strong correlation between Industry 4.0 technology, digital transformation, and organizational performance. Consequently, our study presents numerous pertinent implications that propel the theory of I4.0, digital business transformation (DBT), and organizational performance forward, as well as guide managers in the manufacturing sector.

Keywords: industry 4.0 technologies, digital transformation, digital integration, organizational performance

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Authors: Alan C. Lin, Tzu-Kuan Lin, Tsong Der Lin

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This paper proposes a new method to find the equations of transformation matrix for the rotation angles of the two rotational axes and the coordinates of the three linear axes of an orthogonal multi-axis milling machine. This approach provides intuitive physical meanings for rotation angles of multi-axis machines, which can be used to evaluate the accuracy of the conversion from CL data to NC data.

Keywords: CAM, multi-axis milling machining, transformation matrix, rotation angles

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Authors: Mishu Gupta, Rama Gupta

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It has been elucidated here that non- autonomous discrete non-linear Schrödinger equation is associated with saturable non-linearity through photo-refractive media. We have investigated the localized solution of non-autonomous saturable discrete non-linear Schrödinger equations. The similarity transformation has been involved in converting non-autonomous saturable discrete non-linear Schrödinger equation to constant-coefficient saturable discrete non-linear Schrödinger equation (SDNLSE), whose exact solution is already known. By back substitution, the solution of the non-autonomous version has been obtained. We have analysed our solution for the hyperbolic and periodic form of gain/loss term, and interesting results have been obtained. The most important characteristic role is that it helps us to analyse the propagation of electromagnetic waves in glass fibres and other optical wave mediums. Also, the usage of SDNLSE has been seen in tight binding for Bose-Einstein condensates in optical mediums. Even the solutions are interrelated, and its properties are prominently used in various physical aspects like optical waveguides, Bose-Einstein (B-E) condensates in optical mediums, Non-linear optics in photonic crystals, and non-linear kerr–type non-linearity effect and photo refracting medium.

Keywords: B-E-Bose-Einstein, DNLSE-Discrete non linear schrodinger equation, NLSE-non linear schrodinger equation, SDNLSE - saturable discrete non linear Schrodinger equation

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Authors: Sana Ahrar

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Cities are undergoing rapid transformation with the change in lifestyle and technological advancements. These transformations may be experienced or physically visible in the built form. This paper focuses on the relationship between the social, physical environment, change in lifestyle and the interrelated factors influencing the transformation of any historic city. Shahjahanabad as a city has undergone transformation under the various political powers as well as the various policy implementations after independence. These visible traces of transformation diffused throughout the city may be due to socio-economic, historic, political factors and due to the globalization process. This study shall enable evolving a theory for the study of transformation of Historic cities such as Shahjahanabad: which has been plundered, rebuilt, and which still thrives as a ‘living heritage city’. The theory developed will be the process of studying the transformation and can be used by planners, policy makers and researchers in different urban contexts.

Keywords: heritage, historic cities, Shahjahanabad, transformation

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Authors: Franziska Schaefer, Marlene Kuhn, Heiner Otten

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In the very near future, digitization will be the main challenge a company has to master to survive in a highly competitive market. Developing the right transformation strategy by considering all relevant aspects determines the success or failure of a company. Especially the digital focus on the customer plays a key role in creating sustainable competitive advantages, also leading to new tasks within the quality management. Therefore, quality management needs to be particularly addressed to support the upcoming digital change. In this paper, we present an analysis of existing digital transformation approaches and derive a transformation strategy from a quality management perspective. We identify and classify different transformation dimensions and assess their relevance to quality management tasks, resulting in a quality-adapted digital transformation model. Furthermore, we introduce applicable and customized quality management methods to support the presented digital transformation tasks. With our developed model we provide a digital transformation guideline from a quality perspective to master future disruptive changes.

Keywords: digital transformation, digitization, quality management, strategy

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Authors: Tiexin Wang, Sebastien Truptil, Frederick Benaben

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Model transformation, as a pivotal aspect of Model-driven engineering, attracts more and more attentions both from researchers and practitioners. Many domains (enterprise engineering, software engineering, knowledge engineering, etc.) use model transformation principles and practices to serve to their domain specific problems; furthermore, model transformation could also be used to fulfill the gap between different domains: by sharing and exchanging knowledge. Since model transformation has been widely used, there comes new requirement on it: effectively and efficiently define the transformation process and reduce manual effort that involved in. This paper presents an automatic model transformation methodology based on semantic and syntactic comparisons, and focuses particularly on granularity issue that existed in transformation process. Comparing to the traditional model transformation methodologies, this methodology serves to a general purpose: cross-domain methodology. Semantic and syntactic checking measurements are combined into a refined transformation process, which solves the granularity issue. Moreover, semantic and syntactic comparisons are supported by software tool; manual effort is replaced in this way.

Keywords: automatic model transformation, granularity issue, model-driven engineering, semantic and syntactic comparisons

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Authors: A. Boulanoir, B. Ould Bouamama, A. Debiane, N. Achour

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The paper deals with robust Fault Detection and isolation with respect to parameter uncertainties based on linear fractional transformation form (LFT) Bond graph. The innovative interest of the proposed methodology is the use only one representation for systematic generation of robust analytical redundancy relations and adaptive residual thresholds for sensibility analysis. Furthermore, the parameter uncertainties are introduced graphically in the bond graph model. The methodology applied to the nonlinear industrial Electro-Mechanical Actuators (EMA) used in avionic systems, has determined first the structural monitorability analysis (which component can be monitored) with given instrumentation architecture with any need of complex calculation and secondly robust fault indicators for online supervision.

Keywords: bond graph (BG), electro mechanical actuators (EMA), fault detection and isolation (FDI), linear fractional transformation (LFT), mechatronic systems, parameter uncertainties, avionic system

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Authors: Mounir Gaci, Salim Meziani, Atmane Fouathia

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The purpose of the present paper is to model the behavior of metal alloy, type TRIP steel (Transformation Induced Plasticity), during solid/solid phase transition. A two-dimensional micromechanical model is implemented in finite element software (ZEBULON) to simulate the martensitic transformation in Fe-Ni-C steel grain under mechanical tensile stress of 250 MPa. The effects of non-uniform grain boundary and the criterion of mechanical shear load on the transformation and on the TRIP value during martensitic transformation are studied. The suggested mechanical criterion is favourable to the influence of the shear phenomenon on the progression of the martensitic transformation (Magee’s mechanism). The obtained results are in satisfactory agreement with experimental ones and show the influence of the grain boundary shape and the chosen mechanical criterion (SMF) on the transformation parameters.

Keywords: martensitic transformation, non-uniform Grain Boundary, TRIP, shear Mechanical force (SMF)

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Authors: Wisu Suntoyo, Dedy Sushandoyo

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Innovation and digital transformation are essential for firms’ competitiveness in the digital age. The competition in Indonesia’s banking industry provides an intriguing case study for understanding how digital transformation can generate innovation in established companies. The empirical evidence of this study is mainly based on interviews and annual reports examining four established banks in their various states of digital transformation. The findings of this study reveal that banks’ digital transformations that lead to innovations differ in terms of the activities undertaken and the outcomes achieved depending on the state of advancement in which they are. Digital transformation is a complex and challenging process, and this study finds that with this strategy, established banks have shown capable of generating innovation. Banks can choose types of transformation activities that generate radical, architectural, modular, or even incremental innovations.

Keywords: digital transformation, innovations, banking industry, established banks

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Authors: Zeynep Karacor, Rahime Hulya Ozturk

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In recent years, the rise of population density and the problem of aging population took attention to the health expenditures. In Turkey, some regulations and infrastructure changes in health sector have occurred. These changes are called Health Transformation Program. The productivity of health services, patient satisfaction, quality of services are tried to be improved with this program. Some radical changes are applied in Turkish economy in this context. The aim of this paper is to present the effects of Health Transformation Program on health expenditures. In the first part of the paper, some information’s about health system and applications in Turkey are discussed. In the second part, the aims of Health Transformation Program are explained. And in the third part the effects of Health Transformation Program on health expenditures are examined.

Keywords: health transformation program, Turkey, health services, health expenditures

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Authors: Phuoc Si Nguyen

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Frequency transformation with Pascal matrix equations is a method for transforming an electronic filter (analogue or digital) into another filter. The technique is based on frequency transformation in the s-domain, bilinear z-transform with pre-warping frequency, inverse bilinear transformation and a very useful application of the Pascal’s triangle that simplifies computing and enables calculation by hand when transforming from one filter to another. This paper will introduce two methods to transform a filter into a digital filter: frequency transformation from the s-domain into the z-domain; and frequency transformation in the z-domain. Further, two Pascal matrix equations are derived: an analogue to digital filter Pascal matrix equation and a digital to digital filter Pascal matrix equation. These are used to design a desired digital filter from a given filter.

Keywords: frequency transformation, bilinear z-transformation, pre-warping frequency, digital filters, analog filters, pascal’s triangle

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Authors: Driss Kettani

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In this paper, we shed light on “Digital Divide 2.0,” which we see as COVID-19’s Version of the Digital Divide! We believe that “Fighting” against Digital Divide 2.0 necessitates for a Country to be seriously advanced in the Global Digital Transformation that is, naturally, a complex, delicate, costly and long-term Process. We build an argument supporting our assumption and, from there, we present the foundations of a computational framework to guide and streamline Digital Transformation at all levels.

Keywords: digital divide 2.0, digital transformation, ICTs for development, computational outcomes assessment

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Authors: Bin Li

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In the era of the digital economy, digital transformation has gradually become a strategic choice for enterprise development, but there is a relative lack of systematic research from the perspective of enterprise growth. Based on the sample of Chinese A-share listed companies from 2011 to 2021, this paper constructs A digital transformation index system and an enterprise growth composite index to empirically test the impact of enterprise digital transformation on enterprise growth and its mechanism. The results show that digital transformation can significantly promote corporate growth. The mechanism analysis finds that reducing operating costs, optimizing human capital structure, promoting R&D output and improving digital innovation capability play an important intermediary role in the process of digital transformation promoting corporate growth. At the same time, the level of external digital infrastructure and the strength of organizational resilience play a positive moderating role in the process of corporate digital transformation promoting corporate growth. In addition, while further analyzing the heterogeneity of enterprises, this paper further deepens the analysis of the driving factors and digital technology support of digital transformation, as well as the three dimensions of enterprise growth, thus deepening the research depth of enterprise digital transformation.

Keywords: digital transformation, enterprise growth, digital technology, digital infrastructure, organization resilience, digital innovation

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Authors: Jamal A. Gledan, Othman A. Azzeidani

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During the last decade, Libya established a new Geodetic Datum called Libyan Geodetic Datum 2006 (LGD 2006) by using GPS, whereas the ground traversing method was used to establish the last Libyan datum which was called the Europe Libyan Datum 79 (ELD79). The current research paper introduces ELD79 to LGD2006 coordinate transformation technique, the accurate comparison of transformation between multiple regression equations and the three-parameters model (Bursa-Wolf). The results had been obtained show that the overall accuracy of stepwise multi regression equations is better than that can be determined by using Bursa-Wolf transformation model.

Keywords: geodetic datum, horizontal control points, traditional similarity transformation model, unconventional transformation techniques

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Authors: Dalia Suša Vugec, Ana-Marija Stjepić, Darija Ivandić Vidović

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Digital transformation is one of the latest trends on the global market. In order to maintain the competitive advantage and sustainability, increasing number of organizations are conducting digital transformation processes. Those organizations are changing their business processes and creating new business models with the help of digital technologies. In that sense, one should also observe the role of business process management (BPM) and its maturity in driving digital transformation. Therefore, the goal of this paper is to investigate the role of BPM in digital transformation process within one organization. Since experiences from practice show that organizations from financial sector could be observed as leaders in digital transformation, an insurance company has been selected to participate in the study. That company has been selected due to the high level of its BPM maturity and the fact that it has previously been through a digital transformation process. In order to fulfill the goals of the paper, several interviews, as well as questionnaires, have been conducted within the selected company. The results are presented in a form of a case study. Results indicate that digital transformation process within the observed company has been successful, with special focus on the development of digital strategy, BPM and change management. The role of BPM in the digital transformation of the observed company is further discussed in the paper.

Keywords: business process management, case study, Croatia, digital transformation, insurance company

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Authors: Anod H. Alhazmi, Hanaa A. Yamani

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The lack of digital transformation professionals could prevent Saudi Arabia’s universities from providing digital services. The task of understanding what digital skills are needed within an organization, measuring the existing skills, and developing or attracting talents is a complex task. This paper provides a comprehensive analysis of the digital transformation skills needed in the organizations who seek digital transformation and identifies the skills and competencies framework DigSC built on Skills Framework for the Informational Age (SFIA) framework that is adopted by the Ministry of Communications and Information Technology (MCIT) in Saudi Arabia. The framework adopted identifies the main digital transformation skills clusters, categories and levels of responsibilities for each job description to fill the gap between this requirement and the digital skills supplied by the Umm Alqura University (UQU).

Keywords: competencies, digital transformation, framework, skills, Umm Alqura university

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Authors: Yaxiao Zhang, Yangzhou Chen

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This study investigate the formation problem for high-order continuous-time multi-robot with bounded symmetric time-varying delay protocol under switched directed communication topology. By using a linear transformation, the formation problem is transformed to stability analysis of a switched delay system. Under the assumption that each communication topology has a directed spanning tree, sufficient conditions are presented in terms of linear matrix inequalities (LMIs) that the multi-robot system can achieve a desired formation by the trade-off among the pre-exist topologies with the help of the scheme of average dwell time. A numeral example is presented to illustrate the effectiveness of the obtained results.

Keywords: multi-robot systems, formation, switched directed topology, symmetric time-varying delay, average dwell time, linear matrix inequalities (lmis)

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Authors: Hsiu Hua Hu

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Digital transformation has widely affected various industries. It provides technological innovation, process redesign, new business model construction, and talent value creation. This transformation not only allows organizations to obtain and deploy specific technologies and methods suitable for organizational reengineering but also is an important way to solve management problems in human resource (HR) reengineering, business efficiency, and process redesign. In this study, we present the results of a qualitative study that offers insight into a series of key feature of reengineering related to the digital transformation and how to create talent value when the companies successfully perform digital transformation and human resource reengineering, which is led by business digitalization strategies including talent planning, talent acquisition, talent adjustment, and talent development. Drawing from the qualitative investigation findings, we built an inductive model of HR reengineering, which aims to provide research and practical references on future digital transformation and management inquiry.

Keywords: talent value creation, digital transformation, HR reengineering, qualitative study

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Authors: Skezeer John B. Paz, Ederlina G. Nocon

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Finding an optimal binary linear code is a central problem in coding theory. A binary linear code C = [n, k, d] is called optimal if there is no linear code with higher minimum distance d given the length n and the dimension k. There are bounds giving limits for the minimum distance d of a linear code of fixed length n and dimension k. The lower bound which can be taken by construction process tells that there is a known linear code having this minimum distance. The upper bound is given by theoretic results such as Griesmer bound. One way to find an optimal binary linear code is to make the lower bound of d equal to its higher bound. That is, to construct a binary linear code which achieves the highest possible value of its minimum distance d, given n and k. Some optimal binary linear codes were presented by Andries Brouwer in his published table on bounds of the minimum distance d of binary linear codes for 1 ≤ n ≤ 256 and k ≤ n. This was further improved by Markus Grassl by giving a detailed construction process for each code exhibiting the lower bound. In this paper, we construct new optimal binary linear codes by using some construction processes on existing binary linear codes. Particularly, we developed an algorithm applied to the codes already constructed to extend the list of optimal binary linear codes up to 257 ≤ n ≤ 300 for k ≤ 7.

Keywords: bounds of linear codes, Griesmer bound, construction of linear codes, optimal binary linear codes

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Authors: Sarah E. Stief, Anne Theresa Eidhoff, Markus Voeth

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Despite all progress firms are facing the increasing need to adapt and assimilate digital technologies to transform their business activities in order to pursue business development. By using new digital technologies, firms can implement major business improvements in order to stay competitive and foster new growth potentials. The corresponding phenomenon of digital transformation has received some attention in previous literature in respect to industries such as media and publishing. Nevertheless, there is a lack of understanding of the concept and its organization within firms. With the help of twenty-three in-depth field interviews with German experts responsible for their company’s digital transformation, we examined what digital transformation encompasses, how it is organized and which opportunities and challenges arise within firms. Our results indicate that digital transformation is an inevitable task for all firms, as it bears the potential to comprehensively optimize and reshape established business activities and can thus be seen as a strategy of business development.

Keywords: business development, digitalization, digital strategies, digital transformation

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Authors: Y. Pala, M. O. Ertas

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In this paper, the general Riccati equation is analytically solved by a new transformation. By the method developed, looking at the transformed equation, whether or not an explicit solution can be obtained is readily determined. Since the present method does not require a proper solution for the general solution, it is especially suitable for equations whose proper solutions cannot be seen at first glance. Since the transformed second order linear equation obtained by the present transformation has the simplest form that it can have, it is immediately seen whether or not the original equation can be solved analytically. The present method is exemplified by several examples.

Keywords: Riccati equation, analytical solution, proper solution, nonlinear

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Authors: Ahmed Elaksher, Islam Omar

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For many years, Mars surface has been a mystery for scientists. Lately with the help of geospatial data and photogrammetric procedures researchers were able to capture some insights about this planet. Two of the most imperative data sources to explore Mars are the The High Resolution Imaging Science Experiment (HiRISE) and the Mars Orbiter Laser Altimeter (MOLA). HiRISE is one of six science instruments carried by the Mars Reconnaissance Orbiter, launched August 12, 2005, and managed by NASA. The MOLA sensor is a laser altimeter carried by the Mars Global Surveyor (MGS) and launched on November 7, 1996. In this project, we used MOLA-based DEMs to orthorectify HiRISE optical images for generating a more accurate and trustful surface of Mars. The MOLA data was interpolated using the kriging interpolation technique. Corresponding tie points were digitized from both datasets. These points were employed in co-registering both datasets using GIS analysis tools. In this project, we employed three different 3D to 2D transformation models. These are the parallel projection (3D affine) transformation model; the extended parallel projection transformation model; the Direct Linear Transformation (DLT) model. A set of tie-points was digitized from both datasets. These points were split into two sets: Ground Control Points (GCPs), used to evaluate the transformation parameters using least squares adjustment techniques, and check points (ChkPs) to evaluate the computed transformation parameters. Results were evaluated using the RMSEs between the precise horizontal coordinates of the digitized check points and those estimated through the transformation models using the computed transformation parameters. For each set of GCPs, three different configurations of GCPs and check points were tested, and average RMSEs are reported. It was found that for the 2D transformation models, average RMSEs were in the range of five meters. Increasing the number of GCPs from six to ten points improve the accuracy of the results with about two and half meters. Further increasing the number of GCPs didn’t improve the results significantly. Using the 3D to 2D transformation parameters provided three to two meters accuracy. Best results were reported using the DLT transformation model. However, increasing the number of GCPS didn’t have substantial effect. The results support the use of the DLT model as it provides the required accuracy for ASPRS large scale mapping standards. However, well distributed sets of GCPs is a key to provide such accuracy. The model is simple to apply and doesn’t need substantial computations.

Keywords: mars, photogrammetry, MOLA, HiRISE

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