Alternative Representation Research Articles

A Phase Domain Transmission Line Model Taking into Account the Algebraic Representation of its Eigenvectors

An alternative phase domain representation for transmission lines using ABCD matrices is presented. The proposed representation requests analytical calculation of the [Z][Y] product eigenvalues, where [Z] and[Y] are, respectively, the longitudinal impedance and the transversal admittance matrices of the line. The main idea is to apply the modal domain representation to obtain a direct phase domain model. For this, the analytical development of the conversion phase-mode-phase for the line currents and voltages are done. This way, the phase voltages and currents written as functions of the line longitudinal and transversal parameters are obtained, and these equations can be written as an ABCD matrix. To validate the proposed model, it was applied to represent a typical three-phase line over the entire frequency range during transient conditions. For this, the model was used to simulate the energization by a three-phase sinusoidal generator and lightning striking a phase of the line. The results obtained were compared with those obtained from a classic model developed in the modal domain, and both models are in agreement.

Alternative Representations of Some Arithmetic Functions

This article presents some results of the attempt to simplify the writing of arithmetic functions on the computer so that users can apply them without additional operations, such as summing after a set whose elements must be calculated, such as the set of numbers prime. The important role of the remainder function in defining most arithmetic functions is highlighted. Defining algorithms for the prime factorization of natural numbers highlights the possibility of representing natural numbers in a basis as "natural" as possible for natural numbers, namely the basis of prime numbers. The disadvantage of this natural basis is, for the time being, that it is infinitely dimensional. For now, this representation provides advantages but also disadvantages. Among the arithmetic functions proposed in the article, there are also statistical characterizations of the distribution of prime numbers, given with the hope of helping a better knowledge of the set of prime numbers. The importance of the remainder function in the computational definitions of arithmetic functions leads to reflections on the importance of fundamental operations - addition and multiplication - of natural numbers and the importance of inverse functions - subtraction and division. In turn, these operations can be seen as functions of two variables on the set of natural numbers. From here, readers are invited to reflect on the problem of the origin of natural numbers, the origin based on revelation or the origin provided by set theory, although this may also be a revelation.

Representation of the infimum and supremum of a family of multivariate distribution functions

Sklar's theorem represents a single multivariate distribution function through its univariate marginal distributions and a copula. However, it fails in general when it comes to the representation of the envelopes of a family F of multivariate distribution functions (i.e. its point-wise infimum and supremum), even if we allow more general representing functions than copulas. In this paper we develop an alternative representation which describes the envelopes of a family F in terms of the copulas that correspond to the members of F. Our representation is reminiscent of Sklar's representation but is based on the idea of corner patches of copulas. We prove a series of four representation theorems; (1) a general one, which holds even if the envelopes of the family do not possess a Sklar type representation, (2) a version tailored for the case when the envelopes do possess a Sklar type representation, (3) a theorem for families of continuous distribution functions, and (4) a variant appropriate for modeling dependencies of absolutely continuous random variables. In addition, we demonstrate how our results can be applied to give a Sklar type theorem in the imprecise probability setting, which offers a new approach to multivariate probability boxes.

On Two Fundamental Problems on APN Power Functions

The six infinite families of power APN functions are among the oldest known instances of APN functions, and it has been conjectured in 2000 that they exhaust all possible power APN functions. Another long-standing open problem is that of the Walsh spectrum of the Dobbertin power family, which is still unknown. Those of Kasami, Niho and Welch functions are known, but not the precise values of their Walsh transform, with rare exceptions. One promising approach that could lead to the resolution of these problems is to consider alternative representations of the functions in questions. We derive alternative representations for the infinite APN monomial families. We show how the Niho, Welch, and Dobbertin functions can be represented as the composition <inline-formula> <tex-math notation="LaTeX">$x^{i} \circ x^{1/j}$ </tex-math></inline-formula> of two power functions, and prove that our representations are optimal, i.e. no two power functions of lesser algebraic degree can be used to represent the functions in this way. We investigate compositions <inline-formula> <tex-math notation="LaTeX">$x^{i} \circ L \circ x^{1/j}$ </tex-math></inline-formula> for a linear polynomial <inline-formula> <tex-math notation="LaTeX">$L$ </tex-math></inline-formula>, show how the Kasami functions in odd dimension can be expressed in this way with <inline-formula> <tex-math notation="LaTeX">$i=j$ </tex-math></inline-formula> being a Gold exponent and compute all APN functions of this form for <inline-formula> <tex-math notation="LaTeX">$n \le 9$ </tex-math></inline-formula> and for <inline-formula> <tex-math notation="LaTeX">$L$ </tex-math></inline-formula> with binary coefficients, thereby showing that our theoretical constructions exhaust all possible cases. We present observations and data on power functions with exponent <inline-formula> <tex-math notation="LaTeX">$\sum _{i = 1}^{k-1} 2^{2ni} - 1$ </tex-math></inline-formula> which generalize the inverse and Dobbertin families. We present data on the Walsh spectrum of the Dobbertin function for <inline-formula> <tex-math notation="LaTeX">$n \le 35$ </tex-math></inline-formula>, and conjecture its exact form. As an application of our results, we determine the exact values of the Walsh transform of the Kasami function at all points of a special form. Computations performed for <inline-formula> <tex-math notation="LaTeX">$n\leq 21$ </tex-math></inline-formula> show that these points cover about 2/3 of the field.

다큐멘터리 〈개의 역사〉에 나타난 결정체-이미지: 견자의 영화와 듣기의 영화

This paper intends to analyze the documentary film〈Baek-gu〉, directed by KIM Bo-ram, as a ‘cystal-image’ that appears in Gilles Deleuze’s ‘Cinema Ⅱ: The Time-image’.〈Baek-gu〉 is documentary, showing ‘existence’, ‘memory’, and ‘space/place’ through the live of stray dogs and women. This film begins with the death of Baek-gu, who wandered the neighborhood. Baek-gu’s past times are connected with the lives of countless beings. And the end of the film, Baek-gu and the director’s life are connected. The audience has an opportunity to think about their past while looking at the lives of the main characters in the film 〈Baek-gu〉. So this filme is a cinema of the seer. Furthermore, it is a ‘cinema of the listen’ that allows people to listen not only to their own lives but also the live of others. This paper analyzes the images of clairvoyant and listening in〈Baek-gu〉 as Gilles Deleuze’s crystal-image. Gilles Deleuze called the image that appears when the actual image and the virtual image coalesce and crystallize as a ‘crystal-image’. The crystal-image is the first image of the time-image, and consists of three types : mirror-image, transparent and opaque, and seed and environment. In particular, this paper analyzes the actual image as the image to be seen and the virtual image as the image to be heard, and tries to interpret the crystal-image as the clairvoyant cinema and the listen cinema. Through this, ultimately, we intend to explore the possibility of alternative representation in which the crystal-image gives the audience the experience of ’I am the other’.

A Conditioned Probabilistic Method for the Solution of the Inverse Acoustic Scattering Problem

In the present work, a novel stochastic method has been developed and investigated in order to face the time-reduced inverse scattering problem, governed by the Helmholtz equation, outside connected or disconnected obstacles supporting boundary conditions of Dirichlet type. On the basis of the stochastic analysis, a series of efficient and alternative stochastic representations of the scattering field have been constructed. These novel representations constitute conceptually the probabilistic analogue of the well known deterministic integral representations involving the famous Green’s functions, and so merit special importance. Their advantage lies in their intrinsic probabilistic nature, allowing to solve the direct and inverse scattering problem in the realm of local methods, which are strongly preferable in comparison with the traditional global ones. The aforementioned locality reflects the ability to handle the scattering field only in small bounded portions of the scattering medium by monitoring suitable stochastic processes, confined in narrow sub-regions where data are available. Especially in the realm of the inverse scattering problem, two different schemes are proposed facing reconstruction from the far field and near field data, respectively. The crucial characteristic of the inversion is that the reconstruction is fulfilled through stochastic experiments, taking place in the interior of conical regions whose base belong to the data region, while their vertices detect appropriately the supporting surfaces of the sought scatterers.

New families of mock theta functions and partial fraction decomposition

In 2000, Andrews challenged mathematicians in the 21st century to elucidate the overlap between classes of q-series and modular forms. Motivated by Andrews' challenge, seeking q-hypergeometric series which are mock theta functions in the modern sense and finding their alternative representations have attracted the attention of many mathematicians in recent years. In this paper, we use partial fraction decomposition to give rise to several families of two-parameter mock theta functions and express them in the form of Appell-Lerch sums. In particular, we establish some identities involving several families of mock theta functions and Appell-Lerch sums which imply three identities proved by Cui and Gu.

On the divergence theorem for submanifolds of Euclidean vector spaces within the theory of second-gradient continua

In the theory of second-gradient continua, the internal virtual work functional can be considered as a second-order distribution in which the virtual displacements take the role of test functions. In its easiest representation, the internal virtual work functional is represented as a volume integral over a subset of the three-dimensional Euclidean vector space and involves first and second derivatives of the virtual displacements. In this paper, we show by an iterative integration by parts procedure how an alternative representation of such a functional can be obtained when the integration domain is a subset that contains also edges and wedges. Since this procedure strongly relies on the divergence theorem for submanifolds of a Euclidean vector space, it is a main goal to derive this divergence theorem for submanifolds starting from Stokes’ theorem for manifolds. To that end, results from Riemannian geometry are gathered and applied to the submanifold case.

Violence against Women and Girls: Female Filmmakers Critique the Menace

Violence against Women and Girls: Female Filmmakers Critique the Menace

Chemistry without the Born-Oppenheimer approximation.

Chemistry without the Born-Oppenheimer approximation.

Toward Remaking Software Development to Secure It

Modern software development depends on tools and techniques to represent implied information processing logic to the human engineer, relying chiefly on effortful human reasoning to best determine critical properties of the software system. Current conceptualization, visualization and contextualization of software in development amounts to a significant under-utilization of already limited development resources directed to optimization, prevention, and addressing fundamental security properties of the software system. As a step toward increasing such utilization as a basis for a global ecosystem of secure software, this work explores and evaluates an alternative representation of software source code for the sake of secure development, manifesting universal, critical properties of the system to enhance control of security factors while the bulk of the properties of the system are being determined and the costly skills of the developer are directed to the many aspects of the task.

Problematic Technology Use: The impact of personality and continued use

Modern software development depends on tools and techniques to represent implied information processing logic to the human engineer, relying chiefly on effortful human reasoning to best determine critical properties of the software system. Current conceptualization, visualization and contextualization of software in development amounts to a significant under-utilization of already limited development resources directed to optimization, prevention, and addressing fundamental security properties of the software system. As a step toward increasing such utilization as a basis for a global ecosystem of secure software, this work explores and evaluates an alternative representation of software source code for the sake of secure development, manifesting universal, critical properties of the system to enhance control of security factors while the bulk of the properties of the system are being determined and the costly skills of the developer are directed to the many aspects of the task.

An alternative linear flow model and boundary integral flow representation for ship motions in regular waves

The basic issue of formulating a linear flow model for the analysis of potential flow around a ship advancing at a constant speed in regular waves is considered. Specifically, the ‘rigid-waterplane flow model’, previously considered for diffraction–radiation of regular waves by offshore structures, is applied to analyze flows around ships advancing in regular waves. A straightforward application of Green’s fundamental identity to the rigid-waterplane flow model yields a remarkable new boundary integral flow representation. Indeed, this flow representation does not involve a line integral around the mean waterline of the ship hull surface, is weakly singular, does not involve a distribution of dipoles over the ship-hull surface, and is free from irregular frequencies. In the particular case of flow around a ship steadily advancing in calm water, the boundary integral flow representation obtained in the study via an analysis based on the rigid-waterplane flow model is identical to the flow representation associated with the Neumann–Michell theory, which is based on a different linear flow model that only considers the flow region strictly outside the ship but consistently accounts for the linear contribution of the thin band of water between the wave profile along the ship hull surface and the undisturbed free surface. This result strongly suggests that the classical application of Green’s basic identity to analyze linear potential flow around a ship advancing in regular waves or in calm water, which yields a notoriously troublesome line integral around the ship waterline, may be questionable due to possible incompatibilities between the Neumann boundary condition at the ship hull surface and the linear free surface boundary condition associated with flows around ships advancing in calm water or in regular waves. This fundamental difficulty may be alleviated in the rigid-waterplane flow model, which imposes a compatibility condition between the Neumann boundary condition at the rigid lid that artificially closes the open ship hull surface and the linear boundary condition at the free surface above the waterplane-lid. The boundary integral flow representation given in the study also holds for diffraction–radiation of regular waves by offshore structures. Thus, this new flow representation provides a common mathematical basis, which fundamentally differs from the basis steadfastly adopted over the past fifty years, for the analysis of three basic classes of flows in ship and offshore hydrodynamics, and indeed can be applied more generally to other boundary-value problems such as those associated with flexural-gravity waves for ice sheets or very large floating structures.

Images to Evoke Decision-Making: Building Compelling Representations for Stakeholder-Driven Futures

Contemporary landscape planning challenges require an increasingly diverse ensemble of voices, including regional stakeholders, physical scientists, social scientists, and technical experts, to provide insight into a landscape’s past trends, current uses, and desired future. To impactfully integrate these disparate components, stakeholder-driven research must include clear lines of communication, share data transparently, and slowly develop trust. Alternative future scenario representations aim to generate conversations through discourse, evoke scenario-based stakeholder input, and ensure stakeholder-based revisions to research models. The current literature lacks a metric for gauging effectiveness and a framework for optimal evaluation for future scenario representations. We have developed and applied a metric for a ranked set of compelling scenario representations using stakeholder input from an active research project. Researchers surveyed stakeholders through a case study in Idaho’s Magic Valley to gauge the effectiveness of each representational approach. To improve future stakeholder-driven geodesign projects and gaps in the research literature, this project provides a ranking of graphic strategies based on the stakeholder survey. Additionally, we provide examples and evaluate graphic representation strategies that can stimulate meaningful conversations, create common understandings, and translate research processes and findings to a variety of audiences. The results of this study intend to provide landscape architects, landscape planners, and geodesign specialists with a framework for evaluating compelling future scenario representations for a stakeholder group.

Gossip, the Common Denominator

Gossip, the Common Denominator

An integration by parts formula for the bilinear form of the hypersingular boundary integral operator for the transient heat equation in three spatial dimensions

While an integration by parts formula for the bilinear form of the hypersingular boundary integral operator for the transient heat equation in three spatial dimensions is available in the literature, a proof of this formula seems to be missing. Moreover, the available formula contains an integral term including the time derivative of the fundamental solution of the heat equation, whose interpretation is difficult at second glance. To fill these gaps, we provide a rigorous proof of a general version of the integration by parts formula and an alternative representation of the mentioned integral term, which is valid for a certain class of functions including the typical tensor-product discretization spaces.

Subgrid-scale models of isotropic turbulence need not produce energy backscatter

This investigation questions the importance of inverse interscale energy fluxes, the so-called energy backscatter, for the modelling of the energy cascade in large-eddy simulations (LES) of turbulent flows. The invariance of the filtered Navier–Stokes equations to divergence-preserving transformations of the subgrid-scale (SGS) stress tensor is exploited here to explore alternative representations of the local SGS energy fluxes. Numerical optimisation procedures are applied to the SGS stress tensor – obtained by filtering isotropic turbulence flow fields – to find alternative stresses that satisfy the filtered Navier–Stokes equations, but that produce negligible backscatter. These alternative SGS stresses show that backscatter represents not a flux of energy from the subgrid to the resolved scales, but conservative spatial fluxes, and that it need not be modelled to reproduce the local energetic exchange between the resolved and the subgrid scales in LES. From the perspective of statistical mechanics, it is argued that this is a consequence of the strong statistical irreversibility of inertial-range dynamics, which precludes inverse energy cascades even in a local sense. These findings show that the energy cascade is strongly unidirectional locally, and that it can be modelled as an irreversible sink of energy, justifying the extended use of purely dissipative SGS models in LES.

Contribution to the Hadamard multiplication theorem

In this article we define a binary linear operator T for holomorphic functions in given open sets \(A\) and \(B\) in the complex plane under certain additional assumptions. It coincides with the classical Hadamard product of holomorphic functions in the case where \(A\) and \(B\) are the unit disk. We show that the operator T exists provided \(A\) and \(B\) are simply connected domains containing the origin. Moreover, T is determined explicitly by means of an integral form. To this aim we prove an alternative representation of the star product \(A*B\) of any sets \(A,B\subset\mathbb{C}\) containing the origin. We also touch the problem of holomorphic extensibility of Hadamard product.

‘Don’t worry. It’s just the baby blues’: representations of new motherhood in contemporary graphic memoirs

ABSTRACT All bodies are governed by principles of temporality, yet regarding their roles as (potential) mothers, female bodies are kept under particularly strict observation. I argue that comics’ power to offer ‘a more inclusive perspective of medicine’ can be made fruitful to interrogate the impact that implicit temporal regimes that govern pregnancy, birth and the postnatal period have on new mothers. Analysing two autobiographical comics, Teresa Wong’s Dear Scarlet and Lucy Knisley’s Kid Gloves, I examine how Knisley’s struggles with pre-eclampsia and Wong’s postnatal depression turn their time as new mothers into a period of ‘crip time’ in which their chrono-normative time experience is altered. Both artists use different aesthetic means to illustrate experiences that differ from the positive image of an easy birth, swift recovery and blissful postnatal period perpetuated by contemporary discourses. I suggest that the medium of comics is particularly suited to illustrate these shifts in their subjective time experience. My paper explores how Knisley’s and Wong’s graphic narratives create alternative representations of the corporeal experience of the postpartum period, providing a social commentary on the discursive constraints of motherhood and an underrepresented time in women’s lives.

One View Is Not Enough: Review of and Encouragement for Multiple and Alternative Representations in 3D and Immersive Visualisation

The opportunities for 3D visualisations are huge. People can be immersed inside their data, interface with it in natural ways, and see it in ways that are not possible on a traditional desktop screen. Indeed, 3D visualisations, especially those that are immersed inside head-mounted displays are becoming popular. Much of this growth is driven by the availability, popularity and falling cost of head-mounted displays and other immersive technologies. However, there are also challenges. For example, data visualisation objects can be obscured, important facets missed (perhaps behind the viewer), and the interfaces may be unfamiliar. Some of these challenges are not unique to 3D immersive technologies. Indeed, developers of traditional 2D exploratory visualisation tools would use alternative views, across a multiple coordinated view (MCV) system. Coordinated view interfaces help users explore the richness of the data. For instance, an alphabetical list of people in one view shows everyone in the database, while a map view depicts where they live. Each view provides a different task or purpose. While it is possible to translate some desktop interface techniques into the 3D immersive world, it is not always clear what equivalences would be. In this paper, using several case studies, we discuss the challenges and opportunities for using multiple views in immersive visualisation. Our aim is to provide a set of concepts that will enable developers to perform critical thinking, creative thinking and push the boundaries of what is possible with 3D and immersive visualisation. In summary developers should consider how to integrate many views, techniques and presentation styles, and one view is not enough when using 3D and immersive visualisations.