Two-dimensional Research Papers - Academia.edu (original) (raw)

— Continuous space-time systems, such as transmission lines (TL) with distributed parameters, are normally described by linear 2D partial differential equations, and hence in these cases it is very difficult or even impossible to obtain... more

— Continuous space-time systems, such as transmission lines (TL) with distributed parameters, are normally described by linear 2D partial differential equations, and hence in these cases it is very difficult or even impossible to obtain the space-time response analytically, which brings out the importance of utilizing numerical techniques [1, 2]. In this paper three 2D numerical inverse Laplace transform (NILT) methods are presented, which have the capability of retrieving the space-time response in one single calculation step. Initially the selected 2D-NILT methods, which are devised based on either Fourier series or Padè approximation, are implemented and verified in the Matlab environment. The numerical methods are examined by the use of relevant test functions in the Laplace domain with pre-known originals. Furthermore, the 2D-NILT methods results are analysed from an electrical engineering point of view to observe their performance as for their accuracy, universality and stability. Following, there will be an application of these 2D-NILTs independently on a transmission line described by a Laplace model.

Resumen: Este estudio tiene como objetivo analizar la inundación causada por la falla hipotética de la Presa Mulacorral, cuyo embalse está localizado en la cuenca alta del río Ambato en la cota 3831 msnm. La presa está ubicada a 42... more

Single-crystal In2Se3 thin layers were fabricated, for the first time, using mechanical exfoliation, and the studies of crystalline-crystalline (α → β) phase transformations as well as the corresponding changes of the electrical... more

Single-crystal In2Se3 thin layers were fabricated, for the first time, using mechanical exfoliation, and the studies of crystalline-crystalline (α → β) phase transformations as well as the corresponding changes of the electrical properties in these thin layers. The results show that, in contrast to bulk single crystals, the β phase can persist in single-crystal thin layers at room temperature (RT) and has an electrical resistivity about 1-2 orders of magnitude lower than the α phase. Furthermore, we find that the temperature of the α → β phase transformation increases by as much as 130 K with the layer thickness decreasing from ~ 87 nm to ~ 4 nm. For these In2Se3 thin layers, the accessibility of the β phase at RT, with distinct electrical properties than the α phase, provides the basis for multi-level phase-change memories in a single material system.
Carrier dynamics in single-crystal In2Se3 thin layers with various thicknesses was studied by femtosecond optical pump-probe reflectivity and ultrafast photocurrent measurements. The results suggest that, in thinner (thicker) layers, the carrier recombination dynamics is dominated by three-carrier (bimolecular) Auger process. The Auger time constant was found to decrease with deceasing layer thickness. Surface states were suggested to be the origin of the transition between different Auger processes as the layer thickness varies.
Single-crystal two-dimensional (2D) CuInSe2 with various thicknesses were synthesized, for the first time, by a solid-state chemical reaction between Cu and single-crystal exfoliated In2Se3 nanosheets. The transient optical reflectivity, obtained from femto-second optical pump-probe measurements on single CuInSe2 nanosheets, suggest that the hot carrier cooling process dominates the carrier dynamics within a few ps following the optical excitation. Spatially resolved pump-probe measurements, coupled to simple model calculations, were used to obtain the ambipolar hot carrier diffusion coefficient in single nanosheets. The dependence of the hot carrier diffusion coefficient on the nanosheet thickness provides insight into the limiting mechanisms of hot carrier transport, and can be used to gauge the possibility of efficient hot carrier collection in nanostructured CuInSe2 solar cells.

Recently, the research effort on two-dimensional transition metal dichalcogenides/ graphene (2D-TMDs/Gr) hybrids has grown. These hybrids are emerging as a promising strategy for the preparation of advanced multifunctional materials with... more

Recently, the research effort on two-dimensional transition metal dichalcogenides/ graphene (2D-TMDs/Gr) hybrids has grown. These hybrids are emerging as a promising strategy for the preparation of advanced multifunctional materials with effectively upgraded properties, as well as performances. Due to their outstanding electrical, physical, and chemical properties, these materials have been extensively considered for various applications, both in academia, and industry. This review systematically assesses the important progress to date in the development of 2D-TMDs/Gr hybrids. The synthesis methods of 2D-TMDs/Gr hybrids for fabricating diverse types of nanostructured architec-tures are highlighted. In addition, the relationships between morphological and structural characteristics, and the physicochemical properties of 2D-TMDs/Gr hybrids, are recognized in detail. This review also discusses recent prospective applications of the 2D-TMDs/Gr hybrids in the areas of energy storage, energy conversion, energy harvesting technologies, and sensors. In summary, although there are still challenges for optimizing the synthesis process and performance of the 2D-TMDs/Gr hybrids, they offer unique candidates for a wide range of promising applications in the future.

Analysis would be made amongst National, State and District level players. The study was conducted on the field setting. Standard ball (weight 450 grams) was used for all subjects and for the kick. Two JVC Hard Disk video cameras would be... more

Analysis would be made amongst National, State and District level players. The study was conducted on the field setting. Standard ball (weight 450 grams) was used for all subjects and for the kick. Two JVC Hard Disk video cameras would be used for this study to provide frontal and side view of skill execution. The sampling rate of the video camera was fifty fields per second. The clips were then opened on to the Motion Analysis Tool (MAT) software to identify the angles, displacement, time and number of frames. The result of the study indicated for linear velocity of ankle, knee and hip joint showed no significant difference, during soccer inside instep kick among different level (National, State and District) male soccer players. The variations of the segment kinematics among different level of players are responsible for the no significant difference ball velocity during inside instep soccer kicks.

The purpose of this study is to analyze the angular velocity at various joints for inside instep soccer kick by different level players. To conduct this study ninety-nine players were randomly selected from nation, state and district... more

The purpose of this study is to analyze the angular velocity at various joints for inside instep soccer kick by different level players. To conduct this study ninety-nine players were randomly selected from nation, state and district competition. These players are treated as high, middle and low level players respectively. The subjects wear complete soccer kit. Fifteen minute warm up should be done before the experiment. The subjects performed three trails for instep kick from a preferred distance and with maximum effort on a stationary ball. The kicking motion was recorded using JVC HD video cameras in a field setting. The shutter speed of the camera was fixed at fast speed (1/4000 fast shutter speed allow fast-moving subject to capture one frame at a time vividly) in order to eliminate the blur while video recording. The identified trails were played with the help

Here we take a first step toward tackling the challenge of incomplete optical absorption in monolayers of transition metal dichalcogenides for conversion of photon energy, including solar, into other forms of energy. We present a... more

Here we take a first step toward tackling the challenge of incomplete optical absorption in monolayers of transition metal dichalcogenides for conversion of photon energy, including solar, into other forms of energy. We present a monolayer MoS 2-based photoelectrode architecture that exploits nanophotonic light management strategies to enhance absorption within the monolayer of MoS 2 , while simultaneously integrating an efficient charge carrier separation mechanism facilitated by a MoS 2 /NiO x heterojunction. Specifically, we demonstrate two extremely thin photo-electrode architectures for solar-fuel generation: (i) a planar optical cavity architecture, MoS 2 /NiO x /Al, that improves optical impedance matching and (ii) an architecture employing plasmonic silver nanoparticles (Ag NPs), MoS 2 /Ag NPs/NiO x /Al, that further improves light absorption within the monolayer. We used a combination of numerical simulations, analytical models, and experimental optical characterizations to gain insights into the contributions of optical impedance matching versus plasmonic near-field enhancement effects in our plasmonic photoelectrode structures. By performing three-dimensional electromagnetic simulations, we predict structures that can absorb 37% of the incident light integrated from 400 to 700 nm within a monolayer of MoS 2 , a 5.9× enhanced absorption compared to that of MoS 2 on a sapphire (Al 2 O 3) substrate. Experimentally, a 3.9× absorption enhancement is observed in the total structure compared to that of MoS 2 /Al 2 O 3 , and photoluminescence measurements suggest this enhancement largely arises from absorption enhancements within the MoS 2 layer alone. The results of these measurements also confirm that our MoS 2 /NiO x /Al structures do indeed facilitate efficient charge separation, as required for a photoelectrode. To rapidly explore the parameter space of plasmonic photoelectrode architectures, we also developed an analytical model based on an effective medium model that is in excellent agreement with results from numerical FDTD simulations.

Two fabric composite models are presented for the on-axes elastic analysis of two-dimensional orthogonal plain weave fabric lamina. These are twodimensional models taking into account the actual strand cross-section geometry, possible gap... more

Two fabric composite models are presented for the on-axes elastic analysis of two-dimensional orthogonal plain weave fabric lamina. These are twodimensional models taking into account the actual strand cross-section geometry, possible gap between two adjacent strands and undulation and continuity of strands along both warp and fill directions. The shape functions considered to define the geometry of the woven fabric lamina compare well with the photomicrographs of actual woven fabric lamina cross-sections. There is a good correlation between the predicted results and the experimental values. Certain modifications are suggested to the simple models available in the literature so that these models can also be used to predict the elastic properties of woven fabric laminae under specific conditions. Some design studies have been carried out for graphite/epoxy woven fabric laminae. Effects of woven fabric geometrical parameters on the elastic properties of the laminae have been investigated.

"Contents: От задника к квази-вещи и настоящему мясу: плоскость и трехмерность в кино 1900-1920 Бюсты-Цари Бауэра Оживление вещи в 1910-е годы: Черепки кувшина и жест спинки кресла «Душа декорации» и диковинки Бауeра в... more

The performance graph (PG) hydraulic routing method has been shown to be accurate, numerically efficient, and robust for unsteady flow routing. However, up to present, the performance graphs are constructed using one-dimensional (1D)... more

The performance graph (PG) hydraulic routing method has been shown to be accurate, numerically efficient, and robust for unsteady flow routing. However, up to present, the performance graphs are constructed using one-dimensional (1D) steady flow models only, which are often questioned when simulating flows through complex bathymetries. This paper investigates whether the PG method can still be used when utilizing two-dimensional (2D) models for the construction of PGs. The test case is a stretch around an island in the Fraser River in British Columbia. The results show that the PG method is still applicable when utilizing a 2D steady flow model. The results also show that once the PGs are constructed, the PG routing method (1D and 2D) is computationally more efficient than the unsteady HEC-RAS model and can be several orders of magnitude faster than TELEMAC-2D.

Arithmetics is one of the topics in Mathematics, which deals with logic and detailed process upon generalizing formula. Creativity and flexibility are needed in generalizing formula of arithmetics series. This research aimed at analyzing... more

Arithmetics is one of the topics in Mathematics, which deals with logic and detailed process upon generalizing formula. Creativity and flexibility are needed in generalizing formula of arithmetics series. This research aimed at analyzing students creative thinking skills in generalizing arithmetic series. The triangulation method and research-based learning was used in this research. The subjects were students of the Master Program of Mathematics Education in Faculty of Teacher Training and Education at Jember University. The data was collected by giving assignments to the students. The data collection was done by giving open problem-solving task and documentation study to the students to arrange generalization pattern based on the dependent function formula i and the function depend on i and j. Then, the students finished the next problem-solving task to construct arithmetic generalization patterns based on the function formula which depends on i and i + n and the sum formula of functions dependent on i and j of the arithmetic compiled. The data analysis techniques operative in this study was Miles and Huberman analysis model. Based on the result of data analysis on task 1, the levels of students creative thinking skill were classified as follows; 22,22% of the students categorized as "not creative"; 38.89% of the students categorized as "less creative" category; 22.22% of the students categorized as "sufficiently creative"; and 16.67% of the students categorized as "creative". By contrast, the results of data analysis on task 2 found that the levels of students creative thinking skills were classified as follows; 22.22% of the students categorized as "sufficiently creative", 44.44% of the students categorized as "creative"; and 33.33% of the students categorized as "very creative". This analysis result can set the basis for teaching references and actualizing a better teaching model in order to increase students creative thinking skills.

Low-density nanostructured foams are often limited in applications due to their low mechanical and thermal stabilities. Here we report an approach of building the structural units of three-dimensional (3D) foams using hybrid... more

Low-density nanostructured foams are often limited in applications due to their low
mechanical and thermal stabilities. Here we report an approach of building the structural
units of three-dimensional (3D) foams using hybrid two-dimensional (2D) atomic layers
made of stacked graphene oxide layers reinforced with conformal hexagonal boron nitride
(h-BN) platelets. The ultra-low density (1/400 times density of graphite) 3D porous
structures are scalably synthesized using solution processing method. A layered 3D foam
structure forms due to presence of h-BN and significant improvements in the mechanical
properties are observed for the hybrid foam structures, over a range of temperatures,
compared with pristine graphene oxide or reduced graphene oxide foams. It is found that
domains of h-BN layers on the graphene oxide framework help to reinforce the 2D structural
units, providing the observed improvement in mechanical integrity of the 3D foam structure.

SUMMARY Numerical inverse Laplace transform (NILT) methods are potential methods for time domain simulations, for instance the analysis of the transient phenomena in systems with lumped and/or distributed parameters. This paper proposes a... more

SUMMARY Numerical inverse Laplace transform (NILT) methods are potential methods for time domain simulations, for instance the analysis of the transient phenomena in systems with lumped and/or distributed parameters. This paper proposes a numerical inverse Laplace transform method based originally on hyperbolic relations. The method is further enhanced by properly adapting several convergence acceleration techniques, namely, the epsilon algorithm of Wynn, the quotient-difference algorithm of Rutishauser and the Euler transform. The resulting accelerated models are compared as for their accuracy and computational efficiency. Moreover, an expansion to two dimensions is presented for the first time in the context of the accelerated hyperbolic NILT method, followed by the error analysis. The expansion is done by repeated application of one-dimensional partial numerical inverse Laplace transforms. A detailed static error analysis of the resulting 2D NILT is performed to prove the effectivness of the method. The work is followed by a practical application of the 2D NILT method to simulate voltage/current distributions along a transmission line. The method and application are programmed using the Matlab language.

With the arrival of the new millenium, products, created by varying fields of artistic endeavor, that are usually flat by nature have seen an evolution towards demonstrating the illusion of 3 dimensions. Such a tendency can be observed... more

With the arrival of the new millenium, products, created by varying fields of artistic endeavor, that are usually flat by nature have seen an evolution towards demonstrating the illusion of 3 dimensions. Such a tendency can be observed most noticably in films, painting and in graphic design. Author Steven Heller, states that the illusion of 3 dimensions in graphic design makes the viewer take a second look and thus satisfies the key requirement of any design work. However, Michael Evamy argues that a return to a two dimensional understanding has been on the rise in the past few years due to the fact that, while visually shallow, two dimensional designs are able to provide deeper ideologies. The aim of this paper is to get a better sense of the more efficient approach between graphic design that simulates 3 dimensions and flat design. For the assessment of this, a similarity between design and cinema is drawn where, in movies, the tendency has been mainly to process only the blockbuster movies with 3D technology, while art films have consistently kept their distance with this kind of illusionistic approach. Through the examination of the audiences' interactions with different, both in content and dimension, types of films, it can be observed that both types serve certain purposes, though, with design, honesty and humanity is better achieved through leaving false illusions and taking a 2 dimensional point of view.

Articles you may be interested in Understanding the doping effects on the structural and electrical properties of ultrathin carbon nanotube networks J. Appl. Phys. 118, 215305 (2015); 10.1063/1.4937137 Structure, stability, and electronic... more

Articles you may be interested in Understanding the doping effects on the structural and electrical properties of ultrathin carbon nanotube networks J. Appl. Phys. 118, 215305 (2015); 10.1063/1.4937137 Structure, stability, and electronic property of carbon-doped gold clusters AunC− (n = 1–10): A density functional theory study J. Chem. Phys. 139, 244312 (2013); 10.1063/1.4852179 Ab initio study of semiconducting carbon nanotubes adsorbed on the Si(100) surface: Diameter-and registration-dependent atomic configurations and electronic properties Amphoteric doping of carbon nanotubes by encapsulation of organic molecules: Electronic properties and quantum conductance We present a combined experimental and theoretical study to analyze the structure, electronic properties , and aggregation behavior of hydroxylated multiwalled carbon nanotubes (OH–MWCNT). Our MWCNTs have average diameters of ∼2 nm, lengths of approximately 100–300 nm, and a hydroxyl surface coverage θ ∼0.1. When deposited on the air/water interface the OH–MWCNTs are partially soluble and the floating units interact and link with each other forming extended foam-like carbon networks. Surface pressure-area isotherms of the nanotube films are performed using the Langmuir balance method at different equilibration times. The films are transferred into a mica substrate and atomic force microscopy images show that the foam like structure is preserved and reveals fine details of their microstructure. Density functional theory calculations performed on model hydroxy-lated carbon nanotubes show that low energy atomic configurations are found when the OH groups form molecular islands on the nanotube's surface. This patchy behavior for the OH species is expected to produce nanotubes having reduced wettabilities, in line with experimental observations. OH doping yields nanotubes having small HOMO–LUMO energy gaps and generates a nanotube → OH direction for the charge transfer leading to the existence of more hole carriers in the structures. Our synthesized OH–MWCNTs might have promising applications.

The protein quality of commercial soybeans varieties can be determined from their total protein content, their amino acid composition and from the ratio of glycinin to β-conglycinin, the major seed storage protein components. In this... more

The protein quality of commercial soybeans varieties can be determined from their total protein content, their amino acid composition and from the ratio of glycinin to β-conglycinin, the major seed storage protein components. In this study 14 commercial soybean cultivars were assessed. There were significant differences in storage protein composition (P < 0.05) and in their valine, proline and phenylalanine contents (P < 0.01 to P < 0.001). Mean protein values among these varieties ranged from 29.8% to 36.1%. The total amino acid nitrogen (AAN) ranged from 89.6 to 95.1 g AA/16 g of nitrogen, corresponding to nitrogen values from 16.5 to 17.9 g AAN/100 g protein. All varieties contained a good balance of essential amino acids (EAA9), limited only in methionine. Two-dimensional gel electrophoretic (2-DE) separations, led to the establishment of high-resolution proteome reference maps, enabling polypeptide chain identification and calculation of the ratio of the constituent glycinin and β-conglycinin storage proteins of soybean. This method enables the assessment of the genetic variability of the soybean cultivars, which can then be correlated with their protein quality and food processing properties. These three methods can be used as very effective tools for assisting plant breeders in their selection of high quality soybean varieties.

A study of an efficient blue light-emitting diode based on a fluorescent aryl polyfluorene (aryl-F8) homopolymer in an inverted device architecture is presented, with ZnO and MoO3 as electron- and hole-injecting electrodes, respectively.... more

A study of an efficient blue light-emitting diode based on a fluorescent aryl polyfluorene (aryl-F8) homopolymer in an inverted device architecture is presented, with ZnO and MoO3 as electron- and hole-injecting electrodes, respectively. Charge-carrier balance and color purity in these structures are
achieved by incorporating poly(9,9-dioctylfluorene-co-N-(4-butylphenyl)-diphenylamine (TFB) into aryl-F8. TFB is known to be a hole-transporting material but it is found to act as a hole trap on mixing with aryl-F8. Luminance efficiency of ≈6 cd A−1
and external quantum efficiency (EQE) of 3.1%
are obtained by adding a small amount (0.5% by weight) of TFB into aryl-F8. Study of charge injection and transport in the single-carrier devices shows that the addition of a small fraction of hole traps is necessary for chargecarrier balance. Optical studies using UV–vis and fluorescence spectroscopic measurements, photoluminescence quantum yield, and fluorescence decay
time measurements indicate that TFB does not affect the optical properties of the aryl-F8, which is the emitting material in these devices. Luminance efficiency of up to ≈11 cd A−1 and EQE values of 5.7% are achieved in these structures with the aid of improved out-coupling using index-matched hemispheres.

We introduce a dynamical description based on a probability density φ(σ, x, y, t) of the vorticity σ in two-dimensional viscous flows such that the average vorticity evolves according to the Navier-Stokes equations. A time-dependent... more

We introduce a dynamical description based on a probability density φ(σ, x, y, t) of the vorticity σ in two-dimensional viscous flows such that the average vorticity evolves according to the Navier-Stokes equations. A time-dependent mixing index is defined and the class of probability densities that maximizes this index is studied. The time dependence of the Lagrange multipliers can be chosen in such a way that the masses m(σ, t) := dxdy φ(σ, x, y, t) associated with each vorticity value σ are conserved. When the masses m(σ, t) are conserved then 1) the mixing index satisfies an H-theorem and 2) the mixing index is the time-dependent analogue of the entropy employed in the statistical mechanical theory of inviscid 2D flows [Miller, Weichman & Cross, Phys. Rev. A 45 (1992); Robert & Sommeria, Phys. Rev. Lett. 69, 2776]. Within this framework we also show how to reconstruct the probability density of the quasi-stationary coherent structures from the experimentally determined vorticity-stream function relations and we provide a connection between this probability density and an appropriate initial distribution.

The research aims to describe the level of higher-order thinking skills ability of students in solving generalization patterns in two-dimensional arithmetic series based on revised Bloom's taxonomy. The research method used is a... more

The research aims to describe the level of higher-order thinking skills ability of students in solving generalization patterns in two-dimensional arithmetic series based on revised Bloom's taxonomy. The research method used is a qualitative descriptive approach. The subjects were students of the Master Program of Mathematics Education at Jember University. The data was collected by giving open problem-solving tasks and documentation studies to students to develop patterns of one-dimensional arithmetic series. Then, students are given the task of solving the next problem to draw up a generalization pattern of two-dimensional arithmetic series. The data analysis technique used is qualitative descriptive data analysis. The results showed that the percentage of higher-order thinking skills aspects included analyze (C4) reached 88.89%, evaluate (C5) reached 83.33%, and create (C6) reached 66.67%. The results of this achievement are influenced by several factors, including accuracy in compiling numbers and expanding existing data, mastery of arithmetic series permutation concepts and their application, the tendency of graduate students to rely on memorization and imitations of existing examples. PENDAHULUAN Pendidikan matematika yang diterapkan di sekolah cenderung mengarahkan peserta didik untuk memahami rumus lalu diterapkan dalam menyelesaikan soal atau masalah bila dalam materi yang disampaikan mengandung rumus-rumus tertentu seperti barisan dan deret aritmatika. Padahal, kemampuan berpikir dalam menemukan lalu konstruksi rumus dalam matematika sangat diperlukan agar peserta didik lebih baik dalam memahami materi dan pembelajarannya lebih bermakna. Salah satu kemampuan bepikir yang sangat penting bagi peserta didik agar pembelajarannya lebih bermakna dan meningkatkan kualitas berpikir dalam menyelesaikan masalah sehari-hari yaitu berpikir tingkat tinggi. Berpikir tingkat tinggi merupakan komponen penting yang terdapat pada keterampilan abad ke-21, yaitu berpikir kritis, berpikir kreatif, komunikatif, dan kolaboratif (P21, 2014). Berpikir tingkat tinggi tumbuh ketika seorang individu menghadapi masalah atau persoalan yang belum pernah dipecahkan. atau Higher Order Thinking Skills (HOTS) terjadi ketika seseorang mengambil informasi baru dan informasi yang tersimpan dalam memori saling berhubungan atau menata kembali dan memperluas informasi ini untuk mencapai suatu tujuan atau menemukan jawaban yang mungkin dalam situasi membingungkan. Berbagai

In this paper, a comparative study on two characteristics-based finite element algorithms are presented. Some analytical test problems which embrace many real features of environmental applications in advection-dominated mass transport... more

In this paper, a comparative study on two characteristics-based finite element algorithms are presented. Some analytical test problems which embrace many real features of environmental applications in advection-dominated mass transport phenomenon are modelled: pure advection of a 2-D Gaussian concentration-hill in a rotating flow, diffusion in a plane shear flow and continuous source in an oscillating flow.

Two-dimensional (2D) magnets have evoked tremendous interest within the research community due to their fascinating features and novel mechanisms, as well as their potential applications in magnetic nanodevices. In this review,... more

Two-dimensional (2D) magnets have evoked tremendous interest within the research community due to their fascinating features and novel mechanisms, as well as their potential applications in magnetic nanodevices. In this review, state-of-the-art research into the exploration of 2D magnets from the perspective of their magnetic interaction and order mechanisms is discussed. The properties of these magnets can be effectively modulated by varying the external parameters, such as the charge carrier doping, thickness effect, pressure and strain. The potential applications of heterostructures of these 2D magnets in terms of the interlayer coupling strength are reviewed, and the challenges and outlook for this field are proposed.

Pictorial messages have previously been advocated for interstellar communication because such messages are presumed to be capable of presenting information in a non-arbitrary and easily intelligible manner. In contrast to this view,... more

Pictorial messages have previously been advocated for interstellar communication because such messages are presumed to be capable of presenting information in a non-arbitrary and easily intelligible manner. In contrast to this view, pictorial messages actually represent information in a partially conventional way. This point is demonstrated by examining pictorial representations of human beings from a range of cultures. While such representations may be understood quite readily by individuals familiar with the conventions of a particular culture, to the uninitiated outsider, such representations can be unintelligible. In spite of the partially arbitrary nature of pictorial representation, we may be able to construct messages that would teach extraterrestrial intelligence (ETI) some of the conventions by which we view pictures. One such approach is to pair numerical information about geometrical objects with pictorial representations of the same objects. Problems of conventionality can also be addressed in part through use of (1) multiple representations of the same object, (2) contextual cues, (3) three- and four-dimensional representations and (4) non-visual representations.