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A dual-layer circular polarizer based on FSS (Frequency Selective Surface) composed of two periodic strips in xoy plane. The transmission characteristic of present structure is comprehensively investigated that convert linearly polarized wave into circular polarized wave at operated frequencies. The designed structure has optimal performance for x-band applications. In addition, the designed model of single and dual-layer circular polarizer feature exceptionally strong circular polarization with low loss transmission and attracted for radar and satellite applications. The designed structures of circular polarizers are simple and can be easy fabricated as well. The transmitted waves are achieved with RHCP (Right Handed Circular Polarization) wave at 9.34 GHz and LHCP (Left Handed Circular Polarization) wave at 10.73 GHZ. The corresponding axial ratio bandwidth is enhanced from 9.16-10.85GHz = 16.89%, respectively. Meanwhile, the proposed dual-layer circular polarizer achieves transmission with RHCP wave at 9.59 GHz and axial ratio bandwidth is achieved from9.3-11.31GHz = 19.49%, respectively. [ABSTRACT FROM AUTHOR]

How can building technologies accommodate different and often conflicting user preferences without dissolving the social cohesiveness, intrinsic of every architectural intervention? Individual thermal comfort has often been considered a negligible sensorial experience by modern heating and cooling technologies, and is often influenced by large-group norms. Alternatively, we propose that buildings are repositories of indoor microclimates that can be realized to provide personalized comfort, to create healthier environments, and to enhance the attributes of architectural interventions into haptic dimensions. In response, the goal of this study is to characterize an experimental framework that integrates responsive thermal systems with occupants' direct and indirect experience, which includes stress response and biometric data. A computational model was used up to inform and analyze thermal perception of subjects, and later tested in a responsive physical installation. While results show that thermal comfort assessment is affected by individual differences including cognitive functions and biometrics, further computational efforts are needed to validate biometric indicators. Finally, the implications of personalized built environments are discussed with respect to future technology developments and possibilities of design driven by biometric data. [ABSTRACT FROM AUTHOR]

We present a novel approach for optimizing acoustic parameters using sensitivity analysis for computer-aided design and analysis of architectural models. Our approach builds on recent low-dispersion wave-based acoustic solvers that can accurately compute the pressure field in large models. We present an efficient technique to compute the gradient of the pressure field using automatic differentiation and combine that with a quasi-Newtonian optimization method to automatically compute the optimal material properties. We highlight the performance on many complex CAD models to optimize the strength and clarity acoustic parameters, and thereby improve the acoustic characteristics of large models. To the best of our knowledge, this is the first practical and accurate approach for acoustic material optimization of large indoor CAD models. [ABSTRACT FROM AUTHOR]

We study a single-commodity robust network design problem (sRND) defined on an undirected graph. Our goal is to determine minimum cost capacities such that any traffic demand from a given uncertainty set can be satisfied by a feasible single-commodity flow. We consider two ways of representing the uncertainty set, either as a finite list of scenarios or as a polytope. We propose a branch-and-cut algorithm to derive optimal solutions to sRND, built on a capacity-based integer linear programming formulation. It is strengthened with valid inequalities derived as $$\{0,\frac{1}{2}\}$$ -Chvátal-Gomory cuts. Since the formulation contains exponentially many constraints, we provide practical separation algorithms. Extensive computational experiments show that our approach is effective, in comparison to existing approaches from the literature as well as to solving a flow based formulation by a general purpose solver. [ABSTRACT FROM AUTHOR]

This paper discusses the task of human action recognition. This task is important to applications like video surveillance and video retrieval. Most of the existing local interest points based works on human action analysis, lost the information about spatio-temporal distribution of features and neglected the relationship between features and each defined actions. In this paper, through the analysis of feature distribution and their interactions over spatio-temporal domain, we propose a novel projection transform to take the two factors into account. A video sequence of human action in our perspective can be modeled by three types of features of spatio-temporal interest points: the global projection transform feature, the relative position distribution feature and the bag of visual words based feature. Then a new context-K-nearest-neighbor classifier is utilized to fuse them to form discriminative feature sets for action matching. In most of the case, our experiments have indicated that the novel method outperforms other previous published results on the Weizmann and KTH datasets. [ABSTRACT FROM AUTHOR]

Unmanned aerial vehicle (UAV) and Chinese calligraphy seem like two completely unrelated subjects in today’s world. UAV, as one of the most advanced technology to date, has gathered much attention lately due to its potentially unlimited applications. Contrarily, Chinese calligraphy is one of the most beautiful and ancient calligraphy art originally developed from China few thousand years ago. Today in this manuscript, we present to you the art of autonomous calligraphy writing with UAVs. The proposed UAV calligraphy system is able to trace the user handwritten inputs, and then execute the writing by mimicking the user handwriting with four autonomous UAVs. This manuscript details the design considerations and implementation process of such a system. The UAV calligraphy system was performed in Singapore Airshow 2014. Robustness and reliability of the system has been well tested, and high performance can be seen from the resulting calligraphy writing. [ABSTRACT FROM AUTHOR]

The design of engineering systems often involves multiple disciplines and competing objectives, which requires coordination, information exchange and share amongst the disciplines. However, in practical design environments, designers have to make decisions in isolation due to organization barriers, time schedules and geographical constraints. This paper will propose a new approach for the multi-objective multidisciplinary design optimization (MDO) problems in non-cooperative environments based on gene expression programming (GEP) and Nash equilibrium in the game theory. In this approach, the GEP method is used as a surrogate to construct the approximate rational reaction sets (RRSs) in the Nash model. The effectiveness of the proposed method is demonstrated by the design of a thin-walled pressure vessel and the hull form parameter design of a small waterplane area twin hull (SWATH) ship. The results show that this approach can fully explore and provide the explicit functional relationship between the strategy of an isolated player and the control variables of the other players, thus able to obtain a better Nash equilibrium solution. [ABSTRACT FROM AUTHOR]

In this letter, an iterative approach based on the orthogonal projection (OP) criterion is presented to estimate carrier frequency offset (CFO) for interleaved orthogonal frequency division multiple access (OFDMA) uplink systems. The proposed estimator includes the center-symmetric trimmed correlation matrix and OP technique. It doesn't require eigen-decomposition and only needs single OFDMA data block. To reduce computation complexity, the proposed estimator iteratively searches for the correct CFO vector by minimizing the objective function using a first-order Taylor series approximation of the CFO vector with the one initially given. Computer simulation is also provided for illustrating the effectiveness of the proposed iterative blind CFO estimator. [ABSTRACT FROM AUTHOR]

High-quality inner FoV (Field of View) stitching is currently a prerequisite step for photogrammetric processing and application of image data acquired by spaceborne TDI CCD cameras. After reviewing the technical development in the issue, we present an inner FoV stitching method based on sensor geometry and projection plane in object space, in which the geometric sensor model of spaceborne TDI CCD images is used to establish image point correspondence between the stitched image and the TDI CCD images, using an object-space projection plane as the intermediary. In this study, first, the rigorous geometric sensor model of the TDI CCD images is constructed. Second, principle and implementation of the stitching method are described. Third, panchromatic high-resolution (HR) images of ZY-1 02C satellite and triple linear-array images of ZY-3 satellite are utilized to validate the correctness and feasibility of the method. Fourth, the stitching precision and geometric quality of the generated stitched images are evaluated. All the stitched images reached the sub-pixel level in precision. In addition, the geometric models of the stitched images can be constructed with zero loss in geometric precision. Experimental results demonstrate the advantages of the method for having small image distortion when on-orbit geometric calibration of satellite sensors is available. Overall, the new method provide a novel solution for inner FoV stitching of spaceborne TDI CCD images, in which all the sub-images are projected to the object space based on the sensor geometry, performing indirect image geometric rectification along and across the target trajectory. At present, this method has been successfully applied in the daily processing system for ZY-1 02C and ZY-3 satellites. [ABSTRACT FROM AUTHOR]

Design patterns usually describe abstract systems of interaction between classes, objects, and communication flows. So, a description of a set of interacting classes that provide a generalized solution framework to a generalized/specific design problem in a specific context can be said as a design pattern. There are many design patterns that can be used to solve real-life problems, but it remains very difficult to design, implement and reuse software for complex applications. Examples of these include enterprise system, real -time market data monitoring and analysis system. Design patterns provide an efficient way to create more flexible, elegant and ultimately reusable object-oriented software. Each pattern describes a problem which occurs over and over again in our environment, and then describes the core of the solution to that problem, in such a way that you can use this solution a million times over, without ever doing it the same way twice". The solutions of the given problems are expressed in terms of objects and interfaces. Among 23 design patterns, Strategy pattern defines an interface common to all supported algorithms. Context uses this interface to call the algorithm defined by a Concrete Strategy. In accounting framework one thing is mostly needed that is tax calculation. To solve this problem author in the current study has chosen the strategy pattern. [ABSTRACT FROM AUTHOR]

In an attempt to study the emerging questions about design of mathematical tasks that could support the solving of challenging problems, we designed two settings of interactive diagrams that share an example represented as an animation of multi-process motion but differ in their organizational functions. The interactive settings, each comprising of one task, were designed to support investigation in which the embedded animated example was expected to offer representative and general views. We analyzed the inquiry processes of 13- and 14-year-old interviewees and hypothesized whether these cases could represent more general considerations for the design of animated examples within a setting of interactive diagrams. We argue that (a) self-controlling the number of representations, (b) self-controlling the appearance of simultaneous information, (c) flexibly using links between dynamic and static representations, and (d) establishing links or completing partial links between representations are valuable inquiry processes in solving a problem that includes animated examples to enable viewing the representativeness of a given example. [ABSTRACT FROM AUTHOR]

We show that the space of polygonizations of a fixed planar point set S of n points is connected by O( n2) “moves” between simple polygons. Each move is composed of a sequence of atomic moves called “stretches” and “twangs,” which walk between weakly simple “polygonal wraps” of S. These moves show promise to serve as a basis for generating random polygons. [ABSTRACT FROM AUTHOR]

Let G be a graph. A set S of vertices of G is called a total dominating set of G if every vertex of G is adjacent to at least one vertex in S: The total domination number γt(G) and the matching number α'(G) of G are the cardinalities of the minimum total dominating set and the maximum matching of G; respectively. In this paper, we introduce an upper bound of the difference between γt(G) and α'(G): We also characterize every tree T with γt(T) ⩽ α'(T); and give a family of graphs with γt(G) ⩽ α'(G). [ABSTRACT FROM AUTHOR]

The class of even-hole-free graphs is structurally quite similar to the class of perfect graphs, which was the key initial motivation for their study. The techniques developed in the study of even-hole-free graphs were generalized to other complex hereditary graph classes, and in the case of perfect graphs led to the famous resolution of the Strong Perfect Graph Conjecture and their polynomial time recognition. The class of even-hole-free graphs is also of independent interest due to its relationship to β-perfect graphs. In this survey we describe all the different structural characterizations of even-hole- free graphs, focusing on their algorithmic consequences. [ABSTRACT FROM AUTHOR]

In this paper we present an approach for the analysis of graph transformation rules based on an intermediate OCL representation. We translate different rule semantics into OCL, together with the properties of interest (like rule applicability, conflicts or independence). The intermediate representation serves three purposes: (1) it allows the seamless integration of graph transformation rules with the MOF and OCL standards, and enables taking the meta-model and its OCL constraints (i.e. well-formedness rules) into account when verifying the correctness of the rules; (2) it permits the interoperability of graph transformation concepts with a number of standards-based model-driven development tools; and (3) it makes available a plethora of OCL tools to actually perform the rule analysis. This approach is especially useful to analyse the operational semantics of Domain Specific Visual Languages. We have automated these ideas by providing designers with tools for the graphical specification and analysis of graph transformation rules, including a back-annotation mechanism that presents the analysis results in terms of the original language notation. [ABSTRACT FROM AUTHOR]

Abstract: A hole in a graph is an induced subgraph which is a cycle of length at least four. A hole is called even if it has an even number of vertices. An even-hole-free graph is a graph with no even holes. A vertex of a graph is bisimplicial if the set of its neighbours is the union of two cliques. In this paper we prove that every even-hole-free graph has a bisimplicial vertex, which was originally conjectured by Reed. [Copyright &y& Elsevier]

Abstract: In this paper, we prove that planar graphs without -cycles and without two 5-cycles sharing exactly one edge are 3-colorable. This improves the result in [O.V. Borodin, A.N. Glebov, A. Raspaud, M.R. Salavatipour, Planar graphs without cycles of length from 4 to 7 are 3-colorable, J. Combin. Theory Ser. B 93 (2005) 303–311]. [Copyright &y& Elsevier]

Abstract: Current work presents a set of fault models allowing high coverage for sequential cores in systems-on-a-chip. We propose a novel approach combining a hierarchical fault model for functional blocks, a functional fault model for multiplexers and a mixed hierarchical-functional fault model for comparison operators, respectively. The fault models are integrated into a fast high-level decision diagram based test path activation tool. According to the experiments, the proposed method significantly outperforms state-of-the-art test pattern generation tools. The main new contribution of this paper is a formal definition of high-level decision diagram representations and the combination of the three fault models in order to target high gate-level stuck-at fault coverage for sequential cores. [Copyright &y& Elsevier]

We provide a detailed review of existing object-oriented software development methodologies, focusing on their development processes. The review aims at laying bare their core philosophies, processes, and internal activities. This is done by using a process-centered template for summarizing the methodologies, highlighting the activities prescribed in the methodology while describing the modeling languages used (mainly diagrams and tables) as secondary to the activities. The descriptions produced using this template aim not to offer a critique on the methodologies and processes, but instead provide an abstract and structured description in a way that facilitates their elaborate analysis for the purposes of improving understanding, and making it easier to tailor, select, and evaluate the processes. [ABSTRACT FROM AUTHOR]

Abstract: Any directed graph, even a flow graph representing “spaghetti code”, is shown here to have at least one loop tree, which is a structure of loops within loops in which no loops overlap. The nodes of the graph may be rearranged in such a way that, with respect to their new order, every edge proceeds in the forward direction except for the loopbacks. Here a loopback goes from somewhere in a loop to the head of . We refer to such a rearrangement as a generalized structured program, in which forward goto statements remain unrestricted. Like a min-heap or a max-heap, a loop tree has an array representation, without pointers; it may be constructed in time no worse than for any program written in this fashion. A scalable version of this construction uses a label graph, whose only nodes are the labels of the given program. A graph has a unique loop tree if and only if it is reducible. [Copyright &y& Elsevier]

Petty’s conjectured projection inequality is a famous open problem in the theory of convex bodies. In this paper, it is shown that an inequality relating to L p-version of the Petty’s conjectured projection inequality is developed by using the notions of the L p-mixed volume and the L p-dual mixed volume, the relation of the L p-projection body and the geometric body Γ− p K, the Bourgain-Milman inequality and the L p-Busemann-Petty inequality. In addition, for each origin-symmetric convex body, by applying the Jensen inequality and the monotonicity of the geometric body Γ− p K, the reverses of L p-version of the Petty’s conjectured projection inequality and the L p-Petty projection inequality are given, respectively. [ABSTRACT FROM AUTHOR]

Abstract: Earlier concepts of ultrahigh-cycle fatigue (UHCF) of both ductile single-phase type I materials that do not contain inclusions and type II materials, e.g., high-strength steels containing non-metallic inclusions as (internal) crack initiation sites, are extended. In particular, the multi-stage fatigue life diagrams with a conventional high-cycle fatigue (HCF) limit and a possible lower fatigue limit in the UHCF range are discussed for both classes of materials in terms of the relevant fatigue cracking mechanisms. In this context, it is emphasized that it is important to consider in both cases details of fatigue crack initiation as a life-determining factor in the HCF and, even more so, in the UHCF regime. Different factors such as the density, size, location and distribution of non-metallic inclusions and details of specimen geometry and surface quality in the case of type II materials are discussed with respect to their influence on the transition stress separating the ranges of surface and internal fatigue cracking and with regard to fatigue lives. [Copyright &y& Elsevier]

Mechanical systems have structural organizations—parts, and their relations—and functional organizations—temporal, dynamic, and causal processes—which can be explained using text or diagrams. Two experiments illustrate the role of arrows in diagrams of mechanical systems. In Experiment 1, people described diagrams with or without arrows, interpreting diagrams without arrows as conveying structural information and diagrams with arrows as conveying functional information. In Experiment 2, people produced sketches of mechanical systems from structural or functional descriptions. People spontaneously used arrows to indicate functional processes in diagrams. Arrows can play a powerful role in augmenting structural diagrams to convey dynamic, causal, or functional information. [ABSTRACT FROM AUTHOR]

Packing a maximum number of disjoint triangles into a given graph G is NP-hard, even for most classes of structured graphs. In contrast, we show that packing a maximum number of independent (that is, disjoint and nonadjacent) triangles is polynomial-time solvable for many classes of structured graphs, including weakly chordal graphs, asteroidal triple-free graphs, polygon-circle graphs, and interval-filament graphs. These classes contain other well-known classes such as chordal graphs, cocomparability graphs, circle graphs, circular-arc graphs, and outerplanar graphs. Our results apply more generally to independent packings by members of any family of connected graphs. [ABSTRACT FROM AUTHOR]

Intersection graphs of disks and of line segments, respectively, have been well studied, because of both practical applications and theoretically interesting properties of these graphs. Despite partial results, the complexity status of the Clique problem for these two graph classes is still open. Here, we consider the Clique problem for intersection graphs of ellipses, which, in a sense, interpolate between disks and line segments, and show that the problem is APX-hard in that case. Moreover, this holds even if for all ellipses, the ratio of the larger over the smaller radius is some prescribed number. Furthermore, the reduction immediately carries over to intersection graphs of triangles. To our knowledge, this is the first hardness result for the Clique problem in intersection graphs of convex objects with finite description complexity. We also describe a simple approximation algorithm for the case of ellipses for which the ratio of radii is bounded. [ABSTRACT FROM AUTHOR]

We consider the problem of drawing a graph with a given symmetry such that the number of edge crossings is minimal. We show that this problem is NP-hard, even if the order of orbits around the rotation center or along the reflection axis is fixed. We devise an O(m log m) algorithm for computing a crossing minimal drawing if inter-orbit edges may not cross orbits, showing in particular that intra-orbit edges do not contribute to the NP-hardness of the crossing minimization problem for symmetries. [ABSTRACT FROM AUTHOR]

An independent set of a graph is a set of vertices without edges between them. Every planar graph has an independent set of size at least (1/4)n and there are planar graphs for which any independent set has size at most (1/4)n. In this paper similar bounds are provided for the problem of bounded-degree independent set, i.e., an independent set where additionally all vertices have degree less than a pre-specified bound D. Our upper and lower bounds match (up to a small constant) for D = 16. [ABSTRACT FROM AUTHOR]

In 1975, Lovász conjectured that for any positive integerk, there exists a minimum positive integerf(k) such that, for any two verticesx,yin anyf(k)-connected graphG, there is a pathPfromxtoyinGsuch thatG-V(P) isk-connected. A result of Tutte impliesf(1) = 3. Recently,f(2) = 5 was shown by Chenet al. and, independently, by Kriesell. In this paper, we show thatf(2) = 4 except for double wheels. [ABSTRACT FROM AUTHOR]

We consider the dynamic behavior of a nonlinear vibroprotective system with roller damper of low-frequency oscillations. By using the Ritz averaging method, we deduce the equation of the amplitude-frequency characteristic of the nonlinear system. A new graphic method is proposed for the determination of the parameters of adjustment of the roller damper. [ABSTRACT FROM AUTHOR]

This article presents information on symbol recognition that plays an important role in a variety of applications such as automatic recognition and interpretation of circuit diagrams. In this paper, a new descriptor taking advantage of both statistical and structural information is proposed. It addresses geometric constraint between every pair of pixels. The computation of the descriptor is outlined as follows, First, a histogram is constructed for every pixel to figure out the distribution of the constraints among the other pixels. Second, the information contained in all the histograms is statistically integrated to form a feature vector with fixed dimension.

We study the properties of Schnyder’s realizers and canonical ordering trees of plane graphs. Based on these newly discovered properties, we obtain compact drawings of two styles for any plane graph G with n vertices. First, we show that G has a visibility representation with height at most ? 15n/16 ?. This improves the previous best bound of (n - 1). Second, we show that every plane graph G has a straight-line grid embedding on an (n - d 0 - 1) × (n - d 0 - 1) grid, where d 0 is the number of cyclic faces of G with respect to its minimum realizer. This improves the previous best bound of (n - 1) × (n - 1). We also study the properties of the regular edge labeling of 4-connected plane triangulation. Based on these properties, we show that every such a graph has a canonical ordering tree with at most ? (n + 1)/2 ? leaves. This improves the previously known bound of ? (2n + 1)/3 ?. We show that every 4-connected plane graph has a visibility representation with height at most ? 3n/4 ?. All drawings discussed in this paper can be obtained in linear time. [ABSTRACT FROM AUTHOR]

Abstract: It is proved that every k-colourable graph on n vertices has a grid drawing with area, and that this bound is best possible. This result can be viewed as a generalisation of the no-three-in-line problem. A further area bound is established that includes the aspect ratio as a parameter. [Copyright &y& Elsevier]

Abstract: Given a set S of strings, a DFA accepting S offers a very time-efficient solution to the pattern matching problem over S. The key is how to implement such a DFA in the trade-off between time and space, and especially the choice of how to implement the transitions of each state is critical. Bentley and Sedgewick proposed an effective tree structure called ternary trees. The idea of ternary trees is to ‘implant’ the process of binary search for transitions into the structure of the trees themselves. This way the process of binary search becomes visible, and the implementation of the trees becomes quite easy. The directed acyclic word graph (DAWG) of a string is the smallest DFA that accepts all suffixes of , and requires only linear space. We apply the scheme of ternary trees to DAWGs, introducing a new data structure named ternary DAWGs (TDAWGs). Furthermore, the scheme of AVL trees is applied to the TDAWGs, yielding a more time-efficient structure AVL TDAWGs. We also perform some experiments that show the efficiency of TDAWGs and AVL TDAWGs, compared to DAWGs in which transitions are implemented by linked lists. [Copyright &y& Elsevier]

Let G be a 4-connected graph. For an edge e of G, we do the following operations on G: first, delete the edge e from G, resulting the graph G-e; second, for all the vertices x of degree 3 in G-e, delete x from G-e and then completely connect the 3 neighbors of x by a triangle. If multiple edges occur, we use single edges to replace them. The final resultant graph is denoted by G⊖e. If G⊖e is still 4-connected, then e is called a removable edge of G. In this paper we prove that every 4-connected graph of order at least six (excluding the 2-cyclic graph of order six) has at least (4|G|+16)/7 removable edges. We also give the structural characterization of 4-connected graphs for which the lower bound is sharp. [Copyright &y& Elsevier]

We construct nonconstructible simplicial d-spheres with d + 10 vertices and nonconstructible, nonrealizable simplicial d-balls with d + 9 vertices for d ⩾ 3. [ABSTRACT FROM AUTHOR]

An arrangement graph G is the abstract graph obtained from an arrangement of lines L, in general position by associating vertices of G with the intersection points of L, and the edges of G with the line segments joining the intersection points of L. A simple polygon (respectively path) of n sides in general position, induces a set of n lines by extension of the line segments into lines. The main results of this paper are: • Given a graph G, it is NP-Hard to determine if G is the arrangement graph of some set of lines. • There are non-Hamiltonian arrangement graphs for arrangements of six lines and for odd values of n>6 lines. • All arrangements of n lines contain a subarrangement of size [formula] with an inducing polygon. • All arrangements on n lines contain an inducing path consisting of n line segments. A Java applet implementing the algorithm for determining such a path is also provided. • All arrangements on n hyperplanes in R[sup d] contain a simple inducing polygonal cycle of size n. [ABSTRACT FROM AUTHOR]

This article defines government-industry relations by reference to policy processes and charts expansion of interest, takes an eclectic selection of recent studies, assesses strengths and examines the range of theoretical approaches. It stresses developing tendencies towards comparative studies, empirical verification and theoretical innovation. [ABSTRACT FROM AUTHOR]

This paper proposes a highly accurate gray-level transformation, aiming at the on-line equalization of the discrete histogram. The experimental result is described for the constructed gray level transformation device with NTSC TV rate. The paper first describes the linear interpolation, based on discrete histogram, of the traditional gray-level transformation based on a discrete cumulative histogram. It is shown by computer simulation that the proposed method reduces drastically the effect of error in the gray-level transformation. Then the construction of the 8-bit gray-level transformation device by the proposed method is described together with the realized electrical performances. By giving a low- contrast electron microscope picture of aluminum to a TV camera, the obtained image is given to the gray-level transformation device. It is shown that using the proposed method, the gray-level transformation can be performed with high speed and high accuracy. [ABSTRACT FROM AUTHOR]

Abstract: A method to draw a Pedotti or butterfly diagram is described using Microsoft Excel spreadsheets and charts without the need for knowledge in programming or special software. [Copyright &y& Elsevier]

The article presents the author's views on considering diagrams as a semiotic mode of representation and communication. He states that mathematics is a multimodal discourse which ha different modes of representation and communication. Focusing on geometry, he analyzes the kinds of meanings afforded by diagrams in mathematical discourse. He comments that he considers diagrams as a semiotic mode of representation and communication that leads to construct mathematical meaning. He argues that the author of the diagram creates an imaginary social relation with the viewer.

A diagram proving a sine result for the angles of a triangle is presented.

This article focuses on the preparation of series of bar graphs for a recent publication, "Relation of Size of Community to Marital Status," Memoir 200, Cornell University Agricultural Experiment Station, February, 1937. An experiment was made in the use of printed hatchings to save a large amount of handwork. This seems to have been fairly successful and the method may be of interest to others. A plate was made with eight types of hatching in parallel strips. The plate was 9.5 inches by 12 inches and each strip was approximately 1 and a half inches wide by 12 inches long. This was printed on gummed paper and each type of hatching was cut into strips approximately 5/16 of an inch wide. An outline of each bar graph was made by tracing on tracing cloth over a pencil sketch made on cross-section paper. A strip of the proper type of hatching was then cut for the length of each bar of the graph and was pasted onto the tracing within the outline drawn in ink. The cost of original plate for the printed hatching was $24.