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Defines critical academic skills that should be the hallmark of Kansas community college graduates, in anticipation of a legislative mandate for a common accountability measurement system. Presents five key critical competencies: oral and written communication skills, interpersonal and team skills, critical thinking and complex problem-solving skills, awareness of cultural and social diversity, and basic mathematical skills. (Contains 37 references.) (PGS)

Intends to sketch the research climate in Egypt in such a way that will have relevance to conducting research in the broader developing world. Explains that the problems encountered doing research in Egypt can be expected to occur in most developing countries, not only in Egypt. (CMK)

A literature review, focus groups (n=200), and questionnaire responses from 324 family physicians identified their learning needs related to osteoporosis. The three methods identified different learning issues, suggesting the importance of triangulation to ensure currency and relevance in continuing-education needs-assessment. (SK)

A heuristic study of the methodology used in a civic behavior study examined how data from literary and historical subjects were merged with live interviews, a triangulation that produced rich insights. Suggestions for incorporating nontraditional data sources include considering selection issues and process, media choice, depth, context, and voice. (SK)

Compares students with disabilities and students with no disabilities on the family systems measures of fusion and triangulation. Examines the relationships among fusion, triangulation, and college adjustment. Relationships between fusion and college adjustment and between triangulation and college adjustment were found. (Author/MKA)

Tests the ability of Bowenian family systems theory to explain career-decision problems in young adults. Young adults (N=1,006) completed self-report measures of fusion, triangulation, intimidation, trait anxiety, and career-decision problems. Analyses support the mediating role of anxiety for fusion and intimidation; triangulation was not related to career-decision problems. (Author/MKA)

Describes a method for assessing the effects of an undergraduate environmental history course on student environmental worldviews, the foundation of which is triangulation of method. A grounded survey instrument was used to supply quantitative and qualitative data which were supplemented by data from open-ended interviews. The method was effective in identifying degree and direction of changes in student worldviews. Contains 23 references. (Author/PVD)

Investigates attitudes toward e-mail and e-mail policies through a case study of e-mail users at a university library. Indicates those who use e-mail frequently have more favorable attitudes to it than less frequent users and are more opposed to policies regulating e-mail communication. Notes that employees prefer guidelines to restrictive policies. (PA)

Discusses the components of a new methodology--consensual qualitative research (CQR)--which uses words to describe phenomena and which recognizes the importance of context. Locates CQR within the qualitative research tradition and details ways to develop a focused topic area, choose a team, attend to group dynamics, and other important issues. (RJM)

We introduce the abstract notion of a chain, which is a sequence of n points in the plane, ordered by xcoordinates, so that the edge between any two consecutive points is unavoidable as far as triangulations are concerned. A general theory of the structural properties of chains is developed, alongside a general understanding of their number of triangulations. We also describe an intriguing new and concrete configuration, which we call the Koch chain due to itssimilarities to the Koch curve. A specific construction based on Koch chains is then shown to have Ω(9.08n ) triangulations. This is a significant improvement over the previous and long-standing lower bound of Ω(8.65n ) for the maximum number of triangulations of planar point sets. [ABSTRACT FROM AUTHOR]

In this paper, we present a laser triangulation sensor to measure the distance between the sensor and an object without contact using a diffraction slit rather than a traditional lens. We show that by replacing the lens with a slit, we can exploit the resulting diffraction pattern to have finer and yet simpler image analysis, yielding better estimation of the distance to the object. To test our hypothesis, we build a precision position table and a laser triangulation sensor, generate large data sets to test different estimation algorithms on various materials, and compare data acquisition using a traditional lens versus using a slit. We show that position estimation when using a slit is both more precise and more accurate than comparable methods using a lens. [ABSTRACT FROM AUTHOR]

The variety of equipment implementing laser triangulation technology for 3D scanning makes it difficult to analyse their performance, comparability, and traceability. In this study, three laser triangulation sensors arranged in different configurations are analysed using high precision spheres made of different materials and surface finishes. Three types of reference parameters were used: diameter, form error, and standard deviation of the point cloud. The experimentation was based on studying the quality of the point clouds generated by the three sensors, which enabled us to find and quantify an edge effect in the horizon of the scanned surface. A procedure to reach the optimal filtering conditions was proposed, and a chart of recommended usage of each sphere (material and finish) was created for the different types of sensors. This filter enables removal of both spurious points and those few points that spoil the form error, greatly improving the quality of the measurement. [ABSTRACT FROM AUTHOR]

Golodness of a simplicial complex is defined algebraically in terms of the Stanley–Reisner ring, and it has been a long-standing problem to find its combinatorial characterization. Tightness of a simplicial complex is a combinatorial analogue of a tight embedding of a manifold into Euclidean space, and has been studied in connection to minimal manifold triangulations. In this paper, by using an idea from toric topology, we prove that tight complexes are Golod, and as a corollary, we obtain that a triangulation of a closed connected orientable manifold is Golod if and only if it is tight, which is a combinatorial characterization of Golodness for manifold triangulations. [ABSTRACT FROM AUTHOR]

A new impartial game on a connected graph was introduced, called a feedback game , which is a variant of generalized geography. In this paper, we study the feedback game on 3-chromatic Eulerian triangulations of surfaces. We prove that the winner of the game on every 3-chromatic Eulerian triangulation of a surface all of whose vertices have degree 0 modulo 4 is always fixed. Moreover, we also study the case of 3-chromatic Eulerian triangulations of surfaces which have at least two vertices whose degrees are 2 modulo 4. In addition, as a concrete class of such graphs, we consider the octahedral path, which is obtained from an octahedron by adding octahedra in the same face, and completely determine the winner of the game on those graphs. [ABSTRACT FROM AUTHOR]

In the United States, regions (such as states or counties) are frequently divided into districts for the purpose of electing representatives. How the districts are drawn can have a profound effect on who is elected, and drawing the districts to give an advantage to a certain group is known as gerrymandering. It can be surprisingly difficult to detect when gerrymandering is occurring, but one algorithmic method is to compare a current districting plan to a large number of randomly sampled plans to see whether it is an outlier. Recombination Markov chains are often used to do this random sampling: randomly choose two districts, consider their union, and split this union up in a new way. This approach works well in practice and has been widely used, including in litigation, but the theory behind it remains underdeveloped. For example, it is not known if recombination Markov chains are irreducible, that is, if recombination moves suffice to move from any districting plan to any other. Irreducibility of recombination Markov chains can be formulated as a graph problem: for a planar graph G , is the space of all partitions of G into k connected subgraphs (k districts) connected by recombination moves? While the answer is yes when districts can be as small as one vertex, this is not realistic in real-world settings where districts must have approximately balanced populations. Here we fix district sizes to be k 1 ± 1 vertices, k 2 ± 1 vertices, ... for fixed k 1 , k 2 , ... , a more realistic setting. We prove for arbitrarily large triangular regions in the triangular lattice, when there are three simply connected districts, recombination Markov chains are irreducible. This is the first proof of irreducibility under tight district size constraints for recombination Markov chains beyond small or trivial examples. The triangular lattice is the most natural setting in which to first consider such a question, as graphs representing states/regions are frequently triangulated. The proof uses a sweep-line argument, and there is hope it will generalize to more districts, triangulations satisfying mild additional conditions, and other redistricting Markov chains. [ABSTRACT FROM AUTHOR]

The Ehrhart polynomial ehrP(n) of a lattice polytope P counts the number of integer points in the n-th dilate of P. The f*-vector of P, introduced by Felix Breuer in 2012, is the vector of coefficients of ehrP(n) with respect to the binomial coefficient basis { n − 1 0 , n − 1 1 , ... , n − 1 d } , where d = dim P. Similarly to h/h*-vectors, the f*-vector of P coincides with the f-vector of its unimodular triangulations (if they exist). We present several inequalities that hold among the coefficients of f*-vectors of lattice polytopes. These inequalities resemble striking similarities with existing inequalities for the coefficients of f-vectors of simplicial polytopes; e.g., the first half of the f*-coefficients increases and the last quarter decreases. Even though f*-vectors of polytopes are not always unimodal, there are several families of polytopes that carry the unimodality property. We also show that for any polytope with a given Ehrhart h*-vector, there is a polytope with the same h*-vector whose f*-vector is unimodal. [ABSTRACT FROM AUTHOR]

We construct finite element approximations of the Levi-Civita connection and its curvature on triangulations of oriented two-dimensional manifolds. Our construction relies on the Regge finite elements, which are piecewise polynomial symmetric (0, 2)-tensor fields possessing single-valued tangential-tangential components along element interfaces. When used to discretize the Riemannian metric tensor, these piecewise polynomial tensor fields do not possess enough regularity to define connections and curvature in the classical sense, but we show how to make sense of these quantities in a distributional sense. We then show that these distributional quantities converge in certain dual Sobolev norms to their smooth counterparts under refinement of the triangulation. We also discuss projections of the distributional curvature and distributional connection onto piecewise polynomial finite element spaces. We show that the relevant projection operators commute with certain linearized differential operators, yielding a commutative diagram of differential complexes. [ABSTRACT FROM AUTHOR]

In 1990, Schnyder used a 3-spanning-tree decomposition of a simple triangulation, now known as the Schnyder wood , to give a fundamental grid-embedding algorithm for planar maps. In the framework of mating of trees, a uniformly sampled Schnyder-wood-decorated triangulation can produce a triple of random walks. We show that these three walks converge in the scaling limit to three Brownian motions produced in the mating-of-trees framework by Liouville quantum gravity (LQG) with parameter 1, decorated with a triple of SLE_{16}'s curves. These three SLE_{16}'s curves are coupled such that the angle difference between them is 2\pi /3 in imaginary geometry. Our convergence result provides a description of the continuum limit of Schnyder's embedding algorithm via LQG and SLE. [ABSTRACT FROM AUTHOR]

This article explores the concept of racial triangulation theory, specifically in relation to Asian Americans. The author shares their personal experiences during the 1992 Los Angeles riots and how this theory helped them understand the dynamics between different racial groups. The theory acknowledges the discrimination faced by Asian Americans while recognizing their relative advantages in education and class. However, the author cautions against a limited application of the theory that fails to recognize the unique forms of discrimination faced by Black Americans and can unintentionally reinforce anti-Black attitudes. They stress the importance of a more comprehensive and nuanced understanding of racial dynamics. The article also discusses the need to contextualize the experiences of Asian Americans within the broader racial landscape, particularly in relation to the experiences of Black people. It highlights survey findings that demonstrate the differential racialization experienced by different racial groups, such as the perpetual foreigner stereotype faced by Asian Americans and the higher levels of police brutality experienced by Black and other non-White groups. The author warns against solely focusing on anti-Asian hate crimes and calls for a more comprehensive understanding of systemic racism and discrimination. The article concludes by discussing the significance of intergroup solidarity and the potential consequences of not applying a robust interpretation of racial triangulation theory in contemporary Asian American politics. [Extracted from the article]

The measurement of shape parameters of coarse aggregate is the premise to ensure the quality of concrete engineering. In the measurement of particle shape based on laser triangulation method, the selection of polynomial fitting parameters between different test scene displacement and image offset is often different. For coarse aggregate height measurement, an optimal laser triangulation method is proposed, and the best polynomial fitting times of aggregate measurement is obtained through data extraction and error analysis. Firstly, the laser streak information is collected from the aggregate surface based on the industrial camera, and the laser streak is processed by Gaussian filtering and color space transformation, and then the center line of the laser streak is obtained by the center method to obtain the corresponding aggregate height information. Finally, based on the comparison between the experimental measurements and the height values calculated by different polynomial fits, the laser triangulation solution method is optimized by different error factors analysis. The experimental results show that in the process of aggregate height measurement, the cubic term fitting solution is optimal with an average relative error of only 0.693%. [ABSTRACT FROM AUTHOR]

We show that the order complex of the poset of nonempty intervals, ordered by inclusion, is a Tchebyshev triangulation of the order complex of the original poset. Besides studying the properties of this transformation, we show that the dual of the type B permutohedron is combinatorially equivalent to the suspension of the order complex of the poset of nonempty intervals of a Boolean algebra (with the minimum and maximum elements removed). [ABSTRACT FROM AUTHOR]

Process Analytical Technology (P A T) plays a crucial role in the design of today's manufacturing lines as continuous manufacturing becomes more important. Until now P A T tools to measure the ribbon solid fraction (S F r i b b o n ) in-line are not commonly used in roll compaction. The aim of this study was therefore to establish a new approach as P A T for in-line ribbon solid fraction determination. Different placebo formulations with different binders and one formulation containing active pharmaceutical ingredient were investigated using in-line laser triangulation measurement to detect the ribbon thickness after compaction. With this the ribbon elastic recovery was determined in-line (E R i n − l i n e ) while the ribbons are attached to the roll surface. It was found that the ratio (E R r a t i o ) between the total elastic recovery and E R i n − l i n e is formulation specific and not influenced by any process parameters. This enables E R r a t i o as prediction tool for S F r i b b o n , if the solid fraction at gap (S F g a p ) width is known. S F g a p was determined with ribbon mass flow measurement or based on the Midoux model, a simplified Johanson model, gaining two prediction models for S F r i b b o n . Both models showed good agreement of the predicted S F r i b b o n and the measured one. [Display omitted] • Novel in-line laser triangulation measurement of ribbon elastic recovery in roll compaction. • In-line prediction of ribbon solid fraction as Process Analytical Technology (PAT). • Ribbon mass flow and Midoux number based model were established. • Prediction model based on Midoux number showed superior results and applicability. [ABSTRACT FROM AUTHOR]