The fascinating world of graph theory goes back several centuries and revolves around the study of graphs-mathematical structures showing relations between objects. With applications in biology, ...computer science, transportation science, and other areas, graph theory encompasses some of the most beautiful formulas in mathematics-and some of its most famous problems. For example, what is the shortest route for a traveling salesman seeking to visit a number of cities in one trip? What is the least number of colors needed to fill in any map so that neighboring regions are always colored differently? Requiring readers to have a math background only up to high school algebra, this book explores the questions and puzzles that have been studied, and often solved, through graph theory. In doing so, the book looks at graph theory's development and the vibrant individuals responsible for the field's growth.
Introducing graph theory's fundamental concepts, the authors explore a diverse plethora of classic problems such as the Lights Out Puzzle, the Minimum Spanning Tree Problem, the Königsberg Bridge Problem, the Chinese Postman Problem, a Knight's Tour, and the Road Coloring Problem. They present every type of graph imaginable, such as bipartite graphs, Eulerian graphs, the Petersen graph, and trees. Each chapter contains math exercises and problems for readers to savor.
An eye-opening journey into the world of graphs, this book offers exciting problem-solving possibilities for mathematics and beyond.
In two studies, we investigated whether a recently developed psychometric instrument can differentiate intrinsic, extraneous, and germane cognitive load. Study I revealed a similar three-factor ...solution for language learning (n = 108) and a statistics lecture (n = 174), and statistics exam scores correlated negatively with the factors assumed to represent intrinsic and extraneous cognitive load during the lecture. In Study II, university freshmen who studied applications of Bayes' theorem in example–example (n = 18) or example–problem (n = 18) condition demonstrated better posttest performance than their peers who studied the applications in problem–example (n = 18) or problem–problem (n = 20) condition, and a slightly modified version of the aforementioned psychometric instrument could help researchers to differentiate intrinsic and extraneous cognitive load. The findings provide support for a recent reconceptualization of germane cognitive load as referring to the actual working memory resources devoted to dealing with intrinsic cognitive load.
•We experimentally tested a new instrument for cognitive load measurement.•Results indicate that it could differentiate intrinsic and extraneous cognitive load.•Example/example–problem pairs enhanced learning more than problem/problem–example pairs.•The findings provide support for a recent reconceptualization of germane cognitive load.
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Nonlinear inverse problems appear in many applications, and typically they lead to mathematical models that are ill-posed, i.e., they are unstable under data perturbations. Those problems require a ...regularization, i.e., a special numerical treatment. This book presents regularization schemes which are based on iteration methods, e.g., nonlinear Landweber iteration, level set methods, multilevel methods and Newton type methods.
Group problem solving Laughlin, Patrick R; Laughlin, Patrick R
2011., 20110124, 2011, 2011-01-24
eBook
Experimental research by social and cognitive psychologists has established that cooperative groups solve a wide range of problems better than individuals. Cooperative problem solving groups of ...scientific researchers, auditors, financial analysts, air crash investigators, and forensic art experts are increasingly important in our complex and interdependent society. This comprehensive textbook--the first of its kind in decades--presents important theories and experimental research about group problem solving. The book focuses on tasks that have demonstrably correct solutions within mathematical, logical, scientific, or verbal systems, including algebra problems, analogies, vocabulary, and logical reasoning problems.
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The Vehicle Routing Problem (VRP) has been an especially active and fertile area of research. Over the past five to seven years, there have been numerous technological advances and exciting ...challenges that are of considerable interest to students, teachers, and researchers. The Vehicle Routing Problem: Latest Advances and New Challengeswill focus on a host of significant technical advances that have evolved over the past few years for modeling and solving vehicle routing problems and variants. New approaches for solving VRPs have been developed from important methodological advances. These developments have resulted in faster solutions algorithms, more accurate techniques, and an improvement in the ability to solve large-scale complex problems.
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6.
The traveling salesman problem Applegate, David L; Applegate, David L; Bixby, Robert E ...
2006., 20110919, 2011, 2007, 2007-01-01, Volume:
17
eBook
This book presents the latest findings on one of the most intensely investigated subjects in computational mathematics--the traveling salesman problem. It sounds simple enough: given a set of cities ...and the cost of travel between each pair of them, the problem challenges you to find the cheapest route by which to visit all the cities and return home to where you began. Though seemingly modest, this exercise has inspired studies by mathematicians, chemists, and physicists. Teachers use it in the classroom. It has practical applications in genetics, telecommunications, and neuroscience.
Background
Several inventories have been developed to assess social problem‐solving. However, these instruments originally developed for adult or adolescence and do not capture the full range of main ...interpersonal relationships over which elementary students resolve daily life interpersonal problems and apply elementary‐age typical responses. Therefore, the development of a valid scale to measure interpersonal problem‐solving ability in elementary school students is warranted.
Aims
This study aimed to develop and perform a preliminary psychometric evaluation of an interpersonal problem‐solving inventory for elementary school students (IPSIE).
Samples and Methods
The IPSIE was administered to elementary student samples that consist of 516 Vietnamese elementary school students in grades 3–5. This study examined the reliabilities of International problem behaviour (IPB) and interpersonal problem‐solving inventory (IPSI) as well as the construct validity of IPSI. The construct validity of IPSI was investigated by using exploratory factor analysis (EFA) to explore the emerging factor structure of the data. The confirmatory factor analysis (CFA) was utilized to fit the data.
Results
The reliabilities of IPB and IPSI were assessed by calculating internal consistencies (Cronbach’s α = 0.79 vs. 0.90, McDonald's ω = 0.79 vs. 0.82). The EFA results suggested that the IPSI has two‐factor structure. The CFA was reexamined to define theory‐driven five‐factor structure of the IPSI’s data. The CFA findings indicated that the scores of IPSI have the five‐factor structure as expected with acceptable global fit indices (CFI: 0.943, TLI: 0.939, RMSEA: 0.030, and RMR: 0.046). The concurrent validity of IPSI was tested by calculating correlations between the IPSI and SPSI‐R scores (r = .667) and the IPSI and SPSTE‐A scores (r = .482).
Conclusions
These finding figures suggest that overall the scales of IPSIE are well‐functioning measures with good psychometric properties. Caution and limitations of IPSIE are discussed. Future study and possible applicability are suggested.
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•Instead of focusing on a particular technology or industry, an innovation system must focus on solving problems.•a Problem-oriented Innovation system (PIS) has eight functions.•PIS can be used to ...solve global problems such as global warming and climate change.
The number of theories of innovation systems has grown considerably over the past two decades and several innovation system approaches have been developed. The focus of most has been on the development of technological innovations which create economic value.However, addressing macro-level societal problems – sociotechnical and environmental challengesin which the production, dissemination and use of social and technical knowledge and technology can potentially resolve the problem – has been overlooked. The present study argues that in order to resolve such problems, a combination of technical innovations (covering the technological aspects of the problem) and social innovations (covering the social aspects of the problem) are required.Instead of focusing on the development of a particular technology or industry, an innovation system must focus on solving problems; it must utilize technical innovations alongside economic and social innovations to do so.To this end, the present study highlights the need for a framework for the analysis of macro-level societal problems by reviewing innovation systems literature and proposes a new approach named “Problem-oriented innovation systems”. We conceptualize this approach based on event history analysis and through case study of the US air pollution problem and the way it was successfully resolved by using technical and social innovations.The results show that a problem-oriented innovation system has eight functions: System monitoring and guidance, technical and social knowledge creation, technical and social entrepreneurship, knowledge dissemination, collaboration and synergy, public awareness, standardization and resource mobilization. Finally, a framework for analyzing the innovation process is proposed to solve the macro-level societal problem. This approach can be used to solve global problems such as global warming and climate change which ask for collaboration among different countries.
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Modern electronic devices and novel materials often derive their extraordinary properties from the intriguing, complex behavior of large numbers of electrons forming what is known as an electron ...liquid. This book provides an in-depth introduction to the physics of the interacting electron liquid in a broad variety of systems, including metals, semiconductors, artificial nano-structures, atoms and molecules. One, two and three dimensional systems are treated separately and in parallel. Different phases of the electron liquid, from the Landau Fermi liquid to the Wigner crystal, from the Luttinger liquid to the quantum Hall liquid are extensively discussed. Both static and time-dependent density functional theory are presented in detail. Although the emphasis is on the development of the basic physical ideas and on a critical discussion of the most useful approximations, the formal derivation of the results is highly detailed and based on the simplest, most direct methods.
We consider initial value/boundary value problems for fractional diffusion-wave equation:
∂
t
α
u
(
x
,
t
)
=
L
u
(
x
,
t
)
, where
0
<
α
⩽
2
, where
L is a symmetric uniformly elliptic operator with
...t-independent smooth coefficients. First we establish the unique existence of the weak solution and the asymptotic behavior as the time
t goes to ∞ and the proofs are based on the eigenfunction expansions. Second for
α
∈
(
0
,
1
)
, we apply the eigenfunction expansions and prove (i) stability in the backward problem in time, (ii) the uniqueness in determining an initial value and (iii) the uniqueness of solution by the decay rate as
t
→
∞
, (iv) stability in an inverse source problem of determining
t-dependent factor in the source by observation at one point over
(
0
,
T
)
.
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