Hasil untuk "Mathematics"

M. Sherin, V. Jacobs, Randolph A. Philipp

James Hiebert, P. Lefèvre

S. Shapiro, G. Hellman

H. Freudenthal

H. Hill, S. Schilling, D. Ball

D. Ball

D. Ball, H. Hill, H. Bass

H. Thieme

The formulation, analysis, and re-evaluation of mathematical models in population biology has become a valuable source of insight to mathematicians and biologists alike. This book presents an overview and selected sample of these results and ideas, organized by biological theme rather than mathematical concept, with an emphasis on helping the reader develop appropriate modeling skills through use of well-chosen and varied examples. Part I starts with unstructured single species population models, particularly in the framework of continuous time models, then adding the most rudimentary stage structure with variable stage duration. The theme of stage structure in an age-dependent context is developed in Part II, covering demographic concepts, such as life expectation and variance of life length, and their dynamic consequences. In Part III, the author considers the dynamic interplay of host and parasite populations, i.e., the epidemics and endemics of infectious diseases. The theme of stage structure continues here in the analysis of different stages of infection and of age-structure that is instrumental in optimizing vaccination strategies. Each section concludes with exercises, some with solutions, and suggestions for further study. The level of mathematics is relatively modest; a "toolbox" provides a summary of required results in differential equations, integration, and integral equations. In addition, a selection of Maple worksheets is provided. The book provides an authoritative tour through a dazzling ensemble of topics and is both an ideal introduction to the subject and reference for researchers.

David Burton

D. Geary

R. Siegler, G. Duncan, P. Davis‐Kean et al.

Xin Ma

James Hiebert, D. Grouws

Stuart J. Ritchie, Timothy C. Bates

Rochelle Gutiérrez

Lucy Cragg, C. Gilmore

The successful learning and performance of mathematics relies on a range of individual, social and educational factors. Recent research suggests that executive function skills, which include monitoring and manipulating information in mind (working memory), suppressing distracting information and unwanted responses (inhibition) and flexible thinking (shifting), play a critical role in the development of mathematics proficiency. This paper reviews the literature to assess concurrent relationships between mathematics and executive function skills, the role of executive function skills in the performance of mathematical calculations, and how executive function skills support the acquisition of new mathematics knowledge. In doing so, we highlight key theoretical issues within the field and identify future avenues for research.

R. Bull, Kerry Lee

The Univalent Foundations Program

Homotopy type theory is a new branch of mathematics, based on a recently discovered connection between homotopy theory and type theory, which brings new ideas into the very foundation of mathematics. On the one hand, Voevodsky's subtle and beautiful"univalence axiom"implies that isomorphic structures can be identified. On the other hand,"higher inductive types"provide direct, logical descriptions of some of the basic spaces and constructions of homotopy theory. Both are impossible to capture directly in classical set-theoretic foundations, but when combined in homotopy type theory, they permit an entirely new kind of"logic of homotopy types". This suggests a new conception of foundations of mathematics, with intrinsic homotopical content, an"invariant"conception of the objects of mathematics -- and convenient machine implementations, which can serve as a practical aid to the working mathematician. This book is intended as a first systematic exposition of the basics of the resulting"Univalent Foundations"program, and a collection of examples of this new style of reasoning -- but without requiring the reader to know or learn any formal logic, or to use any computer proof assistant.

Jun Zhang, Chuan Zhang, Mingtao Zhang

ABSTRACT This study integrates embodied intelligence (EI) with a two‐stage two‐sided Hotelling duopoly model to reveal how physical intelligence reshapes digital platform equilibrium in intelligent logistics. By embedding EI‐driven efficiency parameters into market cost functions, the model demonstrates that improved perception and coordination reduce the effective transportation cost and transform pricing dynamics between competing platforms. Experiments in a digital twin warehouse show that when EI strength η increases from 0 to 0.6, throughput rises by 37.5%, Dock‐to‐Stock time decreases by 30.9%, and unit energy consumption drops by 7%–8%, verifying that EI directly enhances operational and economic efficiency. Further analysis confirms that asymmetric advantages in action or data lead to discriminatory pricing as the optimal strategy. Complementary encryption experiments indicate that lightweight security algorithms such as SHA‐1/SHA‐256 add less than 3% latency overhead, maintaining real‐time performance.

Yiannis Kiouvrekis, Theodor Panagiotakopoulos

Electromagnetic field (EMF) exposure mapping is increasingly important for ensuring compliance with safety regulations, supporting the deployment of next-generation wireless networks, and addressing public health concerns. While numerous surveys have addressed specific aspects of radio propagation or radio environment maps, a comprehensive and unified overview of EMF mapping methodologies has been lacking. This review bridges that gap by systematically analyzing computational, geospatial, and machine learning approaches used for EMF exposure mapping across both wireless communication engineering and public health domains. A novel taxonomy is introduced to clarify overlapping terminology—encompassing radio maps, radio environment maps, and EMF exposure maps—and to classify construction methods, including analytical models, model-based interpolation, and data-driven learning techniques. In addition, the review highlights domain-specific challenges such as indoor versus outdoor mapping, data sparsity, and model generalization, while identifying emerging opportunities in hybrid modeling, big data integration, and explainable AI. By combining perspectives from communication engineering and public health, this work provides a broader and more interdisciplinary synthesis than previous surveys, offering a structured reference and roadmap for advancing robust, scalable, and socially relevant EMF mapping frameworks.