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Common map key symbols are discussed alongside full-color examples of many kinds of maps and keys to guide readers through the use and importance of each.

We develop cohomological interpretations for several types of automorphic forms for Hecke triangle groups of infinite covolume. We then use these interpretations to establish explicit isomorphisms between spaces of automorphic forms, cohomology spaces and spaces of eigenfunctions of transfer operators. These results show a deep relation between spectral entities of Hecke surfaces of infinite volume and the dynamics of their geodesic flows.

Detailed examples lead readers through using a compass rose on a map. Full-color images accompany important map skills, engaging readers with content consistent with the social studies curriculum.

Given the ubiquity of handwriting and mathematical content in human transactions, machine recognition of handwritten mathematical text and symbols has become a domain of great practical scope and significance. Recognition of mathematical expression (ME) has remained a challenging and emerging research domain, with mathematical symbol recognition (MSR) as a requisite step in the entire recognition process. Many variations in writing styles and existing dissimilarities among the wide range of symbols and recurring characters make the recognition tasks strenuous even for Optical Character Recognition. The past decade has witnessed the emergence of recognition techniques and the peaking interest of several researchers in this evolving domain. In light of the current research status associated with recognizing handwritten math symbols, a systematic review of the literature seems timely. This article seeks to provide a complete systematic analysis of recognition techniques, models, datasets, sub-stages, accuracy metrics, and accuracy details in an extracted form as described in the literature. A systematic literature review conducted in this study includes pragmatic studies until the year 2021, and the analysis reveals Support Vector Machine (SVM) to be the most dominating recognition technique and symbol recognition rate to be most frequently deployed accuracy measure and other interesting results in terms of segmentation, feature extraction and datasets involved are vividly represented. The statistics of mathematical symbols-related papers are shown, and open problems are identified for more advanced research. Our study focused on the key points of earlier research, present work, and the future direction of MSR.

Several authors have studied homomorphisms from first homology groups of modular curves to $K_2(X)$, with $X$ either a cyclotomic ring or a modular curve. These maps send Manin symbols in the homology groups to Steinberg symbols of cyclotomic or Siegel units. We give a new construction of these maps and a direct proof of their Hecke equivariance, analogous to the construction of Siegel units using the universal elliptic curve. Our main tool is a $1$-cocycle from $\\mathrm {GL}_2(\\mathbb {Z})$ to the second $K$-group of the function field of a suitable group scheme over $X$, from which the maps of interest arise by specialization.

\"A brand is just a logo and a way of charging you more for a product- everyone knows that, don't they? After all, there is no such thing as brand loyalty, and isn't branding all fluff and art, devoid of rigour and science? These myths are all surprisingly entrenched, yet could not be further from the truth. Myths of Branding debunks the most popular misconceptions and replaces them with the reality of what it's really like to work in the world of branding and why it's such an important and effective industry. Branding experts Simon Bailey and Andy Milligan explore the misguided, mistaken and blatantly false myths that abound in the branding arena, using fascinating examples from the world's leading brands and foremost branding agencies. Myths of Branding will give you a deeper and sharper understanding of the realities of branding and brand management.\"--Back cover.

Purpose: The effects of animation on identification of graphic symbols for verbs were studied using the Autism Language Program Graphic Symbols Set in children diagnosed with mild-to-severe autism spectrum disorder between the ages of 3 and 7 years. Method: The participants were randomly assigned to an animated symbol condition or a static symbol condition. Static symbols were spliced from the animated symbols to ensure that the symbols differed only in terms of the absence or presence of movement. The participants were asked to identify a target symbol among foils given the spoken label. Results: There were no significant differences between the groups with respect to chronological age, autism severity, and receptive target verb knowledge. An independent \"t\" test revealed that animated symbols were more readily identified than static symbols. Conclusions: Animation enhances the identification of verbs in children with autism spectrum disorder. Clinicians are encouraged to take advantage of animation when introducing graphic symbols representing verbs. Limitations and implications for future research are discussed.

A useful, inspirational book aimed at graphic design students and practising designers, examining the most successful logo, letterhead and business card designs and how they were created.

Symbolism and symbolic representation serve as mechanisms for ambiguity creation, deepening meaning, engaging the reader in meaning-making, and transitioning from monosemy to polysemy. The advent of modernity, exposure to Western poetic movements—particularly Symbolism—and the oppressive sociopolitical atmosphere following the Constitutional Revolution have significantly influenced both the quantitative and qualitative transformation of symbols in Persian poetry. The interrelation and synergy of symbols, as well as the discovery of their structural connections through the extraction of \"macro-symbols\" and \"organic symbols\", provide novel methodologies for understanding the role of symbolism in contemporary Persian poetry. This study uses a descriptive-analytical approach to examine the structural relationships of symbols and symbolic networks within the poetry of Mohammad Saeed Mirzaei, identifying them as the most significant stylistic component of his literary expression. Through theoretical discussions and the extraction of micro-symbols (as fundamental quantitative units), the research delves into macro-symbols and organic symbols as structural symbolic networks in Mirzaei’s ghazals. The findings indicate that Mirzaei’s poetic symbols achieve meaning through systematic interconnections, wherein the interplay between organic and macro-symbols predominates. That is, the poet strategically positions recurrent macro-symbols at the core of one or multiple ghazals, utilizing them as organic symbols.    Keywords: Symbol, Symbolic Networks, Organic Symbol, Macro-symbol, Mohammad Saeed Mirzaei.     Introduction This research examines the symbolic structures within the poetry of Mohammad Saeed Mirzaei, a prominent neo-ghazal poet of the 1990s. The objective is a systematic analysis of the symbols and uncovering their interrelated patterns throughout his poetry. The scope of the study includes an investigation into the types of symbols employed, the organic structure of symbols within the ghazal, and their network formation across Mirzaei’s poetic compositions.  The primary research question concerns how symbols interact within Mirzaei’s poetry to create a cohesive and meaningful network, and how these structural connections contribute to the comprehension of the deeper semantic layers of his poetry. A thorough examination of the symbolic system within neo-ghazal poetry and the presentation of a precise framework for its analysis are among the core objectives of this study.  While extensive prior research has addressed the role of symbolism in Persian poetry, fewer studies have explored the symbolic networks and their structural relationships in literary texts. Works by Baraheni (2001) and Fotouhi (2006, 2008) in this field serve as foundational references for the present analysis.  The four research questions of the study include:  What connections exist among symbols in Mirzaei’s poetry? Can an organic and structured symbolic system be identified within a single ghazal? Which symbols can be considered the dominant macro-symbols of his poetry? What symbolic networks emerge within his poetry? This study is based on the premise that the symbols employed in Mirzaei’s poetry exhibit structured and meaningful interrelationships, and that their analysis facilitates the identification of symbolic connections and semantic frameworks within his poetic compositions. Additionally, the study addresses the evolution of symbolism in neo-ghazal poetry, providing a comparative perspective on stylistic patterns in contemporary Persian poetry.    Materials and Methods This research adopts a descriptive-analytical approach to examine the symbolic structure in Mohammad Saeed Mirzaei’s poetry. The study is based on a content analysis of the collection Ghazal-e Hezareh-ye Digar, comprising 71 ghazals, conducted through library-based research methods.  The structural analysis of symbols employs an inductive methodology. Initially, micro-symbols are extracted as foundational elements, enabling the identification of macro-symbols and organic symbols. Macro-symbols, due to their high frequency and broad semantic extension in Mirzaei’s poetry, play a pivotal role in his stylistic identity. Conversely, organic symbols emerge within the framework of a single ghazal and, through interaction with other imagery, contribute to the deepening of semantic layers.  The study is centered on two primary analytical axes:  Analysis of Macro-Symbols: Identification of symbols that frequently appear in Mirzaei’s poetry and transcend conventional lexical usage. Examination of Organic Symbols: Analysis of symbolic networks that develop within a single ghazal, influencing the overall semantic framework of the composition. The methodology involves a systematic extraction of symbols, their classification, and the examination of structural relationships among them. Utilizing textual analysis models, this research explores symbolic interactions across different poetic levels, with particular emphasis on ghazals where organic symbolic interconnections are more pronounced.    Research Findings The study aims to explore the symbolic system in Mohammad Saeed Mirzaei’s ghazals by analyzing linguistic data to extract semantic networks of symbols. The symbols used in his poetry primarily fall into two categories: human-related symbols and environmental symbols. Human-related symbols encompass tools, travel, locations, time references, characters, and cultural elements, which are highly prevalent in Mirzaei’s poetry. This reflects the poet’s focus on urban spaces and the psychological dimensions of contemporary life. Objects such as mirrors, chairs, tables, windows, and umbrellas play a central role in shaping themes of identity, memory, anticipation, and existential exploration. Additionally, travel and associated elements such as trains, roads, stations, and bridges symbolize movement, transformation, and the desire to escape environmental constraints.  Conversely, environmental symbols include natural phenomena, animals, plants, and celestial bodies. Frequently recurring elements such as clouds, wind, rain, the sea, and stones symbolize themes of impermanence, longing, sorrow, and hope. Unlike traditional Persian poetry, fish in Mirzaei’s works is employed as a metaphor for the modern individual and their social conditions.  Another significant finding is the role of organic symbols in Mirzaei’s poetry. These symbols function as central thematic pillars within a ghazal, shaping surrounding imagery. Examples such as windows, travel, clouds, and tables form intricate symbolic networks that enhance semantic depth and influence interpretative frameworks.    Discussion of Results and Conclusions The findings of the study indicate that symbols in Mohammad Saeed Mirzaei’s poetry attain meaning through macro-symbolic and organic interconnections rather than as isolated and fragmented elements.  Dominant symbols include mirrors, travel, windows, fish, and chairs, which, when interacting with other poetic elements, construct intricate symbolic networks. Windows and travel represent aspirations for liberation and transformation, whereas mirrors and chairs reflect introspection and mental constraints. Additionally, natural and cosmic symbols such as clouds, rain, stars, and night significantly contribute to the emotional and philosophical dimensions of his poetry.  From a Jungian psychological perspective, Mirzaei’s symbolism embodies an unconscious interplay between confinement and freedom, stillness and movement, past and future. The interconnections among objects and situations underscore the stylistic coherence of his poetic vision.