Hasil Pencarian  ::  Simpan CSV :: Kembali

"In this book the authors take an alternate approach to these theorems and generalize them to the setting of Hilbert modular varieties of arbitrary dimension. The approach is conceptual and uses tools that were not available to Hirzebruch and Zagier, including intersection homology theory, properties of modular cycles, and base change. Automorphic vector bundles, Hecke operators and Fourier coefficients of modular forms are presented both in the classical and adèlic settings. The book should provide a foundation for approaching similar questions for other locally symmetric spaces."

"This book offers something new, every definition and every essential fact concerning classical modular forms of one variable. One of the principal new features of this book is the theory of modular forms of half-integral weight, another being the discussion of theta functions and Eisenstein series of holomorphic and nonholomorphic types. Thus the book is presented so that the reader can learn such theories systematically. Ultimately, we concentrate on the following two themes, (i) the correspondence between the forms of half-integral weight and those of integral weight and (ii) the arithmeticity of various Dirichlet series associated with modular forms of integral or half-integral weight."

"Partitions, q-series, and modular forms contains a collection of research and survey papers that grew out of a Conference on partitions, q-series and modular forms at the University of Florida, Gainesville in March 2008. It will be of interest to researchers and graduate students that would like to learn of recent developments in the theory of q-series and modular and how it relates to number theory, combinatorics and special functions."

"Misalkan 𝐺 = (𝑉(𝐺), 𝐸(𝐺)) adalah suatu graf dengan order 𝑛, dengan 𝑛 merupakan bilangan bulat. Notasi 𝑉(𝐺) menyatakan himpunan simpul dan notasi 𝐸(𝐺) menyatakan himpunan busur. Pemetaan 𝛾: 𝐸(𝐺) → {1,2, … , 𝑘}, dengan 𝑘 adalah bilangan bulat, adalah pelabelan modular tak teratur dari graf G jika terdapat suatu fungsi bijektif 𝜎: 𝑉(𝐺) → 𝑍𝑛 yang didefinisikan sebagai 𝜎(𝑥) = (∑𝛾(𝑥𝑦)) mod 𝑛 untuk setiap y yang bertetangga dengan x sehingga nilai 𝜎(𝑥) berbeda untuk setiap 𝑥 ∈ 𝑉(𝐺). Nilai ketakteraturan modular dari graf 𝐺 adalah nilai minimum 𝑘 sedemikian sehingga terdapat pelabelan modular tak teratur dapat diterapkan ke graf 𝐺. Graf dodecahedral adalah graf planar 3-terhubung yang berhubungan dengan konektivitas simpul dodekahedron. Terdapat 2 macam simpul pada graf dodecahedral yaitu simpul luar dan simpul dalam dan semua simpul memiliki derajat 3. Graf dodecahedral yang diperumum adalah graf yang dibangun dari graf dodecahedral dengan menambahkan 2 busur pada simpul dalam sedemikian sehingga seluruh simpul dalam memiliki derajat 5. Graf dodecahedral yang diperumum dapat dibentuk dengan order bilangan bulat genap lebih dari atau sama dengan 10. Pada skripsi ini, dibahas pelabelan modular tak teratur pada graf dodecahedral yang diperumum.

---

Let 𝐺 = (𝑉(𝐺), 𝐸(𝐺)) be a graph of order 𝑛 , with 𝑛 is an integer. Notation 𝑉(𝐺) represents a set of vertices and 𝐸(𝐺) represents a set of edges. A labeling 𝛾: 𝐸(𝐺) → {1,2, … , 𝑘}, with integer 𝑘, is called modular irregular labelling of the graph 𝐺 if there exist a bijective function 𝜎: 𝑉(𝐺) → 𝑍𝑛 defined by 𝜎(𝑥) = (∑𝛾(𝑥𝑦)) mod 𝑛 for every 𝑦 adjacent to 𝑥, such that the weight 𝜎(𝑥) is different for every 𝑥 ∈ 𝑉(𝐺). The minimal 𝑘 for which the graph 𝐺 admits a modular irregular labelling is called modular irregularity strength of graph 𝐺. Dodecahedral graph is the 3-connected planar graph corresponding to the connectivity of the vertices of dodecahedron. There are 2 kinds of vertices in the dodecahedral graph, inner vertices and outer vertices and all of the vertices has degree 3. Generalized Dodecahedral Graph is a graph that is built from dodecahedral graph by adding 2 additionals edge on each of the inner vertice so that all of the inner vertices have degree 5. Generalized dodecahedral graph can be formed with order of even integer greater than or equal to 10. In this skripsi, it will be discussed the modular irregular labelling of generalized dodecahedral graphs."

"Misalkan $G=(V(G),E(G))$ merupakan suatu graf dengan himpunan simpul tak kosong berhingga $V(G)$ dan himpunan busur $E(G)$. Misalkan $G$ memiliki order $n$. Pelabelan busur $\varphi: E(G) \rightarrow \{1,2,\cdots,k\}$, dengan $k \in \mathbb{Z}^+$, disebut pelabelan-$k$ tak teratur modular jika terdapat fungsi bobot bijektif $\sigma:V(G) \rightarrow \mathbb{Z}_n$ dengan $\mathbb{Z}_n$ merupakan himpunan bilangan bulat modulo $n$. Fungsi $\sigma(v)=\sum_{\forall u \in N(v)} \varphi(uv) \mod n$ disebut bobot modular dari simpul $v\in V(G)$. $N(v)$ merupakan himpunan simpul yang bertetangga dengan simpul $v.$ Kekuatan tak teratur modular dari graf $G$, dinotasikan dengan $ms(G)$, merupakan nilai minimum $k$ sedemikian sehingga graf $G$ memiliki pelabelan-$k$ tak teratur modular. Graf bunga matahari ${Sf}_m$ merupakan graf yang dibangun dari graf roda $W_m,$ $m \geq 3,$ dengan simpul pusat $c$, simpul pada lingkaran-$m$ $v_1,v_2,\ldots,v_m$ dan tambahan $m$ simpul $w_1,w_2,\ldots,w_m$ dengan $w_i$ dihubungkan ke simpul $v_i$ dan $v_{i+1},$ $i=1,2,\ldots,m,$ dengan $v_{m+1}=v_1$ dan $v_0=v_m$. Pada penelitian ini dikontruksi fungsi pelabelan tak teratur modular pada graf bunga matahari ${Sf}_m$, $m\geq 3$, sehingga dapat ditentukan nilai kekuatan tak teratur modularnya.

---

Let $G=(V(G),E(G))$ be a graph with $V(G)$ is a nonempty finite vertex set and $E(G)$ is an edge set, which has order $n$. Edge $k-$labeling $\varphi: E(G) \rightarrow \{1,2,\cdots,k\}$, where $k \in \mathbb{Z}^+$, is called a modular irregular labeling of a graph $G$ if there exists a bijective weight function $\sigma:V(G) \rightarrow \mathbb{Z}_n$ where $\mathbb{Z}_n$ is a set of modulo $n$. Function $\sigma(v)=\sum_{\forall u \in N(v)} \varphi(uv) \mod n$ is called modular weight of vertex $v$. $N(v)$ denotes the set of all vertices that adjacent to $v$. The modular irregularity strength of a graph $G$, denoted by $ms(G)$, is the minimum number $k$ such that a graph $G$ has modular irregular $k$-labeling. The sunflower graph ${Sf}_m$ is a graph which constructed from a wheel graph $W_m$ with center vertex $c$ and $m$-cycle $v_1,v_2,\ldots,v_m$ and additional vertices $w_1,w_2,\ldots,w_m$ where $w_i$ is adjacent to $v_i$ and $v_{i+1}$, $i=1,2,\ldots,m$, with $v_{m+1}=v_1$ and $v_0=v_m$. This research shows the construction of modular irregular labeling on sunflower graph and its modular irregularity strength."

"Finally there is a book that presents real applications of graph theory in a unified format. This book is the only source for an extended, concentrated focus on the theory and techniques common to various types of intersection graphs. It is a concise treatment of the aspects of intersection graphs that interconnect many standard concepts and form the foundation of a surprising array of applications to biology, computing, psychology, matrices, and statistics. The authors emphasize the underlying tools and techniques and demonstrate how this approach constitutes a definite theory within graph theory. Some of the applications are not widely known or available in the graph theoretic literature and are presented here for the first time. The book also includes a detailed literature guide for many specialized and related areas, a current bibliography, and more than 100 exercises."

"Tujuan utama penulisan skripsi ini adalah membahas tentang generalisasi dan Intersection Graph (atau Irisan Graph seperti yang biasa kita lakukan) ke dalam Fuzzy Intersection Graph. Generalisasi ini dilakukan dengan cara menerapkan konsep Fuzzy Set ke dalam teori graph. Representasi Fuzzy Intersection Graph juga akan dibahas dalam skripsi ini."

"The book is a graduate text on unbounded self-adjoint operators on Hilbert space and their spectral theory with the emphasis on applications in mathematical physics (especially, Schrödinger operators) and analysis (Dirichlet and Neumann Laplacians, Sturm-Liouville operators, Hamburger moment problem) . Among others, a number of advanced special topics are treated on a text book level accompanied by numerous illustrating examples and exercises. The main themes of the book are the following, spectral integrals and spectral decompositions of self-adjoint and normal operators, perturbations of self-adjointness and of spectra of self-adjoint operators, forms and operators, and self-adjoint extension theory :boundary triplets, Krein-Birman-Vishik theory of positive self-adjoint extension."