Modular arithmetic的問題，透過圖書和論文來找解法和答案更準確安心。 我們找到下列特價商品、必買資訊和推薦清單

Pillars of Transcendental Number Theory

為了解決Modular arithmetic的問題，作者Natarajan, Saradha,Thangadurai, Ravindranathan 這樣論述：

Saradha Natarajan is an INSA Senior Scientist at the DAE Center for Excellence in Basic Sciences (CEBS) at the University of Mumbai. Earlier, she was a Professor of Mathematics at the Tata Institute of Fundamental Research, Mumbai, until 2016. She was a postdoctoral fellow at Concordia University, C

anada; Macquarie University, Australia; National Board of Higher Mathematics (NBHM), India. She is an elected fellow of the Indian National Science Academy (INSA). She obtained her Ph.D. in 1983 under the guidance of Professor T. S. Bhanumurthy from Ramanujan Institute for Advanced Study in Mathemat

ics, University of Madras, Chennai. Her area of specialization is number theory, in general, and transcendental number theory and Diophantine equations, in particular. She has published several papers in international journals of repute. She has made substantial contributions to the conjectures of E

rdos on perfect powers in arithmetic progressions, where combinatorial and computational methods, linear forms in logarithms and modular method are combined. For instance, it is shown that product of k (>1) successive terms from arithmetic progression with common difference d is cube or higher power

only for d large. She has also made significant contributions to Thue equations and Diophantine approximations, especially towards conjectures of Bombieri, Mueller and Schmidt on number of solutions of Thue inequalities for forms in terms of number of non-zero coefficients of the form. Using new in

duction technique, an old result of Siegel on the number of primitive solutions of Thue inequalities was improved significantly. In the area of transcendence, she has obtained best possible simultaneous approximation measures for values of exponential function and Weierstarss elliptic function. Furt

her, significant lower bounds were shown for the Ramanujan tau-function for almost all primes p. Some problems in elementary number theory have also attracted her attention, for example on a conjecture of Pomerance on residue systems and its generalizations. It is shown that 2, 3, 7 are the only pri

mes p for which there exist p consecutive primes forming complete residue system mod p. She has collaborated with many mathematicians both in India and abroad and guided students for Ph.D. and graduation. She has travelled widely and given invited talks and lectures at seminars and conferences. Ravi

ndranathan Thangadurai is Professor at Harish-Chandra Research Institute, Prayagraj. He earned his Ph.D. in Combinatorial Number Theory, in 1999, from the Mehta Research Institute for Mathematics and Theoretical Physics, Allahabad (now Harish-Chandra Research Institute, Prayagraj) under the supervis

ion of Prof. S. D. Adhikari. He spent two years as a postdoc at the Institute of Mathematical Sciences, Chennai, and two years at Indian Statistical Institute, Kolkata, during 1999-2003. He has been teaching undergraduate and postgraduate students in many summer and winter schools every year, apart

from the regular teaching at HRI. He has been travelling widely in India and abroad for workshops and conferences. His research interests include analytic, combinatorial and transcendental number theory. To be more specific, major contributions in the area of zerosum problems in finite abelian group

s, distribution of residues modulo p, Liouville numbers and Schanuel’s conjecture in transcendental number theory. In this area, he has published his research articles in reputed journals and worked with many reputed mathematicians. He has computed the exact values of Olson’s constant and Alon-Dubin

er constant for subsets for the group. He proved a conjecture of Schmid and Zhuang for large class of finite abelian p-groups and the current best known upper bound for Davenport’s constant for a general finite abelian group. He also has made another major contribution to the theory of distribution

of particular type of elements (specially, quadratic non-residues but not a primitive root) of residues modulo p. He has proved a strong form of Schanuel’s conjecture in transcendental number theory for many n-tuples.

Modular arithmetic進入發燒排行的影片

採用40奈米製程實現之用於軸承故障診斷的低功耗分層卷積神經網路硬體加速器

為了解決Modular arithmetic的問題，作者許堯舜 這樣論述：

現代科技的進步日新月異伴隨著生活品質的成長，近幾年的趨勢技術機器學習充斥在各行各業已經成為現今科技裡面不可或缺的角色。在很多工廠裡充斥著各種各樣的機台，例如:電動機，CNC工具機等不同的機械。這些機器在運行的過程中常常會有故障發生，早期只能以人工的方式或抓取一段大約的時間排除，不僅不準確且危險。而現在使用機器學習的方法進行智慧監控，把工具機或電動機產生的不正常數據行為進行機器學習的訓練萃取該故障數據的特徵，爾後透過在該機器的軸承實施實時監控即可實施預防性維護，不僅可以及早預防工廠的生產線因為機器故障停擺也可以預先防護操作員在操作工具機上的安全。本論文使用分層式卷積神經網路的方式進行訓練，並以

40nm CMOS製程實現。使用分層式卷積神經網路的優點為先將具有相似特徵或類別的圖像資料先分類再進行訓練，相較傳統卷積神經網路需要經過多層運算才能得到每次分類結果，經本實驗數據得知只需少量的運算即可判別並輸出結果且可以大幅的下降神經網路模型所需參數量以及達到辨識軸承故障數據95% 以上的準確度。另外本論文亦使用加入白高斯雜訊的模擬數據，增加到訓練資料集以提升模型的準確度，以及測試此分層式卷積神經網路的抗噪效果，以因應工廠裡面各種不同發生雜訊的情況產生。各項數據結果均確認所提出之分層式卷積神經網路有良好的抗噪效果。本論文在硬體實現的部分使用電源門控技術，將待機狀態的記憶體之電源關閉，達成低功耗

的實現。本論文實現電路使用 TSMC 40nm CMOS 製程，在硬體描述階段，經過調整各階段所需bits數量的實驗結果後，所實現之硬體加速器判斷軸承健康的準確率達到95.31%。後續經由電路合成以及自動佈局繞線後各項數據表明，所提出之硬體電路工作頻率最高可達100MHz，此時功耗為65.608 mW.

實分析與複分析（英文版·原書第3版·典藏版）

為了解決Modular arithmetic的問題，作者（美）沃爾特·魯丁 這樣論述：

本書是分析領域內的一部經典著作。主要內容包括：抽象積分、正博雷爾測度、LP-空間、希爾伯特空間的初等理論、巴拿赫空間技巧的例子、複測度、微分、積空間上的積分、傅裡葉變換、全純函數的初等性質、調和函數、大模原理、有理函數逼近、共形映射、全純函數的零點、解析延拓、HP-空間、巴拿赫代數的初等理論、全純傅裡葉變換、用多項式一致逼近等。另外，書中還附有大量設計巧妙的習題。本書體例優美，實用性很強，列舉的實例簡明精彩，基本上對所有給出的命題都進行了論證，適合作為高等院校數學專業高年級本科生和研究生的教材。 沃爾特·魯丁（Walter Rudin） 1953年于杜克大學獲得數學博士學

位。曾先後執教于麻省理工學院、羅切斯特大學、威斯康星大學麥迪森分校、耶魯大學等。他的主要研究興趣集中在調和分析和複變函數上。除本書外，他還著有《Functional Analysis》（泛函分析）和《Principles of Mathematical Analysis》（數學分析原理）等其他名著。這些教材已被翻譯成十幾種語言，在世界各地廣泛使用。 Preface Prologue: The Exponential Function Chapter 1 Abstract Integration 5 Set-theoretic notations and terminolo

gy 6 The concept of measurability 8 Simple functions 15 Elementary properties of measures 16 Arithmetic in [0, ∞] 18 Integration of positive functions 19 Integration of complex functions 24 The role played by sets of measure zero 27 Exercises 31 Chapter 2 Positive Borel Measures 33 Vector spaces 33

Topological preliminaries 35 The Riesz representation theorem 40 Regularity properties of Borel measures 47 Lebesgue measure 49 Continuity properties of measurable functions 55 Exercises 57 Chapter 3 [WTBX]L[WTBZ]+p-Spaces 61 Convex functions and inequalities 61 The [WTBX]L[WTBZ]+p-spaces 65 Appro

ximation by continuous functions 69 Exercises 71 Chapter 4 Elementary Hilbert Space Theory 76 Inner products and linear functionals 76 Orthonormal sets 82 Trigonometric series 88 Exercises 92 Chapter 5 Examples of Banach Space Techniques 95 Banach spaces 95 Consequences of Baire’s theorem 97 Fouri

er series of continuous functions 100 Fourier coefficients of [WTBX]L[WTBZ]+1-functions 103 The Hahn-Banach theorem 104 An abstract approach to the Poisson integral 108 Exercises 112 Chapter 6 Complex Measures 116 Total variation 116 Absolute continuity 120 Consequences of the Radon-Nikodym theorem

124 Bounded linear functionals on Lp 126 The Riesz representation theorem 129 Exercises 132 Chapter 7 Differentiation 135 Derivatives of measures 135 The fundamental theorem of Calculus 14~ Differentiable transformations 150 Exercises 156 Chapter 8 Integration on Product Spaces 160 Measurability

on cartesian products 160 Product measures 163 The Fubini theorem 164 Completion of product measures 167 Convolutions 170 Distribution functions 172 Exercises 174 Chapter 9 Fourier Transforms 178 Formal properties 178 The inversion theorem 180 The Plancherel theorem 185 The Banach algebra [WTBX]L[W

TBZ]+1 190 Exercises 193 Chapter 10 Elementary Properties of Holomorphic Functions 196 Complex differentiation 196 Integration over paths 200 The local Cauchy theorem 204 The power series representation 208 The open mapping theorem 214 The global Cauchy theorem 217, The calculus of residues 224 Exe

rcises 227 Chapter 11 Harmonic Functions 231 The Cauchy-Riemann equations 231 The Poisson integral 233 The mean value property 237 Boundary behavior of Poisson integrals 239 Representation theorems 245 Exercises 249 Chapter 12 The Maximum Modulus Principle 253 Introduction 253 The Schwarz lemma 25

4 The Phragmen-Lindel6f method 256 An interpolation theorem 260 A converse of the maximum modulus theorem 262 Exercises 264 Chapter 13 Approximation by Rational Functions 266 Preparation 266 Runge's theorem 270 The Mittag-Leffier theorem 273 Simply connected regions 274 Exercises 276 Chapter 14 Co

nformal Mapping 278 Preservation of angles 278 Linear fractional transformations 279 Normal families 281 The Riemann mapping theorem 282 The class [WTHT]S[WTBZ] 285 Continuity at the boundary 289 Conformal mapping of an annulus 291 Exercises 293 Chapter 15 Zeros of Holomorphic Functions 298 Infinit

e products 298 The Weierstrass factorization theorem 301 An interpolation problem 304 Jensen’s formula 307 Blaschke products 310 The Miintz-Szasz theorem 312 Exercises 315 Chapter 16 Analytic Continuation 319 Regular points and singular points 319 Continuation along curves 323 The monodromy theorem

326 Construction of a modular function 328 The Picard theorem 331 Exercises 332 Chapter 17 [WTBX]H[WTBZ]+p-Spaces 335 Subharmonic functions 335 The spaces Hp and N 337 The theorem of F. and M. Riesz 341 Factorization theorems 342 The shift operator 346 Conjugate functions 350 Exercises 352 Chapte

r 18 Elementary Theory of Banach Algebras 356 Introduction 356 The invertible elements 357 Ideals and homomorphisms 362 Applications 365 Exercises 369 Chapter 19 Holomorphic Fourier Transforms 371 Introduction 371 Two theorems of Paley and Wiener 372 Quasi-analytic classes 377 The Denjoy-Carleman t

heorem 380 Exercises 383 Chapter 20 Uniform Approximation by Polynomials 386 Introduction 386 Some lemmas 387 Mergelyan’s theorem 390 Exercises 394 Appendix: Hausdorff’s Maximality Theorem 395 Notes and Comments 397 Bibliography 405 List of Special Symbols 407 Index 409

CKKS全同態加密方案之加解密硬體架構設計

為了解決Modular arithmetic的問題，作者邱奕傑 這樣論述：

近年來物聯網的科技日新月異，許多日常生活會使用到的電子產品都漸漸有了網路的功能，像是家中的冷氣或電燈，現在都可接上網路來進行智能感測，配合適當的感測器去偵測是否有人經過，就能在最佳時機關上燈或冷氣來節省能源。由於網路的蓬勃發展，越來越多的資料在網路上傳遞，不管是自身隱私的資料還是企業公司的機密資料，只要經過網路就有資料外洩的風險，所以為了資料的安全人們開始研究如何將資料進行加密，方便讓資料在網路上傳遞時能夠同時保有安全性。但透過一般加密方式加密過的密文沒辦法在未解密的情況下進行運算，所以當資料交到他人手中時，還是需要先解密才能對資料做處理，像是現在常用的雲端功能。 雲端技術的發展讓很多人選

擇將資料存放在雲端，或是讓需要大量計算的資料透過雲端功能給超級電腦運算。也因為如此，越來越多人開始重視雲端資料的隱私性，像是在機器學習領域中，有時需要龐大的資料去訓練模組，這時就可能用到很多個人的資料，例如醫療研究需要各種生理上的資訊或是金融研究需要各種交易的資料，這些資料有了雲端的功能後，能讓研究者在世界各地透過網路提取。而在資料方便處理的同時，又要讓資料隨時都處於安全的狀態，所以對於資料的隱私性就有了非常大的挑戰。於是同態加密的概念就被提出了，同態加密是一種特殊加密方式，分為全同態加密和部分同態加密，同態加密能夠讓密文資料在不解密的情況下進行運算，且運算後的結果進行解密後會與明文直接運算的

結果相同，讓資料在網路上傳遞時能確保全程都是安全的。本論文針對CKKS全同態加密方案進行專用硬體的設計，架構設計包括加密電路以及解密電路，由於在全同態加密方案中多項式運算的比重很大，多項式乘法的時間複雜度很高，所以若要加速整體電路的速度，就需要對多項式乘法進行設計，其中使用到NTT多項式乘法器來加速主要運算，NTT(Number Theoretic Transform)為與FFT類似的演算法，也使用到蝶形演算法使時間複雜度降低，使用到模數的概念將運算結果限制在一個範圍內讓運算過程中的資料不會過大，這也是本論文選擇NTT的原因。