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In this book, the basic methods of nonlinear analysis are emphasized and illustrated in simple examples. Every considered method is motivated, explained in a general form but in the simplest possible abstract framework. Its applications are shown, particularly to boundary value problems for elementary ordinary or partial differential equations. The text is organized in two levels: a self-contained basic and, organized in appendices, an advanced level for the more experienced reader. Exercises are an organic part of the exposition and accompany the reader throughout the book.

Intended as a self-contained introduction to measure theory, this textbook also includes a comprehensive treatment of integration on locally compact Hausdorff spaces, the analytic and Borel subsets of Polish spaces, and Haar measures on locally compact groups. This second edition includes a chapter on measure-theoretic probability theory, plus brief treatments of the Banach-Tarski paradox, the Henstock-Kurzweil integral, the Daniell integral, and the existence of liftings. Measure Theory provides a solid background for study in both functional analysis and probability theory and is an excellent resource for advanced undergraduate and graduate students in mathematics. The prerequisites for this book are basic courses in point-set topology and in analysis, and the appendices present a thorough review of essential background material.

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In this book, fundamental methods of nonlinear analysis are introduced, discussed and illustrated in straightforward examples. Each method considered is motivated and explained in its general form, but presented in an abstract framework as comprehensively as possible. A large number of methods are applied to boundary value problems for both ordinary and partial differential equations. In this edition we have made minor revisions, added new material and organized the content slightly differently. In particular, we included evolutionary equations and differential equations on manifolds. The applications to partial differential equations follow every abstract framework of the method in question.The text is structured in two levels: a self-contained basic level and an advanced level - organized in appendices - for the more experienced reader. The last chapter contains more involved material and can be skipped by those new to the field. This book serves as both a textbook for graduate-level courses and a reference book for mathematicians, engineers and applied scientists

Intended as a self-contained introduction to measure theory, this textbook also includes a comprehensive treatment of integration on locally compact Hausdorff spaces, the analytic and Borel subsets of Polish spaces, and Haar measures on locally compact groups. This second edition includes a chapter on measure-theoretic probability theory, plus brief treatments of the Banach-Tarski paradox, the Henstock-Kurzweil integral, the Daniell integral, and the existence of liftings. Measure Theory provides a solid background for study in both functional analysis and probability theory and is an excellent resource for advanced undergraduate and graduate students in mathematics. The prerequisites for this book are basic courses in point-set topology and in analysis, and the appendices present a thorough review of essential background material.

This text presents the Eulerian numbers in the context of modern enumerative, algebraic, and geometric combinatorics. The book first studies Eulerian numbers from a purely combinatorial point of view, then embarks on a tour of how these numbers arise in the study of hyperplane arrangements, polytopes, and simplicial complexes. Some topics include a thorough discussion of gamma-nonnegativity and real-rootedness for Eulerian polynomials, as well as the weak order and the shard intersection order of the symmetric group.The book also includes a parallel story of Catalan combinatorics, wherein the Eulerian numbers are replaced with Narayana numbers. Again there is a progression from combinatorics to geometry, including discussion of the associahedron and the lattice of noncrossing partitions.The final chapters discuss how both the Eulerian and Narayana numbers have analogues in any finite Coxeter group, with many of the same enumerative and geometric properties. There are four supplemental chapters throughout, which survey more advanced topics, including some open problems in combinatorial topology. This textbook will serve a resource for experts in the field as well as for graduate students and others hoping to learn about these topics for the first time.

Our purpose and main concern in writing this book is to illuminate classical concepts from the noncommutative viewpoint, to make the language and techniques of noncommutative geometry accessible and familiar to practi­ tioners of classical mathematics, and to benefit physicists interested in the uses of noncommutative spaces. Same may say that ours is a very "com­ mutative" way to deal with noncommutative matters; this charge we readily admit. Noncommutative geometry amounts to a program of unification of math­ ematics under the aegis of the quantum apparatus, i.e., the theory of ope­ rators and of C*-algebras. Largely the creation of a single person, Alain Connes, noncommutative geometry is just coming of age as the new century opens. The bible of the subject is, and will remain, Connes' Noncommuta­ tive Geometry (1994), itself the "3.8-fold expansion" of the French Geome­ trie non commutative ( 1990). Theseare extraordinary books, a "tapestry" of physics and mathematics, in the words of Vaughan jones, and the work of a "poet of modern science," according to Daniel Kastler, replete with subtle knowledge and insights apt to inspire several generations.

The second edition of this classic textbook presents a rigorous and self-contained introduction to real analysis with the goal of providing a solid foundation for future coursework and research in applied mathematics.  Written in a clear and concise style, it covers all of the necessary subjects as well as those often absent from standard introductory texts.  Each chapter features a “Problems and Complements” section that includes additional material that briefly expands on certain topics within the chapter and numerous exercises for practicing the key concepts.The first eight chapters explore all of the basic topics for training in real analysis, beginning with a review of countable sets before moving on to detailed discussions of measure theory, Lebesgue integration, Banach spaces, functional analysis, and weakly differentiable functions.  More topical applications are discussed in the remaining chapters, such as maximal functions, functions of bounded mean oscillation, rearrangements, potential theory, and the theory of Sobolev functions.  This second edition has been completely revised and updated and contains a variety of new content and expanded coverage of key topics, such as new exercises on the calculus of distributions, a proof of the Riesz convolution, Steiner symmetrization, and embedding theorems for functions in Sobolev spaces.  Ideal for either classroom use or self-study, Real Analysis is an excellent textbook both for students discovering real analysis for the first time and for mathematicians and researchers looking for a useful resource for reference or review.Praise for the First Edition:“[This book] will be extremely useful as a text.  There is certainly enough material for a year-long graduate course, but judicious selection would make it possible to use this most appealing book in a one-semester course for well-prepared students.”  ―Mathematical Reviews

Get ready for the future with the 22-Volt Nuron platform - the latest addition to our existing cordless tools. Finally perform your corded and gas-powered applications on a single cordless platform. From breaking and cutting to drilling and fastening, Hilti cordless power tools are designed for maximum performance, enhanced safety and improved user comfort. The new Nuron cordless tools have the flexibility to mix and match tools to suit your needs. There are many different tools to choose from in a range of voltages. Select batteries and chargers compatible across each Nuron platform. Nuron is the latest addition to the Hilti cordless portfolio. It provides you with a single high-performing battery platform for all your Hilti cordless tools. With Nuron, you can help reduce complexity from your business because you can perform your light to heavy-duty jobs - from screwdriving to concrete cutting - using the same set of high-performing interchangeable 22-Volt Nuron batteries. And because the platform is connected, you also get access to a range of data-driven services designed to simplify equipment management.

Become a master of your craft with the Canon EF-S 18-55mm f/3.5-5.6 IS II Lens, a high-quality, durable, and versatile tool that will elevate your photography to new heights. This advanced lens is specifically engineered for APS-C-format Canon EF-S-mount DSLRs, providing a 28.8-88mm equivalent focal length range. This wide range allows for exceptional flexibility, enabling you to capture everything from expansive landscapes to intimate portraits with precision and clarity.The lens features a singular aspherical element that expertly controls spherical aberrations and distortion, delivering unparalleled sharpness across the entire zoom range. The Super Spectra coating battles against ghosting and flare, ensuring vivid contrast and color accuracy, even in challenging lighting conditions.Equipped with an Optical Image Stabilizer, the Canon EF-S 18-55mm f/3.5-5.6 IS II Lens reduces the impact of camera shake by up to four shutter speed stops. This feature is invaluable when capturing memories in low-light settings or using slower shutter speeds, guaranteeing sharp, steady shots every time.The intricate design of this lens, comprising 11 elements in 9 groups, harnesses the power of an aspherical lens element for exceptional image quality. The circular aperture enhances the depth of your shots by rendering sublime out-of-focus backgrounds. Experience autofocus like never before with the Micro Motor autofocus system. This feature ensures precise and swift focusing, with a dedicated AF/MF switch for seamless transitioning when manual touch is required. Embrace the beauty of close-up photography with a minimum focusing distance of 9.8" throughout its zoom range, allowing you to capture intricate details with precision. The lens's rounded six-blade diaphragm ensures a pleasing out-of-focus quality, perfect for emphasizing subjects using shallow depth of field or selective focus techniques.The Canon EF-S 18-55mm f/3.5-5.6 IS II Lens is compatible with a wide range of Canon EOS models, including the 7D Mark II, 7D, 80D, 77D, 70D, 60D, 50D, 40D, 30D, 20D, Rebel T7i, Rebel T6s, Rebel T6i, Rebel T5i, Rebel T4i, Rebel SL1, Rebel T3i, Rebel T6, Rebel T5, Rebel T3, Rebel T2i, Rebel T1i, Rebel Xsi, Rebel XS, Digital Rebel Xti, Digital Rebel XT, and Digital Rebel.

Become a master of your craft with the Canon EF-S 18-55mm f/3.5-5.6 IS II Lens, a high-quality, durable, and versatile tool that will elevate your photography to new heights. This advanced lens is specifically engineered for APS-C-format Canon EF-S-mount DSLRs, providing a 28.8-88mm equivalent focal length range. This wide range allows for exceptional flexibility, enabling you to capture everything from expansive landscapes to intimate portraits with precision and clarity.The lens features a singular aspherical element that expertly controls spherical aberrations and distortion, delivering unparalleled sharpness across the entire zoom range. The Super Spectra coating battles against ghosting and flare, ensuring vivid contrast and color accuracy, even in challenging lighting conditions.Equipped with an Optical Image Stabilizer, the Canon EF-S 18-55mm f/3.5-5.6 IS II Lens reduces the impact of camera shake by up to four shutter speed stops. This feature is invaluable when capturing memories in low-light settings or using slower shutter speeds, guaranteeing sharp, steady shots every time.The intricate design of this lens, comprising 11 elements in 9 groups, harnesses the power of an aspherical lens element for exceptional image quality. The circular aperture enhances the depth of your shots by rendering sublime out-of-focus backgrounds. Experience autofocus like never before with the Micro Motor autofocus system. This feature ensures precise and swift focusing, with a dedicated AF/MF switch for seamless transitioning when manual touch is required. Embrace the beauty of close-up photography with a minimum focusing distance of 9.8" throughout its zoom range, allowing you to capture intricate details with precision. The lens's rounded six-blade diaphragm ensures a pleasing out-of-focus quality, perfect for emphasizing subjects using shallow depth of field or selective focus techniques.The Canon EF-S 18-55mm f/3.5-5.6 IS II Lens is compatible with a wide range of Canon EOS models, including the 7D Mark II, 7D, 80D, 77D, 70D, 60D, 50D, 40D, 30D, 20D, Rebel T7i, Rebel T6s, Rebel T6i, Rebel T5i, Rebel T4i, Rebel SL1, Rebel T3i, Rebel T6, Rebel T5, Rebel T3, Rebel T2i, Rebel T1i, Rebel Xsi, Rebel XS, Digital Rebel Xti, Digital Rebel XT, and Digital Rebel.

Under the umbrella of advanced home connectivity solutions, the Archer AX55 AX3000 Wireless Dual Band Wi-Fi 6 Gigabit Router stands out with its cutting-edge features and superior performance. This Wi-Fi 6 router is engineered to provide a seamless internet experience, with faster speeds, reduced lag, and increased capacity, accommodating multiple simultaneous connections on your home network.The Archer AX55 AX3000 router is equipped with a dual-band gigabit Wi-Fi 6 system, offering 160MHz bandwidth, which is double the standard bandwidth. This feature facilitates smooth 8K video streaming without any lag. The router also boasts a robust Qualcomm chipset and 512 MB RAM, ensuring fast connections with minimal latency, even under heavy transmission loads.This Wi-Fi 6 router is designed with four high-power FEM and gigabit ports, enhancing the strength and reach of your Wi-Fi signals. The inclusion of beamforming technology further boosts signal strength by focusing the wireless signal towards devices, particularly those in previously hard-to-reach areas.The Archer AX55 AX3000 router also features a USB 3.0 port, allowing you to easily share files between connected devices. You can plug in an external drive and transform it into your personal cloud storage, accessible securely from anywhere.With the Archer AX55 AX3000 router, you can create a whole-home Wi-Fi network using TP-Link's OneMesh technology. This feature ensures seamless coverage throughout your home, preventing signal drops and lag when moving between signals.The router also comes with TP-Link HomeShield, offering advanced security features to protect your network's data and privacy. It includes a real-time network scanner for detecting potential threats, parental controls for managing online time and content, and Quality of Service to prioritize your favorite devices for top performance.The Archer AX55 AX3000 router supports the latest Wi-Fi security protocol, WPA3, providing enhanced encryption for Wi-Fi password safety and improved protection against brute-force attacks.Setting up and managing your Archer AX55 AX3000 router is a breeze, whether you prefer the intuitive Tether app or TP-Link's powerful web interface. The router also offers easy firmware upgrades via OTA updates, ensuring your security and functions are always up-to-date.In summary, the Archer AX55 AX3000 Wireless Dual Band Wi-Fi 6 Gigabit Router is a powerful, feature-rich solution for your home connectivity needs, offering high-speed, secure, and seamless internet access across your entire home.

If you're seeking a high-performance lens that delivers exceptional image quality, consider the E 16-55mm f/2.8 G Lens. This standard zoom lens, equivalent to 24-82.5mm in full-frame terms, is a lightweight powerhouse at just 494g. It's designed with the advanced G lens technology, featuring two Advanced Aspherical and two Aspherical elements that effectively suppress aberration. The lens also incorporates three ED (Extra-low Dispersion) glass elements and a Nano AR coating to minimize reflections, flare, and ghosting, ensuring crisp, clear images. The F2.8 max aperture is a standout feature, maintaining exposure and depth of field, and enabling you to isolate your subject with stunning light gathering capabilities when shooting wide open. The E 16-55mm f/2.8 G Lens is also equipped with a 9-blade circular aperture that contributes to a beautiful bokeh effect. This allows your subject to stand out against a smoothly defocused foreground and background, creating impressive images. The lens design ensures the aperture remains almost perfectly circular from its wide-open setting to when it is closed by 2 stops, resulting in smoother, more natural defocusing.The lens features two AA (advanced aspherical) elements and two aspherical elements that work together to deliver outstanding corner-to-corner G Lens resolution. These elements maintain high sharpness and contrast even at maximum aperture and ultra-wide angles, delivering high resolution that meets the expectations of the G Lens brand. The XD Linear Motor technology, also used in G Master series lenses, provides fast, precise, and quiet autofocus, making it ideal for tracking fast-moving subjects and for videography. The lens also includes three ED (Extra-low Dispersion) glass elements that eliminate axial chromatic aberration and chromatic aberration due to differences in magnification, maximizing resolution and bokeh while reducing flare and ghosting.Sony's original Nano AR Coating technology is used to minimize flare and ghosting, providing lifelike detail and gradation with advanced camera sensors. This lens also features a focus hold button that can be programmed for multiple functions, offering versatility and convenience. The E 16-55mm f/2.8 G Lens is designed for robust reliability, with dust and moisture resistance making it suitable for heavy-duty outdoor use. The front lens element features a fluorine coating that repels water, oil, and other contaminants, making it easy to clean. Finally, this lens offers unique close-up shooting capabilities with a minimum focusing distance of 13" (0.33m) and a max. magnification of 0.2x, allowing for dramatic perspectives and beautiful background bokeh. The E 16-55mm f/2.8 G Lens is a versatile and high-quality choice for any photographer or videographer.

If you're seeking a high-performance lens that delivers exceptional image quality, consider the E 16-55mm f/2.8 G Lens. This standard zoom lens, equivalent to 24-82.5mm in full-frame terms, is a lightweight powerhouse at just 494g. It's designed with the advanced G lens technology, featuring two Advanced Aspherical and two Aspherical elements that effectively suppress aberration. The lens also incorporates three ED (Extra-low Dispersion) glass elements and a Nano AR coating to minimize reflections, flare, and ghosting, ensuring crisp, clear images. The F2.8 max aperture is a standout feature, maintaining exposure and depth of field, and enabling you to isolate your subject with stunning light gathering capabilities when shooting wide open. The E 16-55mm f/2.8 G Lens is also equipped with a 9-blade circular aperture that contributes to a beautiful bokeh effect. This allows your subject to stand out against a smoothly defocused foreground and background, creating impressive images. The lens design ensures the aperture remains almost perfectly circular from its wide-open setting to when it is closed by 2 stops, resulting in smoother, more natural defocusing.The lens features two AA (advanced aspherical) elements and two aspherical elements that work together to deliver outstanding corner-to-corner G Lens resolution. These elements maintain high sharpness and contrast even at maximum aperture and ultra-wide angles, delivering high resolution that meets the expectations of the G Lens brand. The XD Linear Motor technology, also used in G Master series lenses, provides fast, precise, and quiet autofocus, making it ideal for tracking fast-moving subjects and for videography. The lens also includes three ED (Extra-low Dispersion) glass elements that eliminate axial chromatic aberration and chromatic aberration due to differences in magnification, maximizing resolution and bokeh while reducing flare and ghosting.Sony's original Nano AR Coating technology is used to minimize flare and ghosting, providing lifelike detail and gradation with advanced camera sensors. This lens also features a focus hold button that can be programmed for multiple functions, offering versatility and convenience. The E 16-55mm f/2.8 G Lens is designed for robust reliability, with dust and moisture resistance making it suitable for heavy-duty outdoor use. The front lens element features a fluorine coating that repels water, oil, and other contaminants, making it easy to clean. Finally, this lens offers unique close-up shooting capabilities with a minimum focusing distance of 13" (0.33m) and a max. magnification of 0.2x, allowing for dramatic perspectives and beautiful background bokeh. The E 16-55mm f/2.8 G Lens is a versatile and high-quality choice for any photographer or videographer.

Callaway's industry-leading, groundbreaking artificial intelligence technology takes a quantum leap forward in the new Paradym Ai Smoke family. Using real player data from thousands of golfers, including swing speed, club delivery, and face orientation just before impact, advanced machine learning created the most sophisticated driver face in Callaway history. Known as Ai Smart Face, this refined design activates micro deflections upon contact, optimizing launch and spin on off-center strikes. The result is a series of sweet spots spanning the entirety of the face that yield an additional seven yards of distance on average and tighten downrange dispersion. If there's anything that modern analytics and purists agree is indisputable, it's that longer, straighter, fairway-finding drives directly correlate to lower scores, and Ai Smoke delivers precisely that. Callaway may have rendered the "golf is a game of misses" cliche obsolete. Positioned firmly in the center of the Ai Smoke lineup in terms of performance characteristics, the MAX model suits the widest variety of golfers and skill sets. The driver features a forgiving shape and adjustable perimeter weighting, offering up to 19 yards of shot shape correction. Callaway Paradym Ai Smoke MAX Driver Features: Ai Smart Face optimizes performance using swing dynamics from thousands of golfers and machine learning to provide optimal launch conditions and maximize accuracy Ai Smart Face technology creates micro deflections at impact to optimize launch and spin on mis-hits, resulting in an exceptionally forgiving, fast face that produces 7 additional yards of distance on average and tightens dispersion Updated 360� Carbon Chassis with a new internal titanium support structure that reduces weight by 15%, allowing mass to be strategically redistributed to add forgiveness and improve launch dynamics Adjustable rear weight offers 19 yards of shot shape correction to dial in the perfect ball flight Adjustable hosel allows for l

Callaway's industry-leading, groundbreaking artificial intelligence technology takes a quantum leap forward in the new Paradym Ai Smoke family. Using real player data from thousands of golfers, including swing speed, club delivery, and face orientation just before impact, advanced machine learning created the most sophisticated driver face in Callaway history. Known as Ai Smart Face, this refined design activates micro deflections upon contact, optimizing launch and spin on off-center strikes. The result is a series of sweet spots spanning the entirety of the face that yield an additional seven yards of distance on average and tighten downrange dispersion. If there's anything that modern analytics and purists agree is indisputable, it's that longer, straighter, fairway-finding drives directly correlate to lower scores, and Ai Smoke delivers precisely that. Callaway may have rendered the "golf is a game of misses" cliche obsolete. Positioned firmly in the center of the Ai Smoke lineup in terms of performance characteristics, the MAX model suits the widest variety of golfers and skill sets. The driver features a forgiving shape and adjustable perimeter weighting, offering up to 19 yards of shot shape correction. Callaway Paradym Ai Smoke MAX Driver Features: Ai Smart Face optimizes performance using swing dynamics from thousands of golfers and machine learning to provide optimal launch conditions and maximize accuracy Ai Smart Face technology creates micro deflections at impact to optimize launch and spin on mis-hits, resulting in an exceptionally forgiving, fast face that produces 7 additional yards of distance on average and tightens dispersion Updated 360� Carbon Chassis with a new internal titanium support structure that reduces weight by 15%, allowing mass to be strategically redistributed to add forgiveness and improve launch dynamics Adjustable rear weight offers 19 yards of shot shape correction to dial in the perfect ball flight Adjustable hosel allows for l

Callaway's industry-leading, groundbreaking artificial intelligence technology takes a quantum leap forward in the new Paradym Ai Smoke family. Using real player data from thousands of golfers, including swing speed, club delivery, and face orientation just before impact, advanced machine learning created the most sophisticated driver face in Callaway history. Known as Ai Smart Face, this refined design activates micro deflections upon contact, optimizing launch and spin on off-center strikes. The result is a series of sweet spots spanning the entirety of the face that yield exceptional distance and tighten downrange dispersion. If there's anything that modern analytics and purists agree is indisputable, it's that longer, straighter, fairway-finding drives directly correlate to lower scores, and Ai Smoke delivers precisely that. Callaway may have rendered the "golf is a game of misses" cliche obsolete. Featuring a neutral-to-fade biased face progression and a compact head shape, the Triple Diamond suits better ball strikers seeking workability off the tee. The driver's adjustable sole weights can be repositioned to drastically reduce spin and increase ball speed. Callaway Paradym Ai Smoke Triple Diamond Driver Features: Smaller 450cc head with a neutral-to-fade face progression designed for better players who like to work the ball Heavier 14g sole weight can be repositioned in the front for increased ball speed and lower spin Ai Smart Face optimizes performance using swing dynamics from thousands of golfers and machine learning to provide optimal launch conditions and maximize accuracy Ai Smart Face technology creates micro deflections at impact to optimize launch and spin on mis-hits, resulting in an exceptionally forgiving, fast face that produces additional distance and a tighter dispersion Updated 360� Carbon Chassis with a new internal titanium support structure that reduces weight by 15%, allowing mass to be strategically redistributed to add forgiveness and