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Probability, Markov Chains, Queues, and Simulation provides a modern and authoritative treatment of the mathematical processes that underlie performance modeling. The detailed explanations of mathematical derivations and numerous illustrative examples make this textbook readily accessible to graduate and advanced undergraduate students taking courses in which stochastic processes play a fundamental role. The textbook is relevant to a wide variety of fields, including computer science, engineering, operations research, statistics, and mathematics. The textbook looks at the fundamentals of probability theory, from the basic concepts of set-based probability, through probability distributions, to bounds, limit theorems, and the laws of large numbers. Discrete and continuous-time Markov chains are analyzed from a theoretical and computational point of view. Topics include the Chapman-Kolmogorov equations; irreducibility; the potential, fundamental, and reachability matrices; random walk problems; reversibility; renewal processes; and the numerical computation of stationary and transient distributions. The M/M/1 queue and its extensions to more general birth-death processes are analyzed in detail, as are queues with phase-type arrival and service processes. The M/G/1 and G/M/1 queues are solved using embedded Markov chains; the busy period, residual service time, and priority scheduling are treated. Open and closed queueing networks are analyzed. The final part of the book addresses the mathematical basis of simulation. Each chapter of the textbook concludes with an extensive set of exercises. An instructor's solution manual, in which all exercises are completely worked out, is also available (to professors only). Numerous examples illuminate the mathematical theories Carefully detailed explanations of mathematical derivations guarantee a valuable pedagogical approach Each chapter concludes with an extensive set of exercises

After a comprehensive upgrade from its first generation, the QSII Series QS600II 600Ws Strobe Flash Modeling Light now boasts a sophisticated design, advanced technology, and an array of functions. This professional studio flash is perfect for capturing stunning images in various settings, including weddings, advertisements, portraits, fashion shoots, and high-speed photography. The QSII Series QS600II is equipped with a built-in Godox 2.4G wireless X system, providing a convenient wireless solution to capture those wonderful moments. With the use of TTL wireless flash trigger X1, power remote control XT16, or FT16, you can wirelessly control the flash's power output, modeling lamp, triggering, and more. This strobe flash modeling light offers excellent flash results with a 0.3-1.5s recycle time and a flash duration ranging from 1/2000 to 1/800s. The power output can be precisely adjusted in 50 steps, from 1/32 to 1/1, in 0.1 increments. The QSII Series QS600II also features a 150W modeling lamp with three modes - OFF, PROP, and percentage. The light brightness of the modeling lamp can be adjusted from 5% to 100%, providing you with the flexibility to create the perfect lighting for your shots. The flash also includes three slave trigger models - OFF, S1, and S2, allowing it to synchronize with cameras that have a one-preflash firing system. The user-friendly design includes a concise keyboard, multifunctional buttons, and an LCD panel for clear display. The settings auto memory and recovery feature ensure that your preferred settings are always at your fingertips. Safety is a priority with the QSII Series QS600II. It comes with alarm display functions, a glass protection cover, and a robust power isolation design to ensure the safety of both the equipment and the users. Experience the versatility and advanced features of the QSII Series QS600II 600Ws Strobe Flash Modeling Light, designed to enhance your photography experience.

QSII Series Professional Studio Flash QSII series high-speed flash has a comprehensive upgrade from the first generation with sophisticated design, advanced technique and abundant functions. With built-in Godox 2.4G wireless X system to offer convenient wireless to capture the wonderful moment, QSII series is excellent for wedding. advertisement, portrait, fashion and high-speed photography. Built-in Godox 2.4G Wireless X System Offers Creative Shooting • Use TTL wireless flash trigger X1, power remote control XT16 or FT16 to wirelessly control flash's power output, modeling lamp, triggering, etc.• QSII series has built-in Godox 2.4G wireless X system to wireless control multiple Godox flashes (built-in Godox X system) with 16 groups and 32 channels Good Flash Results • 0.3-1.5s recycle time and 1/2000 to 1/800s flash duration Precise Power Adjusting • 50 steps (1/32-1/1) of power output in 0.1 increments• 3 modes (OFF, PROP and percentage) of 150W modeling lamp, whose light brightness can be adjusted from 5% to 100% Slave Trigger Model • 3 slave trigger models (OFF, S1 and S2) and the flash can synchronize with cameras having one-preflash firing system Easy Operation • Concise keyboard and multifunctional buttons• LCD panel offers clear display and settings auto memory and recovery Reliable and Safe • Add alarm display functions• With glass protection cover and strong power isolation design to guarantee the safety of the equipment and users

Explore the advanced capabilities of the QSII Series QS1200II 1200Ws Strobe Flash Modeling Light, a professional studio flash designed for high-speed photography. This second-generation model boasts a sophisticated design, advanced technology, and a plethora of features, making it an ideal choice for various photography genres, including wedding, advertisement, portrait, and fashion.The QSII Series QS1200II is equipped with a built-in Godox 2.4G wireless X system, providing a convenient wireless solution to capture those wonderful moments. Utilize the TTL wireless flash trigger X1, power remote control XT16, or FT16 to wirelessly control the flash's power output, modeling lamp, and triggering. This system allows for seamless control of multiple Godox flashes, with 16 groups and 32 channels for maximum flexibility.Experience superior flash results with a 0.3-1.5s recycle time and a flash duration ranging from 1/2000 to 1/800s. The QSII Series QS1200II also offers precise power adjusting with 50 steps of power output in 0.1 increments, ensuring the perfect lighting for every shot.The 150W modeling lamp features three modes (OFF, PROP, and percentage), with light brightness adjustable from 5% to 100%. The flash also includes three slave trigger models (OFF, S1, and S2), enabling synchronization with cameras that have a one-preflash firing system.Operating the QSII Series QS1200II is a breeze, thanks to its concise keyboard and multifunctional buttons. The clear LCD panel displays settings, and the auto memory and recovery function ensure your preferred settings are always at your fingertips.Safety is paramount with the QSII Series QS1200II. It includes alarm display functions and a glass protection cover. The strong power isolation design guarantees the safety of both the equipment and its users. Experience the difference with the QSII Series QS1200II 1200Ws Strobe Flash Modeling Light, your partner in professional, high-speed photography.

After a comprehensive upgrade from its first generation, the QSII Series QS600II 600Ws Strobe Flash Modeling Light now boasts a sophisticated design, advanced technology, and an array of functions. This professional studio flash is perfect for capturing stunning images in various settings, including weddings, advertisements, portraits, fashion shoots, and high-speed photography. The QSII Series QS600II is equipped with a built-in Godox 2.4G wireless X system, providing a convenient wireless solution to capture those wonderful moments. With the use of TTL wireless flash trigger X1, power remote control XT16, or FT16, you can wirelessly control the flash's power output, modeling lamp, triggering, and more. This strobe flash modeling light offers excellent flash results with a 0.3-1.5s recycle time and a flash duration ranging from 1/2000 to 1/800s. The power output can be precisely adjusted in 50 steps, from 1/32 to 1/1, in 0.1 increments. The QSII Series QS600II also features a 150W modeling lamp with three modes - OFF, PROP, and percentage. The light brightness of the modeling lamp can be adjusted from 5% to 100%, providing you with the flexibility to create the perfect lighting for your shots. The flash also includes three slave trigger models - OFF, S1, and S2, allowing it to synchronize with cameras that have a one-preflash firing system. The user-friendly design includes a concise keyboard, multifunctional buttons, and an LCD panel for clear display. The settings auto memory and recovery feature ensure that your preferred settings are always at your fingertips. Safety is a priority with the QSII Series QS600II. It comes with alarm display functions, a glass protection cover, and a robust power isolation design to ensure the safety of both the equipment and the users. Experience the versatility and advanced features of the QSII Series QS600II 600Ws Strobe Flash Modeling Light, designed to enhance your photography experience.

A powerful and versatile addition to any professional photography setup, the QSII Series QS800II 800Ws Strobe Flash Modeling Light boasts a color temperature of 5600K, ideal for capturing natural-looking light in your photos and videos. This high-quality, durable strobe flash is designed with advanced techniques and a sophisticated design, making it an excellent choice for a variety of applications, including wedding, advertisement, portrait, fashion, and high-speed photography.Equipped with the built-in Godox 2.4G wireless X system, this strobe flash offers the convenience of wireless control, allowing you to effortlessly capture those wonderful moments. Use the TTL wireless flash trigger X1, power remote control XT16, or FT16 to wirelessly control the flash's power output, modeling lamp, and triggering. With 16 groups and 32 channels, you can easily control multiple Godox flashes wirelessly, enhancing your creative shooting possibilities.Achieve optimal flash results with a 0.3-1.5s recycle time and a flash duration of 1/2000 to 1/800s. The QS800II offers precise power adjusting with 50 steps of power output in 0.1 increments, and a 150W modeling lamp with three modes (OFF, PROP, and percentage), whose light brightness can be adjusted from 5% to 100%.The QS800II also features three slave trigger models (OFF, S1, and S2), allowing the flash to synchronize with cameras that have a one-preflash firing system. Its user-friendly design includes a concise keyboard, multifunctional buttons, and an LCD panel for clear display and settings auto memory and recovery.For added safety, the QS800II is designed with a glass protection cover and a strong power isolation design. It also includes alarm display functions to ensure the safety of both the equipment and the user. Experience the power and versatility of the QSII Series QS800II 800Ws Strobe Flash Modeling Light, a reliable choice for professional photographers and videographers.

A revolutionary addition to your music gear, the DL4 MkII Delay Modeling Effects Pedal is a comprehensive upgrade from the original DL4 Delay Modeler. This advanced version incorporates 15 new MkII delays, inspired by our renowned HX family of amp and effects processors. It also features both 4-Switch and 1-Switch loopers, providing up to 240 seconds of record time, which can be extended to several hours with an optional microSD card.The DL4 MkII is designed with an XLR microphone input, MIDI In and Out/Thru connectors, robust footswitches, three bypass options, and a jack for connecting an optional expression pedal or two additional footswitches. Despite its extensive features, the DL4 MkII is more compact and lighter than its predecessor, making it a highly portable choice for today's musicians.Constructed from durable cast aluminum, the DL4 MkII is built to withstand the demands of live performances. It maintains the same control layout as the original, with the Legacy button transforming the DL4 MkII into a DL4 at your command.This pedal offers a total of 30 delays: 15 new MkII delays, 14 original DL4 delays, and an Echo Platter, derived from the rackmount Echo Pro. The 4-Switch Classic Looper and the 1-Switch Looper operate in either mono or stereo and can be positioned before or after other effects.The onboard memory provides up to 240 seconds of recording time, which can be expanded with an optional microSD card. This also allows a loop to be stored in memory. The XLR microphone input enables vocal or acoustic instrument processing and looping, with the gain adjustable via the Trim control.MIDI In and Out/Thru DIN connectors allow the DL4 MkII to receive continuous controller, program change, and other MIDI messages from external sources. Bypass options include buffered, DSP, and true bypass, with the latter two avoiding A/D/A conversion by routing analog signals directly from the input(s) to the output(s).The footswitches select presets A, B, and C, and when the Looper is active, they control the Record/Overdub, Play/Stop, and Play Once functions. An optional expression pedal can be connected, automatically assigned to relevant effects parameters, along with two assignable external footswitches.The DL4 MkII is powered by the included 9V DC-1g power supply or most other 9V center-negative power supplies. The Model Selector allows you to choose the delay or reverb type or the Classic Looper, while the ALT/Legacy Button toggles between the MkII and Legacy delays. The Time/SUBDIV adjusts the delay time, and the Repeats control adjusts the delay repeats from one to infinite. The Tweak and Tweez controls are assigned to specific parameters based on the selected delay type, and the Mix control adjusts the blend between the dry and effected signal.

Where innovation meets sophistication, the Volca Drum Physical Modeling Drum Synthesizer emerges as a game-changer in the world of sound design. As the third and most unique entry in the Volca lineup, this advanced drum synthesizer offers a sonic character that sets it apart from its predecessors, the Volca Kick and Beats.The Volca Drum Synthesizer is a digital percussion synthesizer that goes beyond the typical PCM-sampled bass drum, snare drum, or cymbal sounds. Instead, it utilizes a DSP-powered analog modeling system to create its drum sounds. With oscillator waveforms such as sine wave, sawtooth wave, and HPF noise at your disposal, you can craft a wide variety of percussion sounds, from realistic to idiosyncratic.This high-quality drum synthesizer features a 6-part x 2-layer structure, allowing you to assign your unique sounds to any of the six parts without being confined by the traditional drum set conventions. Each part consists of two layers, each of which can be customized with one of five types of oscillator waveform and three types of pitch modulator and amp EG. This flexibility allows you to create thick, layered sounds that are distinctly your own.The Volca Drum Synthesizer also features a newly developed DSP engine that lets you adjust the resulting trigger waveform by applying bit reduction, adjusting the wave folder depth, and using overdrive to control the distortion. This innovative design allows you to create distinctive sounds that are far from typical drum machine outputs.Adding to the richness of the sound is the waveguide resonator effect, based on physical modeling. This effect adds sympathetic resonances to the sound, with two types of waveguide to choose from: "tube" for the resonance of a cylindrical object, and "strings" for the metallic resonance of a string.The Volca Drum Synthesizer also boasts an evolved 16-step sequencer, excellent for improvisation. With the ability to create patterns using the 16 buttons, each corresponding to one of the 16 steps, you can easily construct a pattern while looping the playback. The sequencer also supports real-time recording and the pattern chain function, allowing you to play multiple sequence patterns successively.This professional-grade drum synthesizer is not only a powerful tool for creating unique sounds but also a versatile instrument for live performances. With features like the active step function, step slice function, accent function, and choke function, you can create dynamic performances that are truly original.The Volca Drum Synthesizer also features a custom LCD for easy navigation and a sleek aluminum panel for a sense of quality. With its compact size, battery operation, and built-in speaker, you can take this unit anywhere and enjoy playing on the go. Plus, with a sync jack for easy connection to other Korg groove machines and a standard MIDI IN connector, the Volca Drum Synthesizer can be easily integrated into your existing setup or used as a sound module for...

"Brown is well known for research on mathematical modeling in the social sciences. His book introduces the graph algebra approach to modeling systems in the social sciences."―CHOICEGraph Algebra: Mathematical Modeling with a Systems Approach introduces a new modeling tool to students and researchers in the social sciences. Derived from engineering literature that uses similar techniques to map electronic circuits and physical systems, graph algebra utilizes a systems approach to modeling that offers social scientists a variety of tools that are both sophisticated and easily applied. Key Features:Designed for readers in the social sciences with minimal mathematical training: In this volume, the author assists readers in developing their own difference and differential equation model specificationsIncorporates Social Theory: This book describes an easily applied language of mathematical modeling that uses boxes and arrows to develop very sophisticated algebraic statements of social and political phenomena. Graph algebra can be used to algebraically "flesh-out" even the most complicated and sophisticated of theories. Contains social science examples of graph algebra models: Social science readers can see many examples of how graph algebra can be used to model theories from a wide variety of substantive areas and disciplines. The book also describes how to estimate such models, and two examples are fully worked out. Explains linear and nonlinear model specifications using graph algebra from a social science perspective: Readers can move beyond simple linear regression models by using graph algebra.This text is ideal for use in graduate courses such as Statistical Modeling, Quantitative Methods, and Applied Mathematics.Learn more about "The Little Green Book" - QASS Series! Click Here

This text presents a wide variety of common types of models found in other mathematical modeling texts, as well as some new types. However, the models are presented in a very unique format. A typical section begins with a general description of the scenario being modeled.  The model is then built using the appropriate mathematical tools. Then it is implemented and analyzed in Excel via step-by-step instructions. In the exercises, we ask students to modify or refine the existing model, analyze it further, or adapt it to similar scenarios.

Differential equations are the basis for models of any physical systems that exhibit smooth change. This book combines traditional teaching on ordinary differential equations with an introduction to the more modern theory of dynamical systems, placing this theory in the context of applications to physics, biology, chemistry, and engineering. Beginning with linear systems, including matrix algebra, the focus then shifts to foundational material on non-linear differential equations, drawing heavily on the contraction mapping theorem. Subsequent chapters deal specifically with dynamical systems concepts - flow, chaos, invariant manifolds, bifurcation, etc. An appendix provides simple codes written in Maple®, Mathematica®, and MATLAB® software to give students practice with computation applied to dynamical systems problems. For senior undergraduates and first-year graduate students in pure and applied mathematics, engineering, and the physical sciences. Readers should be comfortable with differential equations and linear algebra and have had some exposure to advanced calculus.

Introduction to Mathematical Modeling helps students master the processes used by scientists and engineers to model real-world problems, including the challenges posed by space exploration, climate change, energy sustainability, chaotic dynamical systems and random processes. Primarily intended for students with a working knowledge of calculus but minimal training in computer programming in a first course on modeling, the more advanced topics in the book are also useful for advanced undergraduate and graduate students seeking to get to grips with the analytical, numerical, and visual aspects of mathematical modeling, as well as the approximations and abstractions needed for the creation of a viable model.

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This book discusses the interplay of stochastics (applied probability theory) and numerical analysis in the field of quantitative finance. The stochastic models, numerical valuation techniques, computational aspects, financial products, and risk management applications presented will enable readers to progress in the challenging field of computational finance. When the behavior of financial market participants changes, the corresponding stochastic mathematical models describing the prices may also change. Financial regulation may play a role in such changes too. The book thus presents several models for stock prices, interest rates as well as foreign-exchange rates, with increasing complexity across the chapters. As is said in the industry, ""do not fall in love with your favorite model."" The book covers equity models before moving to short-rate and other interest rate models. We cast these models for interest rate into the Heath-Jarrow-Morton framework, show relations between the different models, and explain a few interest rate products and their pricing. The chapters are accompanied by exercises. Students can access solutions to selected exercises, while complete solutions are made available to instructors. The MATLAB and Python computer codes used for most tables and figures in the book are made available for both print and e-book users. This book will be useful for people working in the financial industry, for those aiming to work there one day, and for anyone interested in quantitative finance. The topics that are discussed are relevant for MSc and PhD students, academic researchers, and for quants in the financial industry.

This book introduces the basic fundamentals, models, emulators and analyses of mem-elements in the circuit theory with applications. The book starts reviewing the literature on mem-elements, models and their recent applications. It presents mathematical models, numerical results, circuit simulations, and experimental results for double-loop hysteresis behavior of mem-elements. The authors introduce a generalized memristor model in the fractional-order domain under different input and different designs for emulator-based mem-elements, with circuit and experimental results. The basic concept of memristive-based relaxation-oscillators in the circuit theory is also covered. The reader will moreover find in this book information on  memristor-based multi-level digital circuits, memristor-based multi-level multiplier and memcapacitor-based oscillators and synaptic circuits.

From the unique perspective of partial differential equations (PDE), this self-contained book presents a systematic, advanced introduction to the Black-Scholes-Merton's option pricing theory.A unified approach is used to model various types of option pricing as PDE problems, to derive pricing formulas as their solutions, and to design efficient algorithms from the numerical calculation of PDEs. In particular, the qualitative and quantitative analysis of American option pricing is treated based on free boundary problems, and the implied volatility as an inverse problem is solved in the optimal control framework of parabolic equations.

From the unique perspective of partial differential equations (PDE), this self-contained book presents a systematic, advanced introduction to the Black-Scholes-Merton's option pricing theory.A unified approach is used to model various types of option pricing as PDE problems, to derive pricing formulas as their solutions, and to design efficient algorithms from the numerical calculation of PDEs. In particular, the qualitative and quantitative analysis of American option pricing is treated based on free boundary problems, and the implied volatility as an inverse problem is solved in the optimal control framework of parabolic equations.

From the innovative minds at IK Multimedia, the MODO DRUM Acoustic Drum Modeling Software is a groundbreaking virtual instrument that breathes new life into your drum tracks. As IK's pioneering venture into physical modeling for drums, MODO DRUM stands apart with its unique blend of modal synthesis and advanced sampling techniques. This software offers an unparalleled level of customization, allowing you to meticulously craft drum kits that are as authentic and dynamic as if they were played live.Harnessing the power of the award-winning MODO technology, similar to the acclaimed MODO BASS, MODO DRUM delivers drum tracks with an extraordinary level of realism. Every nuance is under your control, from the drum size and tension to the material and playing style, providing an array of sonic possibilities that were previously unattainable with traditional drum libraries.MODO DRUM's real-time sound synthesis is a game-changer. Unlike static sample-based virtual instruments, it employs IK's modal synthesis technology and an ultra-optimized sound engine to generate sounds dynamically. The software meticulously models the physical characteristics of each drum, including dimensions, materials, and skin properties, as well as the drummer's play style and the complex interactions between the drum heads, drum bodies, and the surrounding acoustic environment. This results in a virtual drummer that truly mirrors the energy and variability of a live performance.The software offers a selection of 10 expertly crafted drum kits, each chosen to represent a specific style, genre, or era. From the vintage warmth of the Black Oyster to the cutting-edge punch of the Extreme kit, the sonic palette is vast and versatile. Dive into the customization section to tweak and tailor each drum, adjusting skins, tuning, and damping, or even reshaping the drum's physical dimensions. Fine-tune cymbals, manage sympathetic vibrations, and save your configurations for consistent use across projects.Beyond kit construction, MODO DRUM allows you to sculpt the "drummer's" play style. Adjust the strike location, modify the intensity, and choose the stick type to infuse your grooves with the desired feel. The infinite round robin algorithm ensures that no two hits are identical, delivering a humanized performance every time.The ROOM section of MODO DRUM places your drums in various acoustic spaces, from tight booths to expansive cathedrals, using convolution to ensure natural interactions between the drums and their environment. Apply gates, compression, and other effects to further shape your drum sound.The built-in MIXER offers comprehensive control over your drum mix, with individual levels, panning, phase inversion, and bus grouping. Each channel features an 8-band parametric EQ and four FX slots, drawing from a suite of 19 studio-quality processors and effects from T-RackS and AmpliTube for ultimate sound shaping.Finally, MODO DRUM comes packed with over 1400 MIDI patterns in the...

This accessible and practical book nurtures a "modeling intuition" for readers in a wide range of disciplines, including mathematics, science, engineering, and economics. The numerous examples and mathematical techniques it includes demonstrate that mathematical modeling can be an important tool for revealing the underlying links between apparently disparate phenomena. Its flexible approach also reinforces the idea that there is no fixed set of tools for modeling. Modeling for Industrial Mathematics and Engineering includes many real-world problems related to industry, medicine, and engineering; important topics at the beginning of each chapter; a comprehensive problem section with extensive references in each chapter; and a guide to the literature at the end of each chapter. An important reference book on mathematical modeling for readers in almost any discipline.

This textbook is rich with real-life data sets, uses RStudio to streamline computations, builds "big picture" conceptual understandings, and applies them in diverse settings. Mathematical Modeling and Applied Calculus will develop the insights and skills needed to describe and model many different aspects of our world. This textbook provides an excellent introduction to the process of mathematical modeling, the method of least squares, and both differential and integral calculus, perfectly meeting the needs of today's students.Mathematical Modeling and Applied Calculus provides a modern outline of the ideas of Calculus and is aimed at those who do not intend to enter the traditional calculus sequence. Topics that are not traditionally taught in a one-semester Calculus course, such as dimensional analysis and the method of least squares, are woven together with the ideas of mathematical modeling and the ideas of calculus to provide a rich experience and a large toolbox of mathematical techniques for future studies. Additionally, multivariable functions are interspersed throughout the text, presented alongside their single-variable counterparts. This text provides a fresh take on these ideas that is ideal for the modern student.