Ракета-носитель. Vector. [Редактировать]

Дополнительная классификация

#Наименования
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#Новостная лента.
12016-08-05. Vector Space Systems выиграла конкурс компании Iceye.
Специализирующаяся на малых космических аппаратов, компания Vector Space Systems, подтвердила запуск 21 космического аппарата радиолокационного дистанционного зондирования Земли. В качестве средства выведения в компании планируют использовать свою ракету-носитель Vector Micro Satellite Launch Vehicle, а сроком запуска определен 2018 год. Заказчиком пусков выступает Финляндская Iceye, которая решила начиная с 2017 года развернуть свою орбитальную группировку малых аппаратов ДЗЗ. Тэги: Vector Space SystemsVector
22016-08-16. Компания Vector Space Systems продолжает тестирование своих ракетных блоков.
Разработчик легких ракет провел успешное тестирование своего прототипа P-20, который должен был в ходе испытаний имитировать 12 метровую ракету Vector-1. На этот раз прототип имел размерность около 6 метров в длину. Компания также подтвердила что первый пуск изделия она осуществит в 2018 году. Стоимость пуска объявлена в 1.5 млн. долл. Тэги: VectorVector Space Systems
32016-09-09. Vector Space Systems получила контракт от НАСА.
Оператор пусковых услуг анонсировала заключение с НАСА контракт на продолжение работ по разработке улучшенного прототипа верхней ступени своей ракеты Vector-R. Данный контракт является продолжением работы, которую ранее компания проводила для DARPA с целью оснащения подобным ракетным блоком экспериментального космоплана XS-1. Первые тесты нового блока пройдут в четвертом квартале 2017 года. Согласно новому контракту, в рамках работы Vector Sapce Systems проведет окончательную сборку, интеграцию и проверку полномасштабной версии блока. К проекту также планируется привлечь такие организации как University of Alaska Fairbanks и Alaska Aerospace Corporation (AAC), что позволит Vector SpaceSystems получить доступ к наземной космической инфраструктуре расположенной на острове Кодиак.Тэги: Vector Space SystemsVectorDARPAКосмическое агентство США
42016-10-16. Vector Space Systems решила обосноваться в Аризоне.
Разработчик ракет сверх-легкого класса решил локализовать свое производство в Аризоне. В связи с этим компания объявила что ее перспективные ракеты Vector-R/H будут производиться именно здесь. При этом, территориально производство будет находиться на территории которую местные власти специально выделили для подобных предприятий, запретив на ней строительство жилья и не профильную деятельность.Тэги: Vector Space SystemsVector
52016-10-19. Vector Space Systems анонсировала $60 млн соглашение с York Space Systems.
Компания Vector Space Systems объявила о скором завершении подготовки соглашения с аэрокосмической компанией York Space Systems, которая специализируется на аппаратах малого и среднего размера.
Целью соглашения будет являться запуск шести космических аппаратов в период между 2019 по 2022 года.
Также по условиям будущего контракта заказчик получит опцион на право пуска 14 РН.
Данный заказ будет являться первым в ходе которого будет использоваться РН Vector-H, которая должна будет выводить на орбиту до 100 кг. Также в ходе пусков компании планируют провести испытания полностью электрической верхней ступеней, которая должна будет позволить выводить те-же 100 кг на орбиту с высотой до 1000 км. Тэги: Vector Space SystemsVectorYork Space Systems
62016-12-21. Компания Vector Space Systems провела испытания двигателя первой ступени.
Компания Vector Space Systems анонсировала успешное проведение испытание ДУ первой ступени своей РН Vector R. Испытание проходило в Калифорнии. При этом, в ходе испытаний компания провела также и испытания распечатанного на 3Д принтере инжектора (разработка и проведение испытаний финансировалось НАСА). Также компания обнародовала данные о будущем экономическом эффекте от своего сотрудничества с государством которое выражается в увеличении ВВП региона на 290 млн. долл. (в течении следующих пяти лет) и обеспечение работой порядка 200 человек.Тэги: VectorVector Space SystemsКосмическое агентство США
72017-05-04. Компания Vector Space Systems провела тестирование инженерной модели.
Согласно сообщению оператора пусковых услуг 3 мая компания провела успешное низковысотное испытание инженерной модели своей РН Vector-R. Запуск состоялся в среду с полигона в пустыне Мохаве (штат Калифорния). В ходе испытаний одноступенчатая модель достигла высоты полета около 1.5 км, а целью запуска являлась проверка качества изготовленных при помощи 3Д принтеров инжекторов двигательных установок и других частей двигательной установки. В компании также отметили, что в ближайшее время они проведут еще порядка восьми испытательных пусков с целью набора статистики. Тэги: Vector Space SystemsVector
82017-05-19. Vector Space объявило о желании расширить свои пусковые возможности с минимальными вложениями в наземную инфраструктуру.
Компания Vector Space Systems, которая известна тем, что разрабатывает РН сверхлегкого класса, объявила о желании не только коренным образом снизить стоимость пуска малых КА и повысить оперативность предоставления услуг, но и о готовности рассмотреть возможности запуска своей РН с любой удобной стартовой позиции (включая и морские баржы). В компании также отметили, что характеристики ее РН были рассчитаны на основе предположения о запуске с Мыса Канаверал, что делает потенциально возможным повышение энергоэффективности за счет переноса места пуска ближе к экватору.Тэги: Vector Space SystemsVector
92017-08-05. Компания Vector выполнила второе испытание своей малой ракеты.
Сверхлегкая ракета Vector-R выполнила свой второй тестовый пуск из космопорта Камден в Джорждии (штат США). Компания не решила сразу раскрывать подробности испытаний, но отметила, что пуск прошел успешно. Как и раньше полет не предусматривал полет по траектории высотой более 3 км. Ранее 29 июня компания объявила о получении $21 млн от Sequoia Capital, что должно будет позволить ей ускорить процесс отработки изделия. Тэги: Vector Space SystemsVector
102017-10-21. Vector запланировал три пуска с острова Уоллопс.
Компания Vector, заключила соглашение с Virginia Commercial Space Flight Authority (Virginia Space) на проведение трех коммерческих пусков с регионального космопорта MARS. Как ожидается пуски произойдут в следующие два года. Также компания объявила о том, что она переводит свои инженерные подразделения из Туксона (Аризона) на территорию MARS для проведения испытаний систем заправки. Тэги: Vector Space SystemsVectorУоллопс
112017-10-24. Компания Vector объявила дату первого орбитального пуска.
Компания Vector объявила о том, что она закончила выполнять тестовые полеты из Калифорнии и Джорджии и приступает к подготовке к первому орбитальному пуску с Ванденберга. В качестве даты пуска названо лето 2018 года. Компания не стала конкретизировать технико-экономические аспекты предстоящего пуска, однако известно, что:
1. Стоимость пуска разрабатываемой РН Vector-R (масса ПН НОО 60 кг) составит $1.5 млн.
1. Стоимость пуска перспективной РН Vector-H (масса ПН НОО 150 кг) составит $3 млн. Тэги: VectorVector Space SystemsБаза Ванденберг
122017-11-18. Оператор пусковых услуг объявил о том, что он начал прорабатывать вопросы запуска с Ванденберга.
Оператор пусковых услуг Vector объявила о том, что она прорабатывает вопросы по осуществлению пусковой активности на базе Ванденберг. При этом, в качестве своего партнера в этом проекте компания рассматривает специализирующуюся на разработке оборудования Harris Corporation, которая уже имеет свои производства на территории космодрома. К причинам, которые привели к желанию рассматривать это место, в Vector назвали успешный опыт компании SpaceX.Тэги: Vector Space SystemsVectorБаза Ванденберг
132017-12-08. Компания Vector выбрала подрядчика для создания производства на территории США.
Компания Vector объявила о том, что она выбрала подрядчика (Holladay Properties ) для реализации проекта по созданию производства ракет-носителей в Тусоне (штат Аризона). В качестве архитекторов в проекте будут задействована Swaim Associates LTD. Как ожидается производство будет построено к 2019 году и на нем будет задействовано около 200 человек. Экономический эффект от инвестиций составит около $290 млн за следующие пять лет. Производительность новой фабрики будет составлять до 100 ракет в год и иметь возможности по увеличению этого показателя до 200 шт. в год. Также компания объявила о том, что на существующих в штате Аризона мощностях она уже начала производство новой ракеты, которая должны будет быть запущена во втором квартале 2018 года. Тэги: Vector Space SystemsVector
142017-12-16. Astro Digital выбрала Vector для запуска первых 12 аппаратов.
Оператор пусковых услуг Vector объявил о том, что он осуществит выведение в 2018 году один из КА ДЗЗ компаний Astro Digital (AD). Всего компания должны будет вывести как минимум 12 подобных аппаратов совершая от двух до четырех пусков в год в интересах AD. Средством выведения будет являться ракета Vector R. Тэги: Vector Space SystemsVector
152018-02-15. Vector Space Systems получила новый контракт.
Компания Vector - оператор сверхлегких пусковых услуг, объявил о том, что он получил 5 контрактов на запуски своей ракеты Vector-R в период с 2019 по 2023 годы. Заказчиком пусковых услуг названа компания Open Cosmos, которая является агрегатором заказов на пусковые услуги в интересах клиентов, которые не хотят тратить на их поиск свое время. Также компания оказывает услуги по размещению полезных нагрузок на типовых платформах. Тэги: Vector Space SystemsVector
162018-02-20. Компания Vector объявила о своих ближайших планах.
Компания Vector Space Systems объявила о том, что она планирует летом этого года осуществить свой первый орбитальный пуск. Местом пуска объявлена территория Аляски (Кодиак). Летное испытание будет совмещено с выведением полезной нагрузки и массово-габаритного макета.
Относительно характеристик своей ракеты Vector-R в компании отметили, что она выводит на орбиту до 65 кг, а стоимость ее пуска составляет около $1.5 млн. Тэги: Vector Space SystemsVectorPacific Spaceport Complex – Alaska
172018-03-12. Компания Vector получила новый контракт.
Космическое агентство США объявило о том, что в рамках нового раунда заключения контрактов по программе SBIR оно решило заключить договор с компанией Vector Launch. Размер контракта составляет $0.75 млн., а его срок составляет два года. В рамках проводимых работ стартап должен будет разработать систему микронасосов и связанную с ними, напечатанный на 3Д принтере теплообменник, которые в дальнейшем будут использоваться в составе ее сверхлегкой ракеты. К экономическим последствиям от внедрения этой технологии в компании назвали уменьшение массы (за счет устранения необходимости в дополнительных баков с гелием) и общей стоимости изготовления стоимости ракет. В компании также отметили то обстоятельство, что ее новое изделие будет позволять перекачивать не только керосин и жидкий кислород, но и такие виды топлива как метан и пропан.
С технической точки зрения предлагаемое компанией решение состоит в прокачке через теплообменник части топлива с последующей подачей его бак с горючим.Тэги: VectorVector Space SystemsКосмическое агентство США

Технические характеристики

#ХарактеристикаЗначение
1Длина, метра12
2Масса, кг5100
3Масса (сухая), кг685
4Диаметр (первой ступени), метра1.2

Характеристики орбиты

#ХарактеристикаЗначение
1Масса ПН (Кодиак, 1/3/12 юнитовые аппараты без учета массы системы разделения) (НОО), кг45
2Масса ПН (Мыс канаверал, микроспутники) (НОО), кг35

Экономические характеристики

#ХарактеристикаДата измеренияЗначение
1Страна США
2Стоимость (пуска), млн. долл.2016-08-161.5
3Темп пусков (максимальный), в год100
4Темп пусков (планируемый ), в год12

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... vector, the return value is a row vector, otherwise it is a column vector. If... a row vector if x is a row vector, otherwise it is a column vector. See also... a row vector if x is a row vector; otherwise, it is a column vector. See also... File] Return true if x is a vector. A vector is a 2-D array where one of... # result is a row vector # result is a column vector As a special case, when... vector or matrix. For example: a(:) a(:)’ # result is a column vector # result is a row vector... matrix. "vector" Values are arranged in a single vector (column or vector). See also... plot of the vector x. The input x should be a vector of integers. Any... source location vector lv can be given as a 2-element vector [azimuth, elevation... equivalent. If x is a vector of length M and y is a vector of length N, then...": a four-element vector [x0 y0 width height]. The vector specifies the coordinates... a 3-element RGB vector with the precise TrueColor. If c is a vector of length...: four-element vector, def. [0.25000 2.50000 8.00000 6.00000] Vector [x0 y0 width.... papersize: two-element vector, def. [8.5000 11.0000] Vector [width height] defining..." ticklength: two-element vector, def. [0.010000 0.025000] Two-element vector [2Dlen 3Dlen.... view: two-element vector, def. [0 90] Two-element vector [azimuth elevation] specifying... object. xlim: two-element vector, def. [0 1] Two-element vector [xmin xmax] specifying... object. ylim: two-element vector, def. [0 1] Two-element vector [ymin ymax] specifying... object. zlim: two-element vector, def. [0 1] Two-element vector [zmin zmaz] specifying... not rendered on screen. xdata: vector, def. [0 1] Vector of x data to be... use as x data. ydata: vector, def. [0 1] Vector of y data to be plotted... use as y data. zdata: vector, def. [](0x0) Vector of z data to be... graphics object. position: four-element vector, def. [0 0 0] Vector [X0 Y0 Z0] where.... xdata: two-element vector, def. [1 64] Two-element vector [xmin xmax] specifying...)]. ydata: two-element vector, def. [1 64] Two-element vector [ymin ymax] specifying... screen. xdata: vector | matrix, def. [0; 1; 0] ydata: vector | matrix, def. [1; 1; 0] zdata: vector | matrix, def...] If x is a vector of length n, diff (x) is the vector of first differences... also initialize the state vector from an arbitrary vector of length ≤ 625... matrix formed from an m-vector c, and an n-vector r, has the elements H(i, j) = ci... alpha is a row vector and x is a column vector, the result is a matrix... m. If u is a column vector and m is a row vector, the results are matrices..., given the flag "vector", Q will be returned as a vector such that RT...*housv’)x = -norm (x)*e(j) if x(j) >= 0 Inputs x vector j index into vector z threshold for zero (usually... always requested for a solution vector whose residual vector is already known, and... starting vector for the algorithm. An initial vector close to the final vector... the function with a vector argument to produce a vector result. The second step... and return a vector of output values when given a vector of input values... and return a vector of output values when given a vector of input values... must return a vector of output values if given a vector of input values... z = f (x, y) where x is a vector and y is a scalar. It should return a vector of the... tolerance. May be either vector or scalar. If a vector, it must match... tolerance. May be either vector or scalar. If a vector, it must match... tolerance. May be either vector or scalar. If a vector, it must match... tolerance. May be either vector or scalar. If a vector, it must match... tolerance. May be either vector or scalar. If a vector, it must match... tolerance. May be either vector or scalar. If a vector, it must match... tolerance. May be either vector or scalar. If a vector, it must match... phi{2} must accept one vector argument and return a vector. When supplied, the... functions must accept one vector argument and return a vector. The third and... in a single vector y with groups specified by a corresponding vector of group labels... x is a column vector then return a column vector; Otherwise, return a row vector. x may also... then return a row vector; Otherwise, return a column vector. The inputs may also... then return a row vector; Otherwise, return a column vector. The inputs may also... a is a row vector return a column vector; Otherwise, return a column vector. The inputs may... then return a row vector; Otherwise, return a column vector. The inputs may also... splinefit splinefit splinefit x is a vector, and y is a vector or N-D array. If y is... compute eigenvalues. If x is a vector, poly (x) is a vector of the coefficients of... a vector of length n. y can be either a vector or array. If y is a vector it... as sf. The state vector is a column vector whose length is equal... the length of vector a, l is the length of vector b and e is Gaussian... center of the vector or matrix. If x is a vector of N elements corresponding... n. y can be either a vector or array. If y is a vector then it must... follows. octave:1> x = [some data vector]; octave:2> n = [some coefficient vector]; octave:3> y = filter (n, 1, x); The...



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... и TCH, которые будет представлены векторами: vector > U; vector > GROUPS; vector > TCH; Элементы кортежа вектора... назначению vector > TCRU; 4. TCRC Виды аудиторий по вместимости vector > TCRC; 5. CR Аудитории vector... единиц vector > BAN_U_CR; 8. TW Учебные недели vector > TW; 9. DW Дни недели vector > DW.... PST Должности преподавателей vector > PST; 16. TCH Преподаватели vector > TCH; 17. BAN_TCH_T... дня vector > TD; vector > TP; vector > DU; vector > BAN_TCH_T; vector > GROUPS; Иерархия учебных групп vector > HGR; (дуги графа Γ𝐻 ) Учебные единицы vector... на C++ vector > FAR_CR; Кластеры учебных групп vector > CLGR; vector > SCGR; vector > CIG; vector > SPG; vector >> CU; Т-конкурентность между vector > TCTU...*, tuple , unsigned int, vector *); using F_p = double (*)(Tables*, vector &); Из объявления видно... : vector - genes2 : vector - genes3 : vector + chromosome_p() : + chromosome_p(Tables*, vector , vector , vector ) : + operator=(…) : chromosome_p& + get_genes1() const : vector + get_genes2() const : vector + get_genes3() const : vector Рисунок...(int, int); public: vector > TW; // недели vector > TD; // дни недели vector TP; // таймслоты... номер пары vector > BCR; // учебные корпуса vector FAR_B; // удаленность учебных корпусов vector > CR... корп. - назв-е - вместимость vector FAR_CR; // удаленность аудиторий vector BAN_CR_T; // запрет на аудитории... студентов vector HGR; // иерархические связи между группами vector CLGR; // кластеры учебных групп vector SCGR; // S-конкурентность учебных групп vector CIG; // вхождение групп в кластеры vector U; // учебные....занятия vector U1; // лекции vector U2; // пр. зан. vector U3; // лаб. зан. vector TCTU; // Т-конкурентность учебных единиц vector...*, tuple , unsigned int, vector *); static double SLO(Tables*, vector &); }; #endif /* Fitness_h */ 3.4 Файл... double Fitness::SLO(Tables *t, vector & perm) { GA_binary *g; vector tmp; vector > > CU_tmp; for (auto....end(), cmp); // упорядочивание } template vector population ::get_freq() { vector frec; double z, z_max = 1.01...; vector join(vector &, vector &, vector &); void Mutate_p(vector &); pair , vector > cross_PMX(vector , vector ); pair , vector > cross_OX(vector , vector ); pair , vector > cross_CX(vector , vector ); pair , vector > cross_POX(vector , vector ); pair , vector > cross_PCX(vector , vector ); //---------------------------class chromosome_p : public chromosome , double, double (*)(Tables*, vector &)> { vector genes1; // ген 1 (лекции) vector genes2; // ген 2 (пр.зан.) vector genes3; // ген 3 (лаб.зан.) public: 222 chromosome_p() {} chromosome_p(Tables*t, vector v1, vector v2, vector v3) : genes1(v1), genes2... *this; } vector get_genes1() const {return genes1;} vector get_genes2() const {return genes2;} vector get_genes3... (j < 5); j++) P2 = parent_pool[ui.get_n()]; pair< vector , vector > PP1, PP2, PP3; switch (n_cross....size(); i++) insert(parent_pool[i]); } vector join(vector & v1, vector & v2, vector & v3) { vector tmp = v1; for...(v[i], v[j]); } //Частично отображающий кроссинговер pair , vector > cross_PMX(vector Of1, vector Of2) { int n = (int)Of1... = uni_int(1, n-1).get_n(); for(int i=0; i , vector > cross_OX(vector P1, vector P2) { int n = (int)P1.size(); int crossover = uni_int(1, n-1).get_n(); vector... , vector > cross_CX(vector P1, vector P2) { bool key = true; int w, n = (int)P1.size(); vector... pair , vector > cross_POX(vector P1, vector P2) { int n = (int)P1.size(), k = n / 2, m, j = 0; vector nn(k,-1); uni_int... , vector > cross_PCX(vector P1, vector P2) { int n = (int)P1.size(); vector Of1(n, 0), Of2(n, 0); vector > C; vector Ind...



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...: Software Vector Mode. . . . . . . . . . . . . . . . . . . . . 22 5 INTC: Hardware Vector Mode . . . . . . . . . . . . . . . . . . . . 35 6 INTC: Software Vector Mode, VLE Instructions . . . . . . 48 7 INTC: Hardware Vector... Vector Mode x x x x 5 INTC: Hardware Vector Mode x x x x 6 INTC: Software Vector Mode, VLE x x x 7 INTC: Hardware Vector.../P/S), INTC: SW Vector Mode, VLE Instructions, INTC: HW Vector Mode, VLE Instructions... CPU to vector to the sum of the common Interrupt Vector Prefix... CPU to vector to the sum of the common Interrupt Vector Prefix (IVPR0:15) plus the interrupt’s individual Interrupt Vector Offset... CPU to vector to the sum of the common Interrupt Vector Prefix... CPU to vector to the sum of the common Interrupt Vector Prefix (IVPR0:15) plus the interrupt’s individual Interrupt Vector Offset... Vector Mode 4.1 Description Task: Using the Interrupt Controller (INTC) in software vector... Vector Mode except for the differences between software and hardware vector modes. Note: eMIOS channel 0 interrupt vector numbers are... Vector Mode) Common INTC interrupt request to CPU core Figure 8. Software Vector... ISR vector, re-enable interrupts save registers branch to fetched ISR vector... vector to IVPR0:15 + IVOR416:27 handlers.s file IntcIsrVectors.c file ISR Vector... ISR vector, re-enable interrupts save registers branch to fetched ISR vector... INTC’s ISR vector table with addresses for: Initializations INTC Vector 4 ISR (SW interrupt request 4) INTC Vector 51 ISR (eMIOS...: • Configure for software vector mode (HVEN=0) • Keep vector offset (VTES) at four... for SW vector mode */ INTC.MCR.B.VTES_PRC0 = 0;*/ /* MPC551x Proc'r 0: default vector table... for SW vector mode */ INTC.MCR.B.VTES = 0; /* MPC555x: Use default vector table... Vector Mode 5.1 Description Task: Using the Interrupt Controller (INTC) in hardware vector... Vector Mode, except for the differences between software and hardware vector modes. Note: eMIOS channel 0 interrupt vector numbers are... interrupt 4. INTC vector for eMIOS Channel 0 interrupt taken vector to MPC551x: IVPR0... uses INTC vector 51 for eMIOS channel 0. MPC551x uses INTC vector 58...: Initializations INTC Vector 4 ISR (SW interrupt request 4) INTC Vector 51 ISR (eMIOS... HW vector mode*/ INTC.MCR.B.HVEN = 1; /* MPC555x: initialize for HW vector mode....s - INTC hardware vector mode branch table example Description: INTC vector branch table when using INTC in HW vector mode **** NOTE... #INTC HW vector 0 .align ALIGN_OFFSET hw_vect1: b hw_vect1 #INTC HW vector 1 .align ALIGN_OFFSET hw_vect2: b hw_vect2 #INTC HW vector 2 .align ALIGN_OFFSET hw_vect3: b hw_vect3 #INTC HW vector 3 .align ALIGN_OFFSET... HW vector 5 ... etc. for other vectors hw_vect50: b hw_vect50 #INTC HW vector 50... #INTC HW vector 51 .align ALIGN_OFFSET hw_vect52: b hw_vect52 #INTC HW vector 52 .align ALIGN_OFFSET hw_vect53: b hw_vect53 #INTC HW vector 53 .align ALIGN_OFFSET hw_vect54: b hw_vect54 #INTC HW vector 54 .align ALIGN_OFFSET hw_vect55: b hw_vect55 #INTC HW vector 55 .align ALIGN_OFFSET hw_vect56: b hw_vect56 #INTC HW vector 56 .align ALIGN_OFFSET hw_vect57: b hw_vect57 #INTC HW vector 57... #INTC HW vector 58 .align ALIGN_OFFSET hw_vect59: b hw_vect59 #INTC HW vector 59... ISR vector, re-enable interrupts save registers branch to fetched ISR vector... ISR Vector Table: ... SW IRQ 4 ISR addr ... PIT 1 ISR addr ... ... ... vector to... ISR vector, re-enable interrupts save registers branch to fetched ISR vector...’s ISR vector table with addresses for: • SWirq4ISR: INTC vector #4 • Pit1ISR: INTC vector: MPC551x...: • Configure for software vector mode (HVEN=0) • Keep vector offset (VTES) at 4 bytes... for SW vector mode*/ INTC.MCR.B.VTES_PRC0 = 0; /* MPC551x Proc'r 0: default vector table... for SW vector mode */ INTC.MCR.B.VTES = 0; /* Use default vector table 4B... for SW vector mode */ INTC.MCR.B.VTES = 0; /* Use default vector table 4B... software interrupt 4. INTC vector for PIT1 interrupt taken vector to: MPC551x: IVPR0... for: INTC Vector for SW interrupt request 4 INTC Vector for PIT 1 init... vector 0 #INTC HW vector 1 #INTC HW vector 2 #INTC HW vector 3 # SW IRQ 4 #INTC HW vector... #INTC HW vector 57 .align ALIGN_OFFSET e_b hw_vect58 #INTC HW vector 58 .align ALIGN_OFFSET e_b hw_vect59 #INTC HW vector 59 .align ALIGN_OFFSET e_b Pit1Handler #INTC HW vector 60 .align ALIGN_OFFSET e_b hw_vect61 #INTC HW vector 61 .align ALIGN_OFFSET e_b hw_vect62 #INTC HW vector 62 .align ALIGN_OFFSET e_b hw_vect63 #INTC HW vector 63 .align ALIGN_OFFSET e_b hw_vect64 #INTC HW vector 64...



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... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373 A.1 Deviation bounds for a Gaussian vector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373 A.2 Gaussian integrals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374 B Deviation... norm of a standardized non-Gaussian vector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383 B.2.2 A deviation bound for a general... E Contents Random multiplicity correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415 E.1 Vector case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415 E.2 Max-case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 418... maxima . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423 G Gaussian approximation of a vector sum . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425 G.1 A univariate case with... norm of a vector . . . . . . . . . . . . . . . 433 G.3 GAR for the Euclidean norm of a vector sum . . . . . . . . . . . . . . . . . . . . . . . . . 434 G.4 GAR for the sup-norm of a vector sum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 438 G.5 GAR for the sup-norm of a vector sum... vector in IRn . The log-density of the distribution of the vector... u∗ is the vector of coefficients describing the decomposition of the vector f ∗ w.r.t. this... parameter, Y is the n -vector of responses, ε is the n vector of errors, and...) as 1 L(θ, θ ∗ ) = ξ D(θ − θ ∗ ) − (θ − θ ∗ ) D2 (θ − θ ∗ ), 2 where the random p vector ξ is defined as def ξ = σ −2 D−1 Ψ (Y − Ψ θ ∗ ) = σ −2 D−1 Ψ ε = σ −1 M −1 Ψ ε. (2.16... instrumental regression 55 f (x) = θ1 ψ1 (x) + . . . + θp ψp (x) or in vector form f (x) = ψ(x) θ with ψ(x) = ψ1 (x), . . . , ψp (x) ∈ IRp and θ = (θ1 , . . . , θp ) ∈ IRp.... The observed vector Y follows the model Y = f∗ + ε (3.1) with a homogeneous error vector ε : IEε = 0 , Var... δG (Ψ ) Introduce the random vector bG ∈ of the error vector δG (Ψ ) can be bounded... standard Gaussian vector in IRk and δ be a deterministic vector in IRk with... that each stochastic vector ξ m,m◦ is a linear function of the vector ∇ . A similar representation... Gaussain zero mean vector ξ is given and ξ κ = Πκ ξ . Build a vector X out of the... on the Below for a vector θ ∈ IRp 1 p |θj |, = of the vector θ . we denote p θ 1 -norm... vector process def −1 U(θ, θ ∗G ) = DG ∇ζ(θ) − ∇ζ(θ ∗G ) . (11.18) Further, define υ = V2 (θ − θ ∗G ) and introduce a vector... Proof. The vector QDG the correct noise specification, the vector ξ is standard normal and the vector Q θ ∗ − −2 Dξ is normal... score vector ∇ as ∇= ∇θ ∇η and define efficient Fisher matrix Iθ and the influence vector... mean random vector and bθ is a deterministic non-centrality vector which disappears under... positive: def Iκ = Fκ − Fηκ F−1 η Fηκ > 0. ˘ = η + F−1 For any nuisance vector φ = (η, κ) , it holds with η η Fηκ κ ˘ + κ Iκ κ ˘ Fη η φ F φ = η Fη η + 2η Fηκ κ + κ Fκ κ = η 1/2 ˘ = Fη η 2 2 + I1/2 κ κ . 1/2 −1/2 1/2 ˘ = Fη η+Fη This... and hence, for any vector α and any unit vector u IE u (χ1 − α) exp α χ1 − 2 IE...) Also consider the standardized score vector ξ n ξ = D−1 ∇L(υ ∗ ) = σ −2 D−1 Yi − f (Xi , υ ∗ ) ∇f (Xi , υ ∗ ) i=1 n = σ −2 D−1 n εi ∇f (Xi , υ ∗ ) + σ −2 D−1 i=1 f (Xi... a standard normal vector in IRp . A.1 Deviation bounds for a Gaussian vector The next... of a standard Gaussian vector. Lemma A.1.1. Let µ ∈ (0, 1) . Then for any vector λ ∈ IRp with... Gaussian vector ξ with the n × n covariance matrix V = (σij ) with λmax (V) ≤ λ∗ . Given a unit vector... any unit vector u = (ui ) ∈ IRn , u = 1 , and normal zero mean vector ξ ∼ N(0, V) in IRn...-Gaussian vector The bounds of Corollary B.1.2 heavily use normality of the vector... − µB)−1/2 . 1 1/2 1/2 µ B ξ − µ−1/2 B −1/2 γ 2 2 1I( γ ≤ g)dγ µ−1/2 B 1/2 ε + B 1/2 ξ ≤ g/µ , where ε denotes a standard normal vector in IRp and IPξ means... unit vector ω ∈ IRp = log IEeχ ωω . log IE exp χωω Moreover, for any vector... a bias vector B in IRn , a p × n matrix U , and a stochastic Gaussian zero mean vector ξ , define... of a vector sum This chapter discusses an approximation of a vector sum S of... a vector In this section we consider the squared norm S 2 of a vector sum... G Gaussian approximation of a vector sum for any fixed complex vector u . (Define the... the vector sums S = Denote by vi2 the M × M covariance matrix of the vector... x be a vector in IRM with entries x(η) , and ∆ be the vector with the...η πη (t) = β j u(t)IEπ U j , η 442 G Gaussian approximation of a vector sum |ψ (t)| = β −1 u (t) ≤ IEπ U, u(t) |ψ (t)| = β −1 |u (t)u(t) − u (t)2 | ≤ β Varπ (U ), U 2 (t) |ψ (t)| = β −1 |u (t) − 3u (t)S (t) + 2u...-norm the vector S − z = {S(η) − q(η), η ∈ Ξ} by a similar distribution for the Gaussian vector S = {S(η), η ∈ Ξ} . Let f be... of a vector random process Let Y(υ) , υ ∈ Υ , be a smooth centered random vector process with...



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... scalar product a · b . . . . . . . 1.4 The vector product a × b . . . . . . 1.5 Triple products . . . . . . . . . . . . 1.6 Vector functions of a scalar variable... the rules of vector algebra and differentiation of vector functions of a scalar... differentiation of vector functions of a scalar variable. Unlike the vector algebra sections.... Applications include the tangent vector and normal vector to a curve. These will... concept of a vector as an abstract quantity. Definition 1.2 Vector A vector is an... it represents some abstract vector a.‡ Note that each vector a is represented by... called the zero vector and written 0. The zero vector is not the... 1.4 Negative of a vector Let b be any vector. Then the vector with the same... vectors A vector of unit magnitude is called a unit vector. If any vector a is... segment, −→ O A, which represents some vector a. Conversely, the vector a is sufficient to...finition 1.7 Position vector The vector a is called the position vector of the point... of a vector Definition 1.9 Components of a vector Let n be a unit vector. Then the component of the vector v in... of the vector v in the 1.4 13 The vector product a×b n a×b B b θ FIGURE 1.9 The vector product... 3 = 12 + 3 − 30 = −5. 3 THE VECTOR PRODUCT a×b 1.4 −→ Definition 1.10 Vector product Suppose the... that a × b is a vector quantity.] Laws of algebra for the vector product (i) b×a = −a×b (anti... vector product is not associative. Properties of the vector product (i) a×a = 0. (ii) The vector... example on vector product If a = 2 i − j + 2 k and b = − i − 3 k, find a unit vector perpendicular to both a and b. Solution The vector a×b is perpendicular... magnitude of this vector is 32 + 42 + (−1)2 1/2 unit vector can be either... a triple vector product; its value is a vector. Property of the triple vector product... resulting triple vector product by the formula (1.8), as follows: (a×b) · (c×d) = a · [ b×(c×d)] = a · [(b · d) c − (b · c) d ] = (a · c)(b · d) − (a · d)(b · c) 1.6 VECTOR FUNCTIONS OF... here with vector functions of position. These are called vector fields. † Mathematical... means vector subtraction and its value is a vector; it remains a vector after dividing.... Differentiation rules for vector functions Let u(α) and v(α) be vector functions of the... preserved. Example 1.10 Differentiating vector functions (i) The position vector of a particle P at... chord A A represents the vector r = r(α + α) − r(α) −→ and so r/| r | is a unit vector parallel to the... Find the unit tangent vector, the unit normal vector and the curvature... Find the unit tangent vector, the unit normal vector and the curvature... Find the unit tangent vector, the unit normal vector and the curvature... carefully between the position vector r, which is −→ the vector O P, the co-ordinate... with position vector r D and velocity v D chasing a hare with position vector r H and velocity... derivative of the vector q, that is, q˙ = (q˙1 , . . . , q˙n ). (12.6) The vector q˙ can be regarded... determination of vector potentials is described in textbooks on vector field theory... the column vector with elements {q j }, and q˙ is the column vector with elements... parallel to the unit vector n. Its angular velocity vector is defined... of the vector ω. Let P be a particle of B with position vector r relative to... applies to any vector e that is the position vector (relative to O ) of... a particle P has position vector r relative to F and position vector r relative to F . It... apparent upward vertical vector k (now assumed constant); the vector i is taken so... of the column vector v , where ⎛ ⎞⎛ ⎞ ⎞ ⎛ ⎞ ⎛ 1 √ 0 0 3√ 3 3 v = A · ⎝ −4 ⎠ = ⎝ 0 3/2 √1/2 ⎠ ⎝ −4 ⎠ = ⎝ 1 − 2√ 3 ⎠ . 2 2 0 −1/2 3/2 2+ 3 √ √ The components of the vector v in C are... tensor ⎞ 2 −1 −2 1 A = ⎝2 2 1⎠. 3 1 −2 2 ⎛ The components of the vector v in C vector v , where ⎛ ⎛ ⎞ 2 3 1 v = AT · ⎝ −6 ⎠ = ⎝ −1 3 −2 9 are then... new definition of a vector. Definition 18.3 Vector Let {v1 , v2... time t, {b˙1 (t), b˙2 (t), b˙3 (t)} is a vector. This is, of course, the velocity vector of the...finition of a vector, it is necessary to write the vector transformation formula... and the column vector u represents a vector, then the product T · u represents a vector. Thus pre-multiplicaton by T transforms one vector into another vector. This... angular velocity vector into the angular momentum vector. The angular velocity vector We... that has position vector a relative to G. Since the axial vector a moves with... vector a (= a(t)) is the axial unit vector and the vector n (= n(t)) is the unit vector in... 6, (iii) Yes, order 1 (a vector), (iv) Yes, order 1 (a vector), (v) No, (vi) Yes, order... snooker ball position vector, 8 potential electrostatic, 350 magnetic vector, 350 velocity dependent...–388 vector algebra, 3–16 vector calculus, 16–18 vector geometry, 8–10 vector quantity, 3 vector(s), 4 as...



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... A.2 A.3 A.4 A.5 A.6 A.7 A.8 A.9 A.10 The Scalar Product . . . . . . . . . . . . . . . . . . The Vector Product . . . . . . . . . . . . . . . . . . Differentiation and Integration... , e3 F , F i , F ij Fα F Fi f complex amplitude vector potential acceleration amplitude of oscillation... r∗i T, T ∗ T, T t U V v, v i dW, δW X, Y, Z X, Y x, y, z x, xi , x, y xn , yn α γ δ δ 0 θ Θ, θ, θ∗ λ, λi λi µ µ0 ξ, ξ, η π ρ ρ σ, dσ τ Φ φ ϕ φi ψ position vector relative position position in CM... angular frequencies vector differential operator scalar product of a and b vector product... is called a vector; in this case the Introduction 5 position vector r of P with... a potential energy function V (r) satisfying (3.7). Any vector function F (r) of the form (3.7) obeys... the acceleration due to gravity, a vector of constant magnitude g = 9.81 m s−2 directed... be the vector product G = r ∧ F. (3.18) The components of the vector G are the..., because it is the vector product of a vector with itself. By (1.1), the... convention. A vector of this type is known as an axial vector. It is to be contrasted with an ordinary, or polar, vector... parallel to the position vector r. Since the vector product of two parallel... containing the initial position vector and velocity vector (see Fig. 3.2). This is... components of the momentum vector p and the force vector F — we shall see... momentum vector p in the qi direction. (Here ei is a unit vector in... define the vector angular velocity ω to be a vector of magnitude ω in... an axial vector (see §3.3). For example, for the Earth, ω is a vector pointing... position vector of a point of the rotating body. If a is any vector... = a˙ + ω ∧ a. dt (5.7) Applied to the position vector r, this result is almost obvious... g x ¨ = − x + 2ω y˙ cos θ, l g y¨ = − y − 2ω x˙ cos θ, l (5.24) or, in vector notation, g ˙ r¨ = − r − 2ω cos θ k ∧ r. l (5.25) 118 Classical... momentum vector J is in a different direction from the angular velocity vector...fine an instantaneous angular velocity vector ω and write ˙ + ω ∧ r∗. r˙ = R (9.36) We have... components of a 2n-dimensional velocity vector, v = r˙ = (q˙1 , . . . , q˙n , p˙1 , . . . , p˙ n ). Now suppose that we have... the vector x(t) and the n equations of motion can be written in vector... of n vector fields v j = (∇p Fj , −∇q Fj ), j = 1, . . . , n and the above gradient vector. It is apparent therefore that the vector fields v j at... the lattice vector N has integer components and ω 0 is the vector of normal... that the components of the vector A= p∧J r − m|k| r with p, J respectively linear, angular momentum... vector is the zero vector 0 = (0, 0, 0) of length 0 and indeterminate direction. For a general vector... a vector a and a scalar c is ca = (cax , cay , caz ). If c > 0, it is a vector... = x2 + y 2 + z 2 . (A.7) and in particular, A.3 The Vector Product Any two non-parallel...fine the vector product a∧b (‘a cross b’, sometimes also written a × b) to be a vector along... a to b. 386 Classical Mechanics a∧b ✄ ✄ ✄ ✄ ✄ ✄ ✄ ✄ b ✄ θ ✄ ✄ a ✄ A ✄ ✄ ✄ ✄ ✄ ✄ ✄ ✄ ✄ ✄ ✄ ✄ Fig. A.6 A vector whose sense is merely conventional... an axial vector, as opposed to an ordinary, or polar, vector. For... velocity is an axial vector (see §5.1). The vector product of two polar vectors is thus an axial vector. The vector... expression involving vector products. In particular, the vector product of a vector with itself is the zero vector, a ∧ a = 0. More... be right-handed, then the vector products of i, j, k are i ∧ i = j ∧ j = k ∧ k = 0, i ∧ j = k, j ∧ k = i, k ∧ i = j, j ∧ i = −k, k ∧ j = −i, i ∧ k = −j. (A.10) 387... also form the vector triple product (a ∧ b) ∧ c. Since this vector is perpendicular to... the position vector of a particle as a function of time, r(t). The vector distance... φ(x, y, z) of position in space; a vector field is a vector function A(x, y, z). We can also... written ∇(φψ) = ψ∇φ + φ∇ψ, and similarly ∇ · (φA) = A · ∇φ + φ∇ · A. But, when vector products are involved, we have... when one vector b is given as a linear function of another vector a, according... product of the column vector a and the row vector b, while the scalar... way. For example, for any vector a, 1 · a = a = i(i · a) + j(j · a) + k(k · a) = (ii + jj + kk) · a, whence ii... for the following laws of vector algebra: (a + b) + c = a + (b + c); λ(a + b) = λa + λb; a · (b + c) = a · b + a · c. (Note that a, b, c need not... µ, a vector normal to the loop, of magnitude µ = πa2 I. *Calculate the vector potential... ψ ∓ ae)2 + (b sin ψ)2 = a2 (1 ∓ e cos ψ)2 . 2. Tangent vector is t = (−a sin ψ, b cos ψ), unit vectors..., Dynamical Systems, and Bifurcations of Vector Fields, Springer–Verlag, 1983. Gutzwiller...–Lenz vector, 376 Laplacian, 393 in polar co-ordinates, 400 of vector... velocity in, 56 polar vector, 55, 386 position vector, 5, 6, 381 of composite... vector field, 390 Laplacian of, 393, 406 line integral of, 394 vector potential, 241, 397 vector product, 385 vector triple product, 388...



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... B Partial-Fraction Expansion 867 Appendix C Vector-Matrix Algebra 874 References 882... Appendix B, respectively. • A short summary of vector-matrix analysis is presented in... related to Laplace transforms and vector-matrix analysis are presented separately... variables with suitable weighting. State Vector. If n state variables are needed... of a vector x. Such a vector is called a state vector. A state vector is thus a vector that determines...).] Since the input vector u is r dimensional and the output vector y is m dimensional... a firstorder vector-matrix differential equation. If n elements of the vector are a set of state variables, then the vector-matrix...), see Problem A–2–6.] In terms of vector-matrix equations, Equation (2–36) and... output equations in the standard vector-matrix form, we obtain # x -a 1 x a B # 1R..., the dimensions of “num” vector and “den” vector become the same.An... is that the “num” vector and “den” vector can be directly added... not include “t” explicitly, the time vector is automatically determined. If the... the time vector t (that is, we let the time vector be determined... that x is an n-vector and y is an m-vector.) Similar to case 1, by... the time vector t is not specified (that is, the time vector t is... aa Case B. When the time vector t is specified: t = 0: Δt: tp; % Specify matrices... screen. The gain vector K is automatically determined. (The vector K contains all the...(A,B,C,D,K) use the user-supplied gain vector K. 290 Chapter 6 / Control Systems Analysis... where x y u A B C D = = = = = = = Consider the state vector (n-vector) output vector (m-vector) control vector (r-vector) state matrix (n*n matrix) control... vector at the resonant frequency vr to the magnitude of the vector... x y u A B C D 440 = = = = = = = Consider the state vector (n-vector) output vector (m-vector) control vector (r-vector) state matrix (n*n matrix) control...,w) uses the user-supplied frequency vector w. The vector w specifies the frequencies in...) is the vector sum of the unit vector and the vector G(jv)H(jv), 1+G(jv)H(jv) is identical to the vector... the vector OA is @GAjv1 B @ and the ! ! angle of the vector OA is / GAjv1 B. The vector PA , the vector from the... frequency vector w = logscale(d 1, d 2, n). MATLAB Program 7–19 uses the following frequency vector: w = logscale... a first-order vector-matrix differential equation. The use of vector-matrix notation... x is a state vector, then xˆ , where xˆ = Px is also a state vector, provided the... solve the vector-matrix differential equation # x = Ax (9–28) where x = n-vector A = n * n constant matrix... by # (9–40) x = Ax + Bu where x u A B = = = = n-vector r-vector n * n constant matrix n * r constant matrix By...(t) e-t - e-2t 9–5 SOME USEFUL RESULTS IN VECTOR-MATRIX ANALYSIS In this section... (s I - A)-1 = D 1 s 0 1 s(s + 2) T 1 s + 2 Section 9–5 / Some Useful Results in Vector-Matrix Analysis 671 Hence, eAt... Section 9–5 / Some Useful Results in Vector-Matrix Analysis 673 Substituting 0 for... where x u A B = = = = Consider the (9–51) state vector (n-vector) control signal (scalar) n * n matrix n * 1 matrix... # x = Ax + Bu (9–56) where x = state vector (n-vector) u = control vector (r-vector) A = n * n matrix B = n * r matrix If the... + Du (9–62) where x = state vector (n-vector) u = control vector (r-vector) y = output vector (m-vector) A = n * n matrix B = n * r matrix C = m * n matrix D = m * r matrix... (9–63) y = Cx where x y A C = = = = state vector (n-vector) output vector (m-vector) n * n matrix m * n matrix (9–64) The system... (9–63) and (9–64). The output vector y(t) is y(t) = CeAt x(0) Referring to Equation... + Bu y = Cx where x = state vector (n-vector) u = control vector (r-vector) y = output vector (m-vector) A = n * n matrix B = n * r matrix C = m * n matrix and... defined by # z = A*z + C*v n = B*z where z = state vector (n-vector) v = control vector (m-vector) n = output vector (r-vector) A* = conjugate transpose of A B* = conjugate... by # x = Ax + Bu where x = state vector (n-vector) u = control vector (r-vector) A = n * n constant matrix B = n * r constant matrix... impulse input u(t) as u(t) = d(t) w where w is a vector whose components are the magnitudes... ramp input u(t) as u(t) = t v where v is a vector whose components are magnitudes of...) y = Cx (9–115) where x = state vector (n-vector) u = control vector (r-vector) y = output vector (m-vector) (m Յ n) A = n * n matrix B = n * r matrix C = m * n matrix is... output controllability means that the vector Cx(0) spans the m-dimensional output...–34) where x = state vector of the plant (n-vector) Section 10–4 / Design of... a new (n+1)th-order error vector e(t) by e(t) = B x e(t) R = (n + 1)-vector je(t) Then Equation (10–38... the state vector and m is the dimension of the output vector. An... observed state vector. In many practical cases, the observed state vector ෂ x is... error vector will converge to zero for any initial error vector e(0). That... vector is asymptotically stable and is adequately fast, then any error vector...



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... and Matrices . . . . . . . . . . . . . . . . . . . A.1.1 Linear Vector Spaces . . . . . . . . . . . . . . . A.1.2 Matrix and Vector Algebra . . . . . . . . . . . . A.1.3 Rank and Linear... Operations . . . . . . . . . . . . B.2 Function and Vector Algorithms . . . . . . . . . . . . . . B.2.1 Elementary Functions . . . . . . . . . . . . . . . . B.2.2 Mulprec Vector Algorithms . . . . . . . . . . . . . B.2.3 Miscellaneous . . . . . . . . . . . . . . . . . . . . B.2.4 Using... by means of the matrix-vector equation c = diag (1, z−1 , . . . , z1−n ) P diag (1, z, . . . , zn... B are square n × n matrices and C = x ∈ R n×1 , a column vector of length n, then computing (AB... Numerical Calculations flops. The matrix-vector multiplication y = Ax, where A ∈ R n×n and x ∈ R n , requires... a nonsingular upper triangular matrix U ∈ R n×n and a vector b ∈ R n , the following algorithm computes x ∈ R n such... 1.2. LU Factorization. Given a matrix A = A(1) ∈ R n×n and a vector b = b(1) ∈ R n , the following algorithm computes the... in matrix-vector form we order the unknowns in a vector, u = (u1,1 , . . . , u1... a scalar function y(t) = f (c, t), where c ∈ R n is a parameter vector to be determined. There are... |2 )1/2 = (x T x)1/2 for the Euclidean length of a vector x (see Online Appendix A). We call... y ∈ R m be a vector of observations that is related to a parameter vector c ∈ R n by the..., i.e., E( ) = 0, V ( ) = σ 2 I. The parameter c is then a random vector which we want to estimate... the residual vector r = b − Ax is AT (b − Ax) = 0. (1.4.9) Proof. Let x be a vector for... conditions in vector form dy/dt = f (t, y), y(a) = c, (1.5.9) where y is a column vector that contains... x˜ − x and x˜ − x / x , respectively, where · denotes some vector norm (see Sec. A.3.3 in Online... matrix A˜ ∈ R 2n×2n and real vector z˜ ∈ R 2n defined by B −C x A˜ = , z˜ = . C B y It is... input data vector is transformed into an output data vector. By “operations... have used a vector norm · to measure the size of a vector; see Sec. A.4.3 in Online Appendix A. Common vector norms are... values |A| and |b| of a matrix A and vector b are interpreted componentwise |A|ij = (|aij.... The interval matrix-vector product [A][x] is the smallest interval vector, which contains... vector, caused by the fact that the image of an interval vector under a linear transformation in general is not an interval vector... x = ( 3/2 1/2 )T .) The magnitude of an interval vector or matrix is interpreted componentwise... f˜(g(z)) ˜ = f (g(z)) = h(z). Thus, (3.1.27) and its row vector implementations can be used if... column vector c = (c1 , c2 , . . . , cn )T can be viewed as a coordinate vector of... (xi )]ni,j =1 , (4.1.2) (4.1.3) T and the column vector f = (f (x1 ), f (x2 ), . . . , f (xn )) , then the... µj = 0 x −1/2 x j −1 dx and introduce the row vector µT = (µ1 , µ2 , . . . , µn ). We have that f (x) ≈ p(x) = ni=1 cj... be written I (f ) = a T f , where the coefficient vector is a = Vn−1 µ, i.e., a is the solution... ) = fi , i = 1 : n, is p(x) = (1, x, . . . , x n−1 )a, where the coefficient vector a satisfies the linear system V T a = f . To... linear system for the coefficient vector c becomes V T c = f , where f = (f (z1 ), f (z1 ), f (z1... functions space spanned by φ1 (x), φ2 (x), . . . , φn (x). In a vector space the distance of the... f = 0 (positivity), 2. λf = |λ| f (homogeneity), 3. f +g ≤ f + g (triangle inequality). A normed vector space is a metric space with... to a general vector space B some definitions for a finite-dimensional vector space given... vector space S: A = sup Af S2 . (4.5.5) f S1 Note that A depends on the vector... R = A˜ − A. For any positive , there exists a vector s ∈ S such that f −s = dist (f, s ) < inf dist... also a projection, because (I − P )(I − P ) = I − 2P + P 2 = I − P . Any vector x ∈ B can be written uniquely in... an auxiliary vector f˜ formed by extending the given data vector f either into... , j = 1 : N − 1, form a real data vector f and extend it to a vector f˜ with f˜0 = f˜N = 0 so that... , j = 0 : N , form a real data vector f and extend it to a vector f˜ so that ˜ f = T2N... extending the data vector f . For DST-2 the data vector fj , j = 0 : N − 1, is extended... , j = 1 : N , form a real data vector f and extend it to a vector f˜ so that ˜ f = −T2N... , j = 0 : N − 1, form a real data vector f and extend it to a vector f˜ so that ˜ f = T2N... Fourier matrix and uses matrix-vector multiplication. Algorithm 4.3. Fast Fourier Transform... the inverse FFT of the vector v + g, where gk = −w0cc , g n/2 k = 0 : n/2 − 1, = w0 [(2 − mod... degree n − 1. We introduce the row vector π(x) = [p1 (x), p1 (x), . . . , pn (x)] (5.3.29) containing... be summarized in the (row) vector equation xπ(x) = π(x)C + φn+1 (x)enT , C = (C, cn ). (5.3.36) Here... in R r+s consisting of points (using vector notations) (x, y) such that x ∈ C and y ∈ D. dqbjvol1... be uniquely expressed by the vector equation p = θ1 p1 + θ2 p2 + θ3 p3 , θ1 + θ2 + θ3 = 1. (5.4.15... vector-valued sequences. Then absolute values in (6.1.22) are replaced by a vector...



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................................................. 3-3 Supervisor Stack Pointer .......................................................................... 3-4 Status Register ......................................................................................... 3-4 Vector Base Register................................................................................ 3-4 Alternate Function Code... of {i,d}mem_{read,write}_{b,w,l} .............................................C-25 Vector Table and M68060SP Relationship ......................................................C-28... vs. IPLx Signals......................................................................... 7-74 Exception Vector Assignments .......................................................................... 8-4 Interrupt Levels and Mask... ..................... D-1 M68000 Family Instruction Set.......................................................................... D-6 Exception Vector Assignments for the M68000 Family... processing includes fetching the exception vector, stacking operations, and refilling the... vector base register (VBR) contains the base address of the exception vector... exception vector table in memory. The displacement of an exception vector is... 6-10. Floating-Point Exception Vectors Vector Vector Offset Frame Program Assignment Number... exception corresponds to vector number 11 and shares this vector with the... exception vector number 11 for the unimplemented F-line instruction exception vector, fetches..., and vector number 48 is generated to access the BSUN exception vector. The BSUN entry in the processor’s vector table points... a vector number, it requests an automatically generated vector (autovector). Instead of placing a vector... spurious interrupt vector number 24 ($18) instead of the interrupt vector number... VECTOR GIVEN IN D7–D0 3) IF BUS ERROR TERMINATION, USE VECTOR 24... TERMINATION TAKE EXCEPTION USING VECTOR 4 (ILLEGAL INSTRUCTION EXCEPTION VECTOR) AFTER COMPLETION OF... STACK POINTER FROM VECTOR TABLE 1) FETCH PROGRAM COUNTER FROM VECTOR TABLE 2) PREFETCH...) DETERMINE VECTOR NUMBER SAVE CONTENTS TO STACK FRAME (SEE NOTE) OTHERWISE S➧1 T➧0 VECTOR..., internal logic provides the vector number. This vector number is used in... address of the exception vector. Throughout this section, vector numbers are given... 0 STATUS REGISTER PROGRAM COUNTER FORMAT VECTOR OFFSET ADDITIONAL PROCESSOR STATE INFORMATION... multiplies the vector number by four to determine the exception vector offset... address of the exception vector table, the exception vector table can be... supply vector numbers for some exceptions. External devices that cannot supply vector... to automatically generate a vector number. Table 8-1. Exception Vector Assignments Vector Number(s) 0 1 2 3 4 5 6 7 8 9 10 11... exception vector number 2 for the access error vector. It saves the vector offset...; and an odd vector table entry (e.g., an odd reset vector). A stack frame... a vector number according to the instruction being executed. Vector 5 is for DIVx, vector 6 is for CHK, and vector 7 is... vector number is 32 plus n. The stack frame saves the trap vector... exception corresponds to vector number 11 and shares this vector with the... exception corresponds to vector number 11 and shares this vector with the... illegal instruction exception corresponds to vector number 4. An illegal instruction exception... address contained in the exception vector. 8.2.5 Privilege Violation Exception To provide.... The processor generates vector number 8, saves the privilege violation vector offset, the... vector number 9 for the trace exception and saves the trace exception vector... the spurious interrupt vector number, 24. Once the vector number is obtained... usually returns the vector number for the uninitialized interrupt vector, 15. 8.2.10... FETCH VECTOR FROM INTERRUPTING DEVICE BUS ERROR IF NO VECTOR # SPURIOUS INTERRUPT VECTOR #24 AUTOVECTOR #25–#31 VECTOR OFFSET, PC... $0 FETCH VECTOR #0 OTHERWISE BUS ERROR VECTOR #0 ➧ SP (DOUBLE BUS FAULT) FETCH VECTOR #1 OTHERWISE BUS ERROR VECTOR #1 ➧ PC... Exception Types • Unimplemented FloatingPoint Instruction VECTOR OFFSET ADDRESS • Address Error SIX... the exception type/vector offset equal to $30. The vector pointed to..., and vector offset equal to $24. The trace exception vector pointed to... priority list. Its exception vector number is 12 (vector offset = $30), its... the unimplemented integer instruction exception vector table entry typically points directly... exception vector number fifty-four for the SNAN exception and vector number... to prepare the exception vector table. The appropriate vector table entries must... the vector table to the M68060SP. OR x_060SP: os_code: VECTOR TABLE VECTOR TABLE jmp os_done jmp x_060SP VECTOR ENTRY VECTOR ENTRY OS_done... Table D-3. Exception Vector Assignments for the M68000 Family D-10 Vector Number(s) 0 1 2 3 4 5 6 7 8 9 10...



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... 1.8.2 Circles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 M¨ obius Transformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.9 2 Vector Algebra 11 2.0 Why Study This... Vector Spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.3.1 Algebraic definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.3.2 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.3.3 Properties of Vector Spaces... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 Vector Product . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.5.1 Properties of the vector product . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2.5.2 Vector area of... 3D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 2.8.2 Direction cosines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 Vector Component Identities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2.10 Higher... triple product . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 2.11.10 Vector triple product . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 2.11.11... Schwarz’s inequality (Unlectured) . . . . . . . . . . . . . . . . . . . . 35 2.12 Vector Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 2.13 Lines, Planes... matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 5.3.3 Transformation law for vector components . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 5.3.4 Transformation law for... space is called a vector. Geometric representation. We will represent a vector → v as a line.... • A vector, e.g. force F, that is a function of position (x, y, z) is referred to as a vector... by r. • The position vector is an example of a vector field. (ii) Every... a = 0, where 0 is the null vector or zero vector.12 For all vectors... a unit vector since |a| = a . |a| (2.10) 1 1 |a| = |a| = 1 . |a| |a| A is often used to indicate a unit vector, but... null or zero vector, such that for all a ∈ V a + 0 = a, (2.12c) i.e. vector addition has... redistributed. a + (b + c) = (a + b) + c ; 2.3.3 Properties of Vector Spaces (Unlectured) (i) The zero vector 0 is unique. For... multiplication with the zero vector yields the zero vector. For all λ ∈ R, λ0 = 0. To... vector since λ0 + λa = λ(0 + a) = λa . Next we appeal to the fact that the zero vector... a vector with itself is zero [if and] only if the vector is the zero vector, i.e. SP(iv) Mathematical..., i.e. the only vector of zero norm should be the zero vector, i.e. |a| = 0 Mathematical.../or redistributed. |a · b| 2.5 Vector Product Definition. From a geometric standpoint, the vector product a × b of an ordered pair a, b is a vector such that... 4/08 2.5.1 Properties of the vector product (i) The vector product is anti-commutative... rule): a × b = −b × a . (2.31a) (ii) The vector product of a vector with itself is zero... the vector product a × (λb) = λ (a × b) . (2.31c) (v) For given a and b, suppose that the vector b (a, b) is... vector along OX , be the unit vector along OY , be the unit vector... (x, y, z), then the position vector → OP = r = x i + y j + z k , i.e. r = (x, y, z) . (2.49) (iii) Every vector in 2D/3D... a number of vector identities for components (and one true vector identity). Addition.... with vector addition, scalar multiplication, the zero vector and the inverse vector defined... suffix. Example: the position vector. The position vector r can be written as... . (2.82) Vector triple product Using suffix notation for the vector triple product... − xj yi ) 0. 2.12 Vector Equations When presented with a vector equation one approach... vector equations. 2.13.1 Lines Consider the line through a point A parallel to a vector t, and let P be a point on the line. Then the vector equation... of a vector space V is called a subspace of V if U is a vector space under the same operations (i.e. vector addition and scalar... a vector space, and hence (i) and (ii) hold from the definition of a vector... bold u denoting a vector, italic ui denoting a component of a vector, and sans serif... of a column matrix of vector components, i.e. a column vector, an accepted convention is to use the standard notation for a vector... vector with m rows) Am2 ... xn Amn m × n matrix (m rows, n columns) n × 1 matrix (column vector... x =  .  is a column vector, xT = x1  ..  x2 ... xn is a row vector. xn Remark..., x is a n × 1 column vector of unknowns, and d is a given m × 1 column vector. 4.3.3 Equivalent systems... Q = P−1 . 5.3.3 (5.18) Transformation law for vector components Consider a vector u, and suppose that in... operator that projects the vector w orthogonally onto the vector v by (cf. (3.10b... vector of Cn to a non-negative multiple of the j th basis vector...