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1. Formulation and background. The problem indicated in the title is one of the most important hitherto unsolved problems of the calculus of variations, namely: Given any family of 2" curves (paths) in («+1)-dimensional ü —1, • • • ,n), as represented by a system of differential equations (Li) y'! = F{(x, yj, yj) to determine whether these curves can be identified of some variation problem (1.2) space (x, y,), (l-i, with the totality of extremals ^ and in the affirmative case to find all the corresponding functions The present paper solves this problem for the most important esting case of 3-dimensional space (n = 2), where the given family a>4 curves defined by differential equations of the form (1.3) y" = F(x, y,z, y',z'), and the variation (1.4) •• • ,*); problem sought and interconsists of z" - G(x, y, z, y', z'), for is of the form J 4>(x, z, y', z')dx = min. y, Our essential results and methods have already been published in two preliminary notes(1). Basically, our procedure consists in an application of the Riquier theory of systems of partial differential equations to a certain linear differential system @ on which the inverse problem can be made to depend. This differential system has already appeared—derived in a different way—in the interesting work, of little more than a decade ago, by D. R. Davis on the inverse problem^); but, as he stated, its general solution—even existence-theoretically— presented difficulties which he could not overcome. Presented to the Society, January 1, 1941; received by the editors March 13, 1940. Q) Numbers 8 and 9 of the list of references at the end of §2. (2) See numbers 6 and 7 of the list of references at the end of §2.

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Calculus problems, Education,

The term boundary value problem is applied to the question of determining whether a given system of differential equations (in general, a given system of functional equations) has one or more solutions satisfying certain prescribed end or boundary conditions; and, if so, the determination of the character of these solutions and how their character changes when the differential equations or boundary conditions change. This address is restricted to the discussion of a class of linear boundary problems which are intimately associated with the calculus of variations. These boundary value problems have been used in establishing sufficient conditions, especially for the more complicated problems of the calculus of variations. On the other hand, the principles and theorems of the calculus of variations have been of extreme significance in the advancement of the theory of such boundary value problems. In fact, the calculus of variations has served to unify a certain class of boundary problems much larger than that seemingly represented by the problem that we shall first formulate. In view of the rather extensive interest and study of these problems within recent years, ...

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Calculus problems, Education,

Pololu 3pi Robot Simplified Schematic Diagram J20 + VBAT 1 2 J7 reverse protection Q1 2 1 VIN POWER R4a 1k R4b 1k AVCC B2 2xAAA U3 PB0 PB1 PB4 PB5 32 2 11 PD6 PD5 PB3 PD3 1 3 PD2 (INT0) PD4 (XCK/T0) PD7 (AIN1) 7 8 PC1 R13 220 VCC 19 22 U5 C23 2.2 nF PC2 R14 ADC6 ADC7 220 J4 VCC 29 PC6 VCC PC6 (RESET) U4 C22 2.2 nF VCC R15 10k R16 10k microcontroller U6 C24 2.2 nF 2 1 ATmega168 PD0 PD1 23 24 25 26 27 28 ADC6 ADC7 33 GND 21 GND 5 GND 3 GND 2 Y1 20 MHz 220 VCC PC0 (ADC0) PC1 (ADC1) PC2 (ADC2) PC3 (ADC3) PC4 (ADC4/SDA) PC5 (ADC5/SCL) PB6 (XTAL1/TOSC1) PB7 (XTAL2/TOSC2) VBOOST PC0 R12 30 31 PD0 (RXD) PD1 (TXD) PD6 (OC0A/AIN0) PD5 (OC0B/T1) PB3 (MOSI/OC2A) PD3 (OC2B/INT1) VCC 18 20 AVCC AREF C18 0.1 uF C21 2.2 nF 6 4 VCC VCC PB0 (CLKO/ICP1) PB1 (OC1A) PB4 (MISO) PB5 (SCK) 10 9 15 1 D6 5V zener VCC AVCC PB2 (SS/OC1B) 12 13 16 17 PD2 PD4 PD7 BUZZER D1b T1 D1a BLUE GND + 14 D5 BLUE VOUT pushbutton power circuit BZ1 L2 10 uH GND VIN VOUT 5.0 V linear regulator R33 1k GND B1 2xAAA BTN2 BTN1 + VIN VOUT 9.25 V boost switching regulator SW1 CHARGE VCC VBOOST PC3 R17 220 VCC PB4 PB5 PC6 LCD1 Vss VDD Vo RS E DB0 DB1 DB2 DB3 DB4 DB5 DB6 2 4 6 220 PB3 AVRISP 2 3 4 PB0 6 PD4 VCC PD7 R25a 1k J5 R26b 1k PD1 D4a GREEN R21 220 R23 47k R26a 1k D4b T1 PC5 LEDON Q4 7 8 D3a RED R22 9 D3b T1 10k VCC VBOOST VCC U9 10 11 PB4 13 PB5 14 PD7 AIN1 AIN2 PWMA 17 16 15 BIN1 BIN2 PWMB PC6 19 VM1 VM2 VM3

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Circuit schematic, Hobbies,

Optimal Operation of Photovoltaic Power Conversion Systems: Maximum Power Point Tracking Approach Brief summary of the tutorial contents: As the quantum of available fossil fuels are decreasing day –by- day the world is going towards the use of renewable energy sources either to supplement the existing utility supply are replace completely to mitigate the global warming related problems. Photovoltaic (PV) power generation is one among these renewable sources and has tremendous potential and going to play a key role in the future power generation systems. In view of this it is now becoming essential to look into various aspects of the PV energy conversion into electric energy of form that is suitable to integrate to the conventional utility systems and to drive the versatile electric loads. As the solar radiation/ insolation is changing continuously, right from morning to evening, and hence it’s power output also changes. Further, the photovoltaic cells/ modules exhibits non-linear voltampere characteristics and hence their power output also depends on the type of load connected to it. In order to extract the available power from the solar modules and to improve the overall...

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Power Point 2013 tutorial, Software,

Deep Learning Tutorial ICML, Atlanta, 2013-06-16 Yann LeCun Center for Data Science & Courant Institute, NYU yann@cs.nyu.edu http://yann.lecun.com Marc'Aurelio Ranzato Google ranzato@google.com http://www.cs.toronto.edu/~ranzato Y LeCun MA Ranzato Deep Learning = Learning Representations/Features The traditional model of pattern recognition (since the late 50's) Fixed/engineered features (or fixed kernel) + trainable classifier hand-crafted “Simple” Trainable Feature Extractor Classifier End-to-end learning / Feature learning / Deep learning Trainable features (or kernel) + trainable classifier Trainable Trainable Feature Extractor Classifier Y LeCun MA Ranzato This Basic Model has not evolved much since the 50's Built at Cornell in 1960 The Perceptron was a linear classifier on top of a simple feature extractor The vast majority of practical applications of ML today use glorified linear classifiers or glorified template matching. Designing a feature extractor requires considerable efforts by experts.

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Power Point 2013 tutorial, Software,

SOAL DAN SOLUSI SIAP SBMPTN 2013 MATEMATIKA IPA 1. Jika 0 b a dan a2 b2 4ab maka a+b a-b 2. = 2 (A) (B) (C) (C) 2 (D) 3 3 (D) 5 (E) 20 3 (E) 4 cos 77o cos 33o sin77o sin33o ... . 6. Jika persamaan x2 4x k 1 0 mempunyai akar-akar real dan , maka (D) cos 20o (E) sin 20o (A) cos 20o (B) cos 70o (C) sin 70o 3. Dari 10 pasangan suami istri akan dibentuk tim beranggotakan 6 orang terdiri atas 2 pria dan 4 wanita dengan ketentuan tak boleh ada pasangan suami istri. Banyaknya tim yang dapat dibentuk adalah (A) 3150 (D) 56021 (B) 6300 (E) 141120 (C) 12300 nilai k yang memenuhi (A) (B) (C) (D) (E) (B) (C) (D) 32 3 9 (E) 25 3 16 3 5. Daerah D1 dibatasi oleh parabola y x2 , garis y 4 , dan garis x = c dan daerah D2 dibatasi oleh parabola y = x2, garis x = c, dan sumbu x. Jika luas D1 = luas D2, maka luas siku empat yang dibatasi oleh sumbu x, sumbu y, garis y = 4 dan garis x = c adalah y = x2 y 4 y 3 3(x 3) (B) y 3 3(x 3) (E) y 33 3(x 3) (C) y 33 3(x 3) 8. Jika 36x 2 6x 1 32 0 akar x1 dan x 2 . x1 x2 Jika x1 x2 , maka 9. 1 cos 2 4x …. x 0 1 cos 6x 8 (A) 9 5 (B) 6 1 (C) 3 lim (D) (E) (B) 4 3 8 3 (B) 2 14 dan c // a Jika 14 7 3 ˆ a 3ˆ ˆ 2k i j c b 28 , maka | c | (A) 5 6 ˆ b 2 ˆ 5 ˆ 2k . i j (A) …. (D) 3log 2 (E) 2log3 (A) 1,5 (B) 2 (C) 2,5 c adalah … 5 k 1 atau k 3 5 k 1 atau k 3 k 1 atau 3 k 5 k 1 atau 3 k 5 k 5 atau 1 k 3 10. Diketahui x 1 1 2 f(x) (x 3) 7. Suku banyak dibagi x3 3x 33 dan memberikan hasil bagi sisa 3 . Garis g menyinggung kurva y f(x) di titik berabsis 3, maka persamaan garis g adalah …. (A) y 3 3(x 3) (D) 4. Suatu kerucut memiliki panjang jari-jari r dan tinggi t, Jika r t 6 , maka nilai maksimum volum kerucut adalah … (A) 12 16 3 dan = …. (D) 4 14 (E) 5 14 (C) 3 14 Halaman 1 dari 14 halaman SOAL DAN SOLUSI SIAP SBMPTN 2013 y kx

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Contoh soal snmptn 2013, Education,

Analisis Bedah Soal SBMPTN 2013 SELEKSI BERSAMA MASUK PERGURUAN TINGGI NEGERI Disertai TRIK SUPERKILAT dan LOGIKA PRAKTIS Kimia IPA Disusun Oleh : Pak Anang Roy Handerson Kumpulan SMART SOLUTION dan TRIK SUPERKILAT Analisis Bedah Soal SBMPTN 2013 Kimia IPA By Pak Anang (http://pak-anang.blogspot.com) Berikut ini adalah analisis bedah soal SBMPTN untuk materi Kimia IPA. Soal-soal berikut ini dikompilasikan dari SNMPTN empat tahun terakhir, yaitu SNMPTN 2009, 2010, 2011 dan 2012. Soal-soal berikut disusun berdasarkan ruang lingkup mata pelajaran Kimia SMA, dan juga disertakan tabel perbandingan distribusi soal dan topik materi Kimia yang keluar dalam SNMPTN empat tahun terakhir. Dari tabel tersebut diharapkan bisa ditarik kesimpulan bagaimana prediksi soal SBMPTN yang akan keluar pada SBMPTN 2013 nanti. No Ruang Lingkup Struktur Atom Sistem Periodik Unsur Ikatan Kimia Asam Basa Bronsted-Lowry Ph Asam Basa Titrasi Asam Basa Larutan Penyangga Hidrolisis Garam Tetapan Hasil Kali Kelarutan (Ksp) Reaksi Redoks Sel Volta Sel Elektrolisis Hukum Dasar Kimia (Hukum Proust) Persamaan Reaksi dan Konsep Mol Hitungan Kimia Sifat Koligatif Koloid Kimia Unsur Tata Nama Senyawa Karbon dan Isomer Reaksi-reaksi Senyawa Karbon Identifikasi Senyawa Karbon Benzena dan Turunannya Termokimia Laju Reaksi Kesetimbangan Kimia JUMLAH SOAL SNMPTN 2009 SNMPTN 2010 SNMPTN 2011 SNMPTN 2012 SBMPTN 2013 Bimbel SBMPTN 2013 Kimia IPA by Pak Anang (http://pak-anang.blogspot.com) Halaman 1 1. Struktur Atom 1. (SNMPTN 2010) Konfigurasi ion besi (III), 26 Fe3+ , mempunyai elektron tidak berpasangan sebanyak .... A. Dua B. Tiga C. Empat D. Lima E. Enam

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Contoh soal snmptn 2013, Education,

Electric Fireplaces BUI LT- I N | HD L I N E A R Just plug in one of our electric fireplaces for instant ambience in any room. All of our Built-in and HD Linear models are CSA tested for safety, fit any room style, and are easy to use. They are cool to the touch but will add warmth to any space. Columbia Corner Surround with Arched Rectangle built-in fireplace front shown in Cherry Stain Finish. A division of the Outdoor GreatRoom Company Electric LINEAR Cool to the touch and warm to the eye This hot fireplace feels cool to the touch, yet, puts out heat when you want it. It hangs like a piece of art – easy to install and sets up in minutes. Place it on any interior wall with an electric outlet. Just plug it in and have a beautiful fire instantly. Model GE-58 Select your ideal fire. Fireplace Features Choose from a large range of options – from fire intensity, to backlighting color, to heat range and more! • Ambient backlighting comes standard on all models. • High efficiency LED on fire and backlighting— Uses only 15 watts. • Operating costs as low as a penny per day with flame and backlighting, and 9-18 cents per hour with the heater on.

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Electric fireplaces, Manuals,

APPLICATIONS The LM1949 linear integrated circuit serves as an excellent control of fuel injector drive circuitry in modern automotive systems. The IC is designed to control an external power NPN Darlington transistor that drives the high current injector solenoid. The current required to open a solenoid is several times greater than the current necessary to merely hold it open; therefore, the LM1949, by directly sensing the actual solenoid current, initially saturates the driver until the “peak” injector current is four times that of the idle or “holding” current (Figure 19–Figure 22). This guarantees opening of the injector. The current is then automatically reduced to the sufficient holding level for the duration of the input pulse. In this way, the total power consumed by the system is dramatically reduced. Also, a higher degree of correlation of fuel to the input voltage pulse (or duty cycle) is achieved, since opening and closing delays of the solenoid will be reduced.

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Fuel injector, Automotive,

Product Folder Sample & Buy Technical Documents Support & Community Tools & Software LM35 www.ti.com SNIS159D – AUGUST 1999 – REVISED OCTOBER 2013 LM35 Precision Centigrade Temperature Sensors FEATURES DESCRIPTION The LM35 series are precision integrated-circuit temperature sensors, with an output voltage linearly proportional to the Centigrade temperature. Thus the LM35 has an advantage over linear temperature sensors calibrated in ° Kelvin, as the user is not required to subtract a large constant voltage from the output to obtain convenient Centigrade scaling. The LM35 does not require any external calibration or trimming to provide typical accuracies of ±¼°C at room temperature and ±¾°C over a full −55°C to +150°C temperature range. Low cost is assured by trimming and calibration at the wafer level. The low output impedance, linear output, and precise inherent calibration of the LM35 make interfacing to readout or control circuitry especially easy. The device is used with single power supplies, or with plus and minus supplies. As the LM35 draws only 60 μA from the supply, it has very low self-heating of less than 0.1°C in still air. The LM35 is rated to operate over a −55°C to +150°C temperature range, while the LM35C is rated for a −40°C to +110°C range (−10° with improved accuracy). The LM35 series is available packaged in hermetic TO transistor packages, while the LM35C, LM35CA, and LM35D are also available in the plastic TO-92 transistor package. The LM35D is also available in an 8-lead surface-mount smalloutline package and a plastic TO-220 package.

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Sensor datasheet, Hardware,