text:
## Journal of Mathematics and Computer Science. JMCS

 Short Title: J. Math. Comput. Sci., JMCS Publisher: International Scientific Research Publications (ISRP), Skudai, Johor; International Scientific Research Publications (ISRP), Amol ISSN: 2008-949X/e Online: http://www.isr-publications.com/jmcs Comments: No longer indexed; Published electronic only as of Vol. 1 (2010). This journal is available open access.
 Documents Indexed: 84 Publications (2017–2018) References Indexed: 84 Publications with 1,928 References.
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### Latest Issues

 18, No. 4 (2018) 18, No. 3 (2018) 18, No. 2 (2018) 18, No. 1 (2018) 17, No. 4 (2017) 17, No. 3 (2017) 17, No. 2 (2017) 17, No. 1 (2017)
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### Fields

 21 General topology (54-XX) 18 Ordinary differential equations (34-XX) 13 Operator theory (47-XX) 13 Numerical analysis (65-XX) 10 Biology and other natural sciences (92-XX) 8 Partial differential equations (35-XX) 6 Real functions (26-XX) 6 Dynamical systems and ergodic theory (37-XX) 4 Combinatorics (05-XX) 4 Functions of a complex variable (30-XX) 4 Fluid mechanics (76-XX) 3 Special functions (33-XX) 3 Systems theory; control (93-XX) 2 Number theory (11-XX) 2 Linear and multilinear algebra; matrix theory (15-XX) 2 Group theory and generalizations (20-XX) 2 Integral equations (45-XX) 2 Differential geometry (53-XX) 2 Operations research, mathematical programming (90-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Potential theory (31-XX) 1 Approximations and expansions (41-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Functional analysis (46-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Mechanics of particles and systems (70-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Information and communication theory, circuits (94-XX)

### Citations contained in zbMATH Open

43 Publications have been cited 120 times in 111 Documents Cited by Year
Stability analysis of general humoral immunity HIV dynamics models with discrete delays and HAART. Zbl 1427.92060
Elaiw, A. M.; Elnahary, E. Kh.
2018
Another class of warped product CR-submanifolds in Kenmotsu manifolds. Zbl 1427.53056
Uddin, Siraj; Alghanemi, Azeb; Naghi, Monia Fouad; Al-Solamy, Falleh Rijaullah
2017
Exponential form for Lyapunov function and stability analysis of the fractional differential equations. Zbl 1427.34014
Sene, Ndolane
2018
Strong convergence of modified viscosity implicit approximation methods for asymptotically nonexpansive mappings in complete CAT(0) spaces. Zbl 1427.47023
Pakkaranang, Nuttapol; Kumam, Poom; Cho, Yeol Je; Saipara, Plern; Padcharoen, Anantachai; Khaofong, Chatuphol
2017
Numerical analysis of fractional order pine wilt disease model with bilinear incident rate. Zbl 1427.92090
2017
Generalization of khan fixed point theorem. Zbl 1427.54063
Piri, Hossein; Rahrovi, Samira; Kumam, Poom
2017
Jessen type functionals and exponential convexity. Zbl 1427.26003
Naeem, Rishi; Anwar, Matloob
2017
Fixed point results for multivalued mappings on a sequence in a closed ball with applications. Zbl 1427.54067
2017
Lyapunov functions to Caputo reaction-diffusion fractional neural networks with time-varying delays. Zbl 1427.34104
Agarwal, R. P.; Hristova, S.; O’Regan, Donal
2018
Oscillation of third-order quasilinear neutral dynamic equations on time scales with distributed deviating arguments. Zbl 1427.34094
2017
Dynamic behaviors of a nonautonomous modified Leslie-Gower predator-prey model with Holling-type III schemes and a prey refuge. Zbl 1427.92071
Chen, Fengde; Lin, Qiaoxia; Xie, Xiangdong; Xue, Yalong
2017
Results on soft extremally disconnectedness of soft topological spaces. Zbl 1427.54039
2017
New computational method for solving fractional Riccati equation. Zbl 1427.35310
2017
Asymptotic behavior of third-order neutral differential equations with distributed deviating arguments. Zbl 1427.34095
Wang, Haixia; Chen, Guojuan; Jiang, Ying; Jiang, Cuimei; Li, Tongxing
2017
New type of multivalued F-contraction involving fixed points on closed ball. Zbl 1427.54049
2017
Integral inequalities via generalized convex functions. Zbl 1427.26007
Noor, Muhammad Aslam; Noor, Khalida Inayat; Safdar, Farhat
2017
New Hermite-Hadamard type inequalities for product of different convex functions involving certain fractional integral operators. Zbl 1427.26008
Set, Erhan; Choi, Junesang; Celik, Barıs
2018
Solving fuzzy matrix games through a ranking value function method. Zbl 1427.91007
Qiu, Dong; Xing, Yumei; Chen, Shuqiao
2018
Fuzzy fixed point results of generalized almost F-contraction. Zbl 1427.54042
2018
Explicit solution for some generalized fluids in laminar flow with slip boundary conditions. Zbl 1427.76021
2018
On upper and lower $$(\tau_1,\tau_2)$$-precontinuous multifunctions. Zbl 1427.54030
Boonpok, Chawalit; Viriyapong, Chokchai; Thongmoon, Montri
2018
A reliable analytic study for higher-dimensional telegraph equation. Zbl 1427.65317
2018
Two improved classes of Broyden’s methods for solving nonlinear systems of equations. Zbl 1427.65073
Al-Towaiq, Mohammad H.; Abu hour, Yousef S.
2017
$$\mathsf{F}$$-contraction on asymmetric metric spaces. Zbl 1427.54064
Piri, Hossein; Rahrovi, Samira; Marasi, Hamidreza; Kumam, Poom
2017
Using differential transform method and Padé approximation for solving MHD three-dimensional Casson fluid flow past a porous linearly stretching sheet. Zbl 1427.76277
Yousif, Majeed A.; Mahmood, Bewaar A.; Rashidi, M. M.
2017
The Chebyshev collocation solution of the time fractional coupled Burgers’ equation. Zbl 1427.65276
2017
Some fixed point theorems of self-generalized contractions in partially ordered G-metric spaces. Zbl 1427.54041
2017
The effect of perturbations on the circular restricted four-body problem with variable masses. Zbl 1427.70030
Ansari, Abdullah A.; Alhussain, Ziyad A.; Kellil, Rabah
2017
Proximal forward-backward splitting method for zeros of sum accretive operators for a fixed point set and inverse problems. Zbl 1427.47024
Sitthithakerngkiet, K.; Promluang, K.; Thounthong, P.; Kumam, P.
2017
Classification of a new subclass of $$\xi^{(\mathrm{as})}$$-QSO and its dynamics. Zbl 1427.92081
Qaralleh, Izzat
2017
A note on the $$p$$-adic gamma function and $$q$$-Changhee polynomials. Zbl 1427.11136
Havare, Özge Çolakoğlu; Menken, Hamza
2018
A fixed point theorem on multiplicative metric space with integral-type inequality. Zbl 1427.54053
Khan, Aziz; Khan, Hasib; Baleanu, Dumitru; Jafari, Hossein; Khan, Tahir Saeed; Alqurashi, Maysaa
2018
Stability of switched stochastic nonlinear systems by an improved average dwell time method. Zbl 1427.93259
Guo, Rongwei; Sun, Yuangong; Zhao, Ping
2018
Fixed point theorems for generalized $$\alpha$$-$$\psi$$ type contractive mappings in b-metric spaces and applications. Zbl 1427.54072
Wu, Xianbing; Zhao, Leina
2018
Some new Hermite-Hadamard type inequalities for $$h$$-convex functions via quantum integral on finite intervals. Zbl 1427.26010
Yang, Limin; Yang, Ruiyun
2018
A Grüss type inequality for two weighted functions. Zbl 1427.26006
Choi, Junesang
2018
On $$(\alpha, p)$$-convex contraction and asymptotic regularity. Zbl 1427.54054
Khan, M. S.; Singh, Y. Mahendra; Maniu, Georgeta; Postolache, Mihai
2018
Dynamical analysis on prey refuge in a predator-prey model with square root functional response. Zbl 1427.92072
Chen, Liujuan; Wang, Yiqin
2018
Multi-valued tripled fixed point results via CLR property in metric spaces with application. Zbl 1427.54068
2018
Bitopological spaces on undirected graphs. Zbl 1427.05059
2018
Bounded and sequential $$\sigma$$-approximate amenability of Banach algebras. Zbl 1427.46033
2018
$$F_{m}$$-contractive and $$F_{m}$$-expanding mappings in $$M$$-metric spaces. Zbl 1427.54056
Mlaiki, Nabil
2018
Some new fixed point theorems for compatible mappings in partial metric spaces. Zbl 1427.54043
Alnaser, Laila A.; Lateef, Durdana; Ahmad, Jamshaid
2018
Stability analysis of general humoral immunity HIV dynamics models with discrete delays and HAART. Zbl 1427.92060
Elaiw, A. M.; Elnahary, E. Kh.
2018
Exponential form for Lyapunov function and stability analysis of the fractional differential equations. Zbl 1427.34014
Sene, Ndolane
2018
Lyapunov functions to Caputo reaction-diffusion fractional neural networks with time-varying delays. Zbl 1427.34104
Agarwal, R. P.; Hristova, S.; O’Regan, Donal
2018
New Hermite-Hadamard type inequalities for product of different convex functions involving certain fractional integral operators. Zbl 1427.26008
Set, Erhan; Choi, Junesang; Celik, Barıs
2018
Solving fuzzy matrix games through a ranking value function method. Zbl 1427.91007
Qiu, Dong; Xing, Yumei; Chen, Shuqiao
2018
Fuzzy fixed point results of generalized almost F-contraction. Zbl 1427.54042
2018
Explicit solution for some generalized fluids in laminar flow with slip boundary conditions. Zbl 1427.76021
2018
On upper and lower $$(\tau_1,\tau_2)$$-precontinuous multifunctions. Zbl 1427.54030
Boonpok, Chawalit; Viriyapong, Chokchai; Thongmoon, Montri
2018
A reliable analytic study for higher-dimensional telegraph equation. Zbl 1427.65317
2018
A note on the $$p$$-adic gamma function and $$q$$-Changhee polynomials. Zbl 1427.11136
Havare, Özge Çolakoğlu; Menken, Hamza
2018
A fixed point theorem on multiplicative metric space with integral-type inequality. Zbl 1427.54053
Khan, Aziz; Khan, Hasib; Baleanu, Dumitru; Jafari, Hossein; Khan, Tahir Saeed; Alqurashi, Maysaa
2018
Stability of switched stochastic nonlinear systems by an improved average dwell time method. Zbl 1427.93259
Guo, Rongwei; Sun, Yuangong; Zhao, Ping
2018
Fixed point theorems for generalized $$\alpha$$-$$\psi$$ type contractive mappings in b-metric spaces and applications. Zbl 1427.54072
Wu, Xianbing; Zhao, Leina
2018
Some new Hermite-Hadamard type inequalities for $$h$$-convex functions via quantum integral on finite intervals. Zbl 1427.26010
Yang, Limin; Yang, Ruiyun
2018
A Grüss type inequality for two weighted functions. Zbl 1427.26006
Choi, Junesang
2018
On $$(\alpha, p)$$-convex contraction and asymptotic regularity. Zbl 1427.54054
Khan, M. S.; Singh, Y. Mahendra; Maniu, Georgeta; Postolache, Mihai
2018
Dynamical analysis on prey refuge in a predator-prey model with square root functional response. Zbl 1427.92072
Chen, Liujuan; Wang, Yiqin
2018
Multi-valued tripled fixed point results via CLR property in metric spaces with application. Zbl 1427.54068
2018
Bitopological spaces on undirected graphs. Zbl 1427.05059
2018
Bounded and sequential $$\sigma$$-approximate amenability of Banach algebras. Zbl 1427.46033
2018
$$F_{m}$$-contractive and $$F_{m}$$-expanding mappings in $$M$$-metric spaces. Zbl 1427.54056
Mlaiki, Nabil
2018
Some new fixed point theorems for compatible mappings in partial metric spaces. Zbl 1427.54043
Alnaser, Laila A.; Lateef, Durdana; Ahmad, Jamshaid
2018
Another class of warped product CR-submanifolds in Kenmotsu manifolds. Zbl 1427.53056
Uddin, Siraj; Alghanemi, Azeb; Naghi, Monia Fouad; Al-Solamy, Falleh Rijaullah
2017
Strong convergence of modified viscosity implicit approximation methods for asymptotically nonexpansive mappings in complete CAT(0) spaces. Zbl 1427.47023
Pakkaranang, Nuttapol; Kumam, Poom; Cho, Yeol Je; Saipara, Plern; Padcharoen, Anantachai; Khaofong, Chatuphol
2017
Numerical analysis of fractional order pine wilt disease model with bilinear incident rate. Zbl 1427.92090
2017
Generalization of khan fixed point theorem. Zbl 1427.54063
Piri, Hossein; Rahrovi, Samira; Kumam, Poom
2017
Jessen type functionals and exponential convexity. Zbl 1427.26003
Naeem, Rishi; Anwar, Matloob
2017
Fixed point results for multivalued mappings on a sequence in a closed ball with applications. Zbl 1427.54067
2017
Oscillation of third-order quasilinear neutral dynamic equations on time scales with distributed deviating arguments. Zbl 1427.34094
2017
Dynamic behaviors of a nonautonomous modified Leslie-Gower predator-prey model with Holling-type III schemes and a prey refuge. Zbl 1427.92071
Chen, Fengde; Lin, Qiaoxia; Xie, Xiangdong; Xue, Yalong
2017
Results on soft extremally disconnectedness of soft topological spaces. Zbl 1427.54039
2017
New computational method for solving fractional Riccati equation. Zbl 1427.35310
2017
Asymptotic behavior of third-order neutral differential equations with distributed deviating arguments. Zbl 1427.34095
Wang, Haixia; Chen, Guojuan; Jiang, Ying; Jiang, Cuimei; Li, Tongxing
2017
New type of multivalued F-contraction involving fixed points on closed ball. Zbl 1427.54049
2017
Integral inequalities via generalized convex functions. Zbl 1427.26007
Noor, Muhammad Aslam; Noor, Khalida Inayat; Safdar, Farhat
2017
Two improved classes of Broyden’s methods for solving nonlinear systems of equations. Zbl 1427.65073
Al-Towaiq, Mohammad H.; Abu hour, Yousef S.
2017
$$\mathsf{F}$$-contraction on asymmetric metric spaces. Zbl 1427.54064
Piri, Hossein; Rahrovi, Samira; Marasi, Hamidreza; Kumam, Poom
2017
Using differential transform method and Padé approximation for solving MHD three-dimensional Casson fluid flow past a porous linearly stretching sheet. Zbl 1427.76277
Yousif, Majeed A.; Mahmood, Bewaar A.; Rashidi, M. M.
2017
The Chebyshev collocation solution of the time fractional coupled Burgers’ equation. Zbl 1427.65276
2017
Some fixed point theorems of self-generalized contractions in partially ordered G-metric spaces. Zbl 1427.54041
2017
The effect of perturbations on the circular restricted four-body problem with variable masses. Zbl 1427.70030
Ansari, Abdullah A.; Alhussain, Ziyad A.; Kellil, Rabah
2017
Proximal forward-backward splitting method for zeros of sum accretive operators for a fixed point set and inverse problems. Zbl 1427.47024
Sitthithakerngkiet, K.; Promluang, K.; Thounthong, P.; Kumam, P.
2017
Classification of a new subclass of $$\xi^{(\mathrm{as})}$$-QSO and its dynamics. Zbl 1427.92081
Qaralleh, Izzat
2017
all top 5


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 ${\displaystyle \varphi (\,\,\,93,\,\,\,6)=\varphi (\,\,\,93,\,\,\,5)-\varphi (\,\,\,\,\,\,7,5)=\,\,\,20-\,\,\,\,\,\,1=\,\,\,19}$  ${\displaystyle \varphi (\,\,\,93,\,\,\,5)=\varphi (\,\,\,93,\,\,\,4)-\varphi (\,\,\,\,\,\,8,4)=\,\,\,21-\,\,\,\,\,\,1=\,\,\,20}$  ${\displaystyle \varphi (\,\,\,93,\,\,\,4)=\varphi (\,\,\,93,\,\,\,3)-\varphi (\,\,\,13,3)=\,\,\,25-\,\,\,\,\,\,4=\,\,\,21}$  ${\displaystyle \varphi (\,\,\,93,\,\,\,3)=\varphi (\,\,\,93,\,\,\,2)-\varphi (\,\,\,18,2)=\,\,\,31-\,\,\,\,\,\,6=\,\,\,25}$  ${\displaystyle \varphi (\,\,\,93,\,\,\,2)=\varphi (\,\,\,93,\,\,\,1)-\varphi (\,\,\,31,1)=\,\,\,47-\,\,\,16=\,\,\,31}$  ${\displaystyle \varphi (\,\,\,18,\,\,\,2)=\varphi (18,\,\,\,1)-\varphi (6,1)=\,\,\,\,\,\,9-\,\,\,\,\,\,3}$ ${\displaystyle =}$ ${\displaystyle \,\,\,\,\,\,6}$ ${\displaystyle \varphi (\,\,\,13,\,\,\,3)=\varphi (13,\,\,\,2)-\varphi (2,2)=\,\,\,\,\,\,5-\,\,\,\,\,\,1}$  ${\displaystyle \varphi (\,\,\,13,\,\,\,2)=\varphi (13,\,\,\,1)-\varphi (4,1)=\,\,\,\,\,\,7-\,\,\,\,\,\,2}$ ${\displaystyle =}$ ${\displaystyle =}$ ${\displaystyle \,\,\,\,\,\,4}$ ${\displaystyle \,\,\,\,\,\,5}$ ${\displaystyle \varphi (\,\,\,87,10)=\varphi (\,\,\,87,\,\,\,9)-\varphi (\,\,\,3,\,\,\,9)=\,\,\,15-\,\,\,\,\,\,1=\,\,\,14}$  ${\displaystyle \varphi (\,\,\,87,\,\,\,9)=\varphi (\,\,\,87,\,\,\,8)-\varphi (\,\,\,3,\,\,\,8)=\,\,\,16-\,\,\,\,\,\,1=\,\,\,15}$  ${\displaystyle \varphi (\,\,\,87,\,\,\,8)=\varphi (\,\,\,87,\,\,\,7)-\varphi (\,\,\,4,\,\,\,7)=\,\,\,17-\,\,\,\,\,\,1=\,\,\,16}$  ${\displaystyle \varphi (\,\,\,87,\,\,\,7)=\varphi (\,\,\,87,\,\,\,6)-\varphi (\,\,\,5,\,\,\,6)=\,\,\,18-\,\,\,\,\,\,1=\,\,\,17}$  ${\displaystyle \varphi (\,\,\,87,\,\,\,6)=\varphi (\,\,\,87,\,\,\,5)-\varphi (\,\,\,6,\,\,\,5)=\,\,\,19-\,\,\,\,\,\,1=\,\,\,18}$  ${\displaystyle \varphi (\,\,\,87,\,\,\,5)=\varphi (\,\,\,87,\,\,\,4)-\varphi (\,\,\,7,\,\,\,4)=\,\,\,20-\,\,\,\,\,\,1=\,\,\,19}$  ${\displaystyle \varphi (\,\,\,87,\,\,\,4)=\varphi (\,\,\,87,\,\,\,3)-\varphi (12,\,\,\,3)=\,\,\,23-\,\,\,\,\,\,3=\,\,\,20}$  ${\displaystyle \varphi (\,\,\,87,\,\,\,3)=\varphi (\,\,\,87,\,\,\,2)-\varphi (17,\,\,\,2)=\,\,\,29-\,\,\,\,\,\,6=\,\,\,23}$  ${\displaystyle \varphi (\,\,\,87,\,\,\,2)=\varphi (\,\,\,87,\,\,\,1)-\varphi (29,\,\,\,1)=\,\,\,44-\,\,\,15=\,\,\,29}$  ${\displaystyle \varphi (\,\,\,17,\,\,\,2)=\varphi (17,\,\,\,1)-\varphi (5,1)=\,\,\,\,\,\,9-\,\,\,\,\,\,3}$ ${\displaystyle =}$ ${\displaystyle \,\,\,\,\,\,6}$ ${\displaystyle \varphi (\,\,\,12,\,\,\,3)=\varphi (12,\,\,\,2)-\varphi (2,2)=\,\,\,\,\,\,4-\,\,\,\,\,\,1}$  ${\displaystyle \varphi (\,\,\,12,\,\,\,2)=\varphi (12,\,\,\,1)-\varphi (4,1)=\,\,\,\,\,\,6-\,\,\,\,\,\,2}$ ${\displaystyle =}$ ${\displaystyle =}$ ${\displaystyle \,\,\,\,\,\,3}$ ${\displaystyle \,\,\,\,\,\,4}$ ${\displaystyle \varphi (2439,12)=\varphi (2439,11)-\varphi (\,\,\,65,11)=\,\,\,367-\,\,\,\,\,\,8}$  ${\displaystyle \varphi (2439,11)=\varphi (2439,10)-\varphi (\,\,\,78,10)=\,\,\,379-\,\,\,12}$  ${\displaystyle \varphi (2439,10)=\varphi (2439,\,\,\,9)-\varphi (\,\,\,84,\,\,\,9)=\,\,\,394-\,\,\,15}$  ${\displaystyle \varphi (2439,\,\,\,9)=\varphi (2439,\,\,\,8)-\varphi (106,\,\,\,8)=\,\,\,414-\,\,\,20}$  ${\displaystyle \varphi (2439,\,\,\,8)=\varphi (2439,\,\,\,7)-\varphi (128,\,\,\,7)=\,\,\,439-\,\,\,25}$  ${\displaystyle \varphi (2439,\,\,\,7)=\varphi (2439,\,\,\,6)-\varphi (143,\,\,\,6)=\,\,\,468-\,\,\,29}$  ${\displaystyle \varphi (2439,\,\,\,6)=\varphi (2439,\,\,\,5)-\varphi (187,\,\,\,5)=\,\,\,507-\,\,\,39}$  ${\displaystyle \varphi (2439,\,\,\,5)=\varphi (2439,\,\,\,4)-\varphi (221,\,\,\,4)=\,\,\,557-\,\,\,50}$  ${\displaystyle \varphi (2439,\,\,\,4)=\varphi (2439,\,\,\,3)-\varphi (348,\,\,\,3)=\,\,\,650-\,\,\,93}$  ${\displaystyle \varphi (2439,\,\,\,3)=\varphi (2439,\,\,\,2)-\varphi (487,\,\,\,2)=\,\,\,813-163}$  ${\displaystyle \varphi (2439,\,\,\,2)=\varphi (2439,\,\,\,1)-\varphi (813,\,\,\,1)=1220-407}$  ${\displaystyle \varphi (487,\,\,\,2)=\varphi (487,\,\,\,1)-\varphi (162,1)=244-\,\,\,81}$ ${\displaystyle =}$ ${\displaystyle =}$ ${\displaystyle =}$ ${\displaystyle =}$ ${\displaystyle =}$ ${\displaystyle =}$ ${\displaystyle =}$ ${\displaystyle =}$ ${\displaystyle =}$ ${\displaystyle =}$ ${\displaystyle =}$ ${\displaystyle =}$ ${\displaystyle 359}$ ${\displaystyle 367}$ ${\displaystyle 379}$ ${\displaystyle 394}$ ${\displaystyle 414}$ ${\displaystyle 439}$ ${\displaystyle 468}$ ${\displaystyle 507}$ ${\displaystyle 557}$ ${\displaystyle 650}$ ${\displaystyle 813}$ ${\displaystyle 163}$ ${\displaystyle \varphi (\,\,\,348,\,\,\,3)=\varphi (348,\,\,\,2)-\varphi (\,\,\,69,2)=116-\,\,\,23}$  ${\displaystyle \varphi (\,\,\,348,\,\,\,2)=\varphi (348,\,\,\,1)-\varphi (116,1)=174-\,\,\,58}$  ${\displaystyle \varphi (69,\,\,\,2)=\varphi (69,\,\,\,1)-\varphi (\,\,\,23,1)=\,\,\,35-\,\,\,12}$ ${\displaystyle =}$ ${\displaystyle =}$ ${\displaystyle =}$ ${\displaystyle \,\,\,93}$ ${\displaystyle 116}$ ${\displaystyle \,\,\,23}$

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# If $A$ is the area under the curve $y = e^x$ from 1 to 3, use Exercise 27 to find a value of $n$ such that $R_n - A < 0.0001$.

## $n=10000 \cdot 2 \cdot\left(e^{3}-e\right)$

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### Video Transcript

So Exercise twenty seven tells you a row has made our minds. They will be less land B minus a over on half off being minus f off, eh? So you can estimate Unni, we want this to be last less than this. So we want this to be that zero point zero zero here one. So we want to find someone has to be greater than the inverse of this, which is Ah, I think it's ten thousand ten thousand B minus a F B minus half way. Which is ten thousand b minuses, too. From one to three sizes, too. Half demon surveys. He's e Q my C, and you can use your calculator, the federals and approximate number off this.

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# If $τ_x^k$ is the time of the $k$-th entrance of a Markov chain into $x$, then $\text P_x[τ_y^k<∞]=\text P_x[τ_y^1<∞](\text P_y[τ_y^1<∞])^{k-1}$

Let

• $E$ be at most countable and equipped with the discrete topology and $\mathcal E$ be the Borel $\sigma$-algebra on $E$
• $X=(X_n)_{n\in\mathbb N_0}$ be a discrete Markov chain with values in $(E,\mathcal E$) and distributions $(\operatorname P_x)_{x\in E}$
• $\tau_x^0:=0$ and $$\tau_x^k:=\inf\left\{n>\tau_x^{k-1}:X_n=x\right\}$$ for $x\in E$ and $k\in\mathbb N$

Let $$\varrho(x,y):=\operatorname P_x\left[\tau_y^1<\infty\right]\color{blue}{=\operatorname P_x\left[\exists n\in\mathbb N:X_n=y\right]}\;.$$ I want to prove, that $$\operatorname P_x\left[\tau_y^k<\infty\right]=\varrho(x,y)\varrho(y,y)^{k-1}\;\;\;\text{for all }k\in\mathbb N\tag 1$$ using the strong Markov property: $$\operatorname E_x\left[f\circ (X_{\tau+t})_{t\in \mathbb N_0}\mid\mathcal F_\tau\right]=\operatorname E_{X_\tau}\left[f\circ X\right]\tag 2$$ for all $x\in E$, $\sigma(X)$-stopping times $\tau$ and bounded, $\mathcal E^{\otimes\mathbb N_0}$-measurable $f:E^{\mathbb N_0}\to\mathbb R$.

I want to prove $(1)$ by induction over $k\in\mathbb N$. Since, $k=1$ is trivial, we only need to care about $k-1\to k$. Since $$\left\{\tau_y^{k-1}<\infty\right\}\cap\left\{\tau_y^k<\infty\right\}=\left\{\tau_y^k<\infty\right\}$$ and $$\left\{\tau_y^{k-1}<\infty\right\}\in\mathcal F_{\tau_y^{k-1}}\;,$$ we've got $$\operatorname P_x\left[\tau_y^k<\infty\right]=\operatorname E_x\left[1_{\left\{\tau_y^{k-1}<\infty\right\}}\color{red}{\operatorname P_x\left[\tau_y^k<\infty\mid\mathcal F_{\tau_y^{k-1}}\right]}\right]\;,\tag 4$$ by definition of the conditional expectation. Now, I think, that we somehow need to apply $(2)$ with $\tau=\tau_y^{k-1}$ to the $\color{red}{\text{red}}$ term in order to obtain $$\operatorname E_x\left[1_{\left\{\tau_y^{k-1}<\infty\right\}}\color{red}{\operatorname P_x\left[\tau_y^k<\infty\mid\mathcal F_{\tau_y^{k-1}}\right]}\right]=\operatorname E_x\left[1_{\left\{\tau_y^{k-1}<\infty\right\}}\varrho(y,y)\right]\;,$$ but I can't figure out how I need to choose $f$.

• Yup.    – Did Oct 2 '15 at 12:38
• $$f\circ (X_{t})_{t\in \mathbb N_0}=1_{\left\{\tau_y^{1}<\infty\right\}}$$ – Did Oct 2 '15 at 13:16
• Yes I am sure... Actually, either you apply "my" $f$ at time $\tau^{k-1}_y$, or you apply "your" $f$ at time $\tau^{1}_y$. – Did Oct 2 '15 at 16:30
• Sorry but this cannot go on forever... "Can you provide an answer?" I did. – Did Oct 2 '15 at 17:33
• No mistake, as I said there are two possible solutions. – Did Oct 3 '15 at 10:52

In order to use the strong Markov property $(2)$ at time $\tau:=\tau_y^{k-1}$, we need to find a bounded, $\mathcal E^{\otimes\mathbb N_0}$-measurable function $f:E^{\mathbb N_0}\to\mathbb R$ with $$f\circ\tilde X=1_{\left\{\tau^+<\infty\right\}}\;,$$ where $\tilde X:=\left(X_{\tau+n}\right)_{n\in\mathbb N_0}$ and $\tau^+:=\tau_y^k$. Since
$$\begin{split} \left\{\tau^+<\infty\right\}&=&\left\{\exists n>\tau:X_n=y\right\}\\ &=&\left\{\exists n\in\mathbb N:\tilde X_n=y\right\}\\ &=&\left\{\exists n\in\mathbb N:\pi_n\circ\tilde X=y\right\}\;, \end{split}$$ where $\pi_n:E^{\mathbb N_0}\to E$ denotes the $n$-th coordinate map, we can choose $f$ to be the indicator function of $$\bigcup_{n\in\mathbb N}\left\{\pi_n=y\right\}\;.$$
Noting that $f\circ X$ is the indicator function of $$\bigcup_{n\in\mathbb N}\left\{X_n=y\right\}=\left\{\tau_y^1<\infty\right\}$$ and $X_\tau=y$ on $\left\{\tau<\infty\right\}$, we're now able to conclude, that
$$\begin{split} \operatorname E_x\left[1_{\left\{\tau<\infty\right\}}\operatorname E_x\left[f\circ\tilde X\mid\mathcal F_{\tau}\right]\right]&\stackrel{(2)}=&\;\operatorname E_x\left[1_{\left\{\tau<\infty\right\}}\operatorname E_{X_\tau}\left[f\circ X\right]\right]\\ &=&\;\operatorname E_x\left[1_{\left\{\tau<\infty\right\}}\operatorname P_{X_\tau}\left[\tau_y^1<\infty\right]\right]\\ &=&\;\operatorname E_x\left[1_{\left\{\tau<\infty\right\}}\operatorname P_y\left[\tau_y^1<\infty\right]\right]\\ &\stackrel{\text{def}}=&\;\operatorname E_x\left[1_{\left\{\tau<\infty\right\}}\varrho(y,y)\right]\\ &=&\;\varrho(y,y)\operatorname P_x\left[\tau<\infty\right]\\ &\stackrel{\text{IH}}=&\;\varrho(y,y)\varrho(x,y)\varrho(y,y)^{k-2}\;. \end{split}$$


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# cvode_with_disc.py¶

assimulo.examples.cvode_with_disc.run_example(with_plots=True)[source]

Example of the use of CVode for a differential equation with a iscontinuity (state event) and the need for an event iteration.

on return:

• exp_mod problem instance
• exp_sim solver instance

No initialization defined for the problem.
A discontinuity occured at t = 1.000000e+00.
Current switches: [False, True, True]
Event info: [[0, 0, -1], False]
Final Run Statistics: ODE with discontinuities and a function with consistency problem

Number of steps                                 : 6
Number of function evaluations                  : 10
Number of Jacobian evaluations                  : 1
Number of function eval. due to Jacobian eval.  : 3
Number of error test failures                   : 0
Number of nonlinear iterations                  : 6
Number of nonlinear convergence failures        : 0
Number of state function evaluations            : 8
Number of state events                          : 1

Solver options:

Solver                   : CVode
Linear multistep method  : BDF
Nonlinear solver         : Newton
Linear solver type       : DENSE
Maximal order            : 5
Tolerances (absolute)    : 1e-06
Tolerances (relative)    : 1e-06

No finalization defined for the problem.
Final Run Statistics: ODE with discontinuities and a function with consistency problem

Number of steps                                 : 10
Number of function evaluations                  : 18
Number of Jacobian evaluations                  : 2
Number of function eval. due to Jacobian eval.  : 6
Number of error test failures                   : 0
Number of nonlinear iterations                  : 10
Number of nonlinear convergence failures        : 0
Number of state function evaluations            : 14
Number of state events                          : 1

Solver options:

Solver                   : CVode
Linear multistep method  : BDF
Nonlinear solver         : Newton
Linear solver type       : DENSE
Maximal order            : 5
Tolerances (absolute)    : 1e-06
Tolerances (relative)    : 1e-06

Simulation interval    : 0.0 - 10.0 seconds.
Elapsed simulation time: 0.010479927063 seconds.
Time, t = 1.000000e+00
Event info,  [[0, 0, -1], False]
Number of events:  1

Note

Press [source] (to the top right) to view the example.


text:
# Amateur guitar effects builder.......seeking enlightenment!

Status
Not open for further replies.

#### Millibobs

##### New Member
Hi - I am completely baffled by most aspects of electronic circuit design/build. I am currently up to my armpits in veroboard builds of various overdrives and modulation pedals and thinking there must be a resource or guide that I can buy that covers all the basics? I would really like to move on to a different kind of build process as I find veroboard is tricky to work with - I either cut the spacers in the wrong places or make a mess when soldering.

Recommendations appreciated and of course, I'll be making use of this resource, which looks great.

A question: I need to find an alternative transistor to LM78L05 - can anyone suggest options?

Otherwise, best wishes from Yorkshire, UK and look forward to learning many interesting things through the forum

#### gophert

##### Well-Known Member
Hi - I am completely baffled by most aspects of electronic circuit design/build. I am currently up to my armpits in veroboard builds of various overdrives and modulation pedals and thinking there must be a resource or guide that I can buy that covers all the basics? I would really like to move on to a different kind of build process as I find veroboard is tricky to work with - I either cut the spacers in the wrong places or make a mess when soldering.

Recommendations appreciated and of course, I'll be making use of this resource, which looks great.

A question: I need to find an alternative transistor to LM78L05 - can anyone suggest options?

Otherwise, best wishes from Yorkshire, UK and look forward to learning many interesting things through the forum
LM78L05 is a 5-volt voltage regulator, not a transistor. I am not sure why oneis needed in a guitar stomp box but I guess some effect may need a voltage reference.

Stomp boxes intentionally distort audio signals so there are few "professional" resources because most engineers want to faithfully reproduce audio without distortion.

Your best bet is searching diy effects pedals.

If you know how to design circuits and just want to make better PCBs, search Eagle CAD or DesignSpark for software to draw the pcb.

Pcb toner transfer
Or
Pcb sensitized etching MG chemical

Last edited:

#### Millibobs

##### New Member
Many thanks for that! It won't be the last dumb-ass question I post.........

#### MichaelaJoy

##### Active Member
gophert: I have some op amps that have a max Vcc of +5V. Maybe He's using that same part?

Don't forget Kicad. It's free, which is what I like about it.

Here's a distortion pedal I designed a while back.

It's called "MJ's Hot Mess."

U1A is an input buffer. C1 / R1 as well as C7/R8 control the low frequency cutoff.

Tinker with these values to make a Bass pedal.

U2B is the heart of the distortion pedal. I believe the configuration is called a logarithmic amplifier.
The diode pair makes all the difference here. I use a pair of 1N34As, which are germanium diodes.

U1C and U2A comprise a mixer. You can mix the clean and distorted outputs together.

If you use this circuit, don't forget to mention where you got it.

You won't find it anywhere else but electro-tech-online.

Best o fluck. (This is a typo that I think I want to leave alone, just for the comedic effect.)

Uhhhh...best of luck.

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#### JonSea

##### Well-Known Member
If you are making several copies of your circuits, you can lay out circuit boards as Gorphert suggested, but instead of etching the boards yourself, you can have 10 boards professionally made in China for around $25 all-in ($5 to make the boards, \$20 for shipping). That's just for the printed circuit board to replace the veroboard. Then it would be a lot easier to assemble.

#### AnalogKid

##### Well-Known Member
MJ, when I first looked at your circuit I assumed that the fuzz and direct path gains were independently adjustable. Now I see that the two pots are ganged, so ...

Since R3, R5, R6, R7, and VR2A and B are all equal values, you can eliminate two opamps and 1/2 of the dual pot by summing the fuzz and direct paths into the output buffer and making that stage adjustable gain.

ak

#### MichaelaJoy

##### Active Member
AnalogKid: Thanks for the heads up. I thought it would provide a better control of the percentage
of clean vs distorted output. Like a pan pot.

Problem is, I don't play guitar, so it's difficult to determine what guitarists like.

When I get a chance, I'll try the mod you suggested and ask a few guitarists I know to try it out.

#### AnalogKid

##### Well-Known Member
Now that you say that, I understand why the two pots are connected differently. To improve clarity, add pin numbers to the pots. Pin 3 is the terminal the wiper goes to in the full clockwise direction.

Yes, your dual pot will act as a pan between max fuzz and max clean.

ak

#### audioguru

##### Well-Known Member
Most people who listen to overdrive, fuzz and screamers are so deaf to high audio frequencies that they do not hear the severe distortion then they add more distortion. An acoustic guitar sounds good, even when amplified over a low distortion sound system.

#### unclejed613

##### Well-Known Member
Most people who listen to overdrive, fuzz and screamers are so deaf to high audio frequencies that they do not hear the severe distortion then they add more distortion. An acoustic guitar sounds good, even when amplified over a low distortion sound system.
depends on your taste in music. i happen to like the "these go to 11" version of Neil Young's "Out of the Blue" much better than i like the "unplugged version. but that's the point of effects boxes and amplifiers that go to 11, the whole system is part of the instrument, not just the guitar.

#### Millibobs

##### New Member
Lots of interesting comments/suggestions from original question. All appreciated, guys. I even understood some of it!

#### gophert

##### Well-Known Member
Lots of interesting comments/suggestions from original question. All appreciated, guys. I even understood some of it!
What's a Millibobs ? Is that like 1/1000 of a Robert?

#### JonSea

##### Well-Known Member
Isn't a Bob a fraction of a Robert? So maybe 2000 mBobs = 1 Robert?

#### unclejed613

##### Well-Known Member
a good place to look if you are looking for unusual ideas for effects is [Analog Devices Op Amp Applications 1974] chapters 4 ,5, 6, 9, and 10. i had some unusual boxes i built as prototypes, one of them was a low distortion octave box. if you feed the same signal into both X and Y inputs of a 4-quadrant multiplier, you get an output that is an octave higher. the other prototype i built was a box that distorted the signal, not by clipping the signal, but by simulating crossover notch distortion. there was little or no distortion when playing loud, but the signal would begin getting distorted as the signal level dropped. if you sustained a note, it would gradually get fuzzier as the note decayed. it was an interesting sound.

#### AnalogKid

##### Well-Known Member
Analog Device's books over the years are an outstanding body of work.

But (IMnsHO) -

No one did more to bring the amateur/young designer into the world of professional circuit design than National Semiconductor. "...well into the 1980s." ? I disagree. The Linear Applications Handbook series in general, and the specialty derivatives like the Audio Handbook, are as valuable today as ever - both to fill in what no longer is taught in schools and as a counterpoint to much of the "information" on the innergoogle.

There is a long-running thread on another forum about "bibles". We love our old TI books and the GE Transistor Manual, but NS takes the title.

ak

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#### rjenkinsgb

##### Well-Known Member
For effects schematics, have a look at this site:
http://www.effectsdatabase.com/schematics#list

Or if you want pre-planned stripboard layouts for various types:
http://tagboardeffects.blogspot.com/

I still prototype everything we design for manufacture on either stripboard or square-pad board, though I do tend to use board with a topside ground plane [A "colander" ground plane] for anything that may be sensitive to noise or ground resistance as that eliminates many problems before you start and simplifies wiring.

eg. something like these - the topside copper is show at the very bottom left of the image.
https://uk.rs-online.com/web/p/products/5184046/

That's a square-pad type, you can just bend the component leads over a row of pads to form longer connections or bend a lead to form an angled track..


text:
# Distribution of sum of $n$ i.i.d. symmetric Pareto distributed random variables

Let $X$ be a random variable which follows the symmetric Pareto distribution. For a fix, real parameter set $\alpha > 0$ and $L>0$, its PDF is defined as
$$p_X(x) = \left\{ \begin{array}{ll} \frac{1}{2}\alpha L^\alpha |x|^{-\alpha-1} & |x| \geq L \\ 0 & \mbox{otherwise.} \end{array} \right.$$

If possible, I would like to derive PDF $p_S(x)$, where $S = \sum_{i=1}^n X_i$. Each $X_i$ is i.i.d. according to the PDF given above. I’m particularly interested in the tail distribution $\overline{F}_S(x) = Pr(S > x)$.

My approach is to calculate the $n$-th power of the CF $\varphi_X(\omega)$ and calculate its Fourier transform to obtain $p_S(x)$. However, I’m uncertain if this procedure is valid here. Is it? Do any restrictions emerge inevitably w.r.t. $\alpha$? I observe some “unhandy terms”. Is it possible to obtain $p_S(x)$ analytically and in closed form?

First of all, the CF of a (one sided) Pareto distribution is given by $\varphi_Y(\omega) = \alpha L^\alpha (-i\omega)^\alpha\Gamma(-\alpha, -i\omega L)$. Is the upper incomplete gamma function well defined for a real negative exponent and imaginary integral bounds?

I have
\begin{eqnarray}
\varphi_S(\omega) &=& \frac{1}{2^n}(\varphi_Y(\omega) + \varphi_Y(-\omega))^n\\
&=& \left(\alpha L^\alpha\right)^n|\omega|^{\alpha n}|\Gamma(-\alpha, i\omega L)|^{n} \cos \left( \arg \left( \Gamma(-\alpha, i\omega L)\right)+ \sigma(\omega)\frac{\alpha\pi}{2}\right)\;,
\end{eqnarray}
where $\sigma(\cdot)$ is the signum function.

Alternatively, I have
\begin{eqnarray}
\varphi_S(\omega) &=& \left( \alpha L^\alpha \int\limits_{L}^\infty x^{-\alpha-1} \cos \left(\omega x \right) \,\mathrm{d}x \right)^n.
\end{eqnarray}

Does this help in any way to get $p_S(x)$ or $\overline{F}_S(x)$? How could I proceed?

P.S.: In my case, n is a power of 2. If the inversion has no chance to succeed for a fix $n$, what would be an appropriate approach to investigate $\lim_{n \to \infty} \overline{F}_S(x)$?


text:
# The New Villa

Time Limit: Java: 2000 ms / Others: 2000 ms

Memory Limit: Java: 65536 KB / Others: 65536 KB

## Description

Mr. Black recently bought a villa in the countryside. Only one thing bothers him: although there are light switches in most rooms, the lights they control are often in other rooms than the switches themselves. While his estate agent saw this as a feature, Mr. Black has come to believe that the electricians were a bit absent-minded (to put it mildly) when they connected the switches to the outlets.

One night, Mr. Black came home late. While standing in the hallway, he noted that the lights in all other rooms were switched off. Unfortunately, Mr. Black was afraid of the dark, so he never dared to enter a room that had its lights out and would never switch off the lights of the room he was in.

After some thought, Mr. Black was able to use the incorrectly wired light switches to his advantage. He managed to get to his bedroom and to switch off all lights except for the one in the bedroom.

You are to write a program that, given a description of a villa, determines how to get from the hallway to the bedroom if only the hallway light is initially switched on. You may never enter a dark room, and after the last move, all lights except for the one in the bedroom must be switched off. If there are several paths to the bedroom, you have to find the one which uses the smallest number of steps, where move from one room to another'', switch on a light'' and switch off a light'' each count as one step.

## Input

The input contains several villa descriptions. Each villa starts with a line containing three integers r, d, and s. r is the number of rooms in the villa, which will be at most 10. d is the number of doors/connections between the rooms and s is the number of light switches in the villa. The rooms are numbered from 1 to r; room number 1 is the hallway, room number r is the bedroom.

This line is followed by d lines containing two integers i and j each, specifying that room i is connected to room j by a door. Then follow s lines containing two integers k and l each, indicating that there is a light switch in room k that controls the light in room l.

A blank line separates the villa description from the next one. The input ends with a villa having r = d = s = 0, which should not be processed.

## Output

For each villa, first output the number of the test case (Villa #1', Villa #2', etc.) in a line of its own.

If there is a solution to Mr. Black's problem, output the shortest possible sequence of steps that leads him to his bedroom and only leaves the bedroom light switched on. (Output only one shortest sequence if you find more than one.) Adhere to the output format shown in the sample below.

If there is no solution, output a line containing the statement The problem cannot be solved.'

Output a blank line after each test case.

## Sample Input

3 3 4
1 2
1 3
3 2
1 2
1 3
2 1
3 2
2 1 2
2 1
1 1
1 2
0 0 0

## Sample Output

Villa #1
The problem can be solved in 6 steps:
- Switch on light in room 2.
- Switch on light in room 3.
- Move to room 2.
- Switch off light in room 1.
- Move to room 3.
- Switch off light in room 2.
Villa #2
The problem cannot be solved.`

None

## Source

Southwest Europe 1996


text:
• N H ABDEL-WAHAB

Articles written in Pramana – Journal of Physics

• Dynamic evolution of double $\Lambda$ five-level atom interacting with one-mode electromagnetic cavity field

In this paper, the model describing a double $\Lambda$ five-level atom interacting with a single mode electromagnetic cavity field in the (off) non-resonate case is studied. We obtained the constants of motion for the considered model. Also, the state vector of the wave function is given by using the Schrödinger equation when the atom is initially prepared in its excited state. The dynamical evolutions for the collapse revivals, the antibunching of photons and the field squeezing phenomena are investigated when the field is considered in a coherent state. The influence of detuning parameters on these phenomena is investigated. We noticed that the atom–field properties are influenced by changing the detuning parameters. The investigation of these aspects by numerical simulations is carried out using the Quantum Toolbox in Python (QuTip).

• Pramana – Journal of Physics

Volume 95, 2021
All articles
Continuous Article Publishing mode

• Editorial Note on Continuous Article Publication

Posted on July 25, 2019


text:
# Observed information

Observed information

In statistics, the observed information, or observed Fisher information, is the negative of the second derivative (the Hessian matrix) of the "log-likelihood" (the logarithm of the likelihood function). It is a sample-based version of the Fisher information.

## Definition

Suppose we observe random variables $X_1,\ldots,X_n$, independent and identically distributed with density f(X; θ), where θ is a (possibly unknown) vector. Then the log-likelihood of the parameters θ given the data $X_1,\ldots,X_n$ is

$\ell(\theta | X_1,\ldots,X_n) = \sum_{i=1}^n \log f(X_i| \theta)$.

We define the observed information matrix at θ * as

$\mathcal{J}(\theta^*) = - \left. \nabla \nabla^{\top} \ell(\theta) \right|_{\theta=\theta^*}$
$= - \left. \left( \begin{array}{cccc} \tfrac{\partial^2}{\partial \theta_1^2} & \tfrac{\partial^2}{\partial \theta_1 \partial \theta_2} & \cdots & \tfrac{\partial^2}{\partial \theta_1 \partial \theta_n} \\ \tfrac{\partial^2}{\partial \theta_2 \partial \theta_1} & \tfrac{\partial^2}{\partial \theta_2^2} & \cdots & \tfrac{\partial^2}{\partial \theta_2 \partial \theta_n} \\ \vdots & \vdots & \ddots & \vdots \\ \tfrac{\partial^2}{\partial \theta_n \partial \theta_1} & \tfrac{\partial^2}{\partial \theta_n \partial \theta_2} & \cdots & \tfrac{\partial^2}{\partial \theta_n^2} \\ \end{array} \right) \ell(\theta) \right|_{\theta = \theta^*}$

In many instances, the observed information is evaluated at the maximum-likelihood estimate.[1]

## Fisher information

The Fisher information $\mathcal{I}(\theta)$ is the expected value of the observed information:

$\mathcal{I}(\theta) = \mathrm{E}(\mathcal{J}(\theta))$.

## Applications

In a notable article, Bradley Efron and David V. Hinkley [2] argued that the observed information should be used in preference to the expected information when employing normal approximations for the distribution of maximum-likelihood estimates.

## References

1. ^ Dodge, Y. (2003) The Oxford Dictionary of Statistical Terms, OUP. ISBN 0-19-920613-9
2. ^ Efron, B.; Hinkley, D.V. (1978). "Assessing the accuracy of the maximum likelihood estimator: Observed versus expected Fisher Information". Biometrika 65 (3): 457–487. doi:10.1093/biomet/65.3.457. JSTOR 2335893. MR0521817.

Wikimedia Foundation. 2010.

### Look at other dictionaries:

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• Information bottleneck method — The information bottleneck method is a technique introduced by Tishby et al [1] for finding the best tradeoff between accuracy and complexity (compression) when summarizing (e.g. clustering) a random variable X, given a joint probability… …   Wikipedia

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• traffic information (radar) — Information issued to alert an aircraft to any radar targets observed on the radar display that may be in such proximity to its position or intended route of flight to warrant its attention …   Military dictionary

• traffic information — Information issued by an air traffic services unit to alert a pilot to other known or observed air traffic which may be in proximity to the position or intended route of flight and to help the pilot to avoid a collision (ICAO) …   Aviation dictionary


text:
<img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" />

# Concave Mirrors

## Concave mirrors focus light and create reflected images are of different sizes than the original object.

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Images in a Concave Mirror

Credit: Courtesy of the NASA Marshall Space Flight Center
Source: http://commons.wikimedia.org/wiki/File:Hubble_mirror_polishing.jpg

Concave mirrors are used in a number of applications. They form upright, enlarged images, and are therefore useful in makeup application or shaving. They are also used in flashlights and headlights because they project parallel beams of light, and in telescopes because they focus light to produce greatly enlarged images.

The photograph above shows the grinding of the primary mirror in the Hubble space telescope. The Hubble Space Telescope is a reflecting telescope with a mirror approximately eight feet in diameter, and was deployed from the Space Shuttle Discovery on April 25, 1990.

### Image in a Concave Mirror

Reflecting surfaces do not have to be flat. The most common curved mirrors are spherical. A spherical mirror is called a concave mirror if the center of the mirror is further from the viewer than the edges are. A spherical mirror is called a convex mirror if the center of the mirror is closer to the viewer than the edges are.

To see how a concave mirror forms an image, consider an object that is very far from the mirror so that the incoming rays are essentially parallel. For an object that is infinitely far away, the incoming rays would be exactly parallel. Each ray would strike the mirror and reflect according to the law of reflection (angle of reflection is equal to the angle of incidence). As long as the section of mirror is small compared to its radius of curvature, all the reflected rays will pass through a common point, called the focal point (f).

Credit: Samantha Bacic
Source: CK-12 Foundation

If too large a piece of the mirror is used, the rays reflected from the top and bottom edges of the mirror will not pass through the focal point and the image will be blurry. This flaw is called spherical aberration and can be avoided either by using very small pieces of the spherical mirror or by using parabolic mirrors.

A line drawn to the exact center of the mirror and perpendicular to the mirror at that point is called the principal axis. The distance along the principle axis from the mirror to the focal point is called the focal length. The focal length is also exactly one-half of the radius of curvature of the spherical mirror. That is, if the spherical mirror has a radius of 8 cm, then the focal length will be 4 cm.

### Objects Outside the Center Point

Credit: Samantha Bacic
Source: CK-12 Foundation

Above is a spherical mirror with the principle axis, the focal point, and the center of curvature (C) identified on the image. An object has been placed well beyond C, and we will treat this object as if it were infinitely far away. There are two rays of light leaving any point on the object that can be traced without any drawing tools or measuring devices. The first is a ray that leaves the object and strikes the mirror parallel to the principle axis that will reflect through the focal point. The second is a ray that leaves the object and strikes the mirror by passing through the focal point; this ray will reflect parallel to the principle axis.

These two rays can be seen in the image below. The two reflected rays intersect after reflection at a point between C and F. Since these two rays come from the tip of the object, they will form the tip of the image.

Credit: Samantha Bacic
Source: CK-12 Foundation

If the image is actually drawn in at the intersection of the two rays, it will be smaller and inverted, as shown below. Rays from every point on the object could be drawn so that every point could be located to draw the image. The result would be the same as shown here. This is true for all concave mirrors with the object outside C: the image will be between C and F, and the image will be inverted and diminished (smaller than the object).

Credit: Samantha Bacic
Source: CK-12 Foundation

The heights of the object and the image are related to their distances from the mirror. In fact, the ratio of their heights is the same ratio as their distances from the mirror. If do\begin{align*}d_o\end{align*} is object distance, di\begin{align*}d_i\end{align*} the image distance, ho\begin{align*}h_o\end{align*} the object height and hi\begin{align*}h_i\end{align*} the image height, then

hohi=dodi.\begin{align*}\frac{h_o}{h_i}=\frac{d_o}{d_i}.\end{align*}

It can also be shown that dodi=doff\begin{align*}\frac{d_o}{d_i}=\frac{d_o-f}{f}\end{align*} and from this, we can derive the mirror equation,

1do+1di=1f.\begin{align*}\frac{1}{d_o}+\frac{1}{d_i}=\frac{1}{f}.\end{align*}

In this equation, f is the focal length do is the object distance, and di is the image distance.

The magnification equation for a mirror is the image size divided by the object size, where m gives the magnification of the image.

m=dido\begin{align*}m=\frac{-d_i}{d_o}\end{align*}

#### Example 1

A 1.50 cm tall object is placed 20.0 cm from a concave mirror whose radius of curvature is 30.0 cm. What is the image distance and what is the image height?

1do+1di=1f\begin{align*}\frac{1}{d_o}+\frac{1}{d_i}=\frac{1}{f}\end{align*} The focal length is one-half the center of curvature so it is 15.0 cm. 120.0+1x=115\begin{align*}\frac{1}{20.0}+\frac{1}{x}=\frac{1}{15}\end{align*} multiply both sides by 60x\begin{align*}60x\end{align*} to get 3x+60=4x\begin{align*}3x + 60 = 4x\end{align*} and x=60.0 cm\begin{align*}x = 60.0 \ cm\end{align*}.

The image distance is 60.0 cm. The image is 3 times as far from the mirror as the object so it will be 3 times as large, or 4.5 cm tall.

### Objects Between the Center Point and the Focal Point

Regardless of where the object is, its image's size and location can be determined using the equations given earlier in this section. Nonetheless, patterns emerge in these characteristics. We already know that the image of an object outside the center point is closer and smaller than the object. When an object is between the center point and the focal point, the image is larger and closer. These characteristics can also be determined by drawing the rays coming off of the object; this is called a ray diagram.

Credit: Samantha Bacic
Source: CK-12 Foundation

Look again at the image above that was shown earlier in the lesson. If you consider the smaller arrow to be the object and follow the rays backward, the ray diagram makes it clear that if an object is located between the center point and focal point, the image is inverted, larger, and at a greater distance.

#### Example 2

If an 3.00 cm tall object is held 15.00 cm away from a concave mirror with a radius of 20.00 cm, describe its image.

To solve this problem, we must determine the height of the image and the distance from the mirror to the image. To find the distance, use the mirror equation:

1di=1f1do=110115=130=30cm\begin{align*}\frac{1}{d_i}=\frac{1}{f}-\frac{1}{d_o}=\frac{1}{10}-\frac{1}{15}=\frac{1}{30}=30cm\end{align*}

Next determine the height of the image:

hohi=dodi=3hi=1530\begin{align*}\frac{h_o}{h_i}=\frac{d_o}{d_i}=\frac{3}{h_i}=\frac{15}{30}\end{align*}

Using this equation, we can determine that the height of the image is 6 cm.

This image is a real image, which means that the rays of light are real rays. These are represented in the ray diagram as solid lines, while virtual rays are dotted lines.

### Objects Inside the Focal Point

Consider what happens when the object for a concave mirror is placed between the focal point and the mirror. This situation is sketched at below.

Credit: Samantha Bacic
Source: CK-12 Foundation

Once again, we can trace two rays to locate the image. A ray that originates at the focal point and passes through the tip of the object will reflect parallel to the principal axis. The second ray we trace is the ray that leaves the tip of the object and strikes the mirror parallel to the principal axis.

Below is the ray diagram for this situation. The rays are reflected from the mirror and as they leave the mirror, they diverge. These two rays will never come back together and so a real image is not possible. When an observer looks into the mirror, however, the eye will trace the rays backward as if they had followed a straight line. The dotted lines in the sketch show the lines the rays would have followed behind the mirror. The eye will see an image behind the mirror just as if the rays of light had originated behind the mirror. The image seen will be enlarged and upright. Since the light does not actually pass through this image position, the image is virtual.

Credit: Samantha Bacic
Source: CK-12 Foundation

#### Example 3

A 1.00 cm tall object is placed 10.0 cm from a concave mirror whose radius of curvature is 30.0 cm. Determine the image distance and image size.

Since the radius of curvature is 30.0 cm, the focal length is 15.0 cm. The object distance of 10.0 cm tells us that the object is between the focal point and the mirror.

1do+1di=1f\begin{align*}\frac{1}{d_o}+\frac{1}{d_i}=\frac{1}{f}\end{align*} and plugging known values yields 110.0+1x=115\begin{align*}\frac{1}{10.0}+\frac{1}{x}=\frac{1}{15}\end{align*}

Multiplying both sides of the equation by 30x\begin{align*}30x\end{align*} yields 3x+30=2x\begin{align*}3x + 30 = 2x\end{align*} and x=30.0 cm\begin{align*}x = -30.0 \ cm\end{align*}.

The negative image distance indicates that the image is behind the mirror. We know the image is virtual because it is behind the mirror. Since the image is 3 times as far from the mirror as the object, it will be 3 times as tall. Therefore, the image height is 3.00 cm.

### Summary

• A spherical mirror is concave if the center of the mirror is further from the viewer than the edges.
• For an object that is infinitely far away, incoming rays would be exactly parallel.
• As long as the section of mirror is small compared to its radius of curvature, all the reflected rays will pass through a common point, called the focal point.
• The distance along the principle axis from the mirror to the focal point is called the focal length, f. This is also exactly one-half of the radius of curvature.
• The mirror equation is 1do+1di=1f\begin{align*}\frac{1}{d_o}+\frac{1}{d_i}=\frac{1}{f}\end{align*}.
• The magnification equation is m=dido\begin{align*}m=-\frac{d_i}{d_o}\end{align*}.
• For concave mirrors, when the object is outside C, the image will be between C and F and the image will be inverted and diminished (smaller than the object).
• For concave mirrors, when the object is between C and F, the image will be beyond C and will be enlarged and inverted.
• For concave mirrors, when the object is between F and the mirror, the image will be behind the mirror and will be enlarged and upright.

### Review

1. A concave mirror is designed so that a person 20.0 cm in front of the mirror sees an upright image magnified by a factor of two. What is the radius of curvature of this mirror?
2. If you have a concave mirror whose focal length is 100.0 cm, and you want an image that is upright and 10.0 times as tall as the object, where should you place the object?
3. A concave mirror has a radius of curvature of 20.0 cm. Locate the image for an object distance of 40.0 cm. Indicate whether the image is real or virtual, enlarged or diminished, and upright or inverted.
4. A dentist uses a concave mirror to examine a tooth that is 1.00 cm in front of the mirror. The image of the tooth forms 10.0 cm behind the mirror.
1. What is the mirror’s radius of curvature?
2. What is the magnification of the image?
5. When a man stands 1.52 m in front of a shaving mirror, the image produced is inverted and has an image distance of 18.0 cm. How close to the mirror must the man place his face if he wants an upright image with a magnification of 2.0?

### Explore More

Use this resource to answer the questions that follow.

1. What are the two main rays you need to draw a real image?
2. What is the third ray? What can you use it for?
3. How do light rays through the focal point and vertex behave the same? How are they different?

### Resources

Below is another video about ray diagrams, dealing with drawing virtual images.

For more questions regarding concave mirrors with audio guided solutions, click on the link below. By clicking this link, you will leave the CK-12 site and open an external site in a new tab. This page will remain open in the original tab.

### Notes/Highlights Having trouble? Report an issue.

Color Highlighted Text Notes

1. [1]^ Credit: Courtesy of the NASA Marshall Space Flight Center; Source: http://commons.wikimedia.org/wiki/File:Hubble_mirror_polishing.jpg; License: CC BY-NC 3.0
2. [2]^ Credit: Samantha Bacic; Source: CK-12 Foundation; License: CC BY-NC 3.0
3. [3]^ Credit: Samantha Bacic; Source: CK-12 Foundation; License: CC BY-NC 3.0
4. [4]^ Credit: Samantha Bacic; Source: CK-12 Foundation; License: CC BY-NC 3.0
5. [5]^ Credit: Samantha Bacic; Source: CK-12 Foundation; License: CC BY-NC 3.0
6. [6]^ Credit: Samantha Bacic; Source: CK-12 Foundation; License: CC BY-NC 3.0
7. [7]^ Credit: Samantha Bacic; Source: CK-12 Foundation; License: CC BY-NC 3.0
8. [8]^ Credit: Samantha Bacic; Source: CK-12 Foundation; License: CC BY-NC 3.0

### Explore More

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text:
• Create Account

## Why do we need shadow maps?

Old topic!

Guest, the last post of this topic is over 60 days old and at this point you may not reply in this topic. If you wish to continue this conversation start a new topic.

4 replies to this topic

### #1Telanor  Members

Posted 29 March 2013 - 05:11 PM

Bit of an odd question. In a deferred shading renderer, when you render a point light (for its lighting pass), you have the world space position of the light and the depth value from the viewer's camera to the pixel, from which you can reconstruct the world space position of the pixel. Typical shadowing techniques do a first pass to render the depth value from the light to the pixel and then send that to the lighting pass. Usually it looks something like this:
return length(LightPosition - input.WorldPosition) / FarClip;

If we know the position of the pixel and the light, can't we just do this in the lighting pass:
float shadowFactor = pixelDepth < length(LightPosition - pixelPosition) / FarClip;

I'm sure if this worked someone would have figured it out already, but I can't see why it wouldn't and it's bugging me.

### #2Chris_F  Members

Posted 29 March 2013 - 05:22 PM

It should probably be clear why shadow maps are necessary based solely off the observation that light occluders are often off screen.

### #3phil_t  Members

Posted 29 March 2013 - 05:54 PM

If we know the position of the pixel and the light, can't we just do this in the lighting pass:
float shadowFactor = pixelDepth < length(LightPosition - pixelPosition) / FarClip;

Where did the value pixelDepth come from? pixelDepth needs to be the scene depth as rendered from the light... i.e. the shadow map.

### #4Telanor  Members

Posted 29 March 2013 - 06:03 PM

It should probably be clear why shadow maps are necessary based solely off the observation that light occluders are often off screen.

Ah, of course. Silly me. I always overlook things like that.

### #5Matias Goldberg  Members

Posted 29 March 2013 - 06:24 PM

If we know the position of the pixel and the light, can't we just do this in the lighting pass:

float shadowFactor = pixelDepth < length(LightPosition - pixelPosition) / FarClip;

I'm sure if this worked someone would have figured it out already, but I can't see why it wouldn't and it's bugging me.

There are two possibilities:
1. pixelDepth is the depth from the GBuffer, in which case your formula makes no sense (if the object is further from me than it is from the light, it is shadowed).

2. If pixelDepth is the depth from the light space, then it must have come from a shadow map. Sure, what's confusing you is that you can retrieve the data from the GBuffer and turn it into light space, and obtain "pixelDepth". However in that case your formula would always pass (never shadow). The detail you're omitting is that in the algorithm pixelDepth may not be from the obtained from the object you're evaluating, but rather from another caster that is close to the light (and as pointed out, that caster can be off screen, but even if it isn't, your assumption won't work).


text:
Gravitational Field question

1. Jun 15, 2005

404

1. A person throws a ball upwards with a speed of 15 m/s, calc:
a) the time to the top of the trajectory (1.53s)
b) time the ball is in flight (3.06s)
c) max height of the ball (11.5m)

2. An astronaut is repairing top of her craft while docked on a strange new planet. ( ) She throws a tool down to her partner below at 2.5 m/s. Her partner catches the tool 2.86m below when it has reached a speed of 11.5m/s.
a) What is the gravitational field? (22 N/kg)
b) What is her weight if her mass is 58 kg? (1300 N)

I don't want the solutions, but can someone give me formulas I'm suppose to use for these questions? All I have in my notes is g=F/m...

2. Jun 15, 2005

whozum

The solution is more useful than just a formula. These shouldnt be just "look up the formula and plug it in", you should try to understand why they work, and if tehy dont, how to make them work.

For #1, use energy considerations to solve all three. The kinetic energy initially in the ball will do work against the gravitational field. It will gain potential energy until the KE is dispended, and at the point where KE is zero, the ball will be at its peak. Namely,

$$\frac{1}{2}mv^2 = mgh$$.

3. Jun 15, 2005

404

Well last time I asked for the solution was I given formulas so I thought I'd cut to the chase.

EDIT: ok number 1 worked out. Thanks

Last edited: Jun 15, 2005
4. Jun 15, 2005

404

Oh for Number 2a), I found acceleration to be 22m/s^2. The answer is 22N/kg, so maybe you assume she's dropping at maximum angle 90. a = g sin(theta), sin would be 1, so gravity comes out to be 22? I don't know... Just a crazy guess.

5. Jun 15, 2005

whozum

$$22 m/s^2 = 22 N/kg$$. If you don't see this, write out 1 Newton in terms of its base units (meters, seconds, kilograms). It says the object falls straight down, so we don't need to involve angles.

6. Jun 15, 2005

404

Ok, I see what you are saying now... Just making sure though, even though I included angles, was my thinking correct?

7. Jun 15, 2005

whozum

You didn't show me any thinking, you showed me an answer which matches the one you gave as correct earlier in a different form. I'm guessing that you did it correctly since you came to the correct answer without knowing it.


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# What's a singular model in economics?

What's a singular model in economics? I've tried google, but I didn't find a definition...

In an article by Ingram et al (1994), they state:

This linear model is singular because it predicts that the current value of consumption is an exact(non-stochastic) function of current output and lagged consumption.

Also, the paper says that any model (RBC and extensions) with a number of shocks smaller than the number of observable endogenous variables, has this particular behaviour. So, the models are not 'singular' as a dictionary definition.

From this I get that any stochastic model, which determines some observable endogenous variable to follown a non-stochastic path, then I can call it singular. Is this correct?

Also, does this definition have any relation to bifurcation? In ODE we have a 'bifurcation' of solutions, when

$\dot x = F(x,\mu)$, and at $\mu=\mu^*$, $DF(x,\mu^*)$ is singular, but non-singular at every other value of $\mu$. The equilibrium will depend continuously on $\mu$ and 'after' stability is lost, new stable equilibria will appear. (this lacks mathematical precision, but I think it suits the purpose of stating the intuition of bifurcation)

Any help would be appreciated.

• I'd think singular means non-simultaneous in this context. Meaning that the equation is identifiable. I can be wrong though – EconJohn Apr 25 '18 at 3:19
• Are you referring to Ingram, B., Kocherlakota, N., Savin, N.E., 1994. Explaining business cycles: A multiple shock approach. Journal of Monetary Economics 34, pp 415-428? It would be helpful to include a link in your question. – Adam Bailey Apr 25 '18 at 10:02

The authors are referring to "stochastically singular models". What you state above is basically the definition: a number of shocks smaller than the number of observable endogenous variables. The intro to Zhongjun Qu's working paper "A Composite Likelihood Framework for Analyzing Singular DSGE Models" surveys the literature on the topic.

I assume the term comes from measure theory. If you have $n$ observable variables but they lie in a lower-dimensional subspace, then the probability measure is singular with respect to Lesbesgue measure. (Understanding this is not important for understanding the concept.)

I have tried to grab the article to read it, but my library apparently doesn't subscribe to JME as full text. However, when I have seen the word singular used in economics it is usually in the framework of a singular matrix. As this article appears to be a criticism of another model, it would appear they are arguing the other model would not give rise to an invertible matrix. In the above set of comments, it is implying that the stochastic component is vanishing and that the model is deterministic, despite the fact, there are no actual deterministic models in economics if you have to measure things.

My guess is that they are criticizing the other model by showing it can't work.

• Dave, thanks for the answer. Search for sci-hub. it's a nice thing. ;) – An old man in the sea. Apr 25 '18 at 15:28


text:
# [tex-live] e-TeX schedule

Reinhard Kotucha reinhard.kotucha at web.de
Sun Aug 15 03:24:54 CEST 2004

>>>>> "Gerben" == Gerben Wierda <Gerben.Wierda at rna.nl> writes:

> I understand from another discussion that kpathsea is getting
> that on this list.  Has it been discussed/described on another
> list so that I can have a look?

> The reason is that the Mac TeX working group is talking with
> Apple about a small chance of including TeX by default on the
> next Mac OS release, but we would have to investigate any
> instrument that keeps the initial distribution small. As someone
> caveats) over the last years, I might be able to contribute,
> maybe.

Don't know how small it must be.  But wouldn't it be sufficient if the
programs can read compressed files?  It is probably much easier to
Thus, compression is quite efficient.

There are some files you can omit, for instance the afm files.

Maybe you can omit most of the fonts and some format files like
Context.  If a TeX files requires a particular font (a tfm file), a
script is called.  It shouldn't be too difficult to patch the script

The same can be done with fmtutil.  Context and the Czech, Polish and

you put the files into the user's directory tree, which means that
some users have to download the same files, or you have to set
permissions of the texmf tree to 1777.  This is ok for tfm and pk
files, but tex files can be dangerous with the advent of \write18.

Uncompression of files can either be done on the fly, which is quite
safe if kpathsea uses libz, or it can be done by a script which calls
a setuid program which does nothing else then uncompress files in the
texmf tree.

Regards,
Reinhard

--
----------------------------------------------------------------------------
Reinhard Kotucha			              Phone: +49-511-4592165
Marschnerstr. 25
D-30167 Hannover	                      mailto:reinhard.kotucha at web.de
----------------------------------------------------------------------------
Microsoft isn't the answer. Microsoft is the question, and the answer is NO.
----------------------------------------------------------------------------


text:
## Characterization and computation of closed geodesics on toroidal surfaces.(English)Zbl 1228.53006

Summary: The aim of the present study is to characterize and compute closed geodesics on toroidal surfaces. We show that a closed geodesic must make a number of rotations about the equatorial part ($$k$$ rotations) and the axis of revolution ($$k'$$ rotations) of the surface. We give the relation that exists between the numbers $$k$$ and $$k'$$, and Clairaut’s constant $$C$$ corresponding to the geodesic. Moreover, we prove that the numbers $$k$$ and $$k'$$ are relatively prime. We validate our findings by constructing closed geodesics on some examples of toroidal surfaces using MAPLE. Finally, using experimental data on cardiac fiber direction, we show that the fibers run as geodesies in the left ventricle whose geometrical shape looks like a toroidal surface.

### MSC:

 53A05 Surfaces in Euclidean and related spaces 53C22 Geodesics in global differential geometry 68U05 Computer graphics; computational geometry (digital and algorithmic aspects) 92C05 Biophysics

Maple


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# Need help understanding Current Transformer Sensor

#### shma

Joined Jan 11, 2012
5
Hello,
I am starting a project to compute the power consumed by load so, I came to know about current transformer sensor but have never used it before. Can I get some idea about how current transformer sensor works? does it only measure current or it can measure power too. I would be using microcontroller to do the calculations and displaying result.
Thanks

Last edited:

#### hgmjr

Joined Jan 28, 2005
9,029
A current transformer is typically used to measure AC current. Are you needing to measure AC current or DC current?

hgmjr

#### shma

Joined Jan 11, 2012
5
I need to measure AC current. I have a confusion, if I need to measure current through certain load lets say bulb, do I need two current sensor or the single one would do it. I just got confused because of two live wires and one neutral wire. Thanks for the reply

#### hgmjr

Joined Jan 28, 2005
9,029
One current transformer is all you should require to measure the AC current. The signal from the current transformer will be roughly sinusoidal. Either 50 Hertz or 60 Hertz in frequency depending on what country you are in.

Also since you are looking to calculate power you will need to measure the voltage as well.

hgmjr

#### CDRIVE

Joined Jul 1, 2008
2,219
Keep in mind that a multiplying the AC voltage by the AC current to find power is only valid for non reactive (resistive) loads. Because of this your readings will be 'apparent power' for reactive loads.

#### DickCappels

Joined Aug 21, 2008
7,424
If you are going to measure power to resistive loads like a cloths iron or a light blub, then you can just measure current and assume that it is a complete sine wave in phase with a fixed voltage sine wave. In other words: RMS current X K (where K is a constant you come up with!) = Watts.

If you want to measure anything else, especially motors, you will need to take the waveform and the phase of the current waveform with respect to the voltage waveform. One way is to multiply instantaneous voltage times instantaneous current (at the same instant) for small slices of time, with many samples per cycle, then average that over some number of cycles. This process is discussed by Tom Lancaster in the Tech Musings issue at the URL below.
http://www.tinaja.com/glib/muse112.pdf

Last edited:

#### BillB3857

Joined Feb 28, 2009
2,544
If using a current transformer, be sure to apply a proper load to the output otherwise voltages can rise to dangerous levels, even to the point of destruction of the current transformer.

#### shma

Joined Jan 11, 2012
5
I am trying to measure the power of general loads like lamp, and other daily use instrument so, can you give me more knowledge about what to keep on mind for safety while using current transformer sensor. Thanks for all the replies and help..........

#### shma

Joined Jan 11, 2012
5
Thanks......Can I get some idea about how can I measure dc current? I am using battery as source to some load. I looked at dc current sensor but they are very expensive. Is there some way to measure dc current. Then, I need to take the measurement to microcontroller and display the current the load is consuming. I have some knowledge about microcontroller.

#### shma

Joined Jan 11, 2012
5
Thanks......Can I get some idea about how can I measure dc current? I am using battery as source to some load. I looked at dc current sensor but they are very expensive. Is there some way to measure dc current. Then, I need to take the measurement to microcontroller and display the current the load is consuming. I have some knowledge about microcontroller.

#### crutschow

Joined Mar 14, 2008
27,177
If you don't need isolation you can simply place a small resistor (shunt) in series with the load and then amplify the small shunt voltage for the microcontroller input.

Easiest is to place the shunt in the return line since the shunt voltage is referenced to ground, but that does require that the load not have the same common as your microprocessor.

Otherwise you can place the shunt in the plus supply to the load but that requires measuring a small voltage across a resistor sitting at the supply rails. This requires a differential amp with a good common-mode rejection when measuring at the supply voltage (needs rail-rail type amp). There are also dedicated ICs that are designed to measure this shunt voltage at the supply rails for current measurement.

#### CDRIVE

Joined Jul 1, 2008
2,219
Have you considered an Ammeter?

#### BillB3857

Joined Feb 28, 2009
2,544
Most ammeters won't provide an input to a microprocessor. The low ohm resistor connected to ground on one end is probably the best option. How much current is involved? 1 amp or less or hundreds of amps. Makes a big difference.

#### CDRIVE

Joined Jul 1, 2008
2,219
Most ammeters won't provide an input to a microprocessor.
Really? When did that happen?

Here, for a $4.99 it will measure from 100uA (FS) to 10A (FS). This means it's capable of measuring a few microamps. http://www.harborfreight.com/7-function-digital-multimeter-90899.html FYI: Prior to the digital age we worked with D'arsonval meters. That's analog to the uninitiated. These meters were usually spec'd at 50uA FS @ 100mV. This movement was used in mutimeters that measured Amps, Volts and Ohms, using internal shunts and multiplier resistors and battery for the Ohms function. Last edited: #### BillB3857 Joined Feb 28, 2009 2,544 Really? When did that happen? Here, for a$4.99 it will measure from 100uA (FS) to 10A (FS). This means it's capable of measuring a few microamps.

http://www.harborfreight.com/7-function-digital-multimeter-90899.html

FYI: Prior to the digital age we worked with D'arsonval meters. That's analog to the uninitiated. These meters were usually spec'd at 50uA FS @ 100mV. This movement was used in mutimeters that measured Amps, Volts and Ohms, using internal shunts and multiplier resistors and battery for the Ohms function.

I must be showing my age! When I think of Ammeter, I do think of the moving coil/moving vane types. Otherwise, I think DMM. I would say he would be hard pressed to use the Harbor Freight unit as an input to a micorprocessor. If you can think of a unit that would provide proper inputs to a micro within his budget, please enlighten me. Never too old to learn.

#### CDRIVE

Joined Jul 1, 2008
2,219
If you can think of a unit that would provide proper inputs to a micro within his budget, please enlighten me. Never too old to learn.
Bill, I honestly haven't a clue what you mean by that. What does that mean? Sgt. Wookie uses a Harbor Freight DMM. If it's good enough for him it's good enough for almost anyone.

BTW, that meter is cheap enough to sacrifice for conversion to a permanent panel meter. Also, analog & digital panel meters are readily available.

Some dig & analog panel meters.

http://www.mpja.com/prodinfo.asp?number=12306+ME

http://www.allelectronics.com/index.php?page=seek&id[m]=pattern&id[q]=Dc+Panel+Meter

Chris

Last edited:

#### BillB3857

Joined Feb 28, 2009
2,544
CDrive, enlighten me, please. How do you connect a HF meter to a uProcessor? I do have a Radio Shack meter with serial output, but that's built into the meter.

#### crutschow

Joined Mar 14, 2008
27,177
Originally Posted by BillB3857
If you can think of a unit that would provide proper inputs to a micro within his budget, please enlighten me. Never too old to learn.
Bill, I honestly haven't a clue what you mean by that. What does that mean? ............
Chris
It seems clear to me. It's a meter that has a digital output that a microprocessor can read so the data can be processed by the micro.

#### CDRIVE

Joined Jul 1, 2008
2,219
Bill, tt would appear that the problem here is leakage between my ears. I thought I read the OP's posts thoroughly but evidently not. I totally misinterpreted his requirements. I thought he simply wanted to measure the current draw of a uC, not use a uC to measure current of an another load.... Duh!

My apologies Bill, your brain is working fine. It's mine that's deteriorating. I'm going to go back and read through this thread verrrrrry sloooowly.

Getting old sucks!!

Chris


text:
LaTeX - Multiple pages on a code listing inside a beamer frame

I'm trying to put some Python code on a beamer slide. I would like to take one big file and print it with lstinputlisting.

I've tried to set the frame fragile with:

\begin{frame} [fragile]
\lstinputlisting{my_big_file.py}
\end{frame}

It compiles ok, but LaTeX seems to ignore me =(

Am I missing something?

-

migrated from stackoverflow.comSep 30 '11 at 11:26

This question came from our site for professional and enthusiast programmers.

You're missing a description of which behavior you're observing and how it differs from your expected/desired result. "LaTeX seems to ignore me" is not really informative. –  Henning Makholm Sep 12 '11 at 22:12
Welcome to TeX.sx! Your question was migrated here from Stack Overflow. Please register on this site, too, and make sure that both accounts are associated with each other, otherwise you won't be able to comment on or accept answers or edit your question. –  N.N. Sep 30 '11 at 11:34

1 Answer

Usually the allowframebreaks option allows that overlong content creates several frames. However, this seems not to work with \lstinputlisting. My suggestion is therefore to use a loop to include only e.g. 10 lines of code per slide. If this should really be done for a presentation is an own question, I only answer the technical part.

Here I use \foreach from pgffor to loop in steps of 10 from the first to the last page (120 in this example). Then \only<+> is used to create a new slide as part of the frame. I also added a subtitle to show the current line number. This requires some manually expanding because the loop variable isn't accessible otherwise.

\documentclass{beamer}
\usepackage{listings}
\usepackage{pgffor}
\begin{document}

\begin{frame}{My code}
\lstset{language=python,basicstyle=\sffamily\small}%
\foreach \n in {1,11,...,120} {%
\only<+>{%
\edef\m{\the\numexpr\n+9\relax}%
\edef\thesubtitle{{Lines \n--\m\ / 120}}%
\expandafter\framesubtitle\thesubtitle
\lstinputlisting[firstline=\n,lastline=\m]{my_big_file.py}%
}%
}
\end{frame}

\end{document}

This code creates 12 slides. You only need to adjust the title text and the maximum line number. Note that the fragile option is not required here because the frame doesn't actually include verbatim material directly.

-


text:
# Can Shamir's SSS be augmented so that having the secret as well as half the shares necessary to construct the secret is enough to reconstruct the key?

More generally, is it possible to construct a $$(k,n)$$ threshold secret sharing scheme (i.e. let than k shares leaks no statistical information about the secret) such that possession of the secret along with fewer than $$\left\lfloor \frac{k-1}{2} \right\rfloor$$ is enough to reconstruct the entire key (i.e. the entire polynomial)?

Context: I am trying to use a classical secret sharing scheme in a quantum setting, which requires erasing memory about the key once the secret is constructed.

So, if you have a $$(k,n)$$ threshold scheme, this means that your polynomial is of degree $$k - 1$$. That means you need $$k$$ points to interpolate the polynomial. The secret is just another data point. So, to reconstruct the very same polynomial used initially, possession of the secret should not help. You'd still need enough $$(x,y)$$ pairs to get back to the polynomial.

More generally, is it possible to construct a $$(k,n)$$ threshold secret sharing scheme (i.e. let than k shares leaks no statistical information about the secret) such that possession of the secret along with fewer than $$\left\lfloor \frac{k-1}{2} \right\rfloor$$ is enough to reconstruct the entire key (i.e. the entire polynomial)?

Well, if that's the problem you need to solve, well, sure, it is possible.

One obvious approach would be to extend your secret by including 256 random bits; you then take your extended secret $$S'$$, and construct a $$(k,n)$$ secret sharing scheme with that, using the bits from $$\text{SHAKE}(S')$$ as the source of the bits to construct your polynomial (rather than selecting them at random).

So, when you reconstruct the secret $$S'$$, that secret is sufficient to completely reconstruct the entire polynomial (along with 0 shares, which is fewer than $$\left\lfloor \frac{k-1}{2} \right\rfloor$$); when it comes time to use the secret, you just ignore the 256 random bits you added to $$S'$$

Now, I get the feeling that this doesn't really answer the question you really wanted to ask, but I don't know what that question is...

• Ah, I require that no randomness is added to the secret. Maybe this will help: Alice and Bob each hold 2 shares of a (5,2) and Eve holds 1 share. Alice and Bob deduce from their shares the secret as well as the key. They now have to turn over the information about the key to Eve, but before doing so they are aloud to act on the key with a function that is invertible given the secret (which should contain no information about the key). Given Alice and Bob know what share Eve holds, a natural choice is to turn the key into Eve's share. I am wondering if this is possible. Apr 26 '19 at 16:42
• @cplusplusguru: if your shared secret is unguessable (e.g. it's a random AES key), then you can get away without the 256 random bits (which are there so that the adversary could not verify a guess of the shared secret) Apr 26 '19 at 16:51


text:
# Speed up PyCharm Debugging with Psyco

I’ve been digging what JetBrains is doing with PyCharm, and I’m looking forward to the 1.0 release. Almost everyone doing Python development at work has switched to it. I noticed something a while back that peaked my curiosity, though. While debugging, I came across a cryptic message in PyCharm’s console window:

pydev debugger: warning: psyco not available for speedups (the debugger will still work correctly, but a bit slower)

What’s all this now? Are you saying something on my box isn’t running as fast as it could be? That wouldn’t do at all.

So, I loaded up my web browser. A quick Google search later and I’d found the psyco project on Sourceforge. Psyco is a specialized Python compiler, created by Armin Rigo who is now working on PyPy. Psyco speeds up the execution of most Python programs with a single extension module. Development of psyco was recently taken over by Christian Tismer, who has made many improvements to psyco.

At work, I tend to live in Windows or Ubuntu, and at the moment I was working in Windows, so I followed the link over to Michael Foord’s site where he’d thrown together some 32-bit Windows binaries for psyco 2.0 on Python 2.4, 2.5, and 2.6. I grabbed the 2.6 version, but I didn’t immediately install it.

To gauge the benefit of a psyco-powered debugger versus one without, I first needed to run a baseline benchmark. My work box is a Dell Precision T7400 with an Intel Zeon E5405 @ 2.0Ghz with 8Gb ram on Windows XP SP2 x64. My Python version is 2.6.5 (32-bit – psyco does not as yet work with x64).

I created a new Python project, and copied the pystone.py benchmark file from my Python distribution’s test folder into it. Here’s the results of my first non-psyco debugger run.

C:/Tools/Python26/python.exe "C:\Program Files (x86)\JetBrains\PyCharm 96.742\helpers\pydev\pydevd.py" --client 127.0.0.1 --port 13926 --file C:/Source/PsycoTest/pystone.py
Connected to pydevd (version 1.1)
pydev debugger: warning: psyco not available for speedups (the debugger will still work correctly, but a bit slower)
pydev debugger: starting
Pystone(1.1) time for 50000 passes = 8.70703
This machine benchmarks at 5742.49 pystones/second

Process finished with exit code 0

Next, I installed psyco and ran the test again.

C:/Tools/Python26/python.exe "C:\Program Files (x86)\JetBrains\PyCharm 96.742\helpers\pydev\pydevd.py" --client 127.0.0.1 --port 13936 --file C:/Source/PsycoTest/pystone.py
Connected to pydevd (version 1.1)
pydev debugger: starting
Pystone(1.1) time for 50000 passes = 5.49379
This machine benchmarks at 9101.18 pystones/second

Process finished with exit code 0

Not too shabby. My pystone benchmark went from 5742.49 to 9101.18: a 63% improvement just by installing a Python library! Clearly I’m going to have to experiment using psyco for some of my own projects.

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Hi Dale,

thanks for the nice summary and congrats for the speed improvement.

Sadly, I was not able to get the thing to work (that is, the warning didn’t go away) with my setup, which is:
– Python 2.6.4 (32-bit version)
– psyco 1.6
– pydev 1.6.4
– Windows 7 (64-bit)

I installed psyco in the default directory which it seemed to have picked correctly as C:\Python26\Lib\site-packages and this is (also by default) part of pydev’s “System PYTHONPATH”.

Any clues? Could it be a psyco/Python version issue? Or a 32/64-bit problem?


text:
Articles written in Bulletin of Materials Science

• Structural, elastic, optoelectronic and magnetic properties of CdHo$_2$S$_4$ spinel: a first-principle study

We report the results of the full-potential linearized augmented plane wave (FP-LAPW) calculations on the structural, elastic, optoelectronic and magnetic properties of CdHo$_2$S$_4$ spinel. Both the generalized gradient approximation (GGA) and Trans-Blaha modified Becke-Johnson potential (TB-mBJ) are used to model the exchange-correlation effects. The computed lattice parameter, internal coordinate and bulk modulus are in good agreement with the existing experimentaldata. According to the calculated elastic moduli, CdHo$_2$S$_4$ is mechanically stable with a ductile nature and a noticeableelastic anisotropy. The ferromagnetic phase of CdHo2S4 is energetically favourable compared to non-magnetic one, with ahigh magnetic moment of about 8.15 $\mu$B. The calculated band structure demonstrates that the title compound is a direct bandgap semiconductor. The TB-mBJ yields a band gap of $\sim$1.86 and $\sim$2.17 eV for the minority and majority spins, respectively.The calculated optical spectra reveal a strong response in the energy range between the visible light and the extreme UVregions.

• A study on the vibrational frequencies, elastic properties and sound velocities of vanadium spinel oxides AV$_2$O$_4$ (A $=$ Mn, Fe and Zn) short-range non-Coulomb potential theoretical model

Owing to the fact of the AB$_2$O$_4$ spinel oxide’s chemical and thermal stability, and other intriguing properties make them suitable candidate materials for many applications, including chemical looping and catalytic reactions. To do our investigations, a short-range non-Coulomb potential theoretical model is used to calculate the zone-centre, elastic constants, infrared phonon mode frequencies, Raman phonon mode frequencies, velocities of the sound wave along the highly symmetric three crystallographic-axes and Debye temperature of the vanadium spinel oxides AV$_2$O$_4$ (A $=$ Mn, Fe and Zn). The preliminary results of our calculations show that the interaction inthe second neighbour (V–O) is much stronger than the interaction of the first neighbour (A–O). Moreover, from the analysis of the obtained results of elastic constants, the nature of the studied vanadium spinels are found to beductile.

• Temperature effect to investigate optical and structural properties of AZO nanostructures for optoelectronics

Spin-coating technique is employed to deposit nanostructured zinc oxide (ZnO) doping aluminium (Al) on p-Si substrate. Atomic forces microscopy (AFM), X-ray diffraction (XRD), ultraviolet–visible (UV–Vis) and scanning electron microscopies (SEM) are utilized to investigate the influence of annealing temperature in the range of 200 to 600$^{\circ}$C on the morphological, optical, structural and topographical characteristics of Al NPs-doped ZnO (AZO) nanostructure. The average reflectance is proven by the reflectance spectra to be in the wavelength range of 200–1000 nm, and the absorption spectra provided the optical energy gaps of nanostructured AZO. Crystalline and grain size are correlatedwith annealing temperature variations, thus providing more homogeneous and covered surface morphology. Our resultsare nominated for future researches.

• # Bulletin of Materials Science

Volume 44, 2021
All articles
Continuous Article Publishing mode

• # Dr Shanti Swarup Bhatnagar for Science and Technology

Posted on October 12, 2020

Prof. Subi Jacob George — Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur, Bengaluru
Chemical Sciences 2020


text:
# Proposal: Don't read environment files by default

Michael Peyton Jones me at michaelpj.com
Thu Mar 28 18:33:58 UTC 2019

```+1 to the `cabal ghc`/`cabal ghci` etc. solution. This is the approach used
by many other tools that handle this kind of thing. For example:
- nix-shell
- virtualenv
- rbenv
- sbt
- jenv

The advantage is that the scoping of the special configuration is very
clear: it's the shell that the command launches. Programmers are very used
to this, and changes in shell environments are expected to change the
behaviour of programs.

Plus, as functional programmers this is just the sort of idiom we use all
the time! `cabal ghc` is like writing `withProjectGhc \$ \ghc -> ...`.

On the negative side: I've helped ~6 people at my company alone debug
issues due to environment files. Two of those were novice users (the people
whom this feature is supposed to help). In my experience it breaks people's
assumptions about what sort of things influence compiler invocations.
People don't expect a stateful dependency from a previous run of a build
tool to a later run of a lower-level compiler. Moreover, the failures can
be mystifying, and I was only able to help because I already knew "get rid
of any environment files" as a solution to "weird dependency issues".

*However*, I think Herbert is quite right that this particular proposal
amounts to "remove this feature". The following might be a compromise
solution: we can introduce `cabal ghc` as a parallel feature, and then in a
few releases we can assess the popularity of the two approaches, and
potentially stop generating environment files from Cabal if people aren't
using them.

I think there are enough people that feel strongly about environment files
that we could get together the manpower to write `cabal ghc`.

> This is also a workflow which has been well documented for over a decade
in Haskell's literature and instructions *and* this is the same idiom as
used by many popular package managers out there ("\${pkgmgr} install
somelibrary")

This is an interesting bit of background. FWIW, I would feel a lot better
to run `cabal
save-my-local-dependencies-for-use-by-other-programs-yes-I-know-this-has-side-effects`
that wouldn't bother me (I still wouldn't use it, though). The current
situation is a bit like having `\${pkgmgr} build` imply `\${pkgmgr} install`,
which is a bit surprising.

M

On Thu, Mar 28, 2019 at 5:02 PM Bardur Arantsson <spam at scientician.net>
wrote:

> On 28/03/2019 14.58, Oleg Grenrus wrote:
> >
> >     write-ghc-environment-files: never
> >
> > to your ~/.cabal/config assuming you have cabal-insall-2.4.1.0 or later.
> >
>
> That doesn't really work if you actually want to be able to use both
> ways of working, does it? That same thing applies to
>
>   export GHC_ENVIRONMENT=-
>
> which someone else posted, but at least that can be done by tooling
> before invoking ghc. It's odd to have to change a global setting to
> avoid this. (However, thanks for the hints -- I'll be setting that
> GHC_ENVIRONMENT from now on.)
>
> +1 for changing the default.
>
> It seems really weird to force other tooling to opt out when this could
> easily be solved by just having
>
>    cabal ghci
>    cabal ghc
>
> commands which set up the environment properly and tell users to use
> that if they want to use cabal's environment files. FWIW, I also see
> e.g. ghc as low-level tooling akin to the plain 'gcc' command whereas
> e.g. cabal or stack are more like cmake + make/ninja, i.e. it's not
> something users should really be running unless they know what they're
> doing *and* it should be as tooling-friendly as possible.
>
> Regards,
>
> _______________________________________________
> ghc-devs mailing list