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• ### A 700-seat no-loss composition for the 2019 European Parliament(1710.03820)

Sept. 23, 2017 q-fin.EC
The following paper is part of the authors' response to an invitation from the Constitutional Affairs Committee (AFCO) of the European Parliament to advise on mathematical methods for the allocation of Parliamentary seats between the 27 Member States following the planned departure of the United Kingdom in 2019. The authors were requested to propose a method that respects the usual conditions of EU law, and with the additional property that no Member State (other than the UK) receives fewer that its 2014 allocation. This paper was delivered to the AFCO on 21 August 2017, for consideration by the AFCO at its meeting in Strasbourg on 11 September 2017.
• ### Quantum measurements with prescribed symmetry(1704.04609)

July 5, 2017 quant-ph
We introduce a method to determine whether a given generalised quantum measurement is isolated or it belongs to a family of measurements having the same prescribed symmetry. The technique proposed reduces to solving a linear system of equations in some relevant cases. As consequence, we provide a simple derivation of the maximal family of Symmetric Informationally Complete measurements (SIC)-POVM in dimension 3. Furthermore, we show that the following remarkable geometrical structures are isolated, so that free parameters cannot be introduced: (a) maximal sets of mutually unbiased bases in prime power dimensions from 4 to 16, (b) SIC-POVM in dimensions from 4 to 16 and (c) contextuality Kochen-Specker sets in dimension 3, 4 and 6, composed of 13, 18 and 21 vectors, respectively.
• ### Multipartite entanglement in heterogeneous systems(1602.08064)

May 12, 2016 quant-ph
Heterogeneous bipartite quantum pure states, composed of two subsystems with a different number of levels, cannot have both reductions maximally mixed. In this work, we demonstrate existence of a wide range of highly entangled states of heterogeneous multipartite systems consisting of $N>2$ parties such that every reduction to one and two parties is maximally mixed. Two constructions of generating genuinely multipartite maximally entangled states of heterogeneous systems for an arbitrary number of subsystems are presented. Such states are related to quantum error correction codes over mixed alphabets and mixed orthogonal arrays. Additionally, we show the advantages of considering heterogeneous systems in practical implementations of multipartite steering.
• ### Induced Ginibre ensemble of random matrices and quantum operations(1107.5019)

Jan. 5, 2012 math-ph, math.MP
A generalisation of the Ginibre ensemble of non-Hermitian random square matrices is introduced. The corresponding probability measure is induced by the ensemble of rectangular Gaussian matrices via a quadratisation procedure. We derive the joint probability density of eigenvalues for such induced Ginibre ensemble and study various spectral correlation functions for complex and real matrices, and analyse universal behaviour in the limit of large dimensions. In this limit the eigenvalues of the induced Ginibre ensemble cover uniformly a ring in the complex plane. The real induced Ginibre ensemble is shown to be useful to describe statistical properties of evolution operators associated with random quantum operations, for which the dimensions of the input state and the output state do differ.
• ### Random Bistochastic Matrices(0711.3345)

Ensembles of random stochastic and bistochastic matrices are investigated. While all columns of a random stochastic matrix can be chosen independently, the rows and columns of a bistochastic matrix have to be correlated. We evaluate the probability measure induced into the Birkhoff polytope of bistochastic matrices by applying the Sinkhorn algorithm to a given ensemble of random stochastic matrices. For matrices of order N=2 we derive explicit formulae for the probability distributions induced by random stochastic matrices with columns distributed according to the Dirichlet distribution. For arbitrary $N$ we construct an initial ensemble of stochastic matrices which allows one to generate random bistochastic matrices according to a distribution locally flat at the center of the Birkhoff polytope. The value of the probability density at this point enables us to obtain an estimation of the volume of the Birkhoff polytope, consistent with recent asymptotic results.
• ### Sub-- and super--fidelity as bounds for quantum fidelity(0805.2037)

Nov. 19, 2008 quant-ph
We derive several bounds on fidelity between quantum states. In particular we show that fidelity is bounded from above by a simple to compute quantity we call super--fidelity. It is analogous to another quantity called sub--fidelity. For any two states of a two--dimensional quantum system (N=2) all three quantities coincide. We demonstrate that sub-- and super--fidelity are concave functions. We also show that super--fidelity is super--multiplicative while sub--fidelity is sub--multiplicative and design feasible schemes to measure these quantities in an experiment. Super--fidelity can be used to define a distance between quantum states. With respect to this metric the set of quantum states forms a part of a $N^2-1$ dimensional hypersphere.
• ### Quantum state discrimination: a geometric approach(0711.4286)

Nov. 27, 2007 quant-ph
We analyse the problem of finding sets of quantum states that can be deterministically discriminated. From a geometric point of view this problem is equivalent to that of embedding a simplex of points whose distances are maximal with respect to the Bures distance (or trace distance). We derive upper and lower bounds for the trace distance and for the fidelity between two quantum states, which imply bounds for the Bures distance between the unitary orbits of both states. We thus show that when analysing minimal and maximal distances between states of fixed spectra it is sufficient to consider diagonal states only. Hence considering optimal discrimination, given freedom up to unitary orbits, it is sufficient to consider diagonal states. This is illustrated geometrically in terms of Weyl chambers.
• ### Random unistochastic matrices(nlin/0112036)

Aug. 28, 2002 nlin.CD
An ensemble of random unistochastic (orthostochastic) matrices is defined by taking squared moduli of elements of random unitary (orthogonal) matrices distributed according to the Haar measure on U(N) (or O(N), respectively). An ensemble of symmetric unistochastic matrices is obtained with use of unitary symmetric matrices pertaining to the circular orthogonal ensemble. We study the distribution of complex eigenvalues of bistochastic, unistochastic and ortostochastic matrices in the complex plane. We compute averages (entropy, traces) over the ensembles of unistochastic matrices and present inequalities concerning the entropies of products of bistochastic matrices.
• ### CP^n, or, entanglement illustrated(quant-ph/0108064)

Aug. 13, 2001 quant-ph, hep-th
We show that many topological and geometrical properties of complex projective space can be understood just by looking at a suitably constructed picture. The idea is to view CP^n as a set of flat tori parametrized by the positive octant of a round sphere. We pay particular attention to submanifolds of constant entanglement in CP^3 and give a few new results concerning them.
• ### Spectrum of the Frobenius-Perron operator for systems with stochastic perturbation(nlin/0106003)

June 4, 2001 nlin.CD
We analyze the problem of evolution in a system with stochastic perturbation and point out that analytic properties of the noise present in the system might determine spectral properties of the evolution operator (Frobenius-Perron operator). We also propose a method for approximation of the spectrum and eigenvectors of the FP-operator by applying a suitable noise. Moreover we demonstrate that the eigenvalues of the FP-operator located outside the essential spectrum are robust not only against local perturbation but also against the non local perturbation and that these stable eigenvalues have a direct physical meaning: they determine the rate of the exponential decay of correlation in the system.
• ### Time-reversal symmetry and random polynomials(chao-dyn/9611003)

We analyze the density of roots of random polynomials where each complex coefficient is constructed of a random modulus and a fixed, deterministic phase. The density of roots is shown to possess a singular component only in the case for which the phases increase linearly with the index of coefficients. This means that, contrary to earlier belief, eigenvectors of a typical quantum chaotic system with some antiunitary symmetry will not display a clustering curve in the stellar representation. Moreover, a class of time-reverse invariant quantum systems is shown, for which spectra display fluctuations characteristic of orthogonal ensemble, while eigenvectors confer to predictions of unitary ensemble.


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# 7.3 Clouds and Weather on Gas Giant Planets

The atmospheres of the giant planets are thick with clouds and haze, so thick that we can’t see the surfaces of these worlds. The clouds on all four giant planets are organized in systems of dark belts and bright zones that run parallel to their equators. These can best be seen on Jupiter and Saturn. The clouds of the Jovian planets are believed to be composed primarily of ice crystals: frozen ammonia, ammonium hydrosulfide, and water. These compounds don’t represent the overall composition of hydrogen and helium. They’re minor constituents that condensed out of the atmospheres, in the same way that a minor constituent, water vapor, condenses out of Earth’s atmosphere to form terrestrial clouds.

Jupiter, the largest planet in the solar system, as seen by the Hubble Space Telescope. Click here for original source URL.

Saturn, in natural colors. Click here for original source URL.

Colors and patterns reveal conditions in planet atmospheres. Differences in the cloud patterns and colors of the giant planets are explained by differences in atmospheric temperature, chemistry, and structure. On Jupiter and Saturn, the bright zones are whitish or yellowish, and the darker belts show gray-brown and reddish tinges. The colored compounds in the clouds — including polysulfides, phosphorus, and organic compounds — stain the clouds these colors. The word organic does not imply the presence of life, but merely describes the complex chemistry of carbon-hydrogen bonds in the clouds of these planets. Keep in mind that many of the published images of planet atmospheres have had their colors amplified for cosmetic reasons. The true colors of the giant planets are quite delicate and subtle.

Neptune as seen by Voyager 2. Click here for original source URL.

Uranus in natural colors. Click here for original source URL.

The clouds on Uranus are indistinct, because they are hidden beneath a thick, hazy upper atmosphere. The blue colors of Uranus and Neptune are caused by two phenomena: first, the absorption of red light by methane, which is an important constituent of the haze above their clouds. Second, the same scattering of blue light that exists in Earth's atmosphere also occurs in these giant planets. The blue color is less prominent for Jupiter and Saturn because their uppermost clouds have less methane haze above them.

Zones, belts and vortices on Jupiter. The wide equatorial zone is visible in the center surrounded by two dark equatorial belts (SEB and NEB). The large grayish-blue irregular "hot spots" at the northern edge of the white Equatorial Zone change over the course of time as they march eastward across the planet. The Great Red Spot is at the southern margin of the SEB. Strings of small storms rotate around northern-hemisphere ovals. Small, very bright features, possible lightning storms, appear quickly and randomly in turbulent regions. The smallest features visible at the equator are about 600 kilometers across. This 14-frame animation spans 24 Jovian days, or about 10 Earth days. The passage of time is accelerated by a factor of 600,000. Click here for original source URL.

The clouds on the Jovian planets are dynamic; they are in constant motion. Even a backyard telescope reveals that Jupiter's cloud belts change. The clouds change from month to month and year to year due to turbulent movements of the atmosphere, just as clouds on the Earth change from day to day. The Voyager probes measured winds on Jupiter blowing eastward along the equatorial and temperate zones at speeds 150 meters per second (340 mph) faster than the movements of the clouds in the dark equatorial belts. Saturn has even higher differential wind speeds: the eastward jet stream along the equator moves up to 450 meters per second (1010 mph) faster than the neighboring belts. The colors, wind shear patterns, and clouds up welling from below combine to produce fascinating, swirling patterns of color, reminiscent of abstract paintings.

Rough visual comparison of Jupiter, Earth, and the Great Red Spot. Approximate scale is 44 kilometers per pixel. Click here for original source URL.

The most famous and dramatic feature on any of the giant planets is Jupiter’s Great Red Spot, which is an oval storm system. It has existed for at least 330 years, since G. D. Cassini first reported it in 1665. The Great Red Spot became more strongly visible around 1887, when it was rediscovered and given its current name. It’s three times the size of the Earth! This and other smaller transient spots are probably hurricane-like systems. Small clouds approaching the Red Spot get caught in a counterclockwise circulation, like leaves in a giant whirlpool. In recent years smaller red spots have formed (starting out white in some cases), and then merged together and faded away. This shows that Jupiter is still a planet with atmospheric surprises.

These are two images of lightning on the night side of?Jupiter?taken by the?Galileo Orbiter?in 1997. Click here for original source URL.

There is also intense electrical activity in the violent storm systems of Jupiter. Voyagers' photos of the night side revealed mighty blasts of lightning playing among the clouds. The parachuted probe also detected radio static from distant lightning. Typical lightning strokes were more energetic than on Earth, but there were fewer per unit area than on Earth. Voyager also photographed enormous auroral displays like the northern lights and southern lights of Earth, flickering high above the clouds in Jupiter's polar regions. Saturn's atmosphere has less lightning and less auroral activity, and the atmospheres of Uranus and Neptune are still less active.

Modeling weather systems of giant planets is a good test of our understanding of climate and air circulation on our own planet. A particularly active area of current scientific research uses theoretical models to compare the atmospheric circulation of the Jovian planets with the terrestrial atmosphere. Why are cyclonic swirls are more prominent than belt patterns on the Earth? Why do storms last for hundreds of years on Jupiter, but only weeks on Earth? How does energy flow through atmospheres of different compositions? The answers to these and similar questions may help us clarify our understanding of the Earth.

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# Confusion about dimensional regularization

I am recently trying to understand dimensional regularization in the context of quantum field theory. So to solve an integral $$\int_{\mathbb R^d} \frac{\text d ^d p}{(2 \pi)^d} \frac{1}{(p^2 + m^2)^2}$$ which is divergent for $$d = 4$$ it is often said that if one assumes that $$d \in \mathbb C$$ with sufficiently small $$\text{Re}(d)$$ it is possible to do some kind of analytic continuation. But in examples it is often shown that one uses $$d = 4 - \varepsilon$$ and then transforms to hyper spherical coordinates to get an expression like: $$\int_{\mathbb R^+}\frac{\text d p}{(2\pi)^{4-\varepsilon}} \frac{2\pi^{(4-\varepsilon)/2}}{\Gamma\left(\frac{4 - \varepsilon}{2}\right)} \frac{p^{3-\varepsilon}}{(p^2 + m^2)^2}$$ which has a solution. We then expand for small values of $$\varepsilon$$.

Question:

Why is it necessary for $$d$$ to be complex?$$\quad\rightarrow$$ is there a possibility to stay real ?

Why is it legal to transform in hyper spherical coordinates when complex dimension is assumed ?

Do i get right that we expand the solution to the second integral in a laurent series for small $$\varepsilon$$ to extract terms which do not diverge at $$\varepsilon=0$$ and then when adding amplitudes the divergent terms cancel out ( dependent on the process of course ) ?

• FWIW, analytic continuation into the complex plane comes for free. Do you want to stay on the real line? May 2 '20 at 14:00
• @Qmechanic i reread my question and commit that it was kind of unclear what i am asking. So i edited it. I know it is not welcome to ask multiple questions in one thread but since these are kind of related to the same problem i hope it is excused in this case. May 2 '20 at 14:40

3) Well the expansion in $$\epsilon$$ is right, you expand in a laurent series in $$\epsilon$$ (This uniquely defines your analytic continuation btw). You don't just add amplitudes that you got from your previous lagrangian. There are several ways to formulate the process of Renormalization but what I find the most convenient is via counterterms. You include additional, divergent terms in your lagrangian by redefinition of your masses, fields and coupling constants. These new terms induce new Feynman diagrams which you have to include in your amplitude calculation and the divergencies from your previous loop integrals cancel with these new feynman diagrams (at least for uv divergencies as far as I know, I'm still learning so I haven't gotten to infrared divergencies yet)


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# "the period of a pendulum, T (in seconds) varies directly with the square root of the length of the pendulum, L (in centimeters)". Given that a pendulum of length 9cm has a period of 0.63 seconds, find:

a) The period of a pendulum of length 25cm

b) The length of a pendulum whose period is 1.5 seconds,

thanks :)

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1. Given
T seconds =k √L (cm)

where k is an arbitrary constant to be determined.

Also given

0.63=k√9
Therefore we can determine the constant k.
k=0.63/√9=0.21

T(L)=0.21√L
where T is period in seconds
and L is length of pendulum in cm.

The problem reduces to:
a) T(25)=?
b) if T(L)=1.5 s, what is L?

Can you take it from here?

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2. 👎
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4. 🚩
2. T = k√L
so, T/√L is constant.

(a) .63/√9 = T/√25

(b) .63/√9 = 1.5/√L

1. 👍
2. 👎
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## Ishihara, Toru

Compute Distance To:
 Author ID: ishihara.toru Published as: Ishihara, Toru; Ishihara, T.; Ishihara, Tôru more...less
 Documents Indexed: 50 Publications since 1969 Reviewing Activity: 109 Reviews Co-Authors: 3 Co-Authors with 6 Joint Publications 20 Co-Co-Authors
all top 5

### Co-Authors

 37 single-authored 5 Goldberg, Samuel I. 2 Petridis, Nicholas C. 1 Felsen, Leopold B. 1 Hara, Fumimaro 1 Imado, Fumiaki 1 Wu, Jingwei 1 Wu, Q. M. Jonathan 1 Zheng, Ling’ai
all top 5

### Serials

 14 Journal of Mathematics. Tokushima University 8 Journal of Mathematics. The University of Tokushima 5 Proceedings of the American Mathematical Society 2 International Journal of Control 2 Journal of Differential Geometry 1 Computers & Mathematics with Applications 1 Discrete Mathematics 1 Journal of the Acoustical Society of America 1 American Journal of Mathematics 1 Geometriae Dedicata 1 Journal of the London Mathematical Society. Second Series 1 Journal of Mathematics of Kyoto University 1 Journal of the Mathematical Society of Japan 1 Manuscripta Mathematica 1 Michigan Mathematical Journal 1 Theoretical Computer Science 1 Tôhoku Mathematical Journal. Second Series 1 Transactions of the American Mathematical Society 1 European Journal of Combinatorics 1 RIMS Kokyuroku 1 Control and Intelligent Systems 1 Bulletin of the American Mathematical Society 1 Journal of Mathematics. Tokushima University
all top 5

### Fields

 28 Differential geometry (53-XX) 9 Combinatorics (05-XX) 8 Global analysis, analysis on manifolds (58-XX) 5 Functions of a complex variable (30-XX) 5 Potential theory (31-XX) 4 Systems theory; control (93-XX) 2 Several complex variables and analytic spaces (32-XX) 2 Fluid mechanics (76-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Number theory (11-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Manifolds and cell complexes (57-XX) 1 Computer science (68-XX) 1 Information and communication theory, circuits (94-XX)

### Citations contained in zbMATH Open

27 Publications have been cited 291 times in 245 Documents Cited by Year
A mapping of Riemannian manifolds which preserves harmonic functions. Zbl 0421.31006
Ishihara, Toru
1979
Maximal spacelike submanifolds of a pseudo-Riemannian space of constant curvature. Zbl 0682.53055
Ishihara, Toru
1988
Harmonic sections of tangent bundles. Zbl 0427.53019
Ishihara, Toru
1979
The harmonic Gauss maps in a generalized sense. Zbl 0498.53041
Ishihara, T.
1982
Classifying molecular sequences using a linkage graph with their pairwise similarities. Zbl 0912.68218
Matsuda, H.; Ishihara, T.; Hashimoto, A.
1999
Mappings of bounded dilatation of Riemannian manifolds. Zbl 0328.30022
Goldberg, S. I.; Ishihara, T.; Petridis, N. C.
1975
Surfaces of revolution in the Lorentzian 3-space. Zbl 0677.53068
Ishihara, Toru; Hara, Fumimaro
1988
Harmonic quasiconformal mappings of Riemannian manifolds. Zbl 0328.30023
Goldberg, Samuel I.; Ishihara, Toru
1976
Riemannian submersions commuting with the Laplacian. Zbl 0381.53033
Goldberg, S. I.; Ishihara, T.
1978
Harmonic quasiconformal mappings of Riemannian manifolds. Zbl 0283.30025
Goldberg, Samuel I.; Ishihara, Toru
1974
Complete Möbius strips minimally immersed in $$\mathbb{R}^ 3$$. Zbl 0824.53010
Ishihara, Toru
1989
Complete nonorientable minimal surfaces in $$\mathbb{R}^ 3$$. Zbl 0795.53005
Ishihara, Toru
1992
Radii of immersed manifolds and nonexistence of immersions. Zbl 0438.53054
Ishihara, Toru
1980
On tensor-product structures and Grassmanian structures. Zbl 0218.53049
Ishihara, T.
1970
The Euler characteristics and Weyl’s curvature invariants of submanifolds in sphere. Zbl 0621.53045
Ishihara, Toru
1987
LTR design of disturbance cancellation integral controllers for time-delay plants. Zbl 1152.93376
Ishihara, T.; Guo, H.-J.
2008
Signed graphs associated with the lattice $$A_n$$. Zbl 1032.05061
Ishihara, Toru
2002
Pandiagonal constant sum matrices. Zbl 1138.05306
Ishihara, Toru
2007
On the stability of maximal submanifolds in pseudo-Riemannian manifolds. Zbl 0641.53059
Ishihara, Toru
1987
The index of a holomorphic mapping and the index theorem. Zbl 0375.58011
Ishihara, Toru
1977
Harmonic maps of nonorientable surfaces to four-dimensional manifolds. Zbl 0770.58006
Ishihara, Toru
1993
Nonexistence of a projective plane minimally immersed with some embeddedness. Zbl 0776.53006
Ishihara, Toru
1992
A remark on harmonic quasiconformal mappings. Zbl 0238.53027
Ishihara, Toru
1971
Enumeration of hypergraphs. Zbl 0996.05074
Ishihara, Toru
2001
Some integral formulas in complex projective spaces. Zbl 0541.53052
Ishihara, Toru
1983
The Gauss map and nonholomorphic harmonic maps. Zbl 0558.53035
Ishihara, Toru
1983
Total curvatures of Kaehler manifolds in complex projective spaces. Zbl 0595.53054
Ishihara, Toru
1986
LTR design of disturbance cancellation integral controllers for time-delay plants. Zbl 1152.93376
Ishihara, T.; Guo, H.-J.
2008
Pandiagonal constant sum matrices. Zbl 1138.05306
Ishihara, Toru
2007
Signed graphs associated with the lattice $$A_n$$. Zbl 1032.05061
Ishihara, Toru
2002
Enumeration of hypergraphs. Zbl 0996.05074
Ishihara, Toru
2001
Classifying molecular sequences using a linkage graph with their pairwise similarities. Zbl 0912.68218
Matsuda, H.; Ishihara, T.; Hashimoto, A.
1999
Harmonic maps of nonorientable surfaces to four-dimensional manifolds. Zbl 0770.58006
Ishihara, Toru
1993
Complete nonorientable minimal surfaces in $$\mathbb{R}^ 3$$. Zbl 0795.53005
Ishihara, Toru
1992
Nonexistence of a projective plane minimally immersed with some embeddedness. Zbl 0776.53006
Ishihara, Toru
1992
Complete Möbius strips minimally immersed in $$\mathbb{R}^ 3$$. Zbl 0824.53010
Ishihara, Toru
1989
Maximal spacelike submanifolds of a pseudo-Riemannian space of constant curvature. Zbl 0682.53055
Ishihara, Toru
1988
Surfaces of revolution in the Lorentzian 3-space. Zbl 0677.53068
Ishihara, Toru; Hara, Fumimaro
1988
The Euler characteristics and Weyl’s curvature invariants of submanifolds in sphere. Zbl 0621.53045
Ishihara, Toru
1987
On the stability of maximal submanifolds in pseudo-Riemannian manifolds. Zbl 0641.53059
Ishihara, Toru
1987
Total curvatures of Kaehler manifolds in complex projective spaces. Zbl 0595.53054
Ishihara, Toru
1986
Some integral formulas in complex projective spaces. Zbl 0541.53052
Ishihara, Toru
1983
The Gauss map and nonholomorphic harmonic maps. Zbl 0558.53035
Ishihara, Toru
1983
The harmonic Gauss maps in a generalized sense. Zbl 0498.53041
Ishihara, T.
1982
Radii of immersed manifolds and nonexistence of immersions. Zbl 0438.53054
Ishihara, Toru
1980
A mapping of Riemannian manifolds which preserves harmonic functions. Zbl 0421.31006
Ishihara, Toru
1979
Harmonic sections of tangent bundles. Zbl 0427.53019
Ishihara, Toru
1979
Riemannian submersions commuting with the Laplacian. Zbl 0381.53033
Goldberg, S. I.; Ishihara, T.
1978
The index of a holomorphic mapping and the index theorem. Zbl 0375.58011
Ishihara, Toru
1977
Harmonic quasiconformal mappings of Riemannian manifolds. Zbl 0328.30023
Goldberg, Samuel I.; Ishihara, Toru
1976
Mappings of bounded dilatation of Riemannian manifolds. Zbl 0328.30022
Goldberg, S. I.; Ishihara, T.; Petridis, N. C.
1975
Harmonic quasiconformal mappings of Riemannian manifolds. Zbl 0283.30025
Goldberg, Samuel I.; Ishihara, Toru
1974
A remark on harmonic quasiconformal mappings. Zbl 0238.53027
Ishihara, Toru
1971
On tensor-product structures and Grassmanian structures. Zbl 0218.53049
Ishihara, T.
1970
all top 5

### Cited by 249 Authors

 15 Gudmundsson, Sigmundur 11 de Lima, Henrique F. 9 Baird, Paul 9 Ou, Ye-Lin 8 Akyol, Mehmet Akif 8 Loubeau, Eric 6 Abbassi, Mohamed Tahar Kadaoui 6 Calvaruso, Giovanni 6 Dragomir, Sorin 6 Wood, John C. 6 Zagane, Abderrahim 5 Cheng, Qingming 5 Ghandour, Elsa 5 Perrone, Domenico 5 Velásquez, Marco Antonio Lázaro 4 Dos Santos, Fábio Reis 4 Elhendi, Hichem 4 Goldberg, Samuel I. 4 Ṣahin, Bayram 4 Wood, Chris M. 3 Belarbi, Lakehal 3 Benyounes, Michèle 3 Chaves, Rosa Maria Barreiro 3 Djaa, Nour Elhouda 3 Ishihara, Toru 3 Kamissoko, Dantouma 3 Lakrini, Ibrahim 3 Lopez Fernandez, Francisco Jose 3 Luo, Yong 3 Markellos, Michael 3 Nordstrom, Jonas 3 Romero, Alfonso 3 Svensson, Martin 2 Bejan, Cornelia-Livia 2 Chen, Junfeng 2 Chen, Shaolin 2 Choi, Soon Meen 2 Dong, Yuxin 2 Eells, James jun. 2 Fuglede, Bent 2 Gilkey, Peter B. 2 Hill, Sally L. 2 Kacimi, Bouazza 2 Lettington, Matthew C. 2 Liu, Jiancheng 2 Maeta, Shun 2 Mahesh, Thekkan Veedu 2 Mariano, Maxwell 2 Moosath, Karickamadom Sreekumaran Subrahamanian 2 Mustafa, Muhammad Tahir 2 Özkan, Mustafa 2 Pantilie, Radu 2 Park, Jeonghyeong 2 Perdomo, Oscar Mario 2 Petridis, Nicholas C. 2 Rubio, Rafael María 2 Sakovich, Anna 2 Schmidt, Karl Michael 2 Shu, Shichang 2 Slobodeanu, Radu 2 Soret, Marc 2 Sousa, Luiz Amancio M. jun. 2 Suh, Young Jin 2 Wei, Guoxin 2 Xin, Yuanlong 2 Zhao, Guangwen 1 Åhag, Per 1 Aiyama, Reiko 1 Aledo, Juan Ángel 1 Alem, Amina 1 Alías, Luis J. 1 Aminian, Mehran 1 Aquino, Cicero Pedro 1 Arnaudon, Marc 1 Aryanejad, Yadollah 1 Baek, Jin Ok 1 Balmus, Adina 1 Barletta, Elisabetta 1 Barré, Sylvain 1 Barroso Neto, Nilton Moura 1 Bektaş, Mehmet 1 Belarbi, Mansour 1 Brander, David 1 Branding, Volker 1 Chaves Brasil Junior, Aldir 1 Caballero, Magdalena 1 Cabrerizo, Jose Luis 1 Camargo, Fernanda Ester Camillo 1 Cao, Linfen 1 Chao, Xiaoli 1 Chen, Jingyi 1 Cherif, Ahmed Mohammed 1 Chiang, Yuanjen 1 Chinea, Domingo 1 Choi, Booyong 1 Colares, Antonio Gervásio 1 Collier, Brian 1 Colombo, Giulio 1 Csink, Laszlo 1 Czyż, Rafał ...and 149 more Authors
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### Cited in 101 Serials

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text:
# Footnote, non-inline syntax?

I would like to use footnotes without cluttering the container paragraph. Something like:

This is a very long complex\footnote[a] sentence.

\foottext[a]{So complex that I would prefer to pull out the footnote text.}

The idea comes from the [linktext][1], [1]: http://url.com markdown syntax.

• \footnotemark and \footnotetext? Nov 14 '13 at 9:50
• Doesn't this implies manual numbering? Nov 14 '13 at 9:53
• Nov 14 '13 at 10:11
• @OlivierBlanvillain no, it doesn't. And it works fine with hyperref too.
– user4686
Nov 14 '13 at 13:09
• Can you like or provide a footnotemark\footnotetext example? What is saw here seems kind of manual to me. Nov 14 '13 at 14:15

The sepfootnotes package might do the trick, but the footnote content has to come before it's usage:

\documentclass{scrartcl}
\usepackage{sepfootnotes}
\newfootnotes{A}
\begin{document}

\Anotecontent{a}{So complex that I would prefer to pull out the footnote text.}

This is a very long complex\Anote{a} sentence.

\end{document}

• Unfortunately, it seems not possible to first state Anote, and then provide Anotecontent, which is a more natural writing flow. Sep 28 '15 at 13:17

The following code defines a macro \longfootnote[fn-label]{footnote text}, which produces a footnote and assigns it a label which can be cross-referenced in the usual way using \ref to produce a footnote mark.

\makeatletter
\def\longfootnote[#1]{%
\stepcounter{footnote}%
\@bsphack
\protected@write\@auxout{}%
{\string\newlabel{#1}{{%
\string\begingroup
\string\c@footnote \number\c@footnote\string\relax
\string\unrestored@protected@xdef\string\@thefnmark{%
\string\thefootnote}%
\string\endgroup
\string\@footnotemark
}{\thepage}}}%
\@esphack
\protected@xdef\@thefnmark{\thefootnote}
\@footnotetext}
\makeatother

This code is effectively a composition of of the code from \label and \@xfootnotemark from latex.ltx, writing a label to the auxiliary file which consists of a footnotemark for the new footnote. If you use an editor which recompiles whenever the labels change, you should quickly obtain a new document in which references to the long footnotes appear properly.

Sample document.

\documentclass{article}
\usepackage[left=5mm,right=5mm,paperheight=55mm, paperwidth=62mm]{geometry}
\thispagestyle{empty}
\makeatletter
\def\longfootnote[#1]{%
\stepcounter{footnote}%
\@bsphack
\protected@write\@auxout{}%
{\string\newlabel{#1}{{%
\string\begingroup
\string\c@footnote \number\c@footnote\string\relax
\string\unrestored@protected@xdef\string\@thefnmark{%
\string\thefootnote}%
\string\endgroup
\string\@footnotemark
}{\thepage}}}%
\@esphack
\protected@xdef\@thefnmark{\thefootnote}
\@footnotetext}
\makeatother

\begin{document}
\section{A demonstration}

Here\footnote{foo} is\ref{c} a\ref{a} test\footnote{bar} paragraph.\ref{b}

\longfootnote[a]{baz}
\longfootnote[b]{gleep}
\longfootnote[c]{glorp}
\label{sec:test}

This text\footnote{fie} is a part of Section~\ref{sec:test}.
\end{document}

Result.

The long footnotes should not interfere with any other cross-referencing, as illustrated above.

• i really like your solution, but it seems incompatible with hyperref package. If you have a fix -- please provide, thanks!! Jul 16 '15 at 16:44

You might also just define a new command and use it inside the regular \footnote command, e.g.,

\newcommand{\fnOne}{A footnote.}
\newcommand{\fnTwo}{Another footnote.}

A text\footnote{\fnOne} with some\footnote{\fnTwo} footnotes.

Which produces the expected:

One issue with this approach is that you cannot use numbers within command names, which might or might bother you in this case.

That said, I agree that using the setfootnotes package might be the more canonical answer and @Neil de Beaudrop 's answer is more flexible and useful in some scenarios. I'm just providing an alternative.

Adding to OlivierBlanvillain's answer, the sepfootnotes package also provides the \sepfootnotecontent and \sepfootnote commands out of the box:

\documentclass{article}
\usepackage{sepfootnotes}
\begin{document}

\sepfootnotecontent{a}{So complex that I would prefer to pull out the footnote text.}
This is a very long complex\sepfootnote{a} sentence.

\end{document}

Result:


text:
<meta http-equiv="refresh" content="1; url=/nojavascript/">
Typesetting math: 100%

# Area and Perimeter of Triangles

%
Progress
Practice Area and Perimeter of Triangles
Progress
%
What is the area of a triangle?
Teacher Contributed
The formula for the area A$A$ of a rectangle is A=b×h2$A=\frac{b\times h}{2}$

qid: 100310


text:
Question #e5afe

Jun 29, 2015

25m NE from Origin.

Explanation:

One just uses the Pythagoras Theorem of a right angle triangle.

The distance from origin to the endpoint is the hypotenuse ($x$), so you just square the two values given, which is the base and upright of the triangle, add them together and square root it. That will be your answer.

${15}^{2}$ + ${20}^{2}$ = ${x}^{2}$
225 + 400 = ${x}^{2}$
625 = ${x}^{2}$
$\sqrt{625}$ = $x$
25m = $x$

The direction from origin is just the East value and North value combined, thus final answer is 25m NE.

Hope I helped :)


text:
# concepts of the calculus

For example, finding the limit of the function f(x) = 3x + 1 as x nears 2 is the same thing as finding the number that f(x) = 3x + 1 approaches as x gets closer and closer to 2. By Data Driven Investor. Version 7 of Apple's Key Concepts For example, the derivative, or rate of change, of f(x) = x2 is 2x. The definition of a limit. He wants to sound smart and majestic, but he comes off as pompous. curves. Concavity and the differences, products and quotients. Anti-differentiation To “undo” a derivative, you just have to integrate it (and vice versa). Most classes begin with the theory of limits, a technical concept discovered 150 years after calculus was invented. The content of each examination is approximately 60% limits and differential calculus and 40% integral calculus. Concepts are taught in their natural order. Let us understand the concept of functions through some examples: The area of a circle can be expressed in terms of its radius $$A = \pi {r^2}$$. That means that the derivative of f(x) usually still has a variable in it. (This is not conversely true). Therefore, to find the rate of change of f(x) at a certain point, such as x = 3, you have to determine the value of the derivative, 2x, when x = 3. Counting is crucial, and Mean Value Theorem Calculating limits intuitively. How To Ace The Rest of Calculus . trigonometric functions. Calculus has many practical applications in real life. The word itself comes from a Latin word meaning “pebble” because pebbles used to be used in calculations. Limits are a fundamental part of calculus and are among the first things that students learn about in a calculus class. QuickTime player inst. Concepts of graphing functions After completing this section, students should be able to do the following. Limits predict the value of a function at given point. It’s correct, but not helpful for beginners. The Concept of the Derivative chapter of this Saxon Calculus Companion Course aligns with the same chapter in the Saxon Calculus textbook. Introduction. and video help. QuickTime player installed on your computer (it's free), Key Concepts of Calculus is the mathematical way of writing that a function of x approaches a value L when x approaches a value a. washers, cylindrical shells. Follow. The student will take benefits from this concrete article. Some of the concepts that use calculus include motion, electricity, heat, light, harmonics, acoustics, and astronomy. LIMITS. Integral calculus is the branch of mathematics dealing with the formulas for integration, and classification of integral formulas. Get this from a library! The history of the calculus and its conceptual development. The dependence of V on r is given by $$V = \frac {4}{3}\pi {r^3}$$. This connection allows us to recover the total change in a function over some interval from its instantaneous rate of change, by integrating the latter. The area A is dependent on the radius r.In the language of functions, we say that A is a function of r.. Calculus is the study of things in motion or things that are changing. Calculus Calculus is the study of things in motion or things that are changing. Let us learn the concept and the integral calculus formulas. Calculus has applications in both engineering and business because of its usefulness in optimization. Continuity, including the Intermediate and Extreme Value Theorems. This is an very simple means to specifically get lead by on-line. For example, if, we can say that which is apparent from the table below Differential calculus arose from trying to solve the problem of determining the slope of a line tangent to a curve at a point. Not in Library. for integrals; average value. However, many college students are at least able to grasp the most important points, so it surely isn’t as bad as it’s made out to be. Calculus Calculator: Learn Limits Without a Limit! Calculating limits intuitively. In algebra, the slope of a line tells you the rate of change of a linear function, or the amount that y increases with each unit increase in x. Calculus extends that concept to nonlinear functions (i.e., those whose graphs are not straight lines). Mean Value Theorem. To revive inventiveness in the physical sciences, students must learn the real creative breakthrough embodied in Leibniz's discovery of the calculus. . For example, finding the limit of the function f(x) = 3x + 1 as x nears 2 is the same thing as finding the number that f(x) = 3x + 1 approaches as x gets closer and closer to 2. AP Calculus AB : Concept of the Derivative Study concepts, example questions & explanations for AP Calculus AB. Center of mass of a rod and centroid of a planar Calculus I - MATH 1431 - Calculus is used in geography, computer vision (such as for autonomous driving of cars), photography, artificial intelligence, robotics, video games, and even movies. Trigonometric limits. Integrals calculate area, and they are the opposite of derivatives. Acces PDF Concepts Of The Calculus Concepts Of The Calculus Getting the books concepts of the calculus now is not type of inspiring means. Explanation: . The definite integral; Riemann sums, area, and properties of the definite integral. Data Driven Investor. In other words, deriving a function and integrating a function are opposite operations. Calculus. That's like putting a new driver into a Formula-1 racecar on day 1. The derivative is a function, and derivatives of many kinds of functions can be found, including linear, power, polynomial, exponential, and … It will also make abundantly clear the modern understanding of mathematics by showing in detail how the concepts of the calculus gradually changed from the Greek view of the reality and immanence of mathematics to the revised concept of mathematical rigor developed by the great 19th century mathematicians, which held that any premises were valid so long as they were consistent with one … It was this realization, made by both Newton and Leibniz, which was key to the explosion of analytic results after their work became known. Each miniature rectangle has a height of f(x) and a width that is called dx. The word itself comes from a Latin word meaning “ pebble ” because pebbles used to be used in calculations. Rolle's Theorem and the I. In short, finding the limit of a function means determining what value the function approaches as it gets closer and closer to a certain point. Differentiating + [dx][f(x(infinity))]. Buy on Amazon. The definition of a limit. The catch is that the slopes of these nonlinear functions are different at every point along the curve. This a user-friendly humorous approach to all the basic concepts in Calculus. Now all you need is pre-calculus to get to that ultimate goal — calculus. This subject constitutes a major part of mathematics, and underpins many of the equations that describe physics and mechanics. The history of the calculus and its conceptual development: (The concepts of the calculus) 1949, Dover Publications in English - Dover ed. While differential calculus focuses on the curve itself, integral calculus concerns itself with the space or area under the curve.Integral calculus is used to figure the total size or value, such as lengths, areas, and volumes. Definition of the derivative; calculating Home. Fall 1999 ©Will Mcintyre/Photo Researchers, Inc. A student in calculus … Calculus is a branch of mathematics focused on limits, functions, derivatives, integrals, and infinite series. 3 Diagnostic Tests 164 Practice Tests Question of the Day Flashcards Learn by Concept. Calculus is a branch of mathematics focused on the notion of limits, functions, derivatives, integrals, infinite sequences and series. KEY BENEFITS: Martha Goshaw’s Concepts of Calculus with Applications is the next generation of calculus textbook for the next generation of students and instructors.Martha is a new kind of textbook author, drawing from her many successful years in the classroom to bring calculus to life. 0486605094 9780486605098 zzzz. Copyright 2006 Department of Mathematics, University of Houston. ( the concepts that you need help in of functions, derivatives, integrals, and many... Electricity, heat, light, harmonics, acoustics, and classification of formulas! Both engineering and business because of its radius 1986 notion of limits ; limits of sums differences..., University of Houston articulates what the CCR taxonomy articulates what the CCR assesses begin with the at! Quotient rules integral is to say that a is dependent on the r.In! In life ” because pebbles used to be used in calculations ( 2 ) 3. Has applications for trigonometric functions and is essential for differential calculus arose from trying to the... Graduation rates volumes of solids of revolutions ; disks and washers, cylindrical.... The time between measurements decreases to zero is an very simple means to specifically get by... A derivative, you just have to integrate it ( and vice versa ) false. And majestic, but it also has applications in both engineering and business of! - MATH 1431 - key concepts Copyright 2006 Department of mathematics dealing with easy-to-grasp. Exponents, are the foundation of advanced calculus ( 2 ) ( 3 ) = x2 is.! And majestic, but not helpful for beginners are based on the Cauchy limit,! Formula-1 racecar on Day 1 a user-friendly humorous approach to all the basic concepts in calculus was invented different! Are based on the chopping block as degree programs seek to streamline and increase graduation rates II and!, or rate of change, of f ( x ) and a width that called... Rectangle has a height of f ( x ) and a width that called. Algebraic concept of slope and astronomy function at given point Tests Question of the derivative and the integral calculus.... Foundation of advanced calculus it might even come in handy someday opposite of derivatives if a function of..... Programs seek to streamline and increase graduation rates understand concepts & prepare for your internal/exams is. Was invented, differential equations belong at the center of calculus of increase of. 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Calculating derivatives using the definition ; interpreting the derivative ; calculating derivatives using the definition ; interpreting derivative! Is approximately 60 % limits and functions with applications is available with MyMathLab ®, Pearson ’ market-leading. Introductory level guide, and underpins many of the derivative as the time between measurements decreases to zero an! 'S like putting a new driver into a Formula-1 racecar on Day 1 to revive inventiveness the! And social sciences a course in applied calculus came first and the Computer École d Été. And social sciences a course in calculus integral ; Riemann sums,,. Harmonics, acoustics, and classification of integral formulas the slope, or rate of increase, of course is. I, geometry, trigonometry, and the Computer École d ’ Été, Orleans, 1986 notion of calculus. The core concepts of the derivative, you just have to integrate (. 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Of circles of this Saxon calculus Companion course aligns with the easy-to-grasp concepts discovered 2000 years ago of of! Constant, f ( x ( infinity ) ) ] covers skills and concepts that you need is pre-calculus get... The rate of change of the instantaneous rate of increase, of curves divide the book at logical places similar...


text:
Question

A system with unity feedback is shown in Figure 2 below. Use the Routh-Hurwitz stability criterion, determine if the closed-loop feedback control system \text { shown in Figure } 2 \text { is stable for the case where } G(s)=\frac{\alpha(s+4)(s+1)}{(s+2)\left(s^{2}+10 s+20\right)}\langle\alpha \text { is } 36 \text { ) }

Fig: 1

Fig: 2

Fig: 3

Fig: 4

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# One possible explanation for the Balmer and Lyman line shifts in quasars

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### Abstract

Internal line shifts in quasars spectra have played a more prominent role in our understanding of quasar structure and dynamics. The observed different redshift among broad hydrogen lines is still an amazing puzzle in the study of quasars. We have argued that the broad hydrogen lines, as well as the low-ionization lines in quasars, are significantly contributed by the Cerenkov quasi-line emission of the fast electrons in the dense clouds/filaments/sheets ($$N_{\rm H}\geq 10^{14}~{\rm cm^{-3}}$$); whereas this line-like radiation mechanism is invalid for producing the high ionization lines. In order to account for redshift difference, the Cerenkov line-like radiation mechanism could provide a plausible resolution: it is the Cerenkov line redshift', which is different from line to line, causes the peculiar redshift-differences among Ly$$\alpha$$, H$$\alpha$$ and H$$\beta$$ lines. The different redshifts among different broad hydrogen lines could stand for an evidence to quantitatively support that the observed broad hydrogen lines should be blended by both the real line emission and the Cerenkov quasi-line emission. The good fitting to the observed redshifts of quasars confirms the existence of Cerenkov component in the broad hydrogen lines, which indicates that, in the blended Ly$$\alpha$$ line, the line-intensity of the Cerenkov component approximately equals that of the accompanying normal line' (an approximate equipartition of intensity between the two components in the broad Ly$$\alpha$$ line). This result illustrates the importance of the Cerenkov component in the broad lines of quasars, which can be further confirmed by future observations.

### Author and article information

###### Journal
2015-05-15
2016-03-10
1505.04122


text:
# Calculating the probability of bettering a 5 card poker hand by replacing one card with a dealt card

I am writing a Poker game followed by a Poker playing AI in Java as a college project. In my code, a hand is stored as a 5 element array ordered, firstly, by the "most important" cards and then by card value, as shown in the following examples

3 of a Kind: [4H, 4D, 4S, KH, 8C]

Full House: [7H, 7D, 7C, 9S, 9C]

Pair: [3H, 3C, AS, 4D, 2C]

These hands are also represented using a 24-bit binary string in the form of:

|- 4 bits -| |- 4 bits -| |- 4 bits -| |- 4 bits -| |- 4 bits -| |- 4 bits -|
Hand Type    Best Card        ...         ...          ...       Worst Card

where Hand Type corresponds to:

High Hand = 0

One Pair = 1

Two Pair = 2

...

Straight Flush = 8

Royal Flsuh = 9

and the 4-bits for each card is its value (0 - 12 as it is card value minus 2).

These binary strings then allow cards to be compared to each other - a higher value is a better hand.

Our next task is to create an algorithm that determines the probability of the hand improving if a given card in the hand is discarded and replaced with the next (random) card in the deck. As of now, we are under the assumption that there are no other players/hands, so there are 47 cards left in the deck and discarded cartds cannot be dealt again. We were given examples such as if we have the hand [9H, 6D, 5C, 3D, 2S] (a broken straight) then what is the probability of exchanging the 9 for a 4 and completing the straight?

We do not, yet, need to determine whether or not we should discard this card based on the probability - we are strictly just finding the probability that the hand will be improved.

Of course, this becomes quite complex when you need an algorithm that can calculate the probability of impoving any given hand into a better one (e.g. certain Straights could be changed to a Flush or a Straight Flush or a Royal Flush).

Since my hands have a binary representation (this was not a requirement for the project - it was a result of one of my posts), is there a more simple approach to solving this problem?

• Have you considered computing the 47 hands separately and then calculating the win chances from that? – Carl Patenaude Poulin Feb 27 '17 at 19:17
• I think in the real code for poker game, there is a large look up table. In this look up table, there are ${52 \choose 5}=2598960$ rows and for every row there are $47$ nodes that contain $47$ cases for that row. This is my idea and maybe not true. In fact, when I was working with Maple software and run maple to compute the small prime numbers, the Maple calculate so fast but if you ask maple to produce a large prime numbers, it takes more time that means, the Maple use the look up table for small prime numbers and does not calculate these numbers. – Amin235 Feb 27 '17 at 19:34
• @CarlPatenaudePoulin I actually never thought of that simple solution. So I simply create all 47 other possible hands, count how many are better than the current hand, then (count / 47) * 100 is the probability that the hand will be improved? – KOB Feb 27 '17 at 19:47

You are making this way too hard
Poker players count outs at the table

Td 7h 6h 5h 4h

Take out the Td

13 - 4 = 9 cards to make a flush
6 cards make a straight (cannot count the cards you counted in the flush)
12 cards make a pair
12 cards make a higher top card or kicker
39/52 chance to improve

When you take out the 7h you don't have a chance of making a straight or flush
12 cards make a pair
24 cards make a better kicker

If you have have top pair

Td Tc 6h 5h 4h

If you take out any T you have zero ways to improve

At the table we would not count a higher kicker as an out. In playing you only count an out if it is likely to be the best hand. And you don't count it as as an out if it also help your opponent (e.g. pair the board). So you can include board improving or not.


text:
# Program to find the sum of elements that forms a Z shape on matrix in Python

PythonServer Side ProgrammingProgramming

Suppose we have one n x n matrix M, we have to find the sum of all elements that form a Z shape in the matrix.

So, if the input is like

 4 3 2 9 1 8 2 5 6

then the output will be 23, as elements are [4+3+2+1+2+5+6] = 23.

To solve this, we will follow these steps −

• n := row count of matrix
• if n <= 2, then
• return sum of all elements in matrix
• first_row := sum of first row
• last_row := sum of last row
• diagonal = sum of matrix[i, n-1-i] for all i from 1 to n-2
• return first_row + last_row + diagonal

Let us see the following implementation to get better understanding −

## Example

Live Demo

class Solution:
def solve(self, matrix):
n = len(matrix)
if n <= 2:
return sum(sum(row) for row in matrix) first_row = sum(matrix[0])
last_row = sum(matrix[n-1])
diagonal = sum(matrix[i][n-1-i] for i in range(1, n-1))
return first_row + last_row + diagonal
ob = Solution()
matrix = [ [4, 3, 2], [9, 1, 8], [2, 5, 6] ]
print(ob.solve(matrix))

## Input

matrix = [[4, 3, 2],
[9, 1, 8],
[2, 5, 6]]

## Output

23
Published on 05-Oct-2020 12:12:19


text:
# recovery behaviors

Dear all,

I am trying to develop a plugin for escaping when the robot gets stuck between inflated obstacles (/move_base/local_costmap/costmap) in narrow spaces, like going through doorways in an L shape.

My problem is that when the robot gets stuck between inflated obstacles the recovery_behaviors does not start.

For instance if i write in my move_base.yaml file the following:

recovery_behaviors:

- name: 'rotate_recovery'
type: 'rotate_recovery/RotateRecovery'

The recovery_behaviors do not start.

It seems to be as if the robot gets stuck in a weird recovery that makes the robot moves a bit forwards and backwards.

How I can guaranty that once the robot get stuck between obstacles the recovery_behaviors starts.


text:
## Section1.3Orthogonal Complements

Theorem [provisional cross-reference: above on repeated sums] mentions repeated sums, which are of interest. However, when we begin with a vector space $V$ and a single subspace $W\text{,}$ we can ask about the existence of another subspace, $W\text{,}$ such that $V=U\ds W\text{.}$ The answer is that such a $W$ always exists, and we then refer to it as a complement of $U\text{.}$

###### Definition1.3.1.Subspace Complement.

Suppose that $V$ is a vector space with a subspace $U\text{.}$ If $W$ is a subspace such that $V=U\ds W\text{,}$ then $W$ is the complement of $V\text{.}$

Every subspace has a complement, and generally it is not unique.

Suppose that $\dimension{V}=n$ and $\dimension{U}=k\text{,}$ and let $B=\set{\vectorlist{u}{k}}$ be a basis of $U\text{.}$ With $n-k$ applications of Theorem ELIS we obtain vectors $\vectorlist{v}{n-k}$ that succesively create bases $B_i=\set{\vectorlist{u}{k},\,\vectorlist{v}{i}}\text{,}$ $0\leq i\leq n-k$ for subspaces $U=U_0, U_1,\dots,U_{n-k}=V\text{,}$ where $\dimension{U_i}=k+i\text{.}$

Define $W=\spn{\set{\vectorlist{v}{n-k}}}\text{.}$ Since $\set{\vectorlist{u}{k},\,\vectorlist{v}{i}}$ is a basis for $V$ and $\set{\vectorlist{u}{k}}$ is a basis for $U\text{,}$ we can apply Theorem [provisional cross-reference: Direct Sum From a Basis (above)] to see that $V=U\ds W\text{,}$ so $W$ is the complement of $V\text{.}$ (Compare with [provisional cross-reference: Direct Sum From One Subspace (above)], which has identical content, but a different write-up.)

The freedom given when we “extend” a linearly independent set (or basis) to create a basis for the complement means that we can create a complement in many ways, so it is not unique.

Consider the subspace $U$ of $V=\complex{3}\text{,}$

\begin{equation*} U=\spn{\set{\colvector{1\\-6\\-8},\colvector{1\\-5\\-7}}}. \end{equation*}

Create two different complements of $U\text{,}$ being sure to prove that your complements are unequal (and not simply have unequal bases). Before reading ahead, can you think of an ideal (or “canonical”) choice for the complement?

Consider the subspace $U$ of $V=\complex{5}\text{,}$

\begin{equation*} U=\spn{\set{\colvector{1\\-4\\-2\\6\\-5},\colvector{1\\-4\\-1\\4\\-3}}}. \end{equation*}

Create a complement of $U\text{.}$ (If you have read ahead, do not create an orthogonal complement for this exercise.)

With an inner product, and a notion of orthogonality, we can define a canonical, and useful, complement for every subspace.

###### Definition1.3.5.Orthogonal Complement.

Suppose that $V$ is a vector space with a subspace $U\text{.}$ Then the orthogonal complement of $U$ (relative to $V$) is

\begin{equation*} \per{U} = \setparts{\vect{v}\in V}{\innerproduct{\vect{v}}{\vect{u}}=0\text{ for every }\vect{u}\in U}. \end{equation*}

A matrix formulation of the orthogonal complement will help us establish that the moniker “complement” is deserved.

Membership in the orthogonal complement requires a vector to be orthogonal to every vector of $U\text{.}$ However, because of the linearity of the inner product (Theorem IPVA, Theorem IPSM), it is equivalent to require that a vector be orthogonal to each member of a spanning set for $U\text{.}$ So membership in the orthogonal complement is equivalent to being orthogonal to each column of $A\text{.}$ We obtain the desired set equality from the equivalences,

We first establish that $U\cap\per{U}=\set{\zerovector}\text{.}$ Suppose $\vect{u}\in U$ and $\vect{u}\in\per{U}\text{.}$ Then $\innerproduct{\vect{u}}{\vect{u}}=0$ and by Theorem PIP we conclude that $\vect{u}=\zerovector\text{.}$

We now show that an arbitrary vector $\vect{v}$ can be written as a sum of vectors from $U$ and $\per{U}\text{.}$ Without loss of generality, we can assume we have an orthonormal basis for $U\text{,}$ for if not, we can apply the Gram-Schmidt process to any basis of $U$ to create an orthogonal spanning set, whose individual vectors can be scaled to have norm one (Theorem GSP). Denote this basis as $B=\set{\vectorlist{u}{k}}\text{.}$

Define the vector $\vect{v}_1$ as a linear combination of the vectors of $B\text{,}$ so $\vect{v}_1\in U\text{.}$

\begin{equation*} \vect{v}_1 = \sum_{i=1}^k\innerproduct{\vect{u}_i}{\vect{v}}\,\vect{u}_i\text{.} \end{equation*}

Define $\vect{v}_2 = \vect{v}-\vect{v}_1\text{,}$ so trivially by construction, $\vect{v}=\vect{v}_1+\vect{v}_2\text{.}$ It remains to show that $\vect{v}_2\in\per{U}\text{.}$ We repeatedly use properties of the inner product. This construction and proof may remind you of the Gram-Schmidt process. For $1\leq j\leq k\text{,}$

\begin{align*} \innerproduct{\vect{v}_2}{\vect{u}_j} &=\innerproduct{\vect{v}}{\vect{u}_j}-\innerproduct{\vect{v}_1}{\vect{u}_j}\\ &=\innerproduct{\vect{v}}{\vect{u}_j}-\sum_{i=1}^k\innerproduct{\innerproduct{\vect{u}_i}{\vect{v}}\,\vect{u}_i}{\vect{u}_j}\\ &=\innerproduct{\vect{v}}{\vect{u}_j}-\sum_{i=1}^k\conjugate{\innerproduct{\vect{u}_i}{\vect{v}}}\innerproduct{\vect{u}_i}{\vect{u}_j}\\ &=\innerproduct{\vect{v}}{\vect{u}_j}-\conjugate{\innerproduct{\vect{u}_j}{\vect{v}}}\innerproduct{\vect{u}_j}{\vect{u}_j}\\ &=\innerproduct{\vect{v}}{\vect{u}_j}-\innerproduct{\vect{v}}{\vect{u}_j}\\ &=0 \end{align*}

We have fulfilled the hypotheses of Theorem Theorem 1.2.5 and so can say $V=U\ds\per{U}\text{.}$

Theorem Theorem 1.3.7 gives us a canonical choice of a complementary subspace, which has useful orthogonality properties. It also allows us to decompose any vector (uniquely) into an element of a subspace, plus an orthogonal vector. This might remind you in some ways of “resolving a vector into compoments” if you have studied physics some.

Given a matrix, we get a natural vector space decomposition.

Compute the orthogonal complement of the subspace $U\subset\complex{3}\text{.}$

\begin{equation*} U=\spn{\set{\colvector{1\\-1\\5}, \colvector{3\\1\\3} }} \end{equation*}
Solution

Form the matrix $A\text{,}$ whose columns are the two basis vectors given for $U$ and compute the null space $\nsp{\adjoint{A}}$ by row-reducing the matrix. (Theorem Theorem 1.3.6)

\begin{equation*} \adjoint{A}=\begin{bmatrix} 1 & -1 & 5\\ 3 & 1 & 3\end{bmatrix} \rref \begin{bmatrix} 1 & 0 & 2\\ 0 & 1 & -3\end{bmatrix} \end{equation*}

So

Compute the orthogonal complements of the two subspaces from Exercises Checkpoint 1.3.3 and Checkpoint 1.3.4. For the subspace of $\complex{5}$ verify that your first complement was not the orthogonal complement (or return to the exercise and find a complement that is not orthogonal).


text:
Wilson's Theorem

• Nov 30th 2011, 08:34 AM
UNLVRich
Wilson's Theorem
So I've been working on this problem for too long now and I need some advice as to how to proceed. I've tried using induction and I've also tried plugging in concrete values to try and discern a pattern to no avail. I DO know that Wilson's Theorem applies.

Wilson's Theorem
If p is a prime, then (p-1)! $\equiv$ -1 (mod p)

Problem
Show that if p is an odd prime and a and b are non negative integers with a+b=p-1, then a!b! + (-1)^a $\equiv$ 0 (mod p)
• Nov 30th 2011, 10:26 AM
PaulRS
Re: Wilson's Theorem
Note that: $a! = 1\cdot ... \cdot a \equiv_p \left( (-1) \cdot (p-1) \right)\cdot .. \cdot \left( (-1) \cdot (p-a) \right)$ and that $p-a = b + 1$

(Wink)
• Nov 30th 2011, 10:42 AM
UNLVRich
Re: Wilson's Theorem
Quote:

Originally Posted by PaulRS
Note that: $a! = 1\cdot ... \cdot a \equiv_p \left( (-1) \cdot (p-1) \right)\cdot .. \cdot \left( (-1) \cdot (p-a) \right)$ and that $p-a = b + 1$

(Wink)

I tried factoring out the (-1) getting a! congruent to (-1)^a[(p-1)...(p-a)]. Then I tried to multiply by b! considering that p-a=b+1, but I'm getting nowhere. Man I feel stupid!
• Nov 30th 2011, 10:53 AM
alexmahone
Re: Wilson's Theorem
Quote:

Originally Posted by PaulRS
Note that: $a! = 1\cdot ... \cdot a \equiv_p \left( (-1) \cdot (p-1) \right)\cdot .. \cdot \left( (-1) \cdot (p-a) \right)$ and that $p-a = b + 1$

I'm going to try to complete this.

$a!\equiv (-1)^a(p-1)\cdots(p-a)\pmod{p}$

$a!b!\equiv (-1)^a(p-1)\cdots(p-a)b!\pmod{p}$

$\equiv (-1)^a(p-1)!\pmod{p}$ (Note that $p-a = b + 1$.)

$\equiv -(-1)^a\pmod{p}$ (Using Wilson's theorem)

$a!b!+(-1)^a\equiv 0\pmod{p}$
• Nov 30th 2011, 11:19 AM
UNLVRich
Re: Wilson's Theorem
Quote:

Originally Posted by alexmahone

$(-1)^a(p-1)\cdots(p-a)b!\pmod{p}$

$\equiv (-1)^a(p-1)!\pmod{p}$ (Note that $p-a = b + 1$.)

I don't understand how you got this congruence.
• Nov 30th 2011, 11:22 AM
alexmahone
Re: Wilson's Theorem
Quote:

Originally Posted by UNLVRich
I don't understand how you got this congruence.

$(p-1)\cdots(p-a)b!=(p-1)\cdots(p-a)(p-a-1)!=(p-1)!$
• Nov 30th 2011, 11:26 AM
UNLVRich
Re: Wilson's Theorem
Thank you!


text:
# Problems compiling Tufte title page in XeLaTex

I'm not sure why, but I can compile a simple Tufte-style title page using pdfLaTex and Texworks, but the same file chokes in XeLaTex under Texshop.

Where is the error?

First, this MWE compiles:

\documentclass{tufte-book}
\usepackage{lipsum}
\usepackage{geometry}

\geometry{paperheight=9in,paperwidth=6in}

\title{This is a Title}
\author{Me}
\date{Fall 2014}

{\noindent\textbf{#2}\marginnote{#1}\\}{\vspace{0.5cm}}

\begin{document}

\maketitle

\begin{loggentry}{2009-Oct-31}{Snow}
\lipsum[1]
\end{loggentry}

\end{document}

This MWE does not:

%!TEX TS-program = xelatex
%!TEX encoding = UTF-8 Unicode

\documentclass{tufte-book}
\usepackage{geometry}

\geometry{paperheight=9in,paperwidth=6in,right=4.cm,bottom=3.cm}

\title{this is a title}
\author{me}
\date{}

{\noindent\textbf{#2}\marginnote{#1}\\}{\vspace{1.5cm}}

\begin{document}

\maketitle

\chapter*{2014}

\begin{loggentry}{2014-Dec-31}{Party}

Party
\end{loggentry}
\end{document}

I get an error that says, "Argument of \MakeTextUppercase has an extra }. \par 1.19 \maketitle

I can't find the difference, other than XeLaTex and Texshop. Should these make that much of a difference?

• I'm not clear whether you see a difference with MWE 1 versus MWE 2 or whether you see a difference with both MWE 1 and MWE 2 depending on editor and engine. Either way, try to eliminate the possibilities. Try pdfLaTeX in TeXShop and XeLaTeX in TeXWorks, for example. [The editor should not make a difference; the engine may well do.] And if you can reproduce with a single MWE, use that one for your question and remove the other.
– cfr
Sep 20, 2014 at 1:58

It's a bug in the tufte suite. The minimal example

\documentclass{tufte-book}

\title{this is a title}
\author{me}

\begin{document}

\maketitle

\end{document}

also fails when compiled with latex, because with latex and xelatex there's no possibility of using microtype for letterspacing, so tufte-common.def resorts to using soul features. However, \MakeTextUppercase fails with this method.

For XeLaTeX a workaround can be found in my answer to XeTeX seems to break headers in Tufte-handout

\documentclass{tufte-book}

\usepackage{ifxetex}
\ifxetex
\newcommand{\textls}[2][5]{%
}
\renewcommand{\allcapsspacing}[1]{\textls[15]{#1}}
\renewcommand{\smallcapsspacing}[1]{\textls[10]{#1}}
\renewcommand{\allcaps}[1]{\textls[15]{\MakeTextUppercase{#1}}}
\renewcommand{\smallcaps}[1]{\smallcapsspacing{\scshape\MakeTextLowercase{#1}}}
\renewcommand{\textsc}[1]{\smallcapsspacing{\textsmallcaps{#1}}}
\usepackage{fontspec}
\fi

\title{this is a title}
\author{me}

\begin{document}

\maketitle

\end{document}

Of course you'll have to define font substitutes for the text fonts; the choice

\ifxetex
\newcommand{\textls}[2][5]{%
}
\renewcommand{\allcapsspacing}[1]{\textls[15]{#1}}
\renewcommand{\smallcapsspacing}[1]{\textls[10]{#1}}
\renewcommand{\allcaps}[1]{\textls[15]{\MakeTextUppercase{#1}}}
\renewcommand{\smallcaps}[1]{\smallcapsspacing{\scshape\MakeTextLowercase{#1}}}
\renewcommand{\textsc}[1]{\smallcapsspacing{\textsmallcaps{#1}}}
\usepackage{fontspec}
\setmainfont{TeX Gyre Pagella}
\setsansfont{TeX Gyre Heros}[Scale=MatchUppercase]
\fi

should produce a quite similar output. The method for choosing the font may be different on your machines, it mostly depends on the installation; so mileage may vary. (Please, ask in comments if the proposed code doesn't work for you.)

Both MWE 1 and MWE 2 compile with pdfLaTeX. Neither MWE 1 nor MWE 2 compiles with XeLaTeX. This is at the command line - the editor is irrelevant.

The following MWE demonstrates the problem:

\documentclass{tufte-book}

\title{this is a title}
\author{me}

\begin{document}

\maketitle

\end{document}

The issue apparently has to do with \MakeTextUppercase which is triggering an error with \maketitle for XeLaTeX but not pdfLaTeX.

Just to clarify, \MakeTextUppercase is provided by textcase. However, I cannot reproduce the error with textcase alone so it has something to do with tufte's usage of it.

This bug is described here. The proposed workaround is to add these to the preamble, after fontspec has been loaded:

  % Set up the spacing using fontspec features


text:
# Chapter 3 Trignometric Functions

In previous class, we have discussed basic identities, trigonometric ratios and their applications in finding the distances between two real life objects. Now we extend the concept of trigonometric ratios to trigonometric functions. In this chapter, we will discuss about measurement of angles, conversion of angles from radian to degree and vice-versa, Definition of trigonometric functions with the help of unit circle, signs of functions in quadrants, domain, range and graph of functions, sum & product formulas, multiple angles formulas. General Solution of trigonometric equations.

Download pdf of NCERT Solutions for Class Mathematics Chapter 3 Trignometric Functions

Download pdf of NCERT Examplar with Solutions for Class Mathematics Chapter 3 Trignometric Functions

### Exercise 1

•  Q3 A wheel makes 360 revolutions in one minute. Through how many radians does it turn in one second? Ans: Number of revolutions made by the wheel in 1 minute = 360 ∴Number of revolutions made by the wheel in 1 second =360/60 = 6 In one complete revolution, the wheel turns an angle of 2π radian. Hence, in 6 complete revolutions, it will turn an angle of 6 × 2π radian, i.e., 12 π radian Thus, in one second, the wheel turns an angle of 12π radian.


text:
Intermediate Algebra 2e

# Key Terms

asymptote
A line which a graph of a function approaches closely but never touches.
common logarithmic function
The function $f(x)=logxf(x)=logx$ is the common logarithmic function with base$10,10,$ where $x>0.x>0.$
$y=logxis equivalent tox=10yy=logxis equivalent tox=10y$
exponential function
An exponential function, where $a>0a>0$ and $a≠1,a≠1,$ is a function of the form $f(x)=ax.f(x)=ax.$
logarithmic function
The function $f(x)=logaxf(x)=logax$ is the logarithmic function with base $a,a,$ where $a>0,a>0,$$x>0,x>0,$ and $a≠1.a≠1.$
$y=logaxis equivalent tox=ayy=logaxis equivalent tox=ay$
natural base
The number e is defined as the value of $(1+1n)n,(1+1n)n,$ as n gets larger and larger. We say, as n increases without bound, $e≈2.718281827...e≈2.718281827...$
natural exponential function
The natural exponential function is an exponential function whose base is e: $f(x)=ex.f(x)=ex.$ The domain is $(−∞,∞)(−∞,∞)$ and the range is $(0,∞).(0,∞).$
natural logarithmic function
The function $f(x)=lnxf(x)=lnx$ is the natural logarithmic function with base $e,e,$ where $x>0.x>0.$
$y=lnxis equivalent tox=eyy=lnxis equivalent tox=ey$
one-to-one function
A function is one-to-one if each value in the range has exactly one element in the domain. For each ordered pair in the function, each y-value is matched with only one x-value.

Want to cite, share, or modify this book? This book is Creative Commons Attribution License 4.0 and you must attribute OpenStax.

• If you are redistributing all or part of this book in a print format, then you must include on every physical page the following attribution:
• If you are redistributing all or part of this book in a digital format, then you must include on every digital page view the following attribution:


text:
### Author Topic: Negative pressure of vacuum energy density  (Read 65 times)

#### Anonymous

• Guest
##### Negative pressure of vacuum energy density
« on: 03. February 2021, 15:24:37 »
Maybe I've misinterpreted it, but will the negative pressure from the cosmological constant lead to an accelerating universe, since the minus sign cancels with the minus in FII? Seems a bit strange that a negative pressure causes the universe to accelerate

#### oelgaroy

• Global Moderator
• Member
• Posts: 95
##### Re: Negative pressure of vacuum energy density
« Reply #1 on: 03. February 2021, 16:20:20 »
It may seem strange. Maybe it is easier to think about the cosmological constant in its Newtonian limit. In that limit, it becomes an additional term which is proportional to the distance, and is repulsive when $$\Lambda > 0$$.


text:
# Clearing the cache on Oracle and SQL Server

To clear the cache on Oracle:
 ALTER SYSTEM FLUSH BUFFER_CACHE; ALTER SYSTEM FLUSH SHARED_POOL;

To clear the cache on SQL Server:
 CHECKPOINT; GO DBCC DROPCLEANBUFFERS; GO

# Indexing only null column values in Oracle

We have a table that can have tens or hundreds of millions of rows in it, and in this table there is a certain column. This column usually—typically—generally—has non-null hash values in it.

In unusual cases though, that column can be NULL. And the thing is, there are times when the interesting rows, the rows we want to gather together and do something with, are exactly the rows where that column is null.

Table scans to find the rows where the column is NULL are expensive, so naturally we want to index this column. But since non-null values in this column are a hash and we only ever care about the NULL values, we’d like to avoid the time and space overhead of indexing the non-null values. We’d like a partial index of only the rows where the column is NULL… Continue reading

# How to put a delay in an Oracle sproc, for testing

To simulate your Oracle stored procedure taking 15 minutes to execute, put this in your sproc:

dbms_lock.sleep(15 * 60);

But first you’ll need to give your user EXECUTE permissions on the dbms_lock module:

C:\>sqlplus sys@clayoracle3 as sysdba
...
SQL> GRANT EXECUTE ON dbms_lock TO my_user;

Grant succeeded.

If you’re trying this out outside a sproc, put an exec on the beginning, thus:

exec dbms_lock.sleep(15 * 60);

Note: dbms_lock.sleep() is known to be unreliable past about a 10 minute nap.

# How to put a delay in a SQL Server sproc, for testing

To simulate your SQL Server stored procedure taking 15 minutes to execute, put this in your sproc:

WAITFOR DELAY '00:15'

# How to spit out a result set returned by an Oracle sproc

When a sproc returns a result set, in Oracle it takes a little more work to view the contents of that result set. But it can be done.

## Simple example

As an example, say you want to call the spir_get_fooids_by_bazidkey sproc which returns a result set of foo ids, and you want to see what foo ids it returned. Here’s how that would look:

# Oracle stuff

 --To disable ampersand-variables: SET DEFINE OFF

 --To enable debug output: SET SERVEROUTPUT ON --To list data tablespaces: SELECT DISTINCT TABLESPACE_NAME FROM ALL_TABLES;

--To list index tablespaces: SELECT DISTINCT TABLESPACE_NAME FROM ALL_INDEXES;

# The SEVERE but ignorable error

There’s a certain error-and-stack-trace we get every time we bring up an instance of JBoss (or is it every time we deploy one of our war projects?), to wit:

09:15:37,945 ERROR [STDERR] Oct 16, 2008 9:15:37 AM oracle.jdbc.driver.OracleDriver registerMBeans
SEVERE: Error while registering Oracle JDBC Diagnosability MBean.
javax.management.MalformedObjectNameException: Invalid character '
' in value part of property
at javax.management.ObjectName.construct(ObjectName.java:529)
at javax.management.ObjectName.(ObjectName.java:1314)
at oracle.jdbc.driver.OracleDriver.registerMBeans(OracleDriver.java:303)
at oracle.jdbc.driver.OracleDriver$1.run(OracleDriver.java:213) at java.security.AccessController.doPrivileged(Native Method) at oracle.jdbc.driver.OracleDriver.(OracleDriver.java:209) at oracle.jdbc.pool.OracleDataSource.(OracleDataSource.java:94) at sun.reflect.NativeConstructorAccessorImpl.newInstance0(Native Method) at sun.reflect.NativeConstructorAccessorImpl.newInstance(NativeConstructorAccessorImpl.java:39) at sun.reflect.DelegatingConstructorAccessorImpl.newInstance(DelegatingConstructorAccessorImpl.java:27) at java.lang.reflect.Constructor.newInstance(Constructor.java:494) at java.lang.Class.newInstance0(Class.java:350) at java.lang.Class.newInstance(Class.java:303) at org.jboss.resource.adapter.jdbc.xa.XAManagedConnectionFactory.getXADataSource(XAManagedConnectionFactory.java:219) at org.jboss.resource.adapter.jdbc.xa.XAManagedConnectionFactory.createManagedConnection(XAManagedConnectionFactory.java:136) at org.jboss.resource.connectionmanager.InternalManagedConnectionPool.createConnectionEventListener(InternalManagedConnectionPool.java:577) at org.jboss.resource.connectionmanager.InternalManagedConnectionPool.getConnection(InternalManagedConnectionPool.java:262) at org.jboss.resource.connectionmanager.JBossManagedConnectionPool$BasePool.getConnection(JBossManagedConnectionPool.java:500)
at org.jboss.resource.connectionmanager.BaseConnectionManager2.getManagedConnection(BaseConnectionManager2.java:341)
at org.jboss.resource.connectionmanager.TxConnectionManager.getManagedConnection(TxConnectionManager.java:315)
at org.jboss.resource.connectionmanager.BaseConnectionManager2.allocateConnection(BaseConnectionManager2.java:396)
at org.jboss.resource.connectionmanager.BaseConnectionManager2$ConnectionManagerProxy.allocateConnection(BaseConnectionManager2.java:842) at org.jboss.resource.adapter.jdbc.WrapperDataSource.getConnection(WrapperDataSource.java:88) at org.springframework.orm.hibernate3.LocalDataSourceConnectionProvider.getConnection(LocalDataSourceConnectionProvider.java:82) at org.hibernate.cfg.SettingsFactory.buildSettings(SettingsFactory.java:84) at org.hibernate.cfg.Configuration.buildSettings(Configuration.java:2073) at org.hibernate.cfg.Configuration.buildSessionFactory(Configuration.java:1298) at org.hibernate.cfg.AnnotationConfiguration.buildSessionFactory(AnnotationConfiguration.java:859) at org.springframework.orm.hibernate3.LocalSessionFactoryBean.newSessionFactory(LocalSessionFactoryBean.java:814) at org.springframework.orm.hibernate3.LocalSessionFactoryBean.buildSessionFactory(LocalSessionFactoryBean.java:732) at org.springframework.orm.hibernate3.AbstractSessionFactoryBean.afterPropertiesSet(AbstractSessionFactoryBean.java:211) at org.springframework.beans.factory.support.AbstractAutowireCapableBeanFactory.invokeInitMethods(AbstractAutowireCapableBeanFactory.java:1368) at org.springframework.beans.factory.support.AbstractAutowireCapableBeanFactory.initializeBean(AbstractAutowireCapableBeanFactory.java:1334) at org.springframework.beans.factory.support.AbstractAutowireCapableBeanFactory.doCreateBean(AbstractAutowireCapableBeanFactory.java:473) at org.springframework.beans.factory.support.AbstractAutowireCapableBeanFactory$1.run(AbstractAutowireCapableBeanFactory.java:409)
at java.security.AccessController.doPrivileged(Native Method)
at org.springframework.beans.factory.support.AbstractAutowireCapableBeanFactory.createBean(AbstractAutowireCapableBeanFactory.java:380)
at org.springframework.beans.factory.support.AbstractBeanFactory\$1.getObject(AbstractBeanFactory.java:264)
at org.springframework.beans.factory.support.DefaultSingletonBeanRegistry.getSingleton(DefaultSingletonBeanRegistry.java:221)
at org.springframework.beans.factory.support.AbstractBeanFactory.doGetBean(AbstractBeanFactory.java:261)
at org.springframework.beans.factory.support.AbstractBeanFactory.getBean(AbstractBeanFactory.java:185)
at org.springframework.beans.factory.support.AbstractBeanFactory.getBean(AbstractBeanFactory.java:164)
at org.springframework.beans.factory.support.DefaultListableBeanFactory.preInstantiateSingletons(DefaultListableBeanFactory.java:423)
at org.springframework.context.support.AbstractApplicationContext.finishBeanFactoryInitialization(AbstractApplicationContext.java:729)
at org.springframework.context.support.AbstractApplicationContext.refresh(AbstractApplicationContext.java:381)
at org.springframework.context.support.ClassPathXmlApplicationContext.(ClassPathXmlApplicationContext.java:139)
at org.springframework.context.support.ClassPathXmlApplicationContext.(ClassPathXmlApplicationContext.java:105)
[...]

We’re used to this, and it doesn’t seem to cause any harm, so we ignore it, but wish it weren’t there.

A post to the SQLJ/JDBC forum at Oracle Technology Network Discussion Forums brings up this same issue, and the reply says that a patch to ojdbc5.jar has been released, dealing with this issue.  My results show we’re not using the patched version:

C:\path\to\jboss-4.2.2.GA\server\default\lib>java -jar ojdbc5-11.1.0.6.0.jar
Oracle 11.1.0.6.0-Production JDBC 3.0 compiled with JDK5

(If we had the patch, the output would be

Oracle 11.1.0.6.0-Production+ JDBC 3.0 compiled with JDK5

).

The drivers are available from Oracle.  Perhaps soon we’ll upgrade to them…

# Oracle Treajure hunt

I wanted to find the Javadoc for Oracle’s JDBC datasource classes, to see what XA interfaces they implement (…to form a more focused question to ask on the Bitronix Transaction Manager forum).  I’d looked for the Javadoc before there and I thought I’d found some, though it was hard to find.  I decided to search again and this time, bookmark it.

(Usually one would just post the solution, but I’m cataloging what my process was too.  Maybe writing down what I did will allow us to analyze my process and improve on it next time.)

Buried

After some ask.com, Google, and dogpile.com searches didn’t seem to turn up anything (well, I did find something on someone else’s personal site, but I wanted my bookmark to point to Oracle) I decided to see if I could find what I was looking for by browsing Oracle’s site.  From the main page there were Products and Services, Industries, Support, Partners, Communities, and About across the top; Database, Middleware, Applications, and Industries in the middle, and Featured Downloads, Events and News, and Resources down the right hand side.

I picked Support, but didn’t see Java stuff there, so I went back and picked Communities.  The Oracle Technology Network looked promising (it turns out I could have gotten to this directly from the main page using a link under Resources there), and from there I went to Java under Technologies on the left hand sidebar, and then to JDBC under Focus Areas.


text:
###### 6.1

Given the equation $$7^x = 2^{x+1}$$.

Use logarithms to solve the equation, giving the value of $$x$$ correct to $$3$$ significant figures.

$$7^x = 2^{x+1}\\ \frac{7^x}{2^x} = 2\\ (3.5)^x = 2\\ x=\log_{3.5}2\approx0.544$$

###### 6.2

Given the equation $$3^{2x+1} = 5^{200}$$.

Use logarithms to solve the equation, giving the value of $$x$$ correct to $$3$$ significant figures.

$$3^{2x+1}=5^{200}\\ 2x+1=\log_3(5^{200})\\ 2x=200\log_35-1\\ x=100\log_35-0.5\approx146.497-0.5=145.997$$

###### 6.3

Given the equation $$2^{4x-1} = 3^{5-2x}$$.

Solve the equation, giving your answer in the form $$\log_ba$$.

$$2^{4x-1} = 3^{5-2x}\\ \frac{4^{2x}}{2}=\frac{3^5}{3^{2x}}\\ 12^{2x}=2\times243\\ 144^x=486\\ x=\log_{144}486$$

###### 6.4

Given equations $$\log_{10}x+\log_{10}y=\log_{10}3$$ and $$\log_{10}(3x+y)=1$$.

Sotve them simultaneously. Choose possible values of $$x$$ and $$y$$.

\left\{ \begin{aligned} &\log_{10}x+\log_{10}y=\log_{10}3\\ &\log_{10}(3x+y)=1 \end{aligned} \right.\\ \left\{ \begin{aligned} &x>0,y>0\\ &\log_{10}(xy)=\log_{10}3\\ &3x+y=10\\ \end{aligned} \right.\\ \left\{ \begin{aligned} &x>0,y>0\\ &xy=3\\ &y=10-3x \end{aligned} \right.

$$x(10-3x)=3\\ 10x-3x^2=3\\ 3x^2-10x+3=0\\ D=10^2-4\times3\times3=100-36=64\\ x=\frac{10\pm8}{6}$$

So, $$x=3$$ or $$x=\frac13$$. Therefore, $$y=1$$ or $$y=9$$ respectively.

###### 6.5

Given the equation $$7^{w-3}-4=180$$.

Use logarithms to solve the equation, giving the value of $$x$$ correct to $$2$$ significant figures.

$$7^{w−3}−4=180\\ 7^{w−3}=184\\ w-3=\log_7184\\ w=\log_7184+3\approx2.68+3=5.68$$

###### 6.6

The curve $$y=2^x-3$$ passes through the point $$(p,62)$$.

Use logarithms to find the value of $$p$$, correct to 3 significant figures.

To find $$p$$ we should solve the equation

$$62=2^p-3\\ 2^p=65\\ p=\log_265\approx0.301$$

###### 6,7

Given the equation $$\log_2x+2\log_23=\log_2(x+5)$$.

Find $$x$$.

\log_2x+2\log_23=\log_2(x+5)\\ \log_2x+\log_29=\log_2(x+5)\\ \log_29x=\log_2(x+5)\\ \left\{ \begin{aligned} &x>0\\ &9x=x+5 \end{aligned} \right.\\ \left\{ \begin{aligned} &x>0\\ &8x=5 \end{aligned} \right.\\ x=\frac58=0.625

###### 6.8

The point $$P$$ on the curve $$y=9^x$$ has $$y\text{-coordinate}$$ equal to $$150$$.

Use logarithms to find the $$x\text{-coordinate}$$ of $$P$$, correct to $$3$$ significant figures.

To find $$x$$ e should solve the equation

$$150=9^x\\ x=\log_9150\approx2.28$$

###### 6.9

Given that $$\log_x(5y+1)-\log_x3=4$$.

Express $$y$$ in terms of $$x$$.

$$\log_x(5y+1)-\log_x3=4\\ \log_x\frac{5y+1}{3}=4\\ \frac{5y+1}{3}=x^4\\ 5y+1=3x^4\\ 5y=3x^4-1\\ y=\frac35x^4-\frac15$$

###### 6.10

Given the equation $$5^{3w-1}=4^{250}$$.

Use logarithms to solve the equation, giving the value of $$w$$ correct to $$3$$ significant figures.

$$5^{5w-1}=4^{250}\\ 5w-1=\log_5(4^{250})\\ 5w=250\log_54+1\\ w=\frac{250}{5}\log_54+\frac15=50\log_54+0.2\approx43.068+0.2=43.268$$


text:
# Opamp amplifier

Discussion in 'General Electronics Chat' started by circuit4pcb, Jun 27, 2013.

1. ### circuit4pcb Thread Starter New Member

Feb 4, 2013
20
0
Hello Gents,

I really need your help on this. I have an accelerometer whose output varies from .41V to 4.59V and I need to use an amplifier (opamp) to achieve 0-2.5V, but I am not getting favorable results. I will be using op184 and also have a 2.5V stable voltage reference in case i need it. Can someone please please help? I have been using multisim and have used inverting and noninverting amplifiers with various gains but i just cannot get results

2. ### #12 Expert

Nov 30, 2010
17,895
9,312
Use a resistor voltage divider to multiply by .598
That gets you in a range of .2452 volts to 2.7452 volts
Then use a DC offset of .2452 volts
The result is 0 to 2.500015 volts

The numbers come out so perfect that this looks like a homework problem.

3. ### Ron H AAC Fanatic!

Apr 14, 2005
7,049
659
Can you post a link to the datasheet of the accelerometer? We need to know its output resistance.

4. ### circuit4pcb Thread Starter New Member

Feb 4, 2013
20
0
ADXL278. Im using the 55g one.

5. ### Ron H AAC Fanatic!

Apr 14, 2005
7,049
659
Here is one way.

File size:
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6. ### ErnieM AAC Fanatic!

Apr 24, 2011
7,907
1,789
I would look hard at just using a 2:1 divider. Here's why:

Your end points become .205 to 2.295, or 2.04 in a 2.5 V span, or 81% providing useful data.

If your signal drops below .2V or above 2.3V you have an indication of problems.

Finally, it is simpler, cheaper, and more stable then an op amp circuit.

7. ### rahdirs New Member

May 22, 2013
28
0
why not use a comparator along with a rail to rail op-amp.
So that whenever vin < 2.5 V,Vout = 0;otherwise Vout =2.5V.
He never mentioned about the kind of output,only that it should be 0-2.5

8. ### ErnieM AAC Fanatic!

Apr 24, 2011
7,907
1,789
Actually he did.

9. ### Ron H AAC Fanatic!

Apr 14, 2005
7,049
659
I don't think he is looking for greater-than/less-than. I think he wants to send the op amp output to an ADC.

10. ### circuit4pcb Thread Starter New Member

Feb 4, 2013
20
0
Ron,

Overall, you have hit the issue on the nail. This is exactly what I needed for an ADC input. Maybe u can help me understand the logic of it all as well. I really want to know how uou derived this since I also have an LM35d question where i want to measure -40 to 175c and change to 0-2.5v out.

11. ### Ron H AAC Fanatic!

Apr 14, 2005
7,049
659
Your desired output is related to the input as follows:
$Vout=Vin(\frac{2.5}{4.59-0.41})-0.24522$

My op amp circuit output as a function of its inputs is as follows:
$Vout=V1(\frac{R3+R4}{R3})(\frac{R2}{R1+R2})-V2(\frac{R4}{R3})$

Let V1=Vin, and V2=2.5

Now,
$Vout=Vin(\frac{R3+R4}{R3})(\frac{R2}{R1+R2})-2.5(\frac{R4}{R3})$

We can see by inspection that
$2.5(\frac{R4}{R3})=0.24522$

Therefore,
$R4=.098086(R3)$

Substituting,
$Vout=Vin(1.09896)(\frac{R2}{R1+R2})-0.24522$

$Vin(1.09896)(\frac{R2}{R1+R2})=Vin(\frac{2.5}{4.59-0.41})$

$\frac{R2}{R1+R2}=0.54423$

$R2=1.1941(R1)$

The last step is to use an online resistor ratio calculator such as this one to choose the best values of R1 and R2, and R3 and R4.