content stringlengths 86 994k | meta stringlengths 288 619 |
|---|---|
Assigning Classes
Raphael Mankin raph at mankin.org.uk
Mon Sep 9 15:10:07 BST 2013
This is a classic variation of the transportation problem.
If you can assign (different) costs to being in the wrong class and zero
cost to being in the right class then the Hungarian Algorithm will do
the job.
The standard version of the algorithm has quartic time complexity, but
there is a version due to Wright(?) at Lancaster University that is
quadratic. Both versions have quadratic space complexity. I programmed
it about 20 years ago but I cannot now give you any references. Search
the literature.
On Mon, 2013-09-09 at 09:16 -0400, Mark Fowler wrote:
> On Monday, 9 September 2013 at 08:45, Dave Cross wrote:
> > I have offered to help a friend[1] solve what sounds like an
> > interesting problem.
> No idea on the literature, but here's my two pence worth:
> I'd start by putting everyone in their favourite choice of classes, and seeing how "bad" that is. I assume since you're asking the question that's not a possible solution.
> How feasible is it to randomly select students and move them and see how that works? I ask because this is what we'd do before we had computers, but with a computer you could do this a million times a second and try out all the possibilities (it's key to limit the number of moves to narrow the problem space so we don't have to wait for the heat death of the universe first - hence the putting everyone in the "optimal but broken" place to start with.) You'd need a "unhappiness" score for a student which could be computed from the distance they are from their "ideal" courses. You might want to look at adding some sort of power rule to the distance too, since you'd probably be better off with a bunch of slightly unhappy students verses all happy but one very screwed over student. Obviously junk any 'solution' that doesn't meet your class criteria.
> Mark.
More information about the london.pm mailing list | {"url":"http://london.pm.org/pipermail/london.pm/Week-of-Mon-20130909/024281.html","timestamp":"2014-04-16T13:28:00Z","content_type":null,"content_length":"4312","record_id":"<urn:uuid:20ced126-961e-4d6a-9a85-21ac14ccc9c3>","cc-path":"CC-MAIN-2014-15/segments/1397609523429.20/warc/CC-MAIN-20140416005203-00120-ip-10-147-4-33.ec2.internal.warc.gz"} |
March 18th 2009, 07:50 AM
We are given 3 balls and 10 balls.
a. Suppose the boxes and the balls are all distinguishable. How many ways are there to put 10 balls into the boxes.
b. Suppose the boxes are indistinguishable, and the balls are also indistinguishable. How many ways are there to put 10 balls into the boxes?
March 18th 2009, 09:01 AM
We are given 3 balls and 10 balls.
a. Suppose the boxes and the balls are all distinguishable. How many ways are there to put 10 balls into the boxes.
b. Suppose the boxes are indistinguishable, and the balls are also indistinguishable. How many ways are there to put 10 balls into the boxes?
Part a) is no different from asking "How many function are there from a set of ten to a set of 3"?
Part b) is more complicated. Here we must assume that at least one box is not empty. "How many ways can 10 be partitioned into three or fewer summonds"?
Here are some examples. $\boxed{10} \;;\;\boxed{9,1}\;;\boxed{8,1,1}\;;\;\boxed{7,2,1} \text{ etc}$.
That is not an easy task. | {"url":"http://mathhelpforum.com/statistics/79308-probability-print.html","timestamp":"2014-04-17T03:14:04Z","content_type":null,"content_length":"4892","record_id":"<urn:uuid:e1d14a5c-987a-4736-aaa2-f0cfe9b75d8c>","cc-path":"CC-MAIN-2014-15/segments/1397609526102.3/warc/CC-MAIN-20140416005206-00455-ip-10-147-4-33.ec2.internal.warc.gz"} |
Physics Forums - View Single Post - Intuitive content of Loop Gravity--Rovelli's program
http://arxiv.org/abs/1108.1178v1 Quantum simplicial geometry in the group field theory formalism: reconsidering the Barrett-Crane model
Aristide Baratin, Daniele Oriti
(Submitted on 4 Aug 2011)
Using the non-commutative metric formulation of group field theories (GFT), we define a model of 4-dimensional quantum gravity as a constrained BF theory, without Immirzi parameter, encoding the
quantum simplicial geometry of any triangulation used to define its quantum amplitudes. This involves a generalization of the usual GFT framework, where the usual field variables, associated to the
four triangles of a tetrahedron, are supplemented by an S^3 vector playing the role of the normal to the tetrahedron. This leads naturally to projected spin network states. We give both a simplicial
path integral and a spin foam formulation of the Feynman amplitudes, which correspond to a variant of the Barrett-Crane amplitudes. We then re-examin the arguments against the Barrett-Crane model(s),
in light of our construction. We argue that it can still be considered a plausible quantization of 4d gravity, and that further work is needed to either confirm or refute its validity. | {"url":"http://www.physicsforums.com/showpost.php?p=3436674&postcount=1551","timestamp":"2014-04-20T03:22:24Z","content_type":null,"content_length":"7975","record_id":"<urn:uuid:b5258281-8015-4e95-bcbf-450250344077>","cc-path":"CC-MAIN-2014-15/segments/1397609537864.21/warc/CC-MAIN-20140416005217-00207-ip-10-147-4-33.ec2.internal.warc.gz"} |
Brazilian Journal of Chemical Engineering
Services on Demand
Related links
Print version ISSN 0104-6632
Braz. J. Chem. Eng. vol.21 no.4 São Paulo Oct./Dec. 2004
COMPUTATIONAL FLUID DYNAMICS
A numerical simulation analysis of the effect of the interface drag function on cluster evolution in a CFB riser gas-solid flow
L. C. Gómez^*; F. E. Milioli
Núcleo de Engenharia Térmica e Fluidos, EESC-USP, Av. Trabalhador São-Carlense 400, CEP 13566-590, São Carlos - SP, Brasil, E-mail: milioli@sc.usp.br; E-mail: lubencg@sc.usp.br
The dynamics of formation, dissipation and breaking of coherent structures in the riser gas-solid flow of a circulating fluidized bed (CFB) are evaluated by numerical simulation. The simulation is
performed using the MICEFLOW code, which includes IIT's two-fluid hydrodynamic model B. The methodology for cluster characterization is used from Sharma et al. and is based on determination of four
characteristics, average lifetime, average volumetric fraction of solid, existence time fraction and frequency of occurrence. Clusters are identified applying a criterion for the time average value
of the volumetric solid fraction. A qualitative analysis of the influence of different drag function correlations on the hydrodynamics of the flow, including the evolution of coherent structures, is
performed. The simulation predictions are also compared to experimental results. The results indicate that the choice of a correlation for drag function should be quite judicious. Finally it is shown
that the mean clustering criteria of Sharma et al. should be modified to take into account other factors that influence cluster dynamics.
Keywords: coherent structures, clusters, drag function, numerical simulation, gas-solid flow, circulating fluidized bed.
The hydrodynamics of the gas-solid flow in risers of circulating fluidized beds result in coherent structures generally known as clusters. These structures are regions with higher particle
concentrations than the average concentration of particles in the riser of the bed. These groups of particles move as a single body with little internal relative movement (Helland et al., 2002).
According to Horio and Clift (1992), agglomerates are groups of particles joined together by the action of inter-particle forces, and clusters are groups of particles joined together as a result of
hydrodynamic effects. However, in several articles in the literature the term "agglomerate" is used to refer to clusters. Another important aspect is cluster shape. Horio and Kuroki (1994) found that
clusters are structures with a parabolic geometrical shape in the down region and a gas wake in the upper part. Hori and Kuroki conducted a three-dimensional visualization study of the gas-solid flow
using a laser sheet technique. On the basis of some research in the literature, Davidson (2000) affirms that clusters are groups of particles in the form of vertical sheets with a small width/height
ratio, which are coherent during a considerable traveling distance. Büssing and Reh (2001) indicate that clusters are nonspherical aggregates with a length/diameter ratio of up to 10, contrary to the
descriptions of Horio's group (Horio and Kuroki, 1994; Tsukada et al., 1997; and others). Regarding this discrepancy, Lackermeier et al. (2001) noted that the laser sheet technique used by Horio and
coworkers enables only images external to the flow to be obtained, thereby restricting observations to those of very small solid volumetric fractions (mass flow rates from about 0.01 to 0.05 kg/(m^
2s)). Lackermeier et al. (2001) applied Horio's technique, but tooked a shot of the internal flow through the use of an endoscopic observation technique. This technique allowed studying gas-solid
flows with solid concentrations characteristic of CFB risers. The clusters they observed were very similar to those described by Davidson (2000) and Büssing and Reh (2001).
A number of numerical simulations have been developed for studying clusters. Tsuo and Gidaspow (1990) used a traditional two-fluid model of constant viscosity to study the formation of clusters.
Various characteristics of the clusters were described, including density, size and flow pattern, and a discussion of the effect of several parameters on processes of cluster formation was presented.
The parameters considered were superficial inlet gas velocity, solid mass velocity, particle size, riser diameter, riser height and mixture of fine particles. It was shown that a decrease in mass
flow rate and particle size and an increase in superficial inlet gas velocity, mixture of fine particles and column diameter produced a reduction in cluster population. Work similar to that of Tsuo
and Gidaspow was developed by a number of researchers using Eulerian-Lagrangean formulations (Hoomans et al., 1998; Ouyang and Li, 1999; Helland et al., 2000; Helland et al., 2002; and others).
The similarity between cluster formation in liquid-liquid systems and that in gas-solid systems was addressed by Chen et al. (1991). The authors recognized that the drag force is the only source for
producing relative movement between particles and considered that any two systems must have the same tendency to form clusters if their drag forces are hydrodynamically similar. Currently, the
stationary drag force at the interface is the only one considered in the traditional two-fluid model. Empirical correlations account for this force, by which momentum transport at the interface is
modeled. It is normal to consider the interface drag force as a combination of both the shape and the skin drag in a single empirical parameter (see, for instance, van Wachem et al., 2001).
Most of the data used for drag force correlation in many multiparticle systems were obtained in uniform fluidization and sedimentation studies. Typically, the drag force is determined through
experimental measurement of pressure gradient. Usually the experimental measurements are used to calculate the so-called drag function at the interface, b, either in a straightforward way where b = f
(DP) or as a function of the drag coefficient for a single particle in the suspension, C[Ds], so b = f(C[Ds](DP)). Making use of this methodology various correlations for b have been proposed in the
literature. For instance, Ergun (1952) measured pressure gradient in a fixed liquid-solid bed and developed an expression for DP. Later this correlation was used to calculate b in a straightforward
way, i.e., b = f(DP). Wen and Yu (1966) developed experiments on the sedimentation of solid particles in a liquid for a large range of solid volumetric fraction values. They considered their own data
as well as data from other researchers and derived a correlation for C[Ds], valid for 0.01 < a[s] < 0.63. Later this correlation was used to indirectly calculate b, giving rise to an expression of
the type b = f(C[Ds](DP)).
Helland et al. (2002) describe two opposite effects of the processes of cluster formation on the interface drag. In dilute regions with nonuniformly distributed particles, a descending movement of
one particle can generate a velocity field throughout the fluid, reducing the drag on neighbor particles due to return flow bypass. In dense zones with uniformly distributed particles, the reduced
flow area between particles will impose higher gas velocity gradients, which will produce increased shear stresses and consequently an increased resistance to the gas flow.
In this paper the methodology of identification and characterization of clusters of Sharma et al. (2000) is applied to results of numerical simulation. The main objective is to study the influence of
the drag function on cluster dynamics. Four drag function correlations, taken from Ergun (1952), Wen and Yu (1966), Di Felice (1994) and Gidaspow (1994), are analyzed. The procedure applied in
Gidaspow (1994), here referred to as Gidaspow's procedure, assumes a hybrid approach through which Ergun's correlation is applied for a[s] > 0.2 and Wen and Yu's correlation is applied for a[s] <
0.2. van Wachem et al. (2001) observed that this procedure can cause some numerical instabilities due to the step-change in the drag function for a[s] = 0.2. Otherwise, according to Sanyal and
Cesmebasi (1994) this procedure is the one that best reproduces bubble growth processes in bubbling fluidized beds.
Sharma et al. (2000) presented three different criteria for cluster definition and identification, which were derived from the criteria proposed by Soong et al. (1993) apud Sharma et al. (2000). They
accounted for four basic cluster characteristics that allow quantifying the influence of flow parameters on these structures. The parameters considered were particle size and gas superficial
velocity. Their analyses were of experimental measurements obtained with a capacitance probe, which provided instantaneous local volumetric solid fraction in a 15 cm diameter circulating fluidized
bed. Despite the fact that the methodology was first applied to results of experiments (Soong et al., 1993 apud Sharma et al., 2000; Tuzla et al., 1998; Sharma et al., 2000), it was also recently
applied by Helland et al. (2002) to results of numerical simulation.
Mathematical Model
In the present work the hydrodynamic model B for a gas-solid flow developed at IIT (Illinois Institute of Technology) and included in the numerical code MICEFLOW (Jayaswal, 1991) is applied. A
summary of the governing system of equation is shown in Table 1. More detailed descriptions of the formulation are presented in Jayaswal (1991), Gidaspow (1994), Enwald et al. (1996) and
Cabezas-Gómez and Milioli (2001). The model, called the traditional two-fluid model, uses a Eulerian description for each phase, making possible the use of the kinetic theory of granular flows (KTGF)
as described in Gidaspow (1994). The model includes mass, momentum and energy conservation equations for all the phases and the turbulent kinetic energy equation for all solid phases. The
computational code allows a description of multiphase flows, including various solid phases, each characterized by a mean particle diameter, density and sphericity factor and two different fluid
phases. In the present work a flow containing a single gas phase (air) and a single solid phase (glass beads) is addressed. Both phases are assumed to be isothermal at 300K, and no interface mass
transfer is assumed. A Newtonian rheology is assumed for both phases. The solid phase pressure is modeled empirically through the solid elastic modulus, G, using the empirical correlation of Rietema
and Mutsers (1973) apud Jayaswal (1991). As stated in the previous section, four different correlations are considered for the interface drag function. These are correlations of Ergun (1952), Wen and
Yu (1966), and Di Felice (1994), besides the procedure of Gidaspow and coworkers (Gidaspow, 1994), where Ergun's correlation is used for a[s] > 0.2 and Wen and Yu's correlation is used for a[s] <
In Table 1, the subscripts (g) and (s) respectively stand for gas and solid phases, v[g] and v[s] are local temporal velocities (m/s), r[g] and r[s] are densities (kg/m^3), a[g] and a[s] represent
volumetric fractions, and t[g] and t[s] are viscous stress tensors (Pa). Also, P is the thermodynamic gas pressure (Pa), g is the gravity acceleration (m/s^2), G is the solid-phase elasticity modulus
(N/m^2), and b is an interface drag function (kg/m^2s). C[Ds] characterizes the interface drag coefficient for a single particle in an infinite medium, Re[s] is the Reynolds number based on the
particle mean diameter d[p], f[s] is the particle sphericity, m represents dynamic viscosity (kg/ms), R[g] is the ideal gas constant (kJ/kgK) and t is the time (s).
Cluster Identification and Characterization
Soong et al. (1993) apud Sharma et al. (2000) rely on the following guidelines to define clusters:
The concentration of solids in the cluster must be significantly higher than the local time-averaged solid concentration at a given local position for a particular set of operational conditions.
A perturbation in the concentration of solids due to clusters must be higher than the random ground fluctuations of the solid fraction.
This concentration perturbation should be measured in a sample volume with a characteristic length one or two orders of magnitude longer than the particle diameter.
Considering the above, Soong et al. proposed the following criterion: the value of the local instantaneous volumetric solid fraction for a cluster should be higher than its time-averaged value by two
times the standard deviation (2s). This way the clusters can be identified and considered as such when an instantaneous solid fraction exceeds that limit. This criterion was used by Tuzla et al.
(1998) to detect clusters in a downer fluidized bed. Sharma et al. (2000) slightly changed the above criterion on the basis of experimental evidence. According to the authors, the clusters detected
through the 2s criterion may become a different physical entity as soon as the instantaneous solid fraction becomes larger than the time-averaged solid fraction. This leads to the following criteria
for cluster life-time:
The cluster is detected when the instantaneous solid fraction becomes larger than the time-averaged solid fraction plus two times the standard deviation (2s).
The starting time of a cluster is the last time at which the instantaneous solid fraction exceeds the time-averaged solid fraction before satisfying the 2s criterion.
The end time of a cluster is the first time at which the instantaneous solid fraction falls below the time-averaged solid fraction after falling below the 2s criterion.
The above mean-referenced criterion, as it is referred to by Sharma et al. (2000), renders a cluster duration longer than that provided by the 2s criterion of Soong et al. Sharma et al. point out
that the mean-referenced criterion is rational but also somewhat arbitrary. However, they observe that the use of a different factor to reduce the influence of background noise (e.g., 3s) would
change results in a quantitative way, but would not change the general dynamic characteristics of the clusters. The arbitrariness of the criterion adopted by Sharma et al. is discussed at the end of
the Results section.
An illustrative application of the mean-referenced criterion is presented in Figure 1 for a transient signal of the local volumetric fraction resulting from a typical simulation. The time-averaged
solid fraction [s] and the [s] + 2s threshold are indicated. Figure 1b shows a closer view of the transient signal from 20 to 30 seconds. One cluster is observed between T[a] and T[b].
After a cluster is identified, its four basic characteristics, as defined by Tuzla et al. (1998) and Sharma et al. (2000), can be calculated. These characteristics are the mean duration time, the
frequency of occurrence, the existence time fraction and the mean solid concentration. They are defined as follows:
Mean duration time (t[c]): the mean time of duration of all clusters in a sample volume. (In Sharma et al. the relevant volume is the volume of a capacitance probe; when results of simulation are
used the relevant volume is that of a computational cell.) Assuming t[i] is the duration time of a single cluster,
where n is the total number of clusters detected in the observation period.
Frequency of occurrence (N[c]): the frequency at which the clusters are observed in the sample volume. It is calculated as the mean number of clusters per second that are observed during the entire
observation period (t).
Existence time fraction (F[c]): the fraction of the observation period in which there are clusters in the sample volume.
Mean solid concentration (a[sc]): the sum of the time-averaged solid fractions for all the clusters over the total number of clusters detected in the observation period, i.e.,
The above characteristics can also be calculated for cross-sectional average values, i.e.,
where x is the horizontal coordinate direction and 2R is the cross-sectional length.
Simulation Conditions and Initial and Boundary Conditions
Figure 2 shows the simulation conditions and domain, including the initial, inlet and outlet boundary conditions for both phases. One-dimensional plug flow is assumed at the inlet cross section. At
the outlet the continuity condition is assumed for all variables, except for gas pressure. At the walls the no slip condition is assumed for the gas phase and a partial slip condition is assumed for
the solid phase in agreement with Ding and Gidaspow (1990). A Cartesian coordinate system is used considering a 22´ 297 two-dimensional computational mesh nonuniform in the axial direction. The value
for solid-phase viscosity was taken from Tsuo and Gidaspow (1990).
Simulation Results
In this section a comparison of the radial profiles for axial velocity for both phases and the solid volumetric fraction in the simulation and the experiment is presented. Transient profiles for
solid fraction in the riser column are also presented. Next, simulation results for various drag functions are qualitatively compared using the methodology of cluster identification and
characterization of Sharma et al. Finally some comments on the mean-referenced criterion are offered.
Comparison Between Simulation and Experimental Data
Figure 3 shows radial profiles for time-averaged axial velocity of both phases compared to Luo's experimental data for the various drag function correlations taken into account. In Figure 3a a
significant difference is seen on v[g] profiles and the experimental data for all b correlations except Ergun's for the right-hand side wall. The deviations are still more pronounced at the axis of
the riser. It can be observed that Wen and Yu's correlation and Gidaspow's procedure produce similar behavior for v[g]. Di Felice's correlation also shows behavior that is qualitatively similar to
the above, but with some quantitative differences. It should be pointed out that, despite the fact that the results for Ergun's correlation are similar to those of the experiment (mainly at the
right-hand side wall), they are physically incorrect from the center to left-hand side wall. The reason for this behavior is discussed in Cabezas-Gómez and Milioli (2003a). It appears that in this
case viscous effects lose significance unlike drag effects, resulting in flat distributions of [s ](as seen in Figure 4). This produces a homogenization effect of the solid phase on the gas phase,
i.e., a flow strainer-like effect, that causes the cross-section gas-solid velocity profile to become flat. Also, it can be observed in Figure 3b that Ergun's correlation gives rise to a v[s] radial
profile that deviates more from the experiment that seen in the deviations for all the other b correlations. Figure 3 also shows that all the correlations, except Ergun's, achieve the expected
characteristic core-annulus flow pattern, including the downflow at the walls evidenced by the negative values of v[s]. The physically incoherent results obtained using Ergun's correlation show it
must not be used for the whole range of possible solid volumetric fractions.
Figure 4 shows radial profiles for the time-averaged solid volumetric fraction, [s], for the various b correlations. Except for Ergun's correlation, results are very similar, qualitatively correct
and in good agreement with the experimental data. The largest quantitative differences between simulation and experiment are detected in the region close to the wall. Again, it is clear that Ergun's
correlation alone cannot predict correct hydrodynamic behavior. The other correlations, including Ergun's as applied in Gidaspow's procedure, give rise to coherent solid volumetric fractions, which
are higher close to the walls and lower around the axis.
The temporal variation in the solid volumetric fraction in the column is shown in Figure 5 for the different drag functions considered. Four times are plotted (39.9, 40.0, 79.9 and 80.0 seconds).
Once more the inadequacy of Ergun's correlation when used alone can be seen, since it prevents the model from catching both the expected characteristic low frequency flow oscillations and the
clusters. However, when Ergun's correlation is used for a[s] > 0.2 alongside Wen and Yu's correlation for a[s] < 0.2 (Gidaspow's procedure), the above trends are well represented (Figure 5d). The
same occurs for the other two correlations considered. The predictions for Wen and Yu's correlation and Gidaspow's procedure seem similar, differing more in the lower half of the column. This should
be because Gidaspow's procedure applies Wen and Yu's correlation in dispersed regions. Figure 5 also shows that the instantaneous behavior of the flow is different for each correlation. This
emphasizes the importance of a correct choice of drag function correlation and the need for new studies along this line.
Further analyses of simulations similar to those presented here were presented in Cabezas-Gómez and Milioli (2001, 2003a). The same mathematical model and numerical procedure were employed, using a
different computational mesh. The qualitative behavior found was the same as that in the present simulations. The same behavior was also observed for Ergun's correlation.
Characteristic Analysis of Clusters Using Results of Simulation for Various b Correlations
Radial profiles for the mean solid concentration of clusters, a[sc], are shown in Figure 6. Behavior similar to that seen in Figure 4 for [s] is observed for all the b correlations except for Di
Felice's, which shows a quite different pattern. Again, Wen and Yu's correlation and Gidaspow's procedure produce very similar results. The mean solid concentration of clusters is higher at the
walls. Ergun's correlation gives rise to a flat radial profile (radial homogeneous distribution of a[sc]) that matches the radial profile of [s] both qualitatively and quantitatively. This is
unexpected since the mean concentration of solids in clusters is by definition supposed to be higher than the time-averaged concentration of solids at the same place during the same time interval.
This behavior is also observed for other correlations, as seen in Figure 6. Clearly, for the above situations the mean-referenced criterion is not appropriate. This fact, which is discussed further
below, reinforces the need for improving or formulating new criteria to better characterize and quantify coherent structures in gas-solid flows.
Figure 7 shows axial profiles for the mean cross-sectional values of the time-averaged solid fraction, <[s]>, and the mean concentration of solids in clusters, <a[sc]>. Both parameters show similar
behavior for both Wen and Yu's correlation and Gidaspow's procedure, except for the height of 5.5 m, where <a[sc]> increases while <[s]> decreases. This is clearly a consequence of accumulation of
solids and intensified cluster formation at the outlet. For Di Felice's correlation the axial profile for <a[sc]> shows some variations that are sharper than that of <[s]> and a noticeably sharp
increase at the height of about 3.5 m. Above this height <[s]> considerably decreases and finally slightly increases at the outlet. It should be noted that above 1.5 m <a[sc]> becomes higher than the
values for the other correlations. This is due to the fact that denser clusters are formed for Di Felice's correlation, as seen in Figure 6.
For Ergun's correlation both <a[sc]> and <[s]> were uniform throughout the column, and equal to each other. This shows that Ergun's correlation applied to all possible values of solid fractions does
not allow the model to catch cluster formation and that the mean-referenced criterion of Sharma et al. needs to be revised. The fraction of solids was higher in the lower region of the column for all
correlations except Ergun's. In all cases the mean-referenced criteria applied to this region point to the occurrence of clusters, even though they cannot really exist since the lower bed region
behaves as a bubbling fluidized bed (Johnsson et al., 2000). In these cases, of course, the assumption of the occurrence of clusters is incorrect. The application of any criteria for cluster
identification in this region is an open question and must be studied more systematically. There are considerable differences between the axial profiles for <a[sc]> for the various drag function
correlations considered, making evident the need for experimental validation.
Figure 8 shows radial profiles for cluster mean duration time, t[c], and axial profiles for its cross-sectional average, <t[c]>. Significant relative variations are observed among the radial profiles
for the various drag functions. A considerable increase in t[c] is observed moving towards the right-hand side wall. This happens to a lesser extent moving towards the left-hand side wall. Such
asymmetric behavior seems to be due to the outlet boundary condition that requires the flow to move towards the right-hand side wall, causing a higher concentration of solids in clusters in this
region. It is interesting to note that for Ergun's correlation the cluster mean duration time results in the range from about 1.0 to about 1.75 seconds. In this case the existence of a cluster
duration time is inconsistent, since no cluster is observed when using Ergun's correlation, as previously discussed. Again, this makes clear that the methodology of identification and
characterization of clusters of Sharma et al. (2000) needs revision. Finally, Figure 8 shows that t[c] is higher for Di Felice's correlation at most heights in the column.
The present results for t[c] are quite different from those obtained by Sharma et al. They found the highest t[c] to be about 0.15 seconds at 4.5 meters high in the column. In the present work the
highest t[c] was of about 4.0 seconds at a height of 3.4 meters. The turbulent nature of the flow may be a major cause for the disagreement, since in the present work it is only accounted for to the
extent allowed by the size of the numerical mesh. Scales of turbulence smaller than the mesh size are not observed. This limitation will mainly affect the gas phase, as discussed in Cabezas-Gómez and
Milioli (2003b), since mesh size is considerably fine for the solid phase. Otherwise, caution is required when comparing these results to those of Sharma et al., since those authors assumed radial
symmetry and their operating conditions and bed geometry were not the same as those in the present work. Experimental uncertainties of Sharma et al. and numerical errors in the present simulations
should also be considered.
Radial profiles for cluster existence time fraction are shown in Figure 9 at a column height of 3.4 meters. Cross-sectional averages in the column are also shown. Existence time fraction of the
clusters was quite scattered throughout the cross section, ranging between about 0.07 and 0.27, with most of the points lying between 0.12 and 0.22. No correlation pattern seems to exist between
existence time fraction of the clusters and radial position inside the column. The cross-sectional averages of the existence time fraction of the clusters varied between about 0.07 and 0.23. It's
average on the column height resulted in about 0.17 for all correlations except for those of Di Felice. The same result was obtained by Sharma et al.. The authors observed that <F[c]> is constant and
independent of both inlet gas superficial velocity and mean particle diameter and pointed out that for this there is no explanation at the moment.
Figure 10 shows radial profiles for frequency of cluster occurrence at a column height of 3.4 meters. Cross-sectional averages in the column are also shown. The frequency of occurrence varied within
a broader range than the existence time fraction of the clusters. This effect was stronger for the cross-sectional averages. It can be seen that lower in the column the frequency of clusters was
higher. It oscillated between 0.05 and 0.20 over the entire column height. Di Felice's correlation provided the lowest frequencies of cluster occurrence for all correlations for drag function. The
highest frequency of clusters was observed on the column axis with the exception of Di Felice's correlation. This correlation represents the lower values of N[c] around the axis as well as throughout
the entire cross section. In the upper half of the column the highest of frequency cluster occurrence takes place at 5.5 meters. It was about 0.15 clusters per second for all the drag functions. This
value is very low compared to the maximum of 12 clusters per second found by Sharma et al. This difference in N[c] is consistent with that observed for t[c]. It is reasonable to suppose that a higher
clusters existence time means a lower frequency of occurrence.
Helland et al. (2002) applied an Euler-Lagrange model to simulate the upper side of the experimental rig of Sharma et al. (2000). They found frequencies of cluster occurrence from 6 to 9 clusters per
second, which is relatively close to that of Sharma et al. of 12 clusters per second, and much higher than the 0.15 clusters per second in the present simulation. They also found cluster mean
duration times from 0.12 to 0.15 seconds, which agree with the maximum of 0.15 seconds observed by Sharma et al. and are much lower than the maximum of 4.0 seconds in the present simulation.
Helland et al. used a highly spatial resolved simulation by considering the movement of all the particles in the domain and their interactions with the gas phase. In the present Euler-Euler
simulations, the high frequency hydrodynamic oscillations of the gas phase are filtered by the numerical procedure. This may be a cause for the relatively low values observed for the frequency of
cluster occurrence as well as for the high values found for mean duration time of the clusters. However, the present results are qualitatively supported by Davidson's observation that clusters are
characterized by long residence times and slow movements (Davidson, 2000).
The above are evidence of the need for new and more comprehensive studies on cluster characterization, both experimental and numerical. On the experimental level the reason to require new independent
measurement of solid fractions is clear. On the simulation level more comprehensive and accurate three-dimensional results are required.
Analysis of the Sharma et al. Mean-referenced Criteria
Figure 11 shows the transient behavior of the solid fractions close to the left-hand side wall at a column height of 3.4 meters, using Ergun's correlation for the drag coefficient. As can be seen,
the 2s criteria obtains nine clusters during the time interval considered. The difference between the time-averaged solid's fraction [s] and [s] + 2s, which actually defines what is and what is not a
cluster, is on the order of 10^-7. This very insignificant difference is lower than errors commonly found in experimental measurements and many numerical predictions in fluid mechanics. In fact, the
statistical analysis on the mean-referenced criteria of Sharma et al. (2000) are based will identify clusters independently of the behavior of a[s]. This is so because any signal analyzed will have
some clusters beyond the 2s limit. It seems clear that new criteria need to be formulated, whereby flow hydrodynamic effects are taken into account, rather than only statistical data on a[s]. This
feature was recently addressed by Harris et al. (2002). According to these authors, the lower limit of a[s] influences cluster definition and properties. This suggests that the mean-referenced
criteria should be modified by considering lower limits of a[s], both in time and space. Effects of operating conditions and bed geometry on flow behavior should also be considered. This task seems
to be very difficult to accomplish at the moment.
Simulation results were significantly affected by the particular drag function correlation which was used. The choice of an appropriate correlation was shown to be a critical feature, especially when
quantitative good results are desired. Clearly, further work is required on this matter. Physically incoherent results were obtained with Ergun's correlation, showing that it must not be applied
alone for the whole range of possible solid fractions.
The analyses clearly pointed out that the criteria of Sharma et al. (2000) for identification and characterization of clusters needs to be reformulated. In its present form the criteria indicate the
existence of clusters for any flow pattern, whatever the value of the solid fraction.
The present predictions, evaluated under the criteria of Sharma et al., obtained much lower amounts and much longer lifetimes of clusters than the experiment and other simulations in the literature.
These discrepancies may be caused by experimental uncertainties, numerical errors or differences in both operational conditions and bed geometry. Also, in the present simulations the high frequencies
of hydrodynamic oscillations in the gas phase are filtered by the numerical procedure. This may also be a cause of the above-mentioned discrepancies. In this case the model can by corrected by
including either artificial turbulence models, such as the k-e model, or a large eddy simulation with a well-refined computational mesh, sub-mesh models and the KTGF for solid-phase viscosity
This work was supported by FAPESP (Fundação de Amparo a Pesquisa do Estado de São Paulo) through doctoral and postdoctoral scholarships for the first author (processes 98/13812-1 and 02/12038-8).
List of Symbols
C[Ds] drag coefficient for a single particle in an infinite medium (-)
d[p] particle diameter, (m)
g gravity acceleration, (m/s^2)
G solid elasticity modulus (N/m^2)
P gas pressure (Pa)
Re[s] Reynolds number based on particle diameter (-)
R[g] ideal gas constant, (kJ/kgK)
t time, (s)
v[g] and v[s] control volume average velocities, (m/s)
b interface drag function, (kg/m^2s)
m dynamic viscosity, (kg/ms)
a[g] and a[s] volumetric fractions (-)
r[g] and r[s] densities, (kg/m^3)
s standard deviation (-)
t[g] and t[s] viscous stress tensors, (Pa)
f[s] particle sphericity (-)
(g) and (s) gas and solid phases
(k) gas or solid phase
Agrawal, K., Loezos, P.N., Syamlal, M. and Sundaresan, S., The Role of Meso-Scale Structures in Rapid Gas-Solid Flows, Journal of Fluid Mechanics, 445, 151 (2001). [ Links ]
Büssing, W. and Reh, L., On Viscous Momentum Transfer by Solids in Gas-Solids Flow through Risers, Chemical Engineering Science, 56, 3803 (2001). [ Links ]
Cabezas-Gómez, L. and Milioli, F.E., A Parametric Study of the Gas-Solid Flow in the Riser of a Circulating Fluidized Bed Through Continuous Eulerian Modeling, Powder Technology, 132, 216 (2003a). [
Links ]
Cabezas-Gómez, L. and Milioli, F.E., A Parametric Study of the Gas-Solid Flow in the Riser of a Circulating Fluidized Bed Through Continuous Eulerian Modeling, Submitted to Chemical Engineering
Science (2003b). [ Links ]
Cabezas-Gómez, L. and Milioli, F.E., Gas-Solid Two-phase Flow in the Riser of Circulating Fluidized Bed: Mathematical Modeling and Numerical Simulation, Brazilian Journal of Mechanical Engineering,
19, No. 3, 271 (2001). [ Links ]
Chen, Y-M., Jang, C-S., Cai, P and Fan, L-S., On the Formation and Disintegration of Particle Clusters in a Liquid-Solid Transport, Chemical Engineering Science, 46, No. 9, 2253 (1991). [ Links ]
Davidson, J.F., Circulating Fluidized Bed Hydrodynamics, Powder Technology, 113, 249 (2000). [ Links ]
Di Felice, R., The Voidage Function for Fluid-particle Interaction Systems, International Journal of Multiphase Flow, 20, No. 1, 153 (1994). [ Links ]
Ding, J. and Gidaspow, D., A Bubbling Model Using Kinetic Theory of Granular Flow, AIChE Journal, 36, No. 4, 523 (1990). [ Links ]
Enwald, H., Peirano, E. and Almstedt, A.-E., Eulerian Two-phase Flow Theory Applied to Fluidization, International Journal of Multiphase Flow, 22, (Suppl.), p. 21 (1996). [ Links ]
Ergun, S., Fluid Flow through Packed Columns, Chemical Engineering Progress, 48, No. 2, 89 (1952). [ Links ]
Gidaspow, D., Multiphase Flow and Fluidization: Continuum and Kinetic Theory Descriptions. Academic Press, Boston (1994). [ Links ]
Harris, A.T., Davidson, J.F. and Thorpe, R.B., The Prediction of Particle Cluster Properties in the Near Wall Region of a Vertical Riser (200157), Powder Technology, 127, No. 2, 128 (2002). [ Links ]
Helland, E., Occelli, R. and Tadrist, L., Numerical Study of Cluster Formation in a Gas-Particle Circulating Fluidized Bed, Powder Technology, 110, 210 (2000). [ Links ]
Helland, E., Occelli, R. and Tadrist, L., Computational study of Fluctuating Motions and Cluster Structures in Gas-Particle Flows, International Journal of Multiphase Flow, 28, 199 (2002). [ Links ]
Hoomans, B.P.B., Kuipers, J.A.M. and Van Swaaij, W.P.M., Granular Dynamics Simulation of Cluster Formation in Dense Riser Flow. 3^rd International Conference on Multiphase Flow, Lyon, France (1998).
[ Links ]
Horio, M. and Clift, R., A Note on Terminology: 'Clusters' and 'Agglomerates', Powder Technology, 70, 196 (1992). [ Links ]
Horio, M. and Kuroki, H., Three-Dimensional Flow Visualization of Dilutely Dispersed Solids in Bubbling and Circulating Fluidized Beds, Chemical Engineering Science, 49, 2413 (1994). [ Links ]
Jayaswal, U., Hydrodynamics of Multiphase Flows: Separation, Dissemination and Fluidization. Ph.D. diss., Illinois Institute of Technology, Chicago (1991). [ Links ]
Johnsson, F., Zijerveld, R.C., Schouten, J.C., van den Bleek, C.M. and Leckner, B., Characterization of Fluidization Regimes by Time-series Analysis of Pressure Fluctuations, International Journal of
Multiphase Flow, 26, No. 4, 663 (2000). [ Links ]
Lackermeier, U., Rudnick, J., Werther, J., Bredebusch, A. and Burkhardt, H., Visualization of Flow Structures Inside a Circulating Fluidized Bed by Means of Laser Sheet and Image Processing, Powder
Technology, 114, 71 (2001). [ Links ]
Luo, K.M., Dilute, Dense-Phase and Maximum Solids-Gas Transport. Ph.D. diss., Illinois Institute of Technology, Chicago (1987). [ Links ]
Ouyang, J. and Li, J., Discrete Simulations of Heterogeneous Structure and Dynamic Behavior in Gas-solid Fluidization, Chemical Engineering Science, 54, 5427 (1999). [ Links ]
Sanyal, J. and Cesmebasi, E., On the Effect of Various Momentum Transfer Coefficient Models on Bubble Dynamics in a Rectangular Gas Fluidized Bed, Chemical Engineering Science, 49, No. 23, 3955
(1994). [ Links ]
Sharma, A.K., Tuzla, K., Matsen, J. and Chen, J.C., Parametric Effects of Particle Size and Gas Velocity on Cluster Characteristics in Fast Fluidized Beds, Powder Technology, 111, 114 (2000). [ Links
Tsukada, M., Ito, M., Kamiya, H. and Horio, M., Three-Dimension Imaging of Particle Clusters in Dilute Gas-Solid Suspension Flow, The Canadian Journal of Chemical Engineering, 75, 466 (1997). [ Links
Tsuo, Y., Computation of Flow Regimes in Circulating Fluidized Beds. Ph.D. diss., Illinois Institute of Technology, Chicago (1989). [ Links ]
Tsuo, Y.P. and Gidaspow, D., Computation of Flow Patterns in Circulating Fluidized Beds, AIChE Journal, 36, No. 6, 885 (1990). [ Links ]
Tuzla, K., Sharma, A.K., Chen, J.C., Schiewe, T., Wirth, K.E. and Molerus, O., Transient Dynamics of Solid Concentration in Downer Fluidized Bed, Powder Technology, 100, 166 (1998). [ Links ]
van Wachem, B.G.M., Schouten, J.C., van den Bleek, C.M., Krishna, R. and Sinclair, J.L., Comparative Analysis of CFD Models of Dense Gas-solid Systems, AIChE Journal, 47, No. 5, 1035 (2001). [ Links
Wen, C.Y. and Yu, Y.H., Mechanics of Fluidization, Chemical Engineering Progress Symposium Series, 62, No. 62, 100 (1966). [ Links ]
Received: October 16, 2003
Accepted: July 12, 2004
* To whom correspondence should be addressed | {"url":"http://www.scielo.br/scielo.php?script=sci_arttext&pid=S0104-66322004000400006","timestamp":"2014-04-20T07:14:21Z","content_type":null,"content_length":"84351","record_id":"<urn:uuid:2d972a55-a157-466c-81d6-785cce36cbdc>","cc-path":"CC-MAIN-2014-15/segments/1397609538022.19/warc/CC-MAIN-20140416005218-00506-ip-10-147-4-33.ec2.internal.warc.gz"} |
Kripke-Style Semantics for SDL
We define the frames (structures) for modeling SDL as follows:
F is an Kripke-SDL (or KD) Frame: F = <W,A> such that:
1. W is a non-empty set
2. A is a subset of W × W
3. A is serial: ∀i∃jAij.
A model can be defined in the usual way, allowing us to then define truth at a world in a model for all sentences of SDL (and SDL+):
M is an Kripke-SDL Model: M = <F,V>, where F is an SDL Frame, <W,A>, and V is an assignment on F: V is a function from the propositional variables to various subsets of W (the “truth sets’ for
the variables—the worlds where the variables are true for this assignment).
Let “M ⊨[i] p” denote p's truth at a world, i, in a model, M.
Basic Truth-Conditions at a world, i, in a Model, M:
[PC]: (Standard Clauses for the operators of Propositional Logic.)
[OB]: M ⊨[i] OBp: “∀j[if Aij then M ⊨[j] p]
Derivative Truth-Conditions:
[PE]: M ⊨[i] PEp: ∃j(Aij & M ⊨[j] p)
[IM]: M ⊨[i] IMp: ~∃j(Aij & M ⊨[j] p)
[OM]: M ⊨[i] OMp: ∃j(Aij & M ⊨[j] ~p)
[OP]: M ⊨[i] OPp: ∃j(Aij & M ⊨[j] p) & ∃j(Aij & M ⊨[j] ~p)
p is true in the model, M (M ⊨ p): p is true at every world in M.
p is valid (⊨ p): p is true in every model.
Metatheorem: SDL is sound and complete for the class of all Kripke-SDL models.^[1]
Return to Deontic Logic. | {"url":"http://plato.stanford.edu/entries/logic-deontic/kripke.html","timestamp":"2014-04-18T02:58:45Z","content_type":null,"content_length":"15479","record_id":"<urn:uuid:5ce7a380-15b3-4a08-9065-640f67453e76>","cc-path":"CC-MAIN-2014-15/segments/1398223206120.9/warc/CC-MAIN-20140423032006-00219-ip-10-147-4-33.ec2.internal.warc.gz"} |
integral tables
December 12th 2009, 05:54 PM
integral tables
I need to integrate this integral from -infinity to infinity,
∫▒〖(x^3 e^x)/(e^x+1)^2 dx〗
The question says I can look it up in integral table but I cannot find tables with this type of integral in it.
December 12th 2009, 07:38 PM
note that it is an odd function ( a fantastic odd function (Evilgrin) )
December 12th 2009, 08:28 PM
So it cancels out to 0?
If that is the case then I need to integrate (x^4*e^x)/((e^x+1)^2).
I am doing a sommerfield expansion and I need another term to survive.
December 12th 2009, 08:58 PM
$I = \int_{-\infty}^{\infty} \frac{ x^{2n} e^x }{ ( 1 + e^x )^2 } ~dx = 2(2n)! \zeta(2n)( 1 - 2^{1-2n} )$
when $n = 2$
$I = 2(4)! \zeta(4) ( 1 - 2^{-3} ) = \frac{7}{15} \pi^4$
December 12th 2009, 09:08 PM
Perfect. Thank You.
December 13th 2009, 04:22 AM
mr fantastic
I haven't checked the details here but care must be taken with improper integrals of this type. An odd integrand does not mean that an improper integral of this type is equal to zero. It could be
divergent. A case in point is $\int_{-\infty}^{+\infty} \frac{x}{1 + x^2} eq 0$ ....
December 14th 2009, 01:47 AM
I haven't checked the details here but care must be taken with improper integrals of this type. An odd integrand does not mean that an improper integral of this type is equal to zero. It could be
divergent. A case in point is $\int_{-\infty}^{+\infty} \frac{x}{1 + x^2} eq 0$ ....
Oh , I didn't realise this ... but luckily this integral $\int_0^{\infty} ~(...)~dx$ mentioned above is convergent. | {"url":"http://mathhelpforum.com/calculus/120136-integral-tables-print.html","timestamp":"2014-04-17T07:54:02Z","content_type":null,"content_length":"8076","record_id":"<urn:uuid:677b57fd-b915-47af-ab56-0ecaa13ae424>","cc-path":"CC-MAIN-2014-15/segments/1397609526311.33/warc/CC-MAIN-20140416005206-00155-ip-10-147-4-33.ec2.internal.warc.gz"} |
Find a Caddo Mills Tutor
...After tutoring over 30 hours of Prealgebra, I’ve found that quite a few high school students lack key Prealgebra skills. This knowledge gap can cause problems when trying to learn algebra and
geometry. I tutor pure Prealgebra sessions but also work Prealgebra topics into tutoring sessions for ACT prep, SAT prep, Algebra 1, Algebra 2 and Geometry when needed.
15 Subjects: including reading, writing, geometry, algebra 1
...I hold an elementary certification from the state of Michigan, a Master Reading, special ed and ESL certification in the state of TX. Since I have a Master Reading teacher endorsement on my
certification I have studied extensively how to teach reading. As a teacher of students who have difficulty learning, I have shown them more effective ways to be productive learners.
21 Subjects: including reading, English, writing, geometry
...I would work with manipulatives, diagrams and hands-on materials that your student would be able to touch and feel to learn. For the visual learner, I would work with various visual
illustrations, flash cards and other activities that would aid the student in their studies. Study skills would a...
8 Subjects: including algebra 1, grammar, elementary (k-6th), elementary math
I have been an experienced French professor for nine years. I received my Master's degree from Toulouse University in France. I've also had the privilege to teach this beautiful language in East
Africa for two years, as well as in South and North America for seven years after my Master's degree in France.
1 Subject: French
...Evelyn also is certified to tutor Bilingual Reading and prepare students for the T.O.E.F.L. exam.The reading tutorial I especially love to deliver is for the ESL/ESOL student who is in the
initial stages of learning how to read in English for comprehension. Over the years, I have collected appro...
5 Subjects: including Spanish, reading, ESL/ESOL, TOEFL | {"url":"http://www.purplemath.com/Caddo_Mills_tutors.php","timestamp":"2014-04-18T11:42:56Z","content_type":null,"content_length":"23389","record_id":"<urn:uuid:81c0ffca-85fe-4d46-8a76-b66d2c197481>","cc-path":"CC-MAIN-2014-15/segments/1397609533308.11/warc/CC-MAIN-20140416005213-00269-ip-10-147-4-33.ec2.internal.warc.gz"} |
Operations Research Methods
Central to our discussion of OR Methods is the Teach OR collection of Excel add-ins. These add-ins concentrate on the Mathematical Programming algorithms. This page links to complete
instructions for each add-in.
We provide three units to demonstrate and teach linear programming solution algorithms.
• Primal Simplex Demonstrations are implemented using Flash to illustrate basic concepts of the primal simplex technique.
• The Teach Linear Programming Add-in implements three different algorithms for solving linear programming models.
We provide five units to demonstrate and teach network flow programming solution algorithms.
• The Teach Network Add-in implements the network primal simplex method for both pure and generalized minimum cost flow problems.
• A graphical demonstration using Flash illustrates and contrasts algorithms for finding the minimal spanning tree and shortest path tree.
• The Transportation primal simplex method is implemented in the Teach Transportation Add-in.
• A graphical demonstration using Flash illustrates the network primal simplex method.
The Teach IP Add-in implements three methods for solving linear integer programming problems. The add-in provides demonstrations and hands-on practice for the branch and bound method, the
cutting plane method and Benders' algorithm.
The Teach NLP Add-in demonstrates direct search algorithms for solving nonlinear optimization problems.
The Teach Dynamic Programming Add-in has features that allow almost any system appropriate for dynamic programming to be modeled and solved. The program includes both backward recursion and | {"url":"http://www.me.utexas.edu/~jensen/ORMM/methods/index.html","timestamp":"2014-04-16T10:32:35Z","content_type":null,"content_length":"17392","record_id":"<urn:uuid:47368de6-363a-40e4-9dad-738970f35bdc>","cc-path":"CC-MAIN-2014-15/segments/1398223207046.13/warc/CC-MAIN-20140423032007-00571-ip-10-147-4-33.ec2.internal.warc.gz"} |
Heavy Baggage
When travelling by aircraft, passengers have a maximum allowable weight for their luggage. They are then charged £10 for every kilogram overweight. If a passenger carrying 40 kg of luggage is charged
£50, how much would a passenger carrying 80 kg be charged?
A £50 charge represents 5 kg overweight (5
So 40
Hence 80 kg is 80
Can you find a formula to calculate the charge for a given weight of baggage, W kg?
What would your formula produce if W = 30 kg?
Problem ID: 116 (May 2003) Difficulty: 1 Star | {"url":"http://mathschallenge.net/full/heavy_baggage","timestamp":"2014-04-19T20:18:24Z","content_type":null,"content_length":"5056","record_id":"<urn:uuid:9e250ab2-f7e3-4db1-905a-bac9ca99350c>","cc-path":"CC-MAIN-2014-15/segments/1397609537376.43/warc/CC-MAIN-20140416005217-00623-ip-10-147-4-33.ec2.internal.warc.gz"} |
[Edu-sig] Re: reducing fractions
Steve Litt slitt@troubleshooters.com
Fri, 15 Sep 2000 11:14:50 -0400
At 12:41 PM 8/14/00 -0700, Kirby Urner wrote:
>"Janet Johnson" <johnsonje@adelphia.net> wrote:
>>I teach 6th grade and every year my students seem to have a lot of
>>difficulty with fractions, specifically, reducing or recognizing that a
>>fraction isn't reduced. I have given them many ideas on how to tell, even
>>to the point of writing out the factors for both the numerator and
>>denominator. Does anyone have any suggestions on how to get this concept
>>across to the students? Any suggestions would be greatly appreciated.
>>Janet Johnson
>You could unsimplify some fractions e.g. 2/3 -> 10/15
>i.e. show the inverse of what it means to "simplify".
>If 'prime number' is already a concept, you could try
>'relative prime' meaning no factors in common (i.e.
>"a fraction is in lowest terms when the numerator and
>denominator are both integers and are relative primes").
>Along these lines, I really like your idea of writing
>out the prime factors, crossing out those in common e.g.:
> 150/210 -> (3 x 5 x 2 x 5) / (7 x 3 x 2 x 5) -> 5/7
That's how my 7th grade teacher taught me to simplify fractions, and I've
never been sorry.
Steve Litt
Webmaster, Troubleshooters.Com | {"url":"https://mail.python.org/pipermail/edu-sig/2000-September/000607.html","timestamp":"2014-04-19T17:29:45Z","content_type":null,"content_length":"3687","record_id":"<urn:uuid:3d150d60-9738-46cc-90c0-df2c60ecbe28>","cc-path":"CC-MAIN-2014-15/segments/1397609537308.32/warc/CC-MAIN-20140416005217-00014-ip-10-147-4-33.ec2.internal.warc.gz"} |
Power Topics for Power Supply Users
Many modern power supplies, such as TDK-Lambda's
new Z+ programmable supplies
and the
HFE series of rack mount supplies
, now feature serial data interfaces such as I
C, USB 2.0, and RS485, to name a few. The transmission rates of these serial data interfaces are specified as bits-per-second (bits/s) and/or baud rate. As a refresher, here is a brief review of the
difference between Bit rates and Baud rates.
The Bit rate is the number of bits (binary zeros and ones) that are transmitted during one second (bits/s). The Baud rate refers to the number of signal units (symbols or characters) that are
transmitted per second.
Equation for Baud Rate
baud rate = bit rate (bits/s) ÷ N, where N is the number of bits represented by each signal shift (symbol or character).
For example, if the bit rate is 9,600 bits/s and the communications format require 8 bits per symbol, the baud rate would be 9,600 bits/s divided by 8 bits, which would equal 1200 baud.
Equation for Bit Rate
Bits/s = baud per second x the number of bits per symbol
Therefore, from the above example:
Bits/s = 1200 baud x 8 bits = 9,600 bits/s | {"url":"http://power-topics.blogspot.com/2012_05_01_archive.html","timestamp":"2014-04-16T10:30:19Z","content_type":null,"content_length":"95987","record_id":"<urn:uuid:0489e2da-afe7-4f10-a866-5f277481ebca>","cc-path":"CC-MAIN-2014-15/segments/1397609523265.25/warc/CC-MAIN-20140416005203-00260-ip-10-147-4-33.ec2.internal.warc.gz"} |
Fibonacci Proof (Modelling/Abstract Question)
November 24th 2009, 08:43 AM #1
Oct 2009
Fibonacci Proof (Modelling/Abstract Question)
A certain parking meter will accept only $1 or $2 coins (we're Australian... it's okay!). Parking in this regulated areas costs $1 per hour and a maximum time of six hours of parking is
allowable. Coins can only be inserted into the meter one at a time, and a sequence of, say $1 + $2 is considered to be a different sequence to $2 + $1.
Determine the total number of combinations of $1 and $2 coins that are possible when payment is made for up to the maximum of 6 hours.
I have the combinations (there really aren't many) but this is under Fibonacci proofs and induction and I just can't see how's it relates? Just a couple of hints would be amazing. Please and
Thanks guys
Very nice problem. One hint is to look at the number of ways to pay for exactly n hours. I tried several small n's, and for each n I drew a binary tree. For each node, one child corresponds to
paying $1, the other $2. Each tree node may be labeled with the amount left. After doing an exhaustive search of ways to pay in this manner, I noted that some parts of trees for larger n's are
copies of trees for smaller n's.
Of course, this is just what I tried; this may not be the easiest or the most intuitive way to approach the problem.
Surely there a more... mathematically formulated way?
are you saying do a tree thing??
Parking Meter Tree Diagram..doc
So using this I can see there are 13 ways...
holy moley... that isn't a Fibonacci number I see is it??
okay so maybe there's a formula to the way?? the 7th Fibonacci number is the answer to make a maximum $6 from 1 and 2 dollar coins...
Is there are a math formula or something that can be produced?
Nice trees! Though it would be better to write the remaining amount in the nodes.
So, I understand that if one adds a root to the whole picture, one gets the tree for 6. Well, the top subtree is the tree for 5, and the bottom one is for tree for 4.
One needs to add a child to one of the $2 nodes in the bottom tree. If you go $2, $1, $2, you have only $5, not $6. After that, the bottom tree for 4 is isomorphic to the top subtree of the top
okay what?
Yep, I missed another $1.
Um you mean for the first one go like
etc. etc. rather than
and your saying where directly behind those purple ones would be the way to get $5, behind that, $4....
all Fibonacci numbers...
Except they start at 1.
there's 1 way to get $1
2 ways to get $2
3 ways to get $3
5 ways to get $4
what's isomorphic?
Yes. Branches should be labeled with $1 or $2, and nodes with the remaining amount. So the sum of branch labels from a node to a leaf must be equal to that node's label.
No there not... they are 2 different combinations...
No there not... they are 2 different combinations...
In both cases you have to spend $4. I don't know how this will show because I use OpenOffice, but I am attaching your drawing. I spoiled it
Remember that it is not node labels you are after. What is important is the number of leaves -- each leave corresponds to one way to spend $6. This number is the sum of the corresponding numbers
for $5 and $4.
November 24th 2009, 11:07 AM #2
MHF Contributor
Oct 2009
November 24th 2009, 11:55 AM #3
Oct 2009
November 24th 2009, 12:03 PM #4
MHF Contributor
Oct 2009
November 24th 2009, 12:08 PM #5
MHF Contributor
Oct 2009
November 24th 2009, 12:10 PM #6
Oct 2009
November 24th 2009, 12:13 PM #7
MHF Contributor
Oct 2009
November 24th 2009, 12:20 PM #8
MHF Contributor
Oct 2009
November 24th 2009, 12:21 PM #9
Oct 2009
November 24th 2009, 01:01 PM #10
MHF Contributor
Oct 2009 | {"url":"http://mathhelpforum.com/discrete-math/116505-fibonacci-proof-modelling-abstract-question.html","timestamp":"2014-04-16T20:23:42Z","content_type":null,"content_length":"61081","record_id":"<urn:uuid:40918c33-74c1-4a8c-bc00-5cb685426bce>","cc-path":"CC-MAIN-2014-15/segments/1397609524644.38/warc/CC-MAIN-20140416005204-00103-ip-10-147-4-33.ec2.internal.warc.gz"} |
What is 15 ML EQUALS HOW MANY TEASPOONS?
Mr What? is the first search engine of definitions and meanings, All you have to do is type whatever you want to know in the search box and click WHAT IS!
All the definitions and meanings found are from third-party authors, please respect their copyright.
© 2014 - mrwhatis.net | {"url":"http://mrwhatis.net/15-ml-equals-how-many-teaspoons.html","timestamp":"2014-04-20T16:45:49Z","content_type":null,"content_length":"37287","record_id":"<urn:uuid:348af1b5-5e0c-4983-8393-ea99108e2dc1>","cc-path":"CC-MAIN-2014-15/segments/1398223204388.12/warc/CC-MAIN-20140423032004-00155-ip-10-147-4-33.ec2.internal.warc.gz"} |
Playa Del Rey Algebra 2 Tutor
Find a Playa Del Rey Algebra 2 Tutor
...I have worked with all ages of students, from elementary to college level, and with varying levels of abilities, from students with learning disabilities to the highly gifted. My strongest
subjects are Math and Science but I can also assist with other subjects. I am available almost all hours of the day and am flexible with setting up meeting times and sessions.
11 Subjects: including algebra 2, chemistry, biology, algebra 1
...John's College for 2 years, a teaching assistant for astronomy at Oklahoma State University for 3 years, a teaching assistant for general physics at OSU for 3 years, and currently I am a
physics professor at Marymount College in Palos Verdes, CA I have had glowing student reviews throughout my t...
10 Subjects: including algebra 2, physics, calculus, trigonometry
...I find working with students to be an incredibly rewarding experience and have become versatile to students' different learning modalities. I'm currently working toward a BA, but I have three
Associate Degrees. I have an AS in Biological and Physical Sciences and Math, an AA in Social and Behavioral Sciences, and an AA in Fine and Performing Arts.
7 Subjects: including algebra 2, geometry, precalculus, prealgebra
...My focus is expert, patient, private, high quality, in-home coaching in mathematics at all levels for middle school on up to college level students. I show up prepared, on time, and ready to
lead you through your lesson. I specialize in math chickens!
17 Subjects: including algebra 2, geometry, ASVAB, algebra 1
...I have no professional certification in C++. However, I spend my workdays at my job writing C++ and C# code. Before learning C++ and C# later in my engineering career, I used to program in C. I
am proficient in small- and large-scale project organization in C, as well as program debugging, environment setup, and just about any other topic related with the C programming language.
27 Subjects: including algebra 2, English, physics, calculus | {"url":"http://www.purplemath.com/Playa_Del_Rey_algebra_2_tutors.php","timestamp":"2014-04-21T15:02:01Z","content_type":null,"content_length":"24449","record_id":"<urn:uuid:9bdb6dcd-eac3-4403-8d0d-671a40079ea5>","cc-path":"CC-MAIN-2014-15/segments/1398223201753.19/warc/CC-MAIN-20140423032001-00146-ip-10-147-4-33.ec2.internal.warc.gz"} |
How does cos/sin affect convergence of series
January 7th 2011, 01:08 PM #1
Junior Member
Aug 2010
How does cos/sin affect convergence of series
If for example i had:
{sum 1, inf} cos(r+1)/r^2+1
{sum 1, inf} sin(r^2 +1)/r^2+1
Do i try get rid of the cos/sine? if so how
Or is there a general rule im missing?
Use Dirichlet's test to prove that both these sums converge. Note that since $\displaystyle \sum \cos(r)$ is bounded and $\displaystyle \frac{1}{r^2+1}\to 0$ for example.
Because is...
$\displaystyle \frac{|\cos (r+1)|}{r^{2}+1} < \frac{1}{r^{2}}$ (1)
... and ...
$\displaystyle \frac{|\sin (r^{2}+1)|}{r^{2}+1} < \frac{1}{r^{2}}$ (2)
... and the series $\displaystyle \sum_{n=1}^{\infty} \frac{1}{r^{2}}$ converges, also the two series You proposed converge...
Kind regards
Because is...
$\displaystyle \frac{|\cos (r+1)|}{r^{2}+1} < \frac{1}{r^{2}}$ (1)
... and ...
$\displaystyle \frac{|\sin (r^{2}+1)|}{r^{2}+1} < \frac{1}{r^{2}}$ (2)
... and the series $\displaystyle \sum_{n=1}^{\infty} \frac{1}{r^{2}}$ converges, also the two series You proposed converge...
Kind regards
Maybe I'm being pedantic, but I don't like to use that here. The fact that the absolute convergence of a series implies the convergence of the series is only true since the real (or complex
numbers) is a complete metric space and since this seems like a calculus question I'm not sure if that's ok. I don't know if Dirichlet's test is much easier though :|
So in my first example {sum 1, inf} cos(r+1)/r^2+1
(An)=1/(r^2 +1)
(Bn)= cos(r+1)
i have to show (An) is decreasing & {sum}(Bn) is bounded ?
Not sure how to go about showing {sum}(Bn) is bounded. Although obviously it must as (Bn) must be between 1, -1 for any n.
Maybe I'm being pedantic, but I don't like to use that here. The fact that the absolute convergence of a series implies the convergence of the series is only true since the real (or complex
numbers) is a complete metric space and since this seems like a calculus question I'm not sure if that's ok. I don't know if Dirichlet's test is much easier though :|
I'm not sure of the above: Dirichlet's test's proof does use completeness of the complex (real) field in a very
clear and decisive way (at least the proofs I know of), whereas absolute convergence ==> convergence is true
without using (at least directly, in one of the proofs I know of) completeness...
I'm not sure of the above: Dirichlet's test's proof does use completeness of the complex (real) field in a very
clear and decisive way (at least the proofs I know of), whereas absolute convergence ==> convergence is true
without using (at least directly, in one of the proofs I know of) completeness...
I was just making a remark. There are proofs of Dirichlet's theorem which don't appeal directly to completeness. That said, I do agree that the most common one (the one using summation by parts)
does. I guess it's all kind of irrelevant since everything (and I mean this in a very, very loose sense) depends upon completeness if one goes far enough back.
We now consider the case ot the sums $\displaystyle \sum_{k=1}^{n} \sin k$ and $\displaystyle \sum_{k=1}^{n} \cos k$ and that is valid for all the cases...
We start with the 'geometric sum'...
$\displaystyle \sum_{k=0}^{n-1} a\ r^{k} = a\ \frac{1-r^{n}}{1-r}$ (1)
... and setting $r=a= e^{i}$ we obtain in some steps...
$\displaystyle S= \sum_{k=1}^{n} e^{i k} = e^{i}\ \frac{1-e^{i n}}{1-e^{i}}$
$\displaystyle = \frac{e^{i}}{2} \ \frac{1- \cos 1 - \cos n + \cos (n-1) + i\ \{\sin 1 - \sin n + \sin (n-1) \}} {1 - \cos 1}$ (2)
Without proceeding further it is clear from (2) that both the quantities...
$\displaystyle \sum_{k=1}^{n} \cos k = \mathcal{R} \{S\}$
$\displaystyle \sum_{k=1}^{n} \sin k = \mathcal{I} \{S\}$
... are bounded...
Kind regards
January 7th 2011, 01:13 PM #2
January 7th 2011, 01:41 PM #3
January 7th 2011, 01:46 PM #4
January 7th 2011, 01:49 PM #5
Junior Member
Aug 2010
January 7th 2011, 02:13 PM #6
Oct 2009
January 7th 2011, 02:34 PM #7
January 7th 2011, 11:04 PM #8 | {"url":"http://mathhelpforum.com/differential-geometry/167730-how-does-cos-sin-affect-convergence-series.html","timestamp":"2014-04-18T05:35:49Z","content_type":null,"content_length":"64640","record_id":"<urn:uuid:6ab0d302-38cb-4bb8-9b59-3ee027e2b449>","cc-path":"CC-MAIN-2014-15/segments/1397609532573.41/warc/CC-MAIN-20140416005212-00093-ip-10-147-4-33.ec2.internal.warc.gz"} |
Functioning in the Real World : A Precalculus Experience
Why Rent from Knetbooks?
Because Knetbooks knows college students. Our rental program is designed to save you time and money. Whether you need a textbook for a semester, quarter or even a summer session, we have an option
for you. Simply select a rental period, enter your information and your book will be on its way!
Top 5 reasons to order all your textbooks from Knetbooks:
• We have the lowest prices on thousands of popular textbooks
• Free shipping both ways on ALL orders
• Most orders ship within 48 hours
• Need your book longer than expected? Extending your rental is simple
• Our customer support team is always here to help | {"url":"http://www.knetbooks.com/functioning-real-world-2nd-gordon-sheldon/bk/9780201383898","timestamp":"2014-04-20T11:36:09Z","content_type":null,"content_length":"30317","record_id":"<urn:uuid:932458db-31a5-43a7-bc33-df557ff063cd>","cc-path":"CC-MAIN-2014-15/segments/1397609539447.23/warc/CC-MAIN-20140416005219-00396-ip-10-147-4-33.ec2.internal.warc.gz"} |
Why “syntomic” if “flat, locally of finite presentation, and local complete intersection” is already available?
up vote 8 down vote favorite
Dear everyone,
(i) Who is the father of the adjective “syntomic” in algebraic geometry?
(ii) And why did he choose to introduce a new term for what we already know from EGA IV.19.3.6 and SGA 6.VIII.1.1 as “flat, locally of finite presentation, and local complete intersection”?
ho.history-overview ag.algebraic-geometry names
4 Hi Thanos, Fontaine and Messing claim that Barry Mazur invented the term "syntomic." I'm not sure where the name comes from, but it is a hell of a lot catchier than "flat, locally of finite
presentation, and locally a complete intersection!" – Clark Barwick May 15 '10 at 2:28
Thanks, Clark! You make a reasonable point, but my hope for (ii) would be an answer that also explains why Mazur chose the striking word “syntomic”, which means “cut short, abridged” in Greek. But
now that we know the answer to (i), I'll email Mazur directly. – Thanos D. Papaïoannou May 15 '10 at 3:02
I think the idea is that (possibly with some stretch of interpretation) it is supposed to mean complete cut (tomic, as also in cyclotomic, meaning cut), i.e., complete intersection. I have also
heard Messing attribute it to Mazur. As to why the answer should be obvious (as Clark pointed out), the "flat, locally of finite presentations and local complete intersection topology" is not
something you would want to use more than once in a lecture (if that). – Torsten Ekedahl May 15 '10 at 4:47
1 Ha!, here's a formal improvisation: perhaps Mazur passed from “complete intersection” to the portmanteau “co-section”, which he then translated piece-by-piece to Greek to make “syn-tome”, whose
associated adjective is then “syn-tomic”. – Thanos D. Papaïoannou May 15 '10 at 5:04
add comment
1 Answer
active oldest votes
Mazur gives the following beautiful justification, which explains the “syn-” in “syntomic” as well.
Dear Thanos,
Thanks for your question. I'm thinking of “ local complete intersection” as being a way of cutting out a (sub-) space from an ambient surrounding space; the fact that it is flat
up vote 12 over the parameter space means that each such "cutting" as you move along the parameter space, is---more or less---cut out similarly. I'm also thinking of the word "syntomic" as
down vote built from the verb temnein (i.e., to cut) and the prefix "syn" which I take in the sense of "same" or "together". So I think it fits.
Best wishes,
Excellent! If it is allowed you should mark this the answer... – Torsten Ekedahl May 16 '10 at 5:38
Torsten, apparently it is allowed, after you wait a fixed amount of hours, but it could be bad form. I will go ahead and approve my own answer, but would appreciate comments from the
MO censors on whether it's good form or not. – Thanos D. Papaïoannou May 17 '10 at 0:35
Well, in this case this is the answer (from the horse's mouth so to speak) and you needed to post the question in order to find out that the concept was coined by Mazur so I don't
see how it could be bad form. – Torsten Ekedahl May 17 '10 at 4:09
add comment
Not the answer you're looking for? Browse other questions tagged ho.history-overview ag.algebraic-geometry names or ask your own question. | {"url":"http://mathoverflow.net/questions/24678/why-syntomic-if-flat-locally-of-finite-presentation-and-local-complete-inte?sort=votes","timestamp":"2014-04-20T06:22:47Z","content_type":null,"content_length":"61985","record_id":"<urn:uuid:86f7c205-d5a4-413f-82b2-1b352c5f7490>","cc-path":"CC-MAIN-2014-15/segments/1397609538022.19/warc/CC-MAIN-20140416005218-00206-ip-10-147-4-33.ec2.internal.warc.gz"} |
Conant Prize
Levi L Conant Prize of the AMS
This prize is:-
... to recognize the best expository paper published in either the Notices of the AMS or the Bulletin of the American Mathematical Society in the preceding five years.
The award was endowed though funds provided by the will of the Worcester Polytechnic Institute mathematician Levi L Conant which came to the American Mathematical Society on the death of Conant's
2001 Carl Pomerance
... for his paper "A Tale of Two Sieves".
2002 Elliott H Lieb and Jakob Yngvason
... for their article "A Guide to Entropy and the Second Law of Thermodynamics".
2003 Nicholas Katz and Peter Sarnak
... for their expository paper "Zeroes of zeta functions and symmetry".
2004 Noam D Elkies
... for his enlightening two-part article "Lattices, Linear Codes, and Invariants".
2005 Allen Knutson and Terence Tao
... for their stimulating article "Honeycombs and Sums of Hermitian Matrices".
2006 Ronald Solomon
... for his article "A Brief History of the Classification of the Finite Simple Groups".
2007 Jeffrey Weeks
... for his article "The Poincare Dodecahedral Space and the Mystery of the Missing Fluctuations".
2008 J Brian Conrey
... for his article "The Riemann Hypothesis"
2008 Shlomo Hoory, Nathan Linial, and Avi Wigderson
... for their article "Expander graphs and their applications".
2009 John Morgan
... for his article, "Recent Progress on the Poincaré Conjecture and the Classification of 3-Manifolds".
MacTutor links:
History of the AMS
Presidents of the AMS
AMS Colloquium Lecturers
AMS Gibbs Lecturers
AMS Prizes:
AMS/SIAM Birkhoff Prize
AMS Bôcher Prize
AMS Cole Prize in Algebra
AMS Cole Prize in Number Theory
AMS Conant Prize
AMS Satter Prize
AMS Steele Prize
AMS Veblen Prize
AMS Wiener Prize
Other Web site:
JOC/EFR August 2009
The URL of this page is: | {"url":"http://www-groups.dcs.st-and.ac.uk/~history/Societies/AMSConantPrize.html","timestamp":"2014-04-17T12:32:16Z","content_type":null,"content_length":"5857","record_id":"<urn:uuid:198a5a4f-7c12-42c2-a4e3-5704abe61731>","cc-path":"CC-MAIN-2014-15/segments/1397609530131.27/warc/CC-MAIN-20140416005210-00164-ip-10-147-4-33.ec2.internal.warc.gz"} |
Playa Del Rey Algebra 2 Tutor
Find a Playa Del Rey Algebra 2 Tutor
...I have worked with all ages of students, from elementary to college level, and with varying levels of abilities, from students with learning disabilities to the highly gifted. My strongest
subjects are Math and Science but I can also assist with other subjects. I am available almost all hours of the day and am flexible with setting up meeting times and sessions.
11 Subjects: including algebra 2, chemistry, biology, algebra 1
...John's College for 2 years, a teaching assistant for astronomy at Oklahoma State University for 3 years, a teaching assistant for general physics at OSU for 3 years, and currently I am a
physics professor at Marymount College in Palos Verdes, CA I have had glowing student reviews throughout my t...
10 Subjects: including algebra 2, physics, calculus, trigonometry
...I find working with students to be an incredibly rewarding experience and have become versatile to students' different learning modalities. I'm currently working toward a BA, but I have three
Associate Degrees. I have an AS in Biological and Physical Sciences and Math, an AA in Social and Behavioral Sciences, and an AA in Fine and Performing Arts.
7 Subjects: including algebra 2, geometry, precalculus, prealgebra
...My focus is expert, patient, private, high quality, in-home coaching in mathematics at all levels for middle school on up to college level students. I show up prepared, on time, and ready to
lead you through your lesson. I specialize in math chickens!
17 Subjects: including algebra 2, geometry, ASVAB, algebra 1
...I have no professional certification in C++. However, I spend my workdays at my job writing C++ and C# code. Before learning C++ and C# later in my engineering career, I used to program in C. I
am proficient in small- and large-scale project organization in C, as well as program debugging, environment setup, and just about any other topic related with the C programming language.
27 Subjects: including algebra 2, English, physics, calculus | {"url":"http://www.purplemath.com/Playa_Del_Rey_algebra_2_tutors.php","timestamp":"2014-04-21T15:02:01Z","content_type":null,"content_length":"24449","record_id":"<urn:uuid:9bdb6dcd-eac3-4403-8d0d-671a40079ea5>","cc-path":"CC-MAIN-2014-15/segments/1397609540626.47/warc/CC-MAIN-20140416005220-00146-ip-10-147-4-33.ec2.internal.warc.gz"} |
2014.02.05: Entropy Attacks!
The cr.yp.to blog
2014.02.05: Entropy Attacks!
The conventional wisdom is that hashing more entropy sources can't hurt: if H is any modern cryptographic hash function then H(x,y,z) is at least as good a random number as H(x,y), no matter how
awful z is. So we pile one source on top of another, hashing them all together and hoping that at least one of them is good.
But what if z comes from a malicious source that can snoop on x and y? For example, imagine a malicious "secure randomness" USB device that's actually spying on all your other randomness sources
through various side channels, or—worse—imagine RDRAND microcode that's looking at the randomness pool that it's about to be hashed into. I should note that none of the attacks described below rely
on tampering with x or y, or otherwise modifying data outside the malicious entropy source; you can't stop these attacks by double-checking the integrity of data.
Of course, the malicious device will also be able to see other sensitive information, not just x and y. But this doesn't mean that it's cheap for the attacker to exfiltrate this information! The
attacker needs to find a communication channel out of the spying device. Randomness generation influenced by the device is a particularly attractive choice of channel, as I'll explain below.
Here's an interesting example of an attack that can be carried out by this malicious source:
1. Generate a random r.
2. Try computing H(x,y,r).
3. If H(x,y,r) doesn't start with bits 0000, go back to step 1.
4. Output r as z.
This attack forces H(x,y,z) to start 0000, even if x and y were perfectly random. It's fast, taking just 16 computations of H on average.
Maybe the randomness generator doesn't actually output H(x,y,z); it uses H(x,y,z) as a seed for some generator G, and outputs G(H(x,y,z)). Okay: the attacker changes H to G(H), and again forces the
output G(H(x,y,z)) to start 0000. Similarly, the attack isn't stopped by pre-hashing of the entropy source before it's mixed with other entropy sources. Every mix from the malicious entropy source
lets the attacker produce another "random" number that starts 0000.
More generally, instead of producing "random" numbers that start with 0000, 0000, 0000, etc., the malicious entropy source can produce "random" numbers that start with successive 4-bit components of
AES[k](0),AES[k](1),... where k is a secret key known only to the attacker. Nobody other than the attacker will be able to detect this pattern.
Recall that DSA and ECDSA require random "nonces" for signatures. It's easy to imagine someone grabbing each nonce as a new "random" number from the system's randomness generator. However, it's well
known (see, e.g., http://www.isg.rhul.ac.uk/~sdg/igor-slides.pdf) that an attacker who can predict the first 4 bits of each nonce can quickly compute the user's secret key after a rather small number
of signatures. Evidently hashing an extra entropy source does hurt—in the worst possible way; the attacker has the user's secret key!—contrary to the conventional wisdom stated above.
EdDSA (see http://ed25519.cr.yp.to) is different. It uses randomness once to generate a secret key and is then completely deterministic in its signature generation (following 1997 Barwood, 1997
Wigley, et al.). The malicious entropy source can still control 4 bits of the secret key, speeding up discrete-log attacks by a factor of 4, but this isn't a problem—we use curves with ample security
margins. The source can increase the 4 bits by carrying out exponentially more H computations, but this has to fit into the time available after inspecting x and y and before generating a "random"
Of course, there are many other uses of randomness in cryptography: for example, if you want forward secrecy then you're constantly generating new ECDH keys. Controlling 4 bits of each secret key
isn't nearly as damaging as controlling 4 bits of DSA/ECDSA nonces—it's the same factor of 4 mentioned above—but, as I mentioned above, the malicious entropy source can also use randomness generation
as a communication channel to the attacker. For example, the source controls the low bit of each public key with an average cost of just 2 public-key generations, and uses the concatenation of these
low bits across public keys to communicate an encryption of the user's long-term key. This channel is undetectable, reasonably high bandwidth, and reasonably low cost.
On the other hand, there's no actual need for this huge pile of random numbers. If you've somehow managed to generate one secure 256-bit key then from that key you can derive all the "random" numbers
you'll ever need for every cryptographic protocol—and you can do this derivation in a completely deterministic, auditable, testable way, as illustrated by EdDSA. (If you haven't managed to generate
one secure 256-bit key then you have much bigger problems.)
With this as-deterministic-as-possible approach, the entire influence of the malicious entropy source is limited to controlling a few "random" bits somewhere. There are at least two obvious ways to
further reduce this control:
• Read less-likely-to-be-malicious entropy sources after completing all reading of the more-likely-to-be-malicious entropy sources. Of course, this doesn't help if the last source turns out to be
• Increase the amount of processing, memory, etc. involved in H—as in hashcash, proofs of work in general, password hashing, etc. The costs are negligible, since all of this is done only once.
Let me emphasize that what I'm advocating here, for security reasons, is a sharp transition between
• before crypto: the whole system collecting enough entropy;
• after: the system using purely deterministic cryptography, never adding any more entropy.
This is exactly the opposite of what people tend to do today, namely adding new entropy all the time. The reason that new entropy is a problem is that each addition of entropy is a new opportunity
for a malicious entropy source to control "random" outputs—breaking DSA, leaking secret keys, etc. The conventional wisdom says that hash outputs can't be controlled; the conventional wisdom is
simply wrong.
(There are some special entropy sources for which this argument doesn't apply. For example, an attacker can't exert any serious control over the content of my keystrokes while I'm logged in; I don't
see how hashing this particular content into my laptop's entropy pool can allow any attacks. But I also don't see how it helps.)
Is there any serious argument that adding new entropy all the time is a good thing? The Linux /dev/urandom manual page claims that without new entropy the user is "theoretically vulnerable to a
cryptographic attack", but (as I've mentioned in various venues) this is a ludicrous argument—how can anyone simultaneously believe that
• we can't figure out how to deterministically expand one 256-bit secret into an endless stream of unpredictable keys (this is what we need from urandom), but
• we can figure out how to use a single key to safely encrypt many messages (this is what we need from SSL, PGP, etc.)?
There are also people asserting that it's important for RNGs to provide "prediction resistance" against attackers who, once upon a time, saw the entire RNG state. But if the attacker sees the RNG
state that was used to generate your long-term SSL keys, long-term PGP keys, etc., then what exactly are we gaining by coming up with unpredictable random numbers in the future? I'm reminded of a
Mark Twain quote:
Behold, the fool saith, "Put not all thine eggs in the one basket"—which is but a manner of saying, "Scatter your money and your attention;" but the wise man saith, "Put all your eggs in the one
basket and—WATCH THAT BASKET."
We obviously need systems that can maintain confidentiality of our long-term keys. If we have such systems, how is the attacker supposed to ever see the RNG state in the first place? Maybe
"prediction resistance" can be given a theoretical definition for an isolated RNG system, but I don't see how it makes any sense for a complete cryptographic system.
[Advertisement: If you're interested in these topics, you might want to join the randomness-generation mailing list; I sent this there a few days ago. To subscribe, send email to
randomness-generation+subscribe@googlegroups.com. There's also a mailing list cleverly named dsfjdssdfsd for discussion of randomness in IETF protocols. Randomness is also a frequent topic on more
general cryptographic mailing lists.]
Version: This is version 2014.02.05 of the 20140205-entropy.html web page. | {"url":"http://blog.cr.yp.to/20140205-entropy.html","timestamp":"2014-04-18T13:06:16Z","content_type":null,"content_length":"11430","record_id":"<urn:uuid:cb673898-3c7b-4f80-b87a-7d9a743c9933>","cc-path":"CC-MAIN-2014-15/segments/1397609533689.29/warc/CC-MAIN-20140416005213-00548-ip-10-147-4-33.ec2.internal.warc.gz"} |
Los Gatos Algebra 2 Tutor
Find a Los Gatos Algebra 2 Tutor
...I strongly believe that everyone can be successful at math, and my goal is to give students the tools and confidence they need to achieve success.My years of experience tutoring students (and
teaching Algebra 1 in public schools) has been invaluable for recognizing common misconceptions and devel...
10 Subjects: including algebra 2, calculus, geometry, algebra 1
...By doing this, the students won't just have to memorize formulas, they will be able to derive them if they need to. I am extremely patient with them, and I will explain it in as many times and
different ways I need to until the idea is clear. I find tutoring one of most rewarding experiences one can do.
9 Subjects: including algebra 2, calculus, geometry, algebra 1
...My AP students solve practice questions from previous exams created by CollegeBoard on each topic. AP chemistry is usually an easier course to approach due to the plethora of information
available online and the types of questions on the test administered by CollegeBoard. The SAT chemistry subj...
18 Subjects: including algebra 2, chemistry, physics, calculus
...Over the past three years, I have the privilege to tutor many students in the Cupertino School District, and all of them achieved their GPA goals, i.e., became straight A students. All my
private SAT students earned 790-800 in math and physics, one ACT student earned a perfect score 36, and one ...
15 Subjects: including algebra 2, calculus, physics, statistics
...I have a PhD in Math (from US) and have taught Calculus and other Math classes at San Jose St. U and other colleges. I have taught Discrete Math (Math 42) during Fall 2008 at San Jose State U.
15 Subjects: including algebra 2, calculus, GRE, algebra 1 | {"url":"http://www.purplemath.com/los_gatos_algebra_2_tutors.php","timestamp":"2014-04-16T22:05:00Z","content_type":null,"content_length":"24005","record_id":"<urn:uuid:4f349ecb-234a-459b-8375-e48a8a59850e>","cc-path":"CC-MAIN-2014-15/segments/1398223202457.0/warc/CC-MAIN-20140423032002-00019-ip-10-147-4-33.ec2.internal.warc.gz"} |
[FOM] Predicativity in CZF
[FOM] Predicativity in CZF
Nik Weaver nweaver at math.wustl.edu
Tue Jun 10 03:51:26 EDT 2008
Daniel Mehkeri asked about the predicativity of CZF. In
general I tend to be suspicious of offhand claims that this
or that formal system is predicatively justified, as it is
easy for impredicativity to creep in in subtle ways and
people are not always as careful about this as they should be.
Specifically, he questions whether strong collection and
subset collection are predicative. Strong collection says
(roughly): if for every x in u there exists y such that phi(x,y),
then there exists a set v that contains such a y for every x in a.
The complaint is that v has been constructed with reference to a
condition phi that may involve quantification over the entire
Actually, I think this is okay. The traditional predicativist
concern is directed at constructions that require us, in the
course of constructing a set v, to consult a class of sets that
contains v (e.g., the entire universe). That isn't really the
case here because strong collection takes as a premise that we
know (forall x in u)(exists y)phi(x,y). In other words, we are
not being required to evaluate phi whilst constructing v, but
rather are permitted to construct v only under the assumption
that we have already (somehow) been able to evaluate phi. Is
that clear?
(Incidentally, it was noted by Kreisel in a different setting
that this kind of justification does not work if classical logic
is being used. The premise of strong collection must not only be
classically true; it needs to have been predicatively established.
So the predicative justification of strong collection requires an
intuitionistic interpretation of the logical connective "implies".)
Subset collection, on the other hand, seems to me clearly
impredicative. This axiom scheme is of the form
(forall a,b)(exists u)(forall z)( P implies (exists v in u) Q)
where I am not writing out P and Q. Here every one of an
unbounded class of sets z potentially dictates the appearance
of an element v in u, so we clearly do have to consult the
entire universe in the course of constructing u. I can't
imagine why anyone would think the axiom in this form is
predicatively legitimate.
It is possible to reformulate subset collection so that one
is only consulting all subsets of a x b rather than the entire
universe. However, it is well known that power sets are
generally not predicatively acceptable, so this doesn't really
Nik Weaver
Math Dept.
Washington University
St. Louis, MO 63130 USA
nweaver at math.wustl.edu
More information about the FOM mailing list | {"url":"http://www.cs.nyu.edu/pipermail/fom/2008-June/012931.html","timestamp":"2014-04-21T15:19:31Z","content_type":null,"content_length":"4943","record_id":"<urn:uuid:18fd2e1c-f6d4-4f60-8e54-57690298f712>","cc-path":"CC-MAIN-2014-15/segments/1397609540626.47/warc/CC-MAIN-20140416005220-00403-ip-10-147-4-33.ec2.internal.warc.gz"} |
20.4 Non Integrable Functions
Home | 18.013A | Chapter 20 Tools Glossary Index Up Previous Next
20.4 Non Integrable Functions
Are there functions that are not Riemann integrable?
Yes there are, and you must beware of assuming that a function is integrable without looking at it.
The simplest examples of non-integrable functions are:
There are others as well, for which integrability fails because the integrand jumps around too much.
An extreme example of this is the function that is 1 on any rational number and 0 elsewhere.
Thus the area chosen to represent a single slice in a Riemann sum will be either its width or 0 depending upon whether we pick a rational x or not at which to evaluate our integrand in that interval.
For this function no matter how small the intervals are, you can have a Riemann sum of 0 or of b - a.
In this case it is possible to use a cleverer definition of the area to define it. (You can argue, in essence, that there are so many more irrational points than rational ones, you can ignore the
latter, and the integral will be 0.)
If we consider the area under the curve defined by principle part of the integral and can be and is so defined for functions like | {"url":"http://ocw.mit.edu/ans7870/18/18.013a/textbook/HTML/chapter20/section04.html","timestamp":"2014-04-21T09:51:57Z","content_type":null,"content_length":"3974","record_id":"<urn:uuid:e4c3f2d6-229b-44d1-b250-52dea642b2af>","cc-path":"CC-MAIN-2014-15/segments/1398223207985.17/warc/CC-MAIN-20140423032007-00462-ip-10-147-4-33.ec2.internal.warc.gz"} |
10" Tapped horn project
post #1 of 25
10/2/13 at 6:50pm
Thread Starter
I have 2 drivers that I would like to use in a tapped horn and managed to come up with this design,
The driver parameters are as follows,
FS: 27.7Hz
Qms: 5.6
Vas: 33L
Cms: .22mm/N
Mms: 150g
Xmax: 23mm
Xmech: 32mm
Sd: 325sqcm
Vd p-p: 1.5L
Qes: .53
Le: .46mH
Z: 8ohm
Bl: 12Tm
Pe: 700W
Qts: .48
1WSPL: 83.3db
Im having trouble with the hump at 30hz, and have no idea of how to fold it, any tips?
My other question is regarding sensitivity. Is there any advantage in this design over a ported box?
your tapped horn is...backwards! :-)
s1 is the small enclosed end.
I suppose there is no reason why the large end couldn't be enclosed, it is just atypical.
i played around with it for a bit and the driver has no motor, which is why you ended up with a horn that is backwards.
suggest that you find another driver if horns are in your future. :-(
Hi LTD02,
Just was told that the specs for the driver are incorrect. They are for a dual 4 ohm version, mine are single 8 ohm. Accordingly the BL should be more like 24 and QES .27.
Does that make a difference?
Cheers, Beau.
that would make quite a difference...give it another shot!
Hmmm, cant seem to make it look any good at all now, been playing with sliders for hours...
Tried a new setup with some older caraudio subs I have, thoughts? 2 driver in series.
Ang=0.5 x Pi
"Hmmm, cant seem to make it look any good at all now, been playing with sliders for hours..."
are you sure that you have entered the driver parameters correctly? changing bl will change qes, qtc, fs, vas, and rms. do you have the spec sheet with the t/s parameters on it? what driver is it
that you are working with?
The drivers are acoustic elegance av10h-8 subs. The only specs available are for dual 4ohm versions in series, mine are single 8 ohm. I dont really understand how the parsmeters relate to eachother.
Link to specs.
The other drivers which I seem to be able to get a decent response out of are these, Audiobahn Alum12s
Le 1.61mh
Fs 21hz
Qms 3.46
Qes .39
Qts .35
Vas 117 litres
Re 2 x 5.4ohm
Xmax 16mm
Vcoils in parallel and 2 drivers in series is the setup above.
ah, well, that driver should work and you could enter either the 4 ohm specs from the website or
this version which adjusts for the coil wiring. motor is bl^2/re so that is what goofed you up.
if you want to, try this.
FS: 27.7Hz
Qms: 5.6
Vas: 33L
Cms: .22mm/N
Mms: 150g
Xmax: 23mm
Sd: 325sqcm
Qes: .53
Re: 5.8ohm
Le: .92mH
Bl: 16.97Tm
Qts: .48
but both should model exactly the same. the key is if using the dual 4 ohm, resistance will double, but bl only goes up by root 2 (1.414) and inductance should scale with resistance so 2x resistance
= 2x inductance.
after a few minutes I gave up with the tapped horn too.
it works in a front loaded horn, but it is extremely sensitive to parameters. I wouldn't suggest it for a first horn attempt.
sometimes it helps to have a "starting point". you can use that one to increase length and so on, but again, it is REALLY sensitive to each adjustment and that makes it very difficult to say with
certainty that it will translate once built.
What about the second driver? The results I came up with seem to be pretty good.
Thanks for your help so far
well...post 'em up and let's see what you've got there. :-)
OK results,
The thing im still not sure of is the arrangement of the voice coils. These drivers are also duall voice coil and I don't know if the specs are with the coils in series or not. Is there any way to
it will have no effect on the performance in the horn.
that is what i was trying to get at earlier. if you wire and measure the t/s for the coils in series, you get one set of numbers, measured in parallel, you get another set of numbers, but...both will
perform identically in the horn, except for the change in sensitivity of course.
your tapped horn is looking pretty good...
2 pi space may give a more accurate translation of performance...
s2 is the area in front of the driver and divided into sd gives the "compression ratio" of the horn. at 500/425 your compression ratio is only 1.25. you could increase it by reducing s2 and that may
help smooth things out a little. compression ratios of less than about 3 are pretty conservative.
Edited by LTD02 - 10/6/13 at 12:09pm
Had another go. Got a bit more efficiency out of it but couldn't really smooth it any further. Size is just under 1000l
Now onto folding, another headache. Any tutorials on that?
have you seen lilmike's tutorial? http://www.avsforum.com/t/1212465/simple-tapped-horn-tutorial-using-hornresp
also, for the lengths, using "par" as the expansion rate may better reflect results of a bass horn as it would typically be folded.
for sensitivity, adjusting voltage to provide 1w into the re of the driver in place of 2.83 v may be better.
for space, 2.0 is probably a little better for making comparisons.
that is a lot of wood for such a modest horn and a first attempt...
here is one that we folded up using a simple constant expansion rate that is about as big as what you are talking about. should provide some idea of how it can be done. i hope. :-)
Thanks LTD02. I have had to reduce the size of the box a little. Im planning on putting it inside an old timber dresser so I have fixed dimensions to work with.
Its around 38x118x180cm after the external skin is accounted for. Thats around 800 litres.
"Its around 38x118x180cm"
I'm an American...I don't know wtf a centimeter is. :-)~
minor comment...in your model, s4 is smaller than s5. s5 should be larger if the mouth is expanding.
larger comment...keep at it, sometimes it takes a few complete reworks until the right solution pops out.
Just a couple quick comments... dealing with 10" drivers, in a pair, you need as much Xmech as you can possibly find to do anything in a tapped horn below 20Hz worth doing. Look for as strong a cone
as possible, the smaller the Vas the better (to keep the box size down), the closer you can get to 0.3 Qes the better.
I wouldn't use the AE 10" based on those specs. If they measure better, great, but that's the key - you need confirmed, measured parameters to do a tapped horn well. Sometimes you can get by if the
published specs are close to reality.
For 10s that should work well in a TH, I have a list of them in my signature build thread. You're better off with 12s though if you're intent on going below 20Hz.
post #2 of 25
10/3/13 at 3:39pm
post #3 of 25
10/3/13 at 3:59pm
post #4 of 25
10/3/13 at 5:32pm
Thread Starter
post #5 of 25
10/3/13 at 5:56pm
post #6 of 25
10/3/13 at 6:35pm
Thread Starter
post #7 of 25
10/5/13 at 5:22am
Thread Starter
post #8 of 25
10/5/13 at 5:39am
post #9 of 25
10/5/13 at 5:47am
Thread Starter
post #10 of 25
10/5/13 at 5:51am
Thread Starter
post #11 of 25
10/5/13 at 8:10am
post #12 of 25
10/5/13 at 8:31am
post #13 of 25
10/5/13 at 3:17pm
Thread Starter
post #14 of 25
10/5/13 at 3:36pm
post #15 of 25
10/6/13 at 6:02am
Thread Starter
post #16 of 25
10/6/13 at 11:52am
post #17 of 25
10/6/13 at 11:53am
post #18 of 25
10/6/13 at 11:56am
post #19 of 25
10/6/13 at 9:42pm
Thread Starter
post #20 of 25
10/7/13 at 6:34am
post #21 of 25
10/7/13 at 6:43am
post #22 of 25
10/7/13 at 5:11pm
Thread Starter
post #23 of 25
10/11/13 at 11:09pm
Thread Starter
post #24 of 25
10/11/13 at 11:49pm
post #25 of 25
10/12/13 at 11:26am
• 1,734 Posts. Joined 11/2006
• Location: Eastend, SK, Canada
• Thumbs Up: 25 | {"url":"http://www.avsforum.com/t/1493235/10-tapped-horn-project","timestamp":"2014-04-16T22:25:43Z","content_type":null,"content_length":"184789","record_id":"<urn:uuid:9acd0473-9a6d-419e-be24-a6064eb5ae43>","cc-path":"CC-MAIN-2014-15/segments/1397609525991.2/warc/CC-MAIN-20140416005205-00454-ip-10-147-4-33.ec2.internal.warc.gz"} |
TI-83 vs TI-84 vs TI-89
As an owner of the TI-89 titanium, I strongly suggest it. I am only a senior in high school (taking AP physics/AP calc), and have used a numerous of features that are available in the calculator that
are not available in any lower models.
It's functionality is very widespread, easy to use, and easy to see. The way it displays equations is incredible--everything is perfectly understandable with no confusing super-nested parentheses.
It's got some useful features that are on only the TI-89ti+ such as an explicit differentiation function (only found on certain software versions), 10 times more functions to graph, multi-variable
differentiation (not sure how well this works. I don't know how to do this kind of math!), and the ability to add a slew of different plugins.
It's got an awesome built-in program editor with very basic, easy to understand code style (not sure exactly what language it is, probably Basic). I've used it many times to make my own functions
such as a vector addition program, cross multiplication program, etc.
I strongly suggest this calculator, it's DEFINITELY worth your money. I found it to be one of the best purchases I've had.
P.S. We actually tested the calculators in a speed-run. We had each calculator find sqrt(1+sqrt(1+sqrt(1. . . for a bunch of iterations. We found that for that particular test, the TI-89 was
substantially faster. Whether you'll notice this for any regular calculations, I don't know. | {"url":"http://www.physicsforums.com/showthread.php?t=147197","timestamp":"2014-04-17T09:51:49Z","content_type":null,"content_length":"66777","record_id":"<urn:uuid:f1306ea6-53b5-4081-849e-c6bf8953b091>","cc-path":"CC-MAIN-2014-15/segments/1397609527423.39/warc/CC-MAIN-20140416005207-00351-ip-10-147-4-33.ec2.internal.warc.gz"} |
[R-sig-ME] Bug in weights in lmer
Douglas Bates bates at stat.wisc.edu
Thu Apr 24 14:44:32 CEST 2008
Sorry that I haven't responded on this thread previously. I have had
two computers, a desktop at my office and a desktop at home, go south
in the same week. I have been reduced to using an old Dell laptop
running Windows as my primary computer at work. Those of you who know
my affection for Windows can imagine how cheerful that makes me. :-)
Thank you for pointing out the problem with the weights, Nick, and for
including the example. I haven't worked out what is going wrong yet
because i am still working on some other problems and some examples.
I can tell you where the pieces of information are in a fitted lmer
model (from the version on R-forge) and that may help to isolate the
problem. Fixed weights are stored in the pWt slot and used to
calculate a weighted residual sum of squares, the "wrss" element in
the deviance slot. (The name "pWt" comes from the fact that these are
called the "prior weights" for a generalized linear model.) When
prior weights are not used this slot has length zero.
The mle of sigma^2 in the unweighted case is the penalized weighted
residual sum of squares (the "pwrss" element of the deviance slot)
divided by the number of observations. The "penality" is a quadratic
form in the random effects. It can be expressed as the squared length
of the orthogonal random effects in the u slot.
It is likely that this estimate should be the pwrss divided by either
the sum of the elements in pWt or the sum of the squares of the
elements in pWt when we don't have unit weights. Do either of those
numbers seem reasonable?
Because the variance components are calculated relative to the
estimate of sigma^2, changing sigma^2 will change those too.
On 4/24/08, Nick Isaac <njbisaac at googlemail.com> wrote:
> Harold:
> Could you try the same set of models using lmer2?
> In July last year Sundar Dorai-Raj reported that the weights argument
> was not being used in the CRAN version of lmer (lme4_0.99875-6).
> Therefore, it's possible that you have actually observed the same
> phenomenon in lme4_0.99875-9.
> Sundar found that lmer2 did use weights, but it's not clear whether
> the weighted model is correct. The development version of lmer
> (lme4_0.999375-13) is much closer to the CRAN version of lmer2 than
> lmer.
> See his original post at:
> https://stat.ethz.ch/pipermail/r-sig-mixed-models/2007q3/000262.html
> Best wishes, Nick
> _______________________________________________
> R-sig-mixed-models at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
More information about the R-sig-mixed-models mailing list | {"url":"https://stat.ethz.ch/pipermail/r-sig-mixed-models/2008q2/000897.html","timestamp":"2014-04-19T14:39:28Z","content_type":null,"content_length":"5864","record_id":"<urn:uuid:de0524fe-6fe3-4482-8263-35d1f903a5cb>","cc-path":"CC-MAIN-2014-15/segments/1398223205137.4/warc/CC-MAIN-20140423032005-00636-ip-10-147-4-33.ec2.internal.warc.gz"} |
Department of Mathematics Colloquium
Disease breaks out on a graph! As medicine is expensive, it is unrealistic to send medicine to all vertices in preparation to fight the outbreak, but we still desire to ensure that the disease dies
out quickly on the medicated vertices and escapes the medicated set with low probability. Under a variant of the contact process, a classical model of the spread of disease, we show how to accomplish
such a goal on an arbitrary host graph. In particular,
we show that the probability that the disease escapes a given medicated set can be bounded in terms of the PageRank of the complement. We additionally look at a broad generalization of this, where
multiple interacting processes spread on a graph, where a new vectorized version of PageRank becomes critical to our understanding of the process. | {"url":"http://www.webpages.uidaho.edu/~barannyk/Seminars/Colloquium_Feb15_2013.html","timestamp":"2014-04-18T05:31:34Z","content_type":null,"content_length":"2492","record_id":"<urn:uuid:19a6676c-e017-4052-9feb-97e426767da9>","cc-path":"CC-MAIN-2014-15/segments/1397609532573.41/warc/CC-MAIN-20140416005212-00511-ip-10-147-4-33.ec2.internal.warc.gz"} |
Three Dimensional Drawings of Bounded Degree Trees
Frati, Fabrizio and Di Battista, Giuseppe (2007) Three Dimensional Drawings of Bounded Degree Trees. In: Graph Drawing 14th International Symposium, GD 2006, September 18-20, 2006, Karlsruhe, Germany
, pp. 89-94 (Official URL: http://dx.doi.org/10.1007/978-3-540-70904-6_10).
Full text not available from this repository.
We show an algorithm for constructing 3D straight-line drawings of balanced constant degree trees. The drawings have linear volume and optimal aspect ratio. As a side effect, we also give an
algorithm for constructing 2D drawings of balanced constant degree trees in linear area, with optimal aspect ratio and with better angular resolution with respect to the one of [8]. Further, we
present an algorithm for constructing 3D poly-line drawings of trees whose degree is bounded by n^{1/3} in linear volume and with optimal aspect ratio.
Repository Staff Only: item control page | {"url":"http://gdea.informatik.uni-koeln.de/764/","timestamp":"2014-04-17T15:25:53Z","content_type":null,"content_length":"21684","record_id":"<urn:uuid:45b804e8-0a45-4dbf-853c-f8178c983def>","cc-path":"CC-MAIN-2014-15/segments/1397609530136.5/warc/CC-MAIN-20140416005210-00532-ip-10-147-4-33.ec2.internal.warc.gz"} |
Re: Partial Functions and Logics
Re: Partial Functions and Logics
>>>>> "Hubert" == Hubert Baumeister <hubert@mpi-sb.mpg.de> writes:
In article <41coud$r71@hitchcock.dfki.uni-sb.de> hubert@mpi-sb.mpg.de (Hubert Baumeister) writes:
Hubert> In article <4109ub$kja@newsflash.concordia.ca>,
Hubert> chalin@cs.concordia.ca (CHALIN patrice) writes:
Hubert> As I understand [Sp88] (pp. 69,70-71,91) the equality in
Hubert> Z is to be interpreted as strict equality. Two terms are
Hubert> strictly equal in an interpretation iff they are _both_
Hubert> defined and evalutate to the same value. Thus an equation
I believe that this is often called "existential equality" (and
suspect that Schoet used this phrase) this is apposite because it
gives true only if both terms "exist". "Strong equality" can then be
used for one that gives false if one term is defined and the other is
But the terminology is not the main point.
I have said before that I think the use of "existential equality" fits
well with other decisions in Z. But there is a disadvantage and that
is that the user has also to think about "weak equality" (or
"computational equality" if you prefer: in -for example- a recursive
function definition, the equality between terms (if i=j then ...) has
to be one that can be evaluated by a normal computation.
cliff jones
□ From: chalin@cs.concordia.ca (CHALIN patrice)
□ From: hubert@mpi-sb.mpg.de (Hubert Baumeister) | {"url":"http://www.sds.lcs.mit.edu/spd/larch/archive/msg00296.html","timestamp":"2014-04-21T12:54:19Z","content_type":null,"content_length":"4134","record_id":"<urn:uuid:0da1721f-5932-4dad-892c-741b05211093>","cc-path":"CC-MAIN-2014-15/segments/1398223207046.13/warc/CC-MAIN-20140423032007-00492-ip-10-147-4-33.ec2.internal.warc.gz"} |
Math Forum Discussions - The integration test suites for Sage.
Date: Sep 3, 2013 7:58 AM
Author: Peter Luschny
Subject: The integration test suites for Sage.
I just discovered the recent threads "An independent integration
test suite" and "The Charlwood Fifty".
I looked at the test suites as a Sage user and used the default
('maxima') algorithm.
Martin> It should be possible to switch the Sage integrator from
Martin> "Maxima" to "Sympy"; perhaps somebody could explain how?
That is easy! The docs say:
integral(expression, v=None, a=None, b=None, algorithm=None)
algorithm - (default: ?maxima?) one of
?maxima? - use maxima (the default)
?sympy? - use sympy (also in Sage)
Why does FriCas not provide an interface to the selection box of
Sage's integral function?
My results are in [1]. Please let me know if you spot any errors.
[1] http://www.luschny.de/math/quad/IntegralTestsSage.html | {"url":"http://mathforum.org/kb/plaintext.jspa?messageID=9252394","timestamp":"2014-04-20T22:06:12Z","content_type":null,"content_length":"1893","record_id":"<urn:uuid:4eca8572-244d-4711-9db6-a1c16e2fbfc0>","cc-path":"CC-MAIN-2014-15/segments/1397609539230.18/warc/CC-MAIN-20140416005219-00198-ip-10-147-4-33.ec2.internal.warc.gz"} |
a family uses 12.5lb of paper in a week and recycles about 3/4 of its waste. how many pounds of paper does the family recycle? - WyzAnt Answers
a family uses 12.5lb of paper in a week and recycles about 3/4 of its waste. how many pounds of paper does the family recycle?
Tutors, please sign in to answer this question.
2 Answers
When solving a problem like this, start by having two of the same types of numbers to work with (either both in fractions or both in decimals).
Let's make 3/4 into 0.75
Then multiply 12.5 and 0.75 = 9.375 lbs of waste.
Thank you so much! Putting everything in one conversion is so much easier. That cleared things up a whole lot!
Hi Sarah;
(12.5 pounds)(3/4)
Let's note that 12.5=12 1/2
12 1/2=25/2
[25/2 (pounds)](3/4)
Let's multiply the numerators...(25)(3)=75
Let's multiply the denominators...(2)(4)=8
75/8 pounds
9 3/8 pounds
Do you need help understanding how I converted 12 1/2 into 25/2?
Do you need help understanding how I converted 75/8 into 9 3/8?
Please let me know.
I understand how you got your answer. Making it into an improper fraction and multiply the numerators and the denominators. I cant believe how this word problem beat me up! Thank you so much for
showing your work and breaking it down for me. I am truly thankful. | {"url":"http://www.wyzant.com/resources/answers/26551/a_family_uses_12_5lb_of_paper_in_a_week_and_recycles_about_3_4_of_its_waste_how_many_pounds_of_paper_does_the_family_recycle","timestamp":"2014-04-17T02:39:44Z","content_type":null,"content_length":"50287","record_id":"<urn:uuid:8cf512a1-c903-49fd-8a9e-a9646cdda848>","cc-path":"CC-MAIN-2014-15/segments/1397609526102.3/warc/CC-MAIN-20140416005206-00217-ip-10-147-4-33.ec2.internal.warc.gz"} |
Nurses are often intimidated by the math that occurs in everyday practice. Patient safety depends on the practitioner's ability to calculate medications correctly and in a timely manner. This article
will provide a simple and concise method for accurate computation using basic calculations (see Quick reference: Universal formulas).
Doing the math
Even with the programmable I.V. pumps used in many clinical settings, it's advisable for the nurse to verify the correct dosage by calculation once during the shift; more often if a medication is
being titrated or changed. Verification of correct dosages with another RN is also a widespread practice among many professionals and sometimes mandatory in institutions.
Another resource that's present in many practice settings is the pharmacy. Pharmacists have an abundance of knowledge about medications, as well as an unparalleled proficiency with drug calculations;
utilize their expertise if you're unsure of your computation.
Knowing the therapeutic dosage for the desired effect is as important as knowing the correct calculations for the drug. For example, dopamine at doses of 3 to 5 mcg/kg/minute provides a gentle
dilatation of the renal arteries, increasing urine output with no effect on BP. At higher doses (up to 20 mcg/kg/minute), dopamine is used for BP support. Know the medication and what effect you're
attempting to achieve, as well as the maximum recommended safe infusion dosage.
Next time you have a patient on I.V. medication, try the following simple methods for calculating in a systematic way. Patient medication safety is a goal that all practitioners have in common-it
starts with doing the math!
Basic calculations
The universal formula is:
Figure. No caption available.
Administer heparin 5,000 units I.V. push. Available is heparin 10,000 units/mL. How many mL will you need to administer to achieve a 5,000 unit dose?
Answer: X = 0.5 mL
Figure. No caption available.
Calculations in mcg/minute
Follow these four steps to easily calculate your patient's accurate drug dosage.
1. Find out what's in your I.V. bottle (drug concentration or number of mL of fluid).
2. Determine in which units your drug is measured (units/hour, mg/hour, or mcg/kg/minute).
3. Know the patient's weight in kg if your calculation is weight based.
4. Use the universal formula below and then divide your final answer by the patient's weight in kg to arrive at mcg/kg/minute.
Figure. Quick reference: Universal formulas
Figure. No caption available.
Dopamine is infusing. The bottle states dopamine 800 mg, and it's mixed in 500 mL of D[5]W. The I.V. pump in your patient's room is set at 15 mL, and the patient weighs 60 kg (60,000 g). At how many
mcg/kg/minute is the patient's dopamine infusing?
Answer: X = 6.7 mcg/kg/minute
Figure. No caption available.
Dobutamine 200 mg in 250 mL of D[5]W is ordered to run at 5 mcg/kg/minute. At how many mL/hour will you set the pump?
Answer: X = 22.5 mL/hour
Figure. No caption available.
Calculations in units/hour
To arrive at units/hour, the universal formula is:
Figure. No caption available.
Heparin 20,000 units in 500 mL D[5]W is ordered to run at 1,000 units/hour. How will the I.V. pump be set?
Answer: X = 25 mL/hour
Figure. No caption available.
Heparin 20,000 units in 500 mL D[5]W is infusing at 20 mL/hour. At how many units/hour is the heparin infusing?
Answer: X = 800 units/hour
Figure. No caption available.
Patient safety depends on accurate I.V. drug dosing; precise calculations are essential to this process. Nurses shouldn't be apprehensive when I.V. drug dosages are presented in practice. Use the
simple calculations conveyed in this article as a first step! | {"url":"http://www.nursingcenter.com/lnc/JournalArticle?Article_ID=1502627&Journal_ID=417221&Issue_ID=1502626","timestamp":"2014-04-16T22:52:05Z","content_type":null,"content_length":"75918","record_id":"<urn:uuid:2071c817-a829-4693-98bb-34ad91082c3d>","cc-path":"CC-MAIN-2014-15/segments/1397609525991.2/warc/CC-MAIN-20140416005205-00306-ip-10-147-4-33.ec2.internal.warc.gz"} |
TwistyPuzzles.com > Member Collections > RubiksMaster614 - Wish List
Two 2x2x2 cubes connected by gears.
A Junior variant of the Borg Cube.
Also known as the "Void 2x2x2".
A 2x2x2 consisting only of rails. It uses polarizing filters instead of stickers.
"QUBAMI: 3D sudoku with a twist!" Mini 2x2x2 version. The objective is to scramble the puzzle from its ordered starting state, so that only one copy of each colour and symbol lies on every row and
column on all six faces.
A 2x2x2 with restricted movemements that can be taken apart.
This 3x3x3 allows only halfturns for one axes. Another puzzle deemed impossible before.
Mefferts variant of the "Nine Color Scramble Cube"
Three corners of a 3x3x3 connected with a rope and a ring in between.
A 3x3x3 bandaged in a quite unusual way.
A "bandaged" 3x3x3 with more permutations than the unbandaged one.
A 3x3x3 which looks like the villain spaceship from Star Trek.
A 3x3x3 stickered in an innovative way.
A Crazy 3x3x3 where some of the six circles move together with the surrounding layer and some not. One of a series of eight variants named after the solar systems eight planets.
A Crazy 3x3x3 where some of the six circles move together with the surrounding layer and some not. One of a series of eight variants named after the solar systems eight planets.
A 3x3x3 cube split into eighths, with each having one colour. Eliminates the need to consider corner orientations but introduces face orientations.
A partially truncated 3x3x3 with beautiful stickers.
The world's first in Wavy-style Rubik's 3*3*3 Cube.
A Bump Cube (aka Mirror Blocks) bandaged like a Mefferts Bandaged Cube and colored differently but still in a single color.
A geared Rubik’s Cube with opposite faces moving in opposite directions.
A cube which is hollow and can be opened when solved.
A 3x3x3 that only allows 180-degree turns.
A 3x3x3 with three of non adjacent pieces connected by a bar.
Custom 3x3x3 sticker pattern designed by Mark Longridge. It's pretty challenging with it's 108 triangles
A variant of Oskar van Deventer's original Gift Cube with hinges.
A mass produced Treasure Chest with four pieces replaced. The result resembles the Hinged Gift Cube without being identical.
A 3x3x3 made mostly out of air.
A 3x3x3 with one cut bandaged away.
A special 3x3x3 which comes with becoming a member of Uwe Mefferts Jade Club.
A very innovative "sticker" variation of the 3x3x3.
A 3x3x3 with innovatively restricted movements.
Nine sets of stickers with 6 stickers each distributed over a 3x3x3. The goal is to completely scramble this variant.
A bandaged shape and sticker variant of the 3x3x3. Similar to the "XX of Wander" presented by the same creator.
An ordinary two-color 3x3x3. The astonishing about it is the method it was made.
An attractive colour variation of the Path Cube idea.
A very clever "sticker variation" of a transparent 3x3x3.
"QUBAMI: 3D sudoku with a twist!" The objective is to completely scramble the puzzle from its ordered starting state, so that only one copy of each colour and symbol lies on every row and column of
blocks on every face of the puzzle.
A sticker variant of the MirrorBlocks which is more modern cube art.
A sliding piece puzzle on the sides of a 3x3x3.
3x3x3 with two colors on each face
Kind of a contradiction in a cube: A cube without centers and core was stickered to make the orientation of the core visible.
A brilliant design, filled with symmetries, some of which only become apparent after you scramble it.
Ten Cube - 10mm world's smallest 3x3x3 Rubik's cube. In December 2010 the cube got into Guinness Book of Records as the smallest cube in the world!
An excellent cube for a beginner to try first. A simple piece shuffle variant.
A fully handmade 3x3x3. All pieces are made from solid Titanium!
A custom sticker variation of the 3x3x3.
A sticker variation of a Dayan Guhong (where the pieces itself are colored) which results in a puzzle with three solutions.
A sticker variant of the Mirror Block puzzle which leads into a puzzle with two solutions.
A clever Rubik's Cube variant.
A giveaway from the World Rubik's Games Championships 2003 event in Toronto.
The combination of Circle Cube and Void Cube.
3X3X3 (PICTURE)
A 3x3x3 with a very innovative maze structure as stickers.
A 3x3x3 stickered as if blocks of the famous name-giving game were glued on.
A calendar cube based on cut-out stickers for a cube with silver body.
A bandaged 4x4x4 that simulates a cuboid.
A bandaged 4x4x4 that simulates a cuboid.
A bandaged 4x4x4 that simulates a cuboid.
A bandaged 4x4x4 variation that functions exactly like a 2x2x3.
Another 4x4x4 Sudoku but with just 4 colors.
A Sudoku 4x4x4 which uses colors instead of numbers.
A black-and-white 4x4x4. Still not trivial to solve.
The third 4x4x4 with circles on all six sides. The circles are larger as in the first two variants.
An interesting custom variation of a 4x4x4.
A custom 4x4x4 sticker variation which shows a single closed loop in solved state.
The stickering scheme of the Rubenking Cube adapted to a 4x4x4.
A sticker variant of the 4x4x4. Compared with the traditional stickering scheme the face pieces are distinguishable.
A super 4x4x4 made with small extensions instead of just stickers.
A 5x5x5 which corner-pieces are hidden under extended wing pieces.
A 5x5x5 which corner- and wing-pieces are hidden under extended edges.
A custom 5x5x5 sticker variation which shows a single closed loop in solved state.
The bigger cousin of the Mixup Cube. A fudged and jumbling puzzle.
An Eastsheen 4x4x4 modified to look like a 5x5x5 it internally is. The internal bandaging was NOT removed.
The stickering scheme of the Shepherd cube applied to a 5x5x5
The 5x5x5 super group cube. Unlike the standard 5x5x5, each of the nine center cubies on each face has only one solved position and one solved orientation.
An incredibly confusing customized 5x5x5.
A void 5x5x5 with peep holes where the center corners would be.
6X6X6 & UP
The first working prototype to break the border (11x11x11) set by the Verdes patent.
Also known as "Over the top". A puzzle made just because it is possible.
The logical successor of the Wall Cube.
A 6x6x6 without the corners. The adjacent wing-pieces received additional stickers.
A 6x6x6 without corners. In this case the corners are not only truncated but their remains are hidden under the extended wing pieces.
A V-Cube 7x7x7 modified to give it a true cubic shape.
A Dazzler from V-Cubes twisted into a pattern and stickered to transform it into a Super 7x7x7.
A mass produced 7x7x7 with colored plastic pieces instead of stickers.
A V-Cube 7 "Illusion" color variation with several checkerboards.
A trivial item. The 1x1x2-cousin of the Rainbow Cube.
A Master Skewb which represents the middle between a Master Skewb and a fully Hollow Master Skewb
A 4x4x4 reduced to its face pieces.
A 2x2x2 with 6 circular sectors on each face.
Two 2x2x2's which have to be solved "together".
A hybrid puzzle which combines a 2x2x2 with a Curvy Copter.
A cornerturning hexahedron with four (no more!) logical layers.
The Simple Overlapping Cube with the stickering scheme of the Ultimate Cube
A Simple Overlapping Cube stickered like he 8 Color Cube
A fishered 4x4x4.
An Axis Cube is bumped into this one.
The Golden Cube without stickers but with uniformly colored pieces. Came with a variety of colors.
A Rubik’s Cube with edges that turn by gears.
A Kilominx (or impossiball or corners-only-megaminx) transformed into the shape of hexahedron.
A megaminx transformed into the shape of hexahedron but with differently oriented axis system.
Also known as Royal Floppy.
A super Square-1 reduced to 2 layers.
A highly customized 4x4x4 cube.
Ola Jansson drives the series of cuboids another step further.
A 2x3x3 transformed like a Fisher Cube
A 3x3x10 with the shape of a true cuboid.
A 3x3x10 cuboid. It had to be non-proportionate to be functional.
The name describes it perfectly. Two years earlier this puzzle would have deemed impossible.
A twisty puzzle with corners that hang in the air.
A twisty puzzle with corners that hang in the air.
A megaminx in octahedral shape. It is not a shape transformation but designed from scratch.
A bandaged Dogic extended into the shape of an octahedron.
The octahedral equivalent of the Curvy Copter II.
A non-platonic 2x2x2
A 2x2x2 Octahedron, also called a Gem or Okki, but with a color pattern reminiscent of the Alexander's Star puzzle.
A 3x3x3 in shape of a hexagonal prism.
A bandaged face turning pentadecagonal prism in shape of a (irregular) hexagonal prism.
A 2x2x2 transformed into a hexagonal prism.
The second hexagonal prism made from a 4x4x4. Wider than the first two.
The one layered cousin of the three-, four- and two-layered variants. Made from a puck.
A 5x5x5 transformed into the shape of a hexagonal prism.
A 3x3x3 in shape of hexagonal prism, stickered to resemble the warning symbol for radiation.
The principle of the void cube applied on a hexagonal prism.
A truncated Professor Pyraminx.
A bumped dodecahedral 2x2x2
A megaminx bandaged to resemble the pattern of Mefferts bandaged cube.
The CopterMinx is a hybrid of two puzzles; A megaminx and a Helicopter Dodecahedron.
Built on a 3x3x3 mechanism by Tony Fisher.
A Kilominx (a faceless megaminx) with two additional layers for every face.
"A Megaminx with gears" A brilliant design for a very short description.
A face turning dodecahedron with 4 cuts per axis. The cuts are placed different compared to the Gigaminx.
The all-in-one face turning dodecahedron which collects all the pieces of the Megaminx and Master Pentultimate.
By its time it was the most valuable puzzle known to exists. What else can somebody say about a puzzle sold for $3550?
A face turning dodecahedron with 4 cuts per axis all very close to the puzzle's center.
A dodecahedral twisty puzzle.
The first edgeturning dodecahedron.
A Super Gigaminx. The stickers are handmade in the well-known style created by Stefan Pochmann.
A Teraminx with a stickere scheme resembling the Cube Ultimate.
A sticker variant of the Gigaminx.
A sticker variant of the megaminx adapted from the Ultimate Cube
The hollow version of the Petaminx.
A 1x1x2 in shape of a Reuleaux tetrahedron.
A 6x6x6 Mastermorphix. A 6x6x6 transformed into the shape of a Reuleaux tetrahedron.
A 7x7x7 transformed into the shape of a Reuleaux tetrahedron.
A Golde Cube transformed into a tetrahedron.
Two opposite edges glued to adjacent corners.
Looks like a Master Pyraminx but two layers are linked on every axes.
An Ultimate Skewb transformed into something halfway to a Jings Pyraminx.
Not the first Square-1 in shape of a tetrahedron but this is a pillowed tetrahedron and it was made by truncating only.
A Pyraminx with 7 layers.
A Gear Cube transformed into the shape of Reuleaux tetrahedron.
The "geared" variant of the Pyraminx.
Totally trivial tetrahedral cousin of the 1x1x2.
Looks like a Pyraminx but is closely related to the Mastermorphix.
An even higher-order Pyramorphix. This time a 4x4x4 was transformed into tetrahedral shape.
A pyramorphix in pillowed shape but with several holes in the pieces.
A skewb transformed into a puzzle almost to monstrous to hold and twist.
4 pieces tetrahedral puzzle.
A Pyraminx with 6 layers.
The tetrahedral cousin of the Royal Skewb but invented earlier.
The tetrahedral variant of the 7x7x7.
A 3x3x3 transformed into the shape of a square pyramid.
A 2x3x3 in shape of a square pyramid. One subvariation has a special tip.
The pentagonal cousin of the Floppy Cube.
A fully functional prism with pentagonal shape and 6 layers high.
The first doctrinaire puzzle where all axis don't meet in a single point but in two different ones.
A 3 layered deepcut pentagonal prism which top and bottom faces look like the Pyraminx Crystal its name was taken from.
This is a face turning 5x5x5 pentagonal prism. The sides must be turned 180 degrees.
This CaseCube Version 2.0 is based off of a 3x3x3.
An octagonal prism with two layers.
The first puzzle which implements three axis systems in one.
A Helicopter Cube truncated into the shape of cuboctahedron.
The first face turning icosahedron with planar cuts.
Probably the most sought after of all Twisty Puzzles which went in mass production.
A DLI - A dual layer cornerturning icosahedron.
A face turning icosahedron. Not the first one but the first to reveal the jumbling geometry of this type of puzzles.
A Pentultimate in shape of a icosahedron => A deepcut cornerturning icosahedron.
The Tutt's Icosahedron with an additional set of layers.
A corners only megaminx with twenty holes through the solid.
The third implementation of the diamond shape. This time from a 2x2x2.
A 5x5x5 truncated into a hexagonal dipyramid and then further truncated.
The "fudged" cousin of the tuttminx which allows more movements.
A heptagonal prism with 3 layers stacked upon each other.
A heavily truncated megaminx.
A transformation of the 3x3x3 with the shape of the namegiving grenade.
A Teraminx truncated into the shape of an Icosidodecahedron which is a archimedean solid.
A Void cube transformed into a sphere like shape.
A 7x7x7 truncated into the shape of a barrel, aka pillowed cylinder.
A megaminx in shape of a cylinder.
A Dino Cube in cylindral shape with bright black plastic and very reduced stickers.
A two-layered hexagonal prism in shape of a cylinder and stickered like a rainbow puck.
A three-layered puck with an additional orthogonal cut.
A Gear Cube truncated on four edges.
A 2x2x2 combined with a moving hole (aka sliding piece) puzzle.
The cube version of Lights Out.
An electronic Rubiks Cube completely playable. | {"url":"http://www.twistypuzzles.com/cgi-bin/cm-view.cgi?ckey=3068","timestamp":"2014-04-18T19:06:09Z","content_type":null,"content_length":"99024","record_id":"<urn:uuid:d1a2d137-4200-4752-b4f6-f7ec05d19ff3>","cc-path":"CC-MAIN-2014-15/segments/1397609535095.7/warc/CC-MAIN-20140416005215-00295-ip-10-147-4-33.ec2.internal.warc.gz"} |
Wolfram Demonstrations Project
Euler's Method for the Exponential Function
For each value of , the sequence converges to . Also, if is the Euler method approximation to the solution of the differential equation , on the interval with , then (the red curve) converges to for
each in the interval. The points generated by Euler's method are marked in green. Observe that for any , the error between the approximation and the real value increases with the value of . | {"url":"http://demonstrations.wolfram.com/EulersMethodForTheExponentialFunction/","timestamp":"2014-04-19T20:14:37Z","content_type":null,"content_length":"43926","record_id":"<urn:uuid:8fff6522-0962-4d0e-a452-117b7e76a238>","cc-path":"CC-MAIN-2014-15/segments/1397609537376.43/warc/CC-MAIN-20140416005217-00606-ip-10-147-4-33.ec2.internal.warc.gz"} |
Differentiation Word Problem! please help
October 2nd 2008, 09:09 PM #1
Oct 2008
Differentiation Word Problem! please help
I don't get how you suppose to use differentiation to solve these 3 problems, please help! I been trying to do it for hours, ahhh!
1. Recall that the area A of a circle with radius r is pi r^2 and that the circumference C is 2 pi r. Notice that dA/dr=C. Explain in terms of geometry why the instantaneous rate of change of the
area with respect to the radius should equal the circumference.
2.An apple farmer currently has 156 trees yielding an average of 12 bushels of apples per tree. He is expanding his farm at a rate of 13 trees per year, while improved husbandry is improving his
average annual yield by 1.5 bushels per tree. What is the current (instantaneous) rate of increase of his total annual production of apples? Answer in appropriate units of measure.
3.If gas in a cylinder is maintained at a constant temperature T, the pressure P is related to the volume V by a formula of the form:
P= (nRT/V-nb)-(an^2/V^2)
in which a, b, n, and R are constants. Find dP/dV.
Hi JimDavid,
For the last one we have
$P=\left(\frac{nRT}{V-nb}\right)-\left(\frac{an^2}{V^2}\right)$ , where $a$ , $b$ , $n$ and $R$ are constants.
Note the phrase "constant temperature $T$" thus $T$ is also constant. Hence re-write the equation as follows an differentiate as normal.
$<br /> \frac{dP}{dV}=-nRT(V-nb)^{-2}+an^2V^{-3}=\left(\frac{-nRT}{(V-nb)^2}\right)+\left(\frac{an^2}{V^3}\right)<br />$
October 3rd 2008, 10:49 AM #2
Aug 2007 | {"url":"http://mathhelpforum.com/calculus/51792-differentiation-word-problem-please-help.html","timestamp":"2014-04-18T00:50:18Z","content_type":null,"content_length":"34722","record_id":"<urn:uuid:ad1dcab1-d0dc-431a-ba57-a6f6a1b898dd>","cc-path":"CC-MAIN-2014-15/segments/1397609532374.24/warc/CC-MAIN-20140416005212-00469-ip-10-147-4-33.ec2.internal.warc.gz"} |
Re: Java API for MATHML
From: Stan Devitt <jsdevitt@stratumtek.ca> Date: Mon, 24 Feb 2003 18:15:32 -0500 (EST) Message-Id: <200302242315.h1ONFWC13407@radical.stratumtek.ca> To: paul@activemath.org (Paul Libbrecht) Cc:
RobertM@dessci.com (Robert Miner), www-math@w3.org
The content definitions for the arc trig functions
used in appendix C were largely based on Abromovitz
and Stegun, Section 4.4 -- see, for example,
and more generally, were chosen to be consistent
with OpenMath.
> Robert Miner wrote:
> >>Although it looks interesting for an amount of task... do I understand that
> >>you're opening the door to yet another system with possibly, say, yet another
> >>interpretation of the arccos ?
> >>
> >>
> >
> >Yes. But as this is true for any new piece of software that has an
> >interpretation for functions like arccos, I'm not sure what the
> >implication is? That no new mathematical software should be written?
> >
> >
> What it means is that when one starts to write a software which is
> expected to be connected to the rest of the world, one has to ask how
> good this connection is to happen.
> In the case of MathML-content, I thought the lack of specification of,
> at least to my knowledge, the inverse-trigonometric functions have made
> Mathematica and Maple MathML-content behave inconsistently.
> Based on this experience (which I'd like to see one day written
> somewhere under an "interoperability" heading in the w3c.org/math
> pages), a new software being written should then declare something like:
> the inversed trigonometric functions shall behave the same as Maple,
> Mathematica (or OpenMath) ones.
> Hence my statement which was, sorry for that, sort of sketchy.
> I would surely not prevent new software to be written!
> Paul
Received on Monday, 24 February 2003 18:10:06 GMT
This archive was generated by hypermail 2.2.0+W3C-0.50 : Saturday, 20 February 2010 06:12:54 GMT | {"url":"http://lists.w3.org/Archives/Public/www-math/2003Feb/0016.html","timestamp":"2014-04-16T22:52:12Z","content_type":null,"content_length":"10331","record_id":"<urn:uuid:3ec41cee-0e13-4216-92fa-14721d7d6159>","cc-path":"CC-MAIN-2014-15/segments/1397609525991.2/warc/CC-MAIN-20140416005205-00281-ip-10-147-4-33.ec2.internal.warc.gz"} |
Logic error in Math.pow(a,b) using JOptionPane
February 7th, 2013, 05:33 PM #1
Junior Member
Join Date
Feb 2013
Thanked 0 Times in 0 Posts
I've been trying to figure out one part of my code for around 3 hours.
I've been rewriting it different ways, only running what the logic error is and not the other parts and I still can't seem to get what I want.
I think that if I can figure out this one part of the program that it will help me with the whole program as I'll know what I did wrong.
I'll tell you what I'm having problems at in the program at the bottom of the code.
I'm a beginner so i'm sure it's not a very difficult problem to solve.
This is the program directions:
/* Write a program that prompts the user to enter three points (x1,
*y1), (x2, y2), (x3, y3) of a triangle and displays its area. The
*formula for computing the area of a triangle is
*S = (side1 + side2 + side3)/2;
*Area = √(s(s-side1)(s-side2)(s-side3))
I'm trying to be consistent with this problem by only using certain numbers.
If you run the program it will ask you these numbers in the order I listed them.
The number's I am using are:
x1 = 3
y1 = 4
x2 = 5
y2 = 6
x3 = 7
y3 = 4
(i hope the code is easy to read i tried to make it so)
Here is the code:
import javax.swing.JOptionPane;
public class AreaOfATriangle {
* @param args
public static void main(String[] args) {
// TODO Auto-generated method stub
/* Write a program that prompts the user to enter three points (x1,
*y1), (x2, y2), (x3, y3) of a triangle and displays its area. The
*formula for computing the area of a triangle is
*S = (side1 + side2 + side3)/2;
*Area = √(s(s-side1)(s-side2)(s-side3))
String x1String = JOptionPane.showInputDialog("Enter a point for x1 of (P(x and y)) for a triangle: ");
double x1 = Double.parseDouble(x1String);
String y1String = JOptionPane.showInputDialog("Enter a point for y1 of (P(x and y)) for a triangle: ");
double y1 = Double.parseDouble(y1String);
String x2String = JOptionPane.showInputDialog("Enter a point for x2 of (P(x and y)) for a triangle: ");
double x2 = Double.parseDouble(x2String);
String y2String = JOptionPane.showInputDialog("Enter a point for y2 of (P(x and y)) for a triangle: ");
double y2 = Double.parseDouble(y2String);
String x3String = JOptionPane.showInputDialog("Enter a point for x3 of (P(x and y)) for a triangle: ");
double x3 = Double.parseDouble(x3String);
String y3String = JOptionPane.showInputDialog("Enter a point for y3 of (P(x and y)) for a triangle: ");
double y3 = Double.parseDouble(y3String);
double side1 = Math.pow(Math.pow((x2-x1),2) + Math.pow((y2-y1),2),(0.5));/*this should be 4 but for some reason it's giving me 2.82364723723 (i'm calculating the side of a triangle here)
*i'm using the distance formula to find the side, the program didn't give this to me, I don't know why
double side2 = Math.pow(Math.pow((x3-x2),2) + Math.pow((y3-y2),2),(0.5));//this is another side of a triangle i'm calculating
double side3 = Math.pow(Math.pow((x1-x3),2) + Math.pow((y1-y3),2),(0.5));//another side to calculate
double s = (side1 + side2 + side3) / 2;//s means semiperimeter (calculating)
double area = Math.pow((s * (s - side1) * (s - side2) * (s - side3)), (0.5));//calculates the area
String output = "The area of the triangle is: " + area + ".";//creating a result
JOptionPane.showMessageDialog(null, output, "Result", JOptionPane.WARNING_MESSAGE);//displaying the result
To avoid typing too much in the code, I'll tell you exactly what my problem is.
I'm trying to get an area, but I figured out that in my code there is a logic error in the following piece of code:
I noticed that it was giving me 2.8 instead of 4.0. I couldn't figure this out, why is it doing this? What's wrong in the code and how do i make it 4.0?
Also, in Math.pow in the piece of code I just mentioned, why can't I use (1/2) instead of (0.5)? Does it have something to do with the datatype i'm using?
When i run my code with everything included it says there are errors in the project, but it doesn't say where. When i run it anyway (on eclipse), the area is give as 3.999999999982 when it
should be 11 (I calculated the area using the numbers I gave and it gave 11).
I assuming that once i correct then it will fix the errors in the program and it will run.
Thank you for taking the time to look at this.
says there are errors in the project,
Are those compiler errors or execution errors?
Can you use the javac compiler to get good compiler error messages?
If you don't understand my answer, don't ignore it, ask a question.
It doesn't have any errors marked in the program when i have typed it all in, but when i compile and try to run it, it says:
Errors in Workspace:
Errors exist in required project(s):
Proceed with launch?
and then I proceed with executing it and it runs the program fine, although my errors in that code (i think they are called logic errors) are still there.
I was running this program in Eclipse when it said this, I tried using JGrasp and it compiles and runs without giving me an error though.
Can I use the javac compiler to get good compiler error messages? I'm not sure what you mean by this, Eclipse marks errors when i'm typing the code, but there aren't any errors it's marking in
the program.
If you can do the computation manually and get the correct answer, you need to compare your results at each step with the programs results for that step. When your results and the program's
results are different, you need to break the compound statements down into simple, single steps and compare your manual results with what the program produces. At some point you should find the
If you don't understand my answer, don't ignore it, ask a question.
Also, in Math.pow in the piece of code I just mentioned, why can't I use (1/2) instead of (0.5)? Does it have something to do with the datatype i'm using?
Yes, those are integer literals and Java will use integer math. 1/2 = 0 in integer land.
Are you sure your hand-calculated answer is correct?
Try graphing your triangle and see if you can estimate approximate lengths and area.
Side note:
There's a sqrt function available in Java. Personally I prefer this over pow(x,0.5).
I tried doing what Norm said,
I'm using:
x1 = 2, x2 = 2
y1 = 4, y2 = 4
then I added another Math.pow()
double side1 = Math.pow((x2-x1),2) + Math.pow((y2-y1),2);//this equals 8.0 ((4-2)^2) + ((4-2)^2) = 8.0
Then I added a Math.pow (also did Math.sqrt) to this.
I thought the above would equal 4.0? Isn't it (4+4)^0.5 ?
I also tried the Math.sqrt and got the same answer: 2.8284
I did the hand calculations to this part of the program and its just 4.0 as well.
I'm assuming it has to do with me not correctly putting a Math.pow inside another Math.pow, however, I've never done anything like this. I've only used a single Math.pow one at a time.
No, sqrt(8) != 4. sqrt(8) ~= 2.8284
You can verify this easily because 4*4 = 16, and likewise 2.8284*2.8284 ~= 8
Thank you, Wow i feel like an idiot. My code was actually correct I just thought when I was typing in integer numbers into the program that for some reason the Area couldn't be a decimal number
and that sqrt(8) != 4.
I appreciate everyone taking the time to reply to my problem. I thought my problem was more complicated than it actually was.
February 7th, 2013, 05:48 PM #2
Super Moderator
Join Date
May 2010
Eastern Florida
Thanked 1,956 Times in 1,930 Posts
February 7th, 2013, 06:08 PM #3
Junior Member
Join Date
Feb 2013
Thanked 0 Times in 0 Posts
February 7th, 2013, 06:31 PM #4
Super Moderator
Join Date
May 2010
Eastern Florida
Thanked 1,956 Times in 1,930 Posts
February 7th, 2013, 06:32 PM #5
Super Moderator
Join Date
Jun 2009
Thanked 619 Times in 561 Posts
Blog Entries
February 7th, 2013, 07:19 PM #6
Junior Member
Join Date
Feb 2013
Thanked 0 Times in 0 Posts
February 7th, 2013, 11:03 PM #7
Super Moderator
Join Date
Jun 2009
Thanked 619 Times in 561 Posts
Blog Entries
February 8th, 2013, 12:18 AM #8
Junior Member
Join Date
Feb 2013
Thanked 0 Times in 0 Posts | {"url":"http://www.javaprogrammingforums.com/whats-wrong-my-code/23547-logic-error-math-pow-b-using-joptionpane.html","timestamp":"2014-04-18T18:46:21Z","content_type":null,"content_length":"111208","record_id":"<urn:uuid:8dc7da63-8232-4822-b88a-ff10cefea9d3>","cc-path":"CC-MAIN-2014-15/segments/1397609535095.7/warc/CC-MAIN-20140416005215-00252-ip-10-147-4-33.ec2.internal.warc.gz"} |
How a CPU Adds Decimal Numbers
Date: 10/22/2000 at 17:31:08
From: Farina
Subject: 8-bit CPU
Hi, Dr. Math. Can you help me? How does an 8-bit CPU add up two
four-digit numbers and why does it take four operations to do so?
Please explain.
Date: 10/23/2000 at 14:00:01
From: Doctor TWE
Subject: Re: 8-bit CPU
Hi Farina - thanks for writing to Dr. Math.
Are you referring to 4-digit _decimal_ numbers? I'll assume that the
numbers are stored in normal Binary Coded Decimal (BCD), and that you
want the result in BCD as well. (Note that there are other forms of
Binary Coded Decimal, like Excess-3 code, 2'421 code, or BCD Gray
code, but the most commonly used form is 8421 BCD, called normal BCD
or simply BCD.)
First, let me briefly explain BCD. In BCD, each digit of a decimal
number is represented by a 4-bit value (similar to the way hexadecimal
digits are represented by 4-bit groups in "pure" binary). Since
decimal only has the digits 0 through 9, only the following values are
valid "4-bit groups" in BCD:
DEC BCD DEC BCD
The combinations 1010, 1011, 1100, 1101, 1110, and 1111 are invalid
because they don't add up to a decimal digit.
Since each decimal digit requires 4 BCD bits, we need 16 bits to
represent a 4-digit decimal value. Your CPU, however, can only work
with 8 bits at a time. So we'll need to break up the numbers into two
parts (bytes) and work with one byte at a time. Let's call the bytes
(or the registers where the bytes are stored) A1 and A0 for the first
number - with A1 being the more significant byte (MSB) and A0 being
the less significant (LSB.) Let's call the bytes B1 and B0 for the
second number - again letting B1 be the more significant byte and B0
the less significant. For example, let's say we want to add the
+ 1795
The 2483 would be represented as 0010 0100 1000 0011 (I'll put spaces
in between each group of 4 bits for readability) and so:
A1 = 0010 0100
A0 = 1000 0011
The 1795 would be represented as 0001 0111 1001 0101 and so:
B1 = 0001 0111
B0 = 1001 0101
When adding large numbers with pencil and paper, we start with the
least significant digits (the units place) and work our way from right
to left. Similarly, our CPU will begin with the LSBs and work over to
the MSBs.
First we'll add the LSBs; A0 + B0:
1 111 <- carry bits
+ 1001 0101
Note that the CPU will do a straight binary addition. The answer is
0001 1000 (18 decimal) with a carry-out of 1. The carry-out is stored
as the "C-flag" in a register, usually called the Condition Code
Register (CCR) or Status Register (SR), depending on the CPU's
Of course, this answer is wrong: 83 + 95 = 178, not 118. Why did it
get the wrong result? Because when it added the 8 and the 9 in the
tens digit, it got 17 and carried 16 of them into the carry-out. (This
is because it did the addition in pure binary.) It should have only
carried 10, not 16, into the carry out, so to compensate, we'll
add 6 back into the tens digit (0110 0000 in BCD), like this:
+ 1001 0101
+ 0110 0000
That's better. Let's store that as S0. Now the MSBs. We'll add
A1 + B1:
_____ Carry-over from the LSBs (in the C-flag)
+ 0001 0111
This time, we got the answer 0011 1100, but that doesn't make sense in
BCD (1100 is an invalid 4-bit group in BCD.) Why? Because again the
CPU did the addition in pure binary. When it added 4 + 7 + 1 it got 12
and represented it in binary as 1100. But for BCD it should have
carried 10 of them over to the tens digit and only kept 0010 (2 in
decimal). To "force" the half-carry (i.e. the carry from the 4th bit
to the 5th), we'll add 6 to the units digit (0000 0110 in BCD) to make
the group of 10 that should have been carried a group of 16 that the
CPU will carry:
+ 0001 0111
+ 0000 0110
Let's store that as S1. Now we have our answer in S1 and S0:
0100 0010 0111 1000, or 4278 decimal.
How do we know if and when to use "fudge factors" like the 0110 0000
and 0000 0110 that we used here? Most CPUs have either a "BCD Mode"
that will automatically determine the proper fudge factor and add it
after every ADD (or ADC - Add with Carry) operation, or they have a
special instruction like DAA (Decimal Adjust Accumulator). Here are
the rules the CPU uses when determining what "fudge factor" to add:
(The H is the half-carry flag and the C is the carry-out flag.)
1. If H = 1 or the last 4 bits > 1001, add 0000 0110
2. If C = 1 of the first 4 bits > 1001, add 0110 0000
Note that both can occur (thus adding 0110 0110), and the first step
can cause the second to occur - that's why they must be tested
sequentially. Sometimes no adjustment is necessary.
Here's a bit of pseudocode that adds two 4-digit BCD values. A1, A0,
B1 and B0 are registers that are storing the inputs as defined above,
and S1 and S0 are registers that are storing the outputs also as
defined above:
LDA A0 ; Load accumulator with LSB of addend
ADD B0 ; Add LSB of augend to accumulator
DAA ; Add "fudge factor" to adjust result to BCD
STA S0 ; Store LSB of sum
LDA A1 ; Load accumulator with MSB of addend
ADC B1 ; Add MSB of augend to accumulator with carry from LSB
DAA ; Add "fudge factor" to adjust result to BCD
STA S1 ; Store MSB of sum
I hope this helps. If you have any more questions, write back.
- Doctor TWE, The Math Forum | {"url":"http://mathforum.org/library/drmath/view/51901.html","timestamp":"2014-04-16T07:36:38Z","content_type":null,"content_length":"11085","record_id":"<urn:uuid:551e139e-2e51-44ed-8012-b5240e3c8971>","cc-path":"CC-MAIN-2014-15/segments/1397609521558.37/warc/CC-MAIN-20140416005201-00089-ip-10-147-4-33.ec2.internal.warc.gz"} |
Math Solve Rational Formulas For A Specified Variable
The Algebra Buster Software is marvelous. Complex numbers always scared me and I wanted a way out. The step-by-step way of your software really cleared my concepts and now I look forward to solve
other types of algebra problems.
Gary Sterns, CA
What a great tool! I would recommend this software for anyone that needs help with algebra. All the procedures were so simple and easy to follow.
Lakeysha Smith, OH
What a great step-by-step explanations. As a father, sometimes it helps me explaining things to my children more clearly, and sometimes it shows me a better way to solve problems.
Marsha Stonewich, TX
Be it any equation, within seconds not only you have the answers but also the steps to refer to. This is awesome.
David Brown, CA
I can no longer think of math without the Algebra Buster . It is so easy to get spoiled you enter a problem and here comes the solution. Recommended!
N.J., Colorado | {"url":"http://www.algebra-online.com/math-software/math-solve-rational-formulas-f.html","timestamp":"2014-04-20T06:37:59Z","content_type":null,"content_length":"19840","record_id":"<urn:uuid:2a324436-eff1-4b76-ac6b-021e237d9a67>","cc-path":"CC-MAIN-2014-15/segments/1398223207985.17/warc/CC-MAIN-20140423032007-00472-ip-10-147-4-33.ec2.internal.warc.gz"} |
Re: Semantic information for math representations of physics
From: John Fletcher <J.P.Fletcher@aston.ac.uk> Date: Thu, 03 Feb 2005 13:06:46 -0000 To: Paul Libbrecht <paul@activemath.org> CC: www-math@w3.org Message-ID: <420221E6.22244.C670B4@localhost>
I would like to join in this discussion as a potential user, at the stage
of knowing what I want to do and having some design choices.
I have computer programs which can compute algebraic
expressions. I want to compute, output and store results. It would
be good also to attach metadata e.g. data, time, purpose to the
I idenitified content MathML as providing the basic coding, except
that I need to go beyond that, as I am working in Clifford Algebra,
so I need to extend MathML.
I could extend it in an arbitrary way, or use RDF to define a set of
As an example of what I am doing
x{1} + y{2} is the vector (1,2)
1 + {1,2} is the sum of a scalar and a bivector.
I need the capability to represent terms {i,j,k....} in a simlar way to a
complex number or a quaternion.
I can provide more information
John Fletcher
is m
Copies to: RobertM@dessci.com, www-math@w3.org
From: Paul Libbrecht <paul@activemath.org>
Date sent: Thu, 3 Feb 2005 13:51:16 +0100
To: JB Collins <joebmath@yahoo.com>
Subject: Re: Semantic information for math representations of physics
Forwarded by: www-math@w3.org
Date forwarded: Thu, 03 Feb 2005 12:51:55 +0000
> Le 3 févr. 05, à 13:20, JB Collins a écrit :
> > [...] Those things being said, I am going to take your
> > response as guidance that says something like "when
> > concepts are defined in MathML, use them; when they
> > are not, for user extensibility, rely on OpenMath."
> What we know:
> - OpenMath and MathML are informally compatible (that is, everyone
> believes so) - the policy in the two bodies (W3C Math Working/Interest
> Groups and the OpenMath society) converge (which was not the case at
> the time MathML content was created, I think).
> MathML-content has been started with a view that an element-name is
> the best representation for a mathematical symbol... thus it needs to
> declare all these element-names, for example, in the DTD, hence
> specify them all part of the language specification. Extensibility is
> not normalized
> OpenMath has started with extensibility in mind from the start on.
> There is no element in the OpenMath language that denotes a precise
> mathematical "notion", "symbol", "concept". All of them are described
> in content-dictionaries the management of which is somewhat easier.
> Content-dictionaries can be contributed and modified easier than a
> language specification.
> There has been some discussions, probably not enough, about bringing
> MathML and OpenMath in sync but this has not been finalized.
> There are intents to promote a tighter compatibility declaration such
> as cross-pointing between OpenMath symbols and MathML symbols and
> indicating best practice for the usage of OpenMath along with MathML.
> Comments and suggestions about this would be most welcome!
> Both OpenMath and MathML, however, do not treat the problematic of
> grounding the extension of a symbol, for example, using a definition.
> That definition could be formal or informal, it would, typically, need
> further developments such as theorems, proofs, or axioms. This last
> step, an attempt at complete representation of mathematical documents
> is the goal of the OMDoc language, http://www.mathweb.org/omdoc/.
> OMDoc's user-base or gang of tools is not as rich...
> Physics has not been touched much in OMDoc, as far as I know. I would
> view such statements as the formal statement about the nature of an
> observable as being a possible extension of OMDoc. (which could even
> be something like the statement of the type of a symbol).
> OMDoc theories are not, yet, convertible back into an OpenMath content
> dictionary. This is a known issue which we intend to tackle in the
> ActiveMath authoring gang of tools (headed by jEditOQMath,
> http://www.activemath.org/projects/jEditOQMath).
> OMDoc documents are the base of our ActiveMath learning environment.
> The formal part of OMDocs are not much used yet though there are some
> intents in the direction of proof-planning usage for education...
> The content in the Mizar Mathematical Library is one of the most
> famous formal mathematics libraries and, clearly, conversion from
> there to OMDoc is something that interests many involved in OMdoc and
> a start of it has been attempted by Michael Kohlhase (on this list
> usually) among others. I heard of no results thus far.
> I did not know of the goal of Mizar encoding to provide a platform for
> the exchange of mathematical documents between theorem provers... the
> conversion of the logical foundation is, as far as I know, often a
> very tough problem when considering such exchange and the logical
> foundation of Mizar documents is very high level, I heard.
> paul
> > As an additional question to throw in, I am also
> > interested in knowing if MathML / OpenMath borrow or
> > cooperate with the MIZAR project. While I started this
> > thread on the MathML reflector, you pointed to
> > OpenMath and its use for interchanging documents for
> > theorem provers. The MIZAR project provides a similar
> > capability. While they seem primarily focused on
> > supporting mathematicians, there seems to be a lot to
> > borrow from.
Dr John P. Fletcher Tel: (44) 121 204 3389 (direct line)
Chemical Engineering and Applied Chemistry (CEAC),
School of Engineering and Applied Science (SEAS),
Aston University, Fax: (44) 121 359 4094
Aston Triangle, Email: J.P.Fletcher@aston.ac.uk
BIRMINGHAM B4 7ET U.K. CEAC Web site
Received on Thursday, 3 February 2005 13:04:13 GMT | {"url":"http://lists.w3.org/Archives/Public/www-math/2005Feb/0004.html","timestamp":"2014-04-19T20:34:13Z","content_type":null,"content_length":"16865","record_id":"<urn:uuid:28bfcfa7-e1cc-44d8-8554-30faba54b4e6>","cc-path":"CC-MAIN-2014-15/segments/1397609537376.43/warc/CC-MAIN-20140416005217-00192-ip-10-147-4-33.ec2.internal.warc.gz"} |
Today We Broke the Bernoulli Record: From the Analytical Engine to
Today We Broke the Bernoulli Record: From the Analytical Engine to Mathematica
April 29, 2008 — Oleksandr Pavlyk, Kernel Technology
In Mathematica, a core principle is that everything should be scalable. So in my job of creating algorithms for Mathematica I have to make sure that everything I produce is scalable.
Last week I decided to test this on one particular example. The problem I chose happens to be a classic. In fact, the very first nontrivial computer program ever written—by Ada Lovelace in 1842—was
solving the same problem.
The problem is to compute Bernoulli numbers.
Bernoulli numbers have a long history, dating back at least to Jakob Bernoulli’s 1713 Ars Conjectandi.
Bernoulli’s specific problem was to find formulas for sums like
Before Bernoulli, people had just made tables of results for specific n and m. But in a Mathematica-like way, Bernoulli pointed out that there was an algorithm that could automate this.
For any given n, the answer is a polynomial in m, and the coefficients are constants that Bernoulli showed could be computed by a simple recurrence formula.
It could have been that Bernoulli numbers would be useful only for solving this particular problem. But in fact over the past 300 years they have found their way into a remarkable range of areas of
mathematics. They appear in the formula for the Riemann zeta function at even integers. They are in the coefficients in the series expansion for tan(x). They appear in the Euler-Maclaurin formula for
approximating integrals by sums and in the Stirling series for the gamma function. They even relate to Fermat’s last theorem—which was first proved by Ernst Kummer for “regular primes” characterized
by Bernoulli numbers.
In 1713 Bernoulli was rather proud of being able to compute the first ten Bernoulli numbers in “a quarter of an hour”.
Of course, in Mathematica, it’s now instantaneous:
But just how far can we go—295 years after Bernoulli, and now with Mathematica?
I decided to try scaling up Bernoulli’s computation—by a factor of a million—and computing the 10 millionth Bernoulli number.
Until recently, doing this would have been impractical, even in Mathematica. Because Mathematica used essentially the same classic recurrence relation for computing Bernoulli numbers that Jakob
Bernoulli himself used, and that Ada Lovelace described programming on Charles Babbage’s Analytical Engine.
This algorithm has the feature (already recognized by Lovelace) that it takes about n^2 steps to compute the nth Bernoulli number. So even if one could compute the 10th Bernoulli number in a
millisecond, it’d take several thousand years to compute the 10 millionth Bernoulli number.
But a few years ago I programmed a quite different algorithm into Mathematica. Instead of directly computing the Bernoulli numbers using a recurrence relation, I instead used a trick recently
suggested by Bernd Kellner: computing Bernoulli numbers by computing the Riemann zeta function.
It’s the integrated nature of Mathematica that makes things like this practical. Without Mathematica, one has to use the simplest building blocks to make efficient algorithms. But with Mathematica,
one can take for granted access to efficient very-high-level operations—like computing Riemann zeta functions.
Bernoulli numbers are related to the zeta function by:
The denominator of a Bernoulli number can be computed using a corollary to the von Staudt-Clausen theorem as:
To get the numerator, one then just has to use the relation to the zeta function. The right-hand side is, then, evaluated approximately and multiplied by the already-known denominator of the
Bernoulli number. Provided the approximation is done with enough significant digits, the numerator of the Bernoulli number is a mere integer part of the product.
But there’s still a problem: to get all the digits in a Bernoulli number, one has to compute powers of pi to extreme precision.
Of course, Mathematica can do that—to billions of digits if necessary.
A week ago, I took our latest development version of Mathematica, and I typed BernoulliB[10^7].
And then I waited.
Yesterday—5 days, 23 hours, 51 minutes, and 37 seconds later—I got the result! [Download 24MB bzip2 file]
The denominator is simple; it’s just 9601480183016524970884020224910.
But the numerator is not so simple; in fact it’s 57,675,292 digits long. It took less than 1 gigabyte of memory to compute, and required computing pi to about 66 million digits.
The numerator is negative, it begins with -47845869850733698144899338333210878162030638218660 and ends with 57164275665935124168181176013725629647185402960697.
Its digits seem almost random. I counted occurrences of all possible k-digit subsequences in the numerator of the 10 millionth Bernoulli number for k=1, 2, 3, and 4. The ratio of the standard
deviation to the mean stays low, though grows with k.
So how can we tell if it’s correct?
Bernoulli numbers have lots of interesting properties. One that’s particularly revealing was discovered by Kummer in 1843, and goes by the name of p-adic continuity. In particular, for two integers n
and m, and a prime number p such that neither n nor m is divisible by p-1, and a natural number r, such that:
the p-adic continuity asserts that:
This property is completely independent of the way we computed the Bernoulli number.
So let’s start checking. Obviously n=10^7. I checked the p-adic continuity for p=43, r=3, m=59776; p=59, r=2, m=916; p=7919, r=1, m=7484; and p=27449, r=1, m=8928. Every one of these congruences is
0, as it should be.
We’ve successfully found the 10 millionth Bernoulli number.
We’ve done what Ada Lovelace believed should be possible: we’ve mechanized the computation of Bernoulli numbers—so well, in fact, that 295 years after Jakob Bernoulli, it’s taken us only 500 times
longer to compute a million-times-as-large Bernoulli number.
And all with a single line of Mathematica input. | {"url":"http://blog.wolfram.com/2008/04/29/today-we-broke-the-bernoulli-record-from-the-analytical-engine-to-mathematica/","timestamp":"2014-04-16T21:58:55Z","content_type":null,"content_length":"66897","record_id":"<urn:uuid:7f59fb82-ae29-4e63-9dec-f12ad4408880>","cc-path":"CC-MAIN-2014-15/segments/1397609525991.2/warc/CC-MAIN-20140416005205-00147-ip-10-147-4-33.ec2.internal.warc.gz"} |
Math Forum Discussions
Math Forum
Ask Dr. Math
Internet Newsletter
Teacher Exchange
Search All of the Math Forum:
Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.
Topic: Optimization with external simulator (SPICE)?
Replies: 5 Last Post: Jul 14, 2013 3:52 AM
Messages: [ Previous | Next ]
Optimization with external simulator (SPICE)?
Posted: Nov 1, 2005 9:40 AM
Hello everybody,
I have a circuit simulator (SPICE) that runs a high frequency model of an
electrical device. I want to tune the parameters of this model to fit my
measurements. I am considering using the Optimization toolbox for this.
Basically I have two sets of frequency dependant variables m(f) and s(f),
and I need to tune about 20 variables (values of resistors, capacitors,
etc) within quite restrictive constraints (factor 10 at most) so that
|| m(f) - s(f) ||² == min
All circuit elements are linear, within certain limits. Just R, L, C.
Normally this would be simple (using \), however s(f) can only be provided
with an external circuit simulator (SPICE in this case), it is too
complicated to be formulated mathematically.
So I need to find a way to make the Matlab optimizer decide on the values
for the next iteration, but perform the actual calculation of s(f) by an
external program (and then read the external program's output file).
The idea is:
Matlab decides on initial values for all variables
Matlab writes SPICE netlist with those values
Matlab calls SPICE simulator
Matlab reads results
... loop until max iterations or required min. difference reached
My ultimate goal is to do this with m(f) and s(f) being matrices instead of
vectors, considering multiple "versions" of the circuit with different m(f)
and parameter constraints for each one (e.g. one circuit with filter, one
without filter), and running seperate external simulations for each one.
Any ideas? Is this possible with the opt. toolbox? Is it feasible? CPU power
and RAM is not the problem (I can order a new 8GB Dual Opteron if that's
what it takes). But I would like to have an idea whether Matlab is the
right tool for this at all beforehand. :-)
Thank you!
Jens Benecke
Date Subject Author
11/1/05 Optimization with external simulator (SPICE)? Jens Benecke
11/1/05 Re: Optimization with external simulator (SPICE)? Marcelo Marazzi
11/2/05 Re: Optimization with external simulator (SPICE)? Jens Benecke
11/1/05 Re: Optimization with external simulator (SPICE)? Marcus M. Edvall
11/2/05 Re: Optimization with external simulator (SPICE)? Jens Benecke
7/14/13 Re: Optimization with external simulator (SPICE)? Sandeep Sulakhe | {"url":"http://mathforum.org/kb/message.jspa?messageID=4060521","timestamp":"2014-04-20T18:52:50Z","content_type":null,"content_length":"23725","record_id":"<urn:uuid:a7c2020c-7a51-4b3b-bedd-b04078a7b497>","cc-path":"CC-MAIN-2014-15/segments/1397609539066.13/warc/CC-MAIN-20140416005219-00172-ip-10-147-4-33.ec2.internal.warc.gz"} |
What is the
10 Answers
Circumference equation is =2 x (Pie) x (R)
Wher Pie =3.1417
R-Radius of Circle
The circumfrance of a circle can be found out using the equation C= 2
Circumference is the measurement surrounding around a circle using the "middle" of a circle.
To find the circumference you need to use one of the following formulas. First you have to find out what information you are given or can measure. Depending on the information you have, you may
need to calculate the diameter of the circle before you can find the circumference. If you are only given a radius, you will either need to calculate the diameter or use a different formula.
(A VIDEO explaining this can be found here: "http://video.about.com/math/How-to-Calculate-Circumference.htm")
Circumference = π × diameter
Circumference = π × 2 × radius
Pi = π = 3.14159265359...
In circles the circumference is 3.14 (p) times the Diameter.
Thus the formula looks like:
Area= pd.
And since diameter(d) is 2 times radius(r) i.e. d=2r
Area= pd=2pr
The distance around a circle is called the circumference. The distance across a circle through the center is called the diameter.
The equation for thecircumference of a cicle is 2r
where the value of
and r is the radius of the circle i.e length of a straight line drawn from the centre of the circle to its circumference.
The distance around a circle is called the circumference. The distance across a circle through the center is called the diameter.
The circumference of a circle can be calculated from its diameter using the formula: Circumference of a circle = 2*pi*radius
First measure the diameter (the width) of the circle.
Then times it by Pi (or just 3.142)
So if the diameter of a circle is 10 cm across the circumference would be 31.42 cm
Suggested reading…
How to calculate the area of a Circle: C=πr^2
But what does this mean?
Some facts you might need to know first:
A circle is a shape where every point on its edge is the same distance from the centre.
The distance from the centre to the edge of the circle is called the Radius.
The distance from one side of the circle to the other, going through the centre, is called the Diameter. This is also double the length of the Radius.
π (pronounced Pi) is a special number that is calculated by dividing the circumference of a circle by the diameter. No matter what size circle you have, this number always stays the same. In reality,
this number is never ending, but we can approximate it to 3.14, but to make it easier for us, since this number never changes, we just call it Pi and write it π.
The Area of a circle
C = circumference
d = diameter
r = radius
The formula for an area circle, if you know its radius, is given by:
A= π r^2
But what if you know the diameter?
You can either divide the diameter by 2 which gives you the radius and then use the formula above or use:
A=(1/4) x πd^2
Remember, the area of a circle is given in square units! (e.g cm^2) | {"url":"http://cribbd.com/question/what-is-the-equation-for-circumference-of-a-circle","timestamp":"2014-04-18T13:36:00Z","content_type":null,"content_length":"60460","record_id":"<urn:uuid:607e00c9-8d8e-49fb-b6b5-a0fa657d5ff6>","cc-path":"CC-MAIN-2014-15/segments/1398223205375.6/warc/CC-MAIN-20140423032005-00621-ip-10-147-4-33.ec2.internal.warc.gz"} |
Gaussian curvature radius
up vote 3 down vote favorite
In the paper Surface sampling and the intrinsic Voronoi diagram (2008), Ramsay Dyer defines the Gaussian curvature radius at a point $x$ of a surface $S$ to be $\rho_K(x) = 1/\sqrt{K(x)}$ where $K(x)
=\kappa_1(x) \kappa_2(x)$ is the Gaussian curvature at $x$.
Trying to track back the notion in Berger's A panoramic view of Riemannian geometry, and in Lee's Riemannian manifolds and in Chavel's Riemannian Geometry yielded nothing.
My question is two-folded:
1. Where can I find more information about this notion?
2. Is there a reason not to define it as $\rho_K(x) = 1/|K(x)|$? Otherwise, this definition is only valid for non-negatively curved surfaces.
EDIT As pointed out by Deane Yang, there is no sense in the definition I suggested. Nevertheless, if one wants to relate the Gaussian curvature to a radius (for either negatively or positively curved
surfaces) how about this alternative: $\rho_{K}(x)=1/\sqrt{|K(x)|}$?
add comment
3 Answers
active oldest votes
As for question #2, why does your definition make sense for a negatively curved surface? For a positively curved surface it does not give the right answer for spheres, since presumably you
would want a sphere of radius $r$ to have a Gauss curvature radius of $r$. In particular, the word "radius" reflects a linear measurement and therefore should scale linearly if you rescale
the surface.
The "radius of curvature" at a point on a curve is the radius of an osculating circle and turns out to be the reciprocal of the geodesic curvature.
up vote 3 On a point of a surface in $R^3$, you get a radius of curvature for each tangent direction, corresponding to the osculating circle in that direction. In particular, there are the two
down vote principal radii of curvature corresponding to the principal directions. The Gauss curvature radius, as defined above, is the geometric average. Since it can be defined in terms of Gauss
curvature only, it has the advantage of being intrinsic. You could also define the "mean radius" by taking the arithmetic average. I don't recall seeing this before, but it also seems
reasonable to study.
I recommend working out the example of $z = f(x,y)$ at the origin, where $f(0, 0) = \partial_xf(0,0) = \partial_yf(0,0) = 0$.
@Deane: By mean radius, do you refer to $1/H(p)$ where $H(p)=\kappa_1(p)+\kappa_2(p)/2$ is the mean curvature at the point $p$. – Dror Atariah Feb 8 '11 at 15:53
I defined "mean radius" to be the mean of the principal radii of curvature. That's not the same as the reciprocal of the mean of the principal curvatures. – Deane Yang Feb 8 '11 at 18:47
@Deane: Considering eq. (3) mathworld.wolfram.com/MeanCurvature.html what you actually defined is nothing but the quotient $H/K$. Is it correct? Is there some standard geometrical meaning
of this quantity? – Dror Atariah Feb 10 '11 at 9:13
Dror, it's what I said it is, namely the average radius of curvature. It is indeed half of $H/K$. Any function of the principal radii of curvature can also be written as a function of $H$
and $K$. – Deane Yang Feb 15 '11 at 16:29
@Deane: I don't know what is the hidden message in your example. Here, the Gaussian curvature at $(0,0)$ is nothing but the determinant of the Hessian of $f$ and the mean curvature is the
trace. Were you aiming at something more specific? – Dror Atariah Feb 21 '11 at 15:39
show 1 more comment
It so happens that $1/\sqrt{K}$, where $K$ is the Gaussian curvature, is, in a sense, the average of the arithmetic mean radius of curvature and the radius of harmonic mean curvature. The
up vote 0 calculation is explained in the "Merged radius of curvature" subsection of the Wikipedia article on radius of curvature. It is called the arithmetic-harmonic mean radius of curvature.
down vote
1 In short, and hopefully as correct, $\sqrt{\frac{1}{K}}$ is the arithmetic-harmonic mean of the two principal curvature radii $\frac{1}{\kappa_i}$. – Dror Atariah Feb 8 '11 at 15:15
add comment
Deane's answer is similar to what I would have tried to say if I'd got here on time. I don't recall seeing the "Gaussian curvature radius" defined before, so I can't point you to other
references. The definition is natural. On the one hand the bound on the distance to a conjugate point (Morse-Schönberg lemma) is given in terms of a bound on the Gaussian curvature radius,
and on the other hand the Gaussian curvature radius provides an upper bound to the "maximal curvature radius"(reciprocal of the maximum of the absolute values of the principal curvatures).
As Deane pointed out, these two curvature radii coincide on the sphere.
up vote Since we are only using it as an upper bound, we just define it to be infinite if the curvature is non-positive. In flat or negatively curved spaces, conjugate points are not an issue;
0 down geodesics diverge.
As to your alternative, $\rho_K(x) = 1/\sqrt{|K(x)|}$, I guess it depends on what you want to do. You are making a smaller sizing function, but why? The spirit of the Morse-Schönberg lemma
is better captured without the absolute value signs. If the infinite values disturb you, you have not avoided them when the Gaussian curvature vanishes.
@Ramsay: Why is this smaller? Smaller then what? I agree that it is not very helpful definition w.r.t. Morse-Schoenberg lemma. But it is a sizing function which is well defined for
non-flat surfaces. At the moment I'm not sure what I want to do with this definition; I found it a natural generalization to a negatively curved surface case and I was wondering if it was
investigated in the literature. – Dror Atariah Feb 18 '11 at 10:22
By smaller I mean that $\rho_K(x) \leq \rho_G(x)$ for all $x$, where $\rho_G$ is the original definition. They agree everywhere except when the curvature is negative and $\rho_G$ provides
no bound. I would be surprised if you found this to be a useful way to capture the geometry of negatively curved surfaces. Since it is purely intrinsic, you will never be able to control
triangle normals this way, for example. It is not clear to me what is represented by the bound you're proposing to introduce. I don't recall seeing it anywhere previously. – Ramsay Feb 18
'11 at 17:04
add comment
Not the answer you're looking for? Browse other questions tagged riemannian-geometry dg.differential-geometry curves-and-surfaces or ask your own question. | {"url":"http://mathoverflow.net/questions/54742/gaussian-curvature-radius/54765","timestamp":"2014-04-17T07:33:30Z","content_type":null,"content_length":"68885","record_id":"<urn:uuid:810e5489-fb55-4cf9-a1dd-2b7bcff06917>","cc-path":"CC-MAIN-2014-15/segments/1397609526311.33/warc/CC-MAIN-20140416005206-00490-ip-10-147-4-33.ec2.internal.warc.gz"} |
Chestnut Ridge, NY
Tenafly, NJ 07670
Math Made Easy & Computer Skills Too
...I go beyond mere educational content, cultivating students' problem-solving skills through the use of authentic, real-world scenarios. I am a certified K-12
ematics teacher. I scored a perfect 200 on the Praxis Middle School
ematics exam and received...
Offering 10+ subjects including algebra 1, algebra 2 and geometry | {"url":"http://www.wyzant.com/Chestnut_Ridge_NY_Math_tutors.aspx","timestamp":"2014-04-19T04:38:18Z","content_type":null,"content_length":"61531","record_id":"<urn:uuid:918fbe14-9d09-456f-8249-3c2c261d3510>","cc-path":"CC-MAIN-2014-15/segments/1397609535775.35/warc/CC-MAIN-20140416005215-00502-ip-10-147-4-33.ec2.internal.warc.gz"} |
How to show a limit superimposed on a graph
I'd like to Plot the following graph with the Limit superimposed on it. If I enter the following as freeform, then the suggestions back from Alpha include exactly the graph I'm looking for
with a red circle showing the limit, but I can't figure out how to make Mathematica create the same chart.
Peter Plot[(x - 5)/(x^2 - 25), {x, -2.752, 12.752}]
Brown Limit[(x - 5)/(x^2 - 25), x -> 5]
2 Votes Any suggestions gratefully received.
First, set your xlim and ylim values:
xlim = 5;
ylim = Limit[(x - 5)/(x^2 - 25), x -> xlim];
Then, use Epilog to draw a dot:
Plot[(x - 5)/(x^2 - 25), {x, -2.752, 12.752},
Epilog -> {AbsolutePointSize[5], Red, Point[{xlim, ylim}]}]
Arnoud Buzing
Or to draw a circle:
2 Votes
Plot[(x - 5)/(x^2 - 25), {x, -2.752, 12.752}, Epilog -> {Red, Circle[{xlim, ylim}, Scaled[{.02/GoldenRatio, .02}]]}]
Or something more fun:
Plot[(x - 5)/(x^2 - 25), {x, -2.752, 12.752},
Epilog -> {Text[Style["\[FreakedSmiley]", 36], {xlim, ylim}]}]
You could also search Demonstration Project - our largest online repository of interactive code published by users - all open source. So click on this
to see the search results. There are many apps there on the topic of limits - you can view, download and update code easily. There is also
huge general calculus section
Vitaliy Kaurov
. I think most suitable Demonstration for you on limits is:
1 Vote
Finite Limit at a Finite Point
Another functionality to consider is integration with Wolfram|Alpha. So of course you could just do this on W|A site:
Vitaliy Kaurov . But if you want to get the graph in Mathematica then this simple thing will do (note it is just natural langauge query and the graph is interactive and you can see the steps):
1 Vote WolframAlpha["limit (x - 5)/(x^2 - 25) for x -> 5"]
Arnoud, thanks much, Epilog is exactly what I'm looking for and thanks for your multiple examples.
Vitaly, thanks for your answers. I had taken a look in the demonstrations projects but it's hard to find demonstrations of the simple stuff for beginners like me. I had checked the freeform
Alpha and got that graph you showed, but when I pulled the code back into Mathematica it didn't draw that red circle, and my son needs to save to PDF for his teacher so I wanted it in
Peter Mathematica.
Thanks all, question answered. | {"url":"http://community.wolfram.com/groups/-/m/t/119118?p_p_auth=phJ6wFG5","timestamp":"2014-04-17T18:23:35Z","content_type":null,"content_length":"80131","record_id":"<urn:uuid:642b2b26-0928-4b48-b9cc-b93df6dded0b>","cc-path":"CC-MAIN-2014-15/segments/1397609530895.48/warc/CC-MAIN-20140416005210-00004-ip-10-147-4-33.ec2.internal.warc.gz"} |
Frege structures and the notion of proposition, truth and set
Results 1 - 10 of 46
, 1992
"... In computer science we speak of implementing a logic; this is done in a programming language, such as Lisp, called here the implementation language. We also reason about the logic, as in
understanding how to search for proofs; these arguments are expressed in the metalanguage and conducted in the me ..."
Cited by 57 (15 self)
Add to MetaCart
In computer science we speak of implementing a logic; this is done in a programming language, such as Lisp, called here the implementation language. We also reason about the logic, as in
understanding how to search for proofs; these arguments are expressed in the metalanguage and conducted in the metalogic of the object language being implemented. We also reason about the
implementation itself, say to know it is correct; this is done in a programming logic. How do all these logics relate? This paper considers that question and more. We show that by taking the view
that the metalogic is primary, these other parts are related in standard ways. The metalogic should be suitably rich so that the object logic can be presented as an abstract data type, and it must be
suitably computational (or constructive) so that an instance of that type is an implementation. The data type abstractly encodes all that is relevant for metareasoning, i.e., not only the term
constructing functions but also the...
- Annals of Pure and Applied Logic , 2003
"... 1 Introduction Induction-recursion is a powerful definition method in intuitionistic type theory in the sense of Scott ("Constructive Validity") [31] and Martin-L"of [17, 18, 19]. The first
occurrence of formal induction-recursion is Martin-L"of's definition of a universe `a la T ..."
Cited by 28 (11 self)
Add to MetaCart
1 Introduction Induction-recursion is a powerful definition method in intuitionistic type theory in the sense of Scott ("Constructive Validity") [31] and Martin-L"of [17, 18, 19]. The
first occurrence of formal induction-recursion is Martin-L"of's definition of a universe `a la Tarski [19], which consists of a set U
- In Proc. 14 th LICS , 1999
"... Abstract We develop a theory of abstract syntax with variable binding. To every binding signature we associate a category of models consisting of variable sets endowed with both a (binding)
algebra and a substitution structure compatible with each other. The syntax generated by the signature is the ..."
Cited by 21 (0 self)
Add to MetaCart
Abstract We develop a theory of abstract syntax with variable binding. To every binding signature we associate a category of models consisting of variable sets endowed with both a (binding) algebra
and a substitution structure compatible with each other. The syntax generated by the signature is the initial model. This gives a notion of initial algebra semantics encompassing the traditional one;
besides compositionality, it automatically verifies the semantic substitution lemma.
, 1998
"... . Milner introduced action calculi as a framework for investigating models of interactive behaviour. We present a type-theoretic account of action calculi using the propositions-as-types
paradigm; the type theory has a sound and complete interpretation in Power's categorical models. We go on to give ..."
Cited by 19 (7 self)
Add to MetaCart
. Milner introduced action calculi as a framework for investigating models of interactive behaviour. We present a type-theoretic account of action calculi using the propositions-as-types paradigm;
the type theory has a sound and complete interpretation in Power's categorical models. We go on to give a sound translation of our type theory in the (type theory of) intuitionistic linear logic,
corresponding to the relation between Benton's models of linear logic and models of action calculi. The conservativity of the syntactic translation is proved by a model-embedding construction using
the Yoneda lemma. Finally, we briefly discuss how these techniques can also be used to give conservative translations between various extensions of action calculi. 1 Introduction Action calculi arose
directly from the ß-calculus [MPW92]. They were introduced by Milner [Mil96], to provide a uniform notation for capturing many calculi of interaction such as the ß-calculus, the -calculus, models of
- IN GODEL '96 , 1996
"... From 1931 until late in his life (at least 1970) Gödel called for the pursuit of new axioms for mathematics to settle both undecided number-theoretical propositions (of the form obtained in his
incompleteness results) and undecided set-theoretical propositions (in particular CH). As to the nature of ..."
Cited by 16 (6 self)
Add to MetaCart
From 1931 until late in his life (at least 1970) Gödel called for the pursuit of new axioms for mathematics to settle both undecided number-theoretical propositions (of the form obtained in his
incompleteness results) and undecided set-theoretical propositions (in particular CH). As to the nature of these, Gödel made a variety of suggestions, but most frequently he emphasized the route of
introducing ever higher axioms of in nity. In particular, he speculated (in his 1946 Princeton remarks) that there might be a uniform (though non-decidable) rationale for the choice of the latter.
Despite the intense exploration of the "higher infinite" in the last 30-odd years, no single rationale of that character has emerged. Moreover, CH still remains undecided by such axioms, though they
have been demonstrated to have many other interesting set-theoretical consequences. In this paper, I present a new very general notion of the "unfolding" closure of schematically axiomatized formal
systems S which provides a uniform systematic means of expanding in an essential way both the language and axioms (and hence theorems) of such systems S. Reporting joint work with T. Strahm, a
characterization is given in more familiar terms in the case that S is a basic
, 1990
"... this paper we present a non-standard logic for our structures. It is a type-free intensional logic, and is also in the tradition of Curry's illative logic [HS86]; see also [AczN, FM87, Smi84,
MA88]. The logic has two judgments: that an object is a fact and that an object is a state-of-a#airs (cf. tr ..."
Cited by 15 (2 self)
Add to MetaCart
this paper we present a non-standard logic for our structures. It is a type-free intensional logic, and is also in the tradition of Curry's illative logic [HS86]; see also [AczN, FM87, Smi84, MA88].
The logic has two judgments: that an object is a fact and that an object is a state-of-a#airs (cf. truth and proposition). Objects are given using a variant of the traditional situation theory
notation which is more standard, logically speaking, with explicit negation and quantification (see also [Bar87]). No metalinguistic apparatus is employed
- In LICS’06 , 2006
"... U. Berger, [11] significantly simplified Tait’s normalisation proof for bar recursion [27], see also [9], replacing Tait’s introduction of infinite terms by the construction of a domain having
the property that a term is strongly normalizing if its semantics is. The goal of this paper is to show tha ..."
Cited by 13 (1 self)
Add to MetaCart
U. Berger, [11] significantly simplified Tait’s normalisation proof for bar recursion [27], see also [9], replacing Tait’s introduction of infinite terms by the construction of a domain having the
property that a term is strongly normalizing if its semantics is. The goal of this paper is to show that, using ideas from the theory of intersection types [2, 6, 7, 21] and Martin-Löf’s domain
interpretation of type theory [18], we can in turn simplify U. Berger’s argument in the construction of such a domain model. We think that our domain model can be used to give modular proofs of
strong normalization for various type theory. As an example, we show in some details how it can be used to prove strong normalization for Martin-Löf dependent type theory extended with bar recursion,
and with some form of proof-irrelevance. 1
, 1991
"... A rst-order language is interpreted in the following way: terms are regarded as referring to situations and the truth of formulae is relativized to a situation. The language is then extended to
include formulae of the form t : (where t is a term and is a formula) meaning that is true in the s ..."
Cited by 10 (3 self)
Add to MetaCart
A rst-order language is interpreted in the following way: terms are regarded as referring to situations and the truth of formulae is relativized to a situation. The language is then extended to
include formulae of the form t : (where t is a term and is a formula) meaning that is true in the situation referred to by t. Gentzen's sequent calculus for classical rst-order logic is extended with
rules which capture this interpretation. Variants of the calculus and extensions of the language are discussed and the Cut rule is shown to be eliminable from some of the proposed calculi. Situation
theory has been concerned with a range of issues centring around the partiality, context dependency and intensional structure of information. In formalizing situation theory one must focus on a
specic aspect of the whole package | there is too much uncertainty and equivocation about the connections between the various parts. A dominant approach in recent years has been to focus on build...
- of Software Science and Computation Structures (FOSSACS 2005 , 2005
"... Abstract. The general aim of this talk is to advocate a combinatorial perspective, together with its methods, in the investigation and study of models of computation structures. This, of course,
should be taken in conjunction with the wellestablished views and methods stemming from algebra, category ..."
Cited by 9 (3 self)
Add to MetaCart
Abstract. The general aim of this talk is to advocate a combinatorial perspective, together with its methods, in the investigation and study of models of computation structures. This, of course,
should be taken in conjunction with the wellestablished views and methods stemming from algebra, category theory, domain theory, logic, type theory, etc. In support of this proposal I will show how
such an approach leads to interesting connections between various areas of computer science and mathematics; concentrating on one such example in some detail. Specifically, I will consider the line
of my research involving denotational models of the pi calculus and algebraic theories with variable-binding operators, indicating how the abstract mathematical structure underlying these models fits
with that of Joyal’s combinatorial species of structures. This analysis suggests both the unification and generalisation of models, and in the latter vein I will introduce generalised species of
structures and their calculus. These generalised species encompass and generalise various of the notions of species used in combinatorics. Furthermore, they have a rich mathematical structure (akin
to models of Girard’s linear logic) that can be described purely within Lawvere’s generalised logic. Indeed, I will present and treat the cartesian closed structure, the linear structure, the
differential structure, etc. of generalised species axiomatically in this mathematical framework. As an upshot, I will observe that the setting allows for interpretations of computational calculi
(like the lambda calculus, both typed and untyped; the recently introduced differential lambda calculus of Ehrhard and Regnier; etc.) that can be directly seen as translations into a more basic
elementary calculus of interacting agents that compute by communicating and operating upon structured data. | {"url":"http://citeseerx.ist.psu.edu/showciting?cid=763379","timestamp":"2014-04-18T02:09:02Z","content_type":null,"content_length":"37965","record_id":"<urn:uuid:8b3cdd75-320d-40a6-98b0-41a43dd2f106>","cc-path":"CC-MAIN-2014-15/segments/1397609532374.24/warc/CC-MAIN-20140416005212-00080-ip-10-147-4-33.ec2.internal.warc.gz"} |
Binary Menu
16.3 Binary Menu
|AND | OR |XOR |NOT |LSH |RSH |
|DEC |HEX |OCT |BIN |WSIZ|ARSH|
| A | B | C | D | E | F |
The keys in this menu perform operations on binary integers. Note that both logical and arithmetic right-shifts are provided. <INV LSH> rotates one bit to the left.
The “difference” function (normally on b d) is on <INV AND>. The “clip” function (normally on b c) is on <INV NOT>.
The <DEC>, <HEX>, <OCT>, and <BIN> keys select the current radix for display and entry of numbers: Decimal, hexadecimal, octal, or binary. The six letter keys <A> through <F> are used for entering
hexadecimal numbers.
The <WSIZ> key displays the current word size for binary operations and allows you to enter a new word size. You can respond to the prompt using either the keyboard or the digits and <ENTER> from the
keypad. The initial word size is 32 bits. | {"url":"http://www.gnu.org/software/emacs/manual/html_node/calc/Keypad-Binary-Menu.html","timestamp":"2014-04-20T20:13:54Z","content_type":null,"content_length":"3324","record_id":"<urn:uuid:033f61a1-f88f-45df-96f2-38c8d1c49c21>","cc-path":"CC-MAIN-2014-15/segments/1397609539066.13/warc/CC-MAIN-20140416005219-00164-ip-10-147-4-33.ec2.internal.warc.gz"} |
Math Forum Discussions
Math Forum
Ask Dr. Math
Internet Newsletter
Teacher Exchange
Search All of the Math Forum:
Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.
Topic: Alignment of 3D Points
Replies: 10 Last Post: Dec 16, 2012 2:46 AM
Messages: [ Previous | Next ]
Anu Re: Alignment of 3D Points
Posted: Dec 15, 2012 10:43 AM
Posts: 64
Registered: "Matt J" wrote in message <kafkp8$83i$1@newscl01ah.mathworks.com>...
2/22/05 > "Anusha " <anusha@cs.usm.my> wrote in message <kafjg0$3ta$1@newscl01ah.mathworks.com>...
> >
> > Actually what I need to do is aligning A and B into a standard coordinate system. When I say aligning to the centroid, it means that during aligning A and B to standard coordinate,
maybe the centroid of either A or B can be utilized to give the center of gravity for alignment. Hope Im making myself clear.
> ============
> No, I'm afraid not. What makes you think A and B aren't already measured in the same coordinate system right now? After all, they're already both in R^3 and R^3 is a pretty standard
coordinate system.
> Is A a transformation of B? If so, what does that transformation look like and why aren't there the same number of points before and after the transformation?
Actually A and B represents points on a surface of medical structure. Capturing the medical structure at different time wil not provide an aligned point set representastion. I have
checked this, and the structure A and B are not aligned at the same axis. thts why I need to aligned them to a common axis/center of gravity so tht further processing can be done.
Date Subject Author
12/13/12 Anu
12/13/12 Re: Alignment of 3D Points Matt J
12/13/12 Re: Alignment of 3D Points Roger Stafford
12/14/12 Re: Alignment of 3D Points Anu
12/14/12 Re: Alignment of 3D Points Matt J
12/14/12 Re: Alignment of 3D Points Anu
12/14/12 Re: Alignment of 3D Points Matt J
12/15/12 Re: Alignment of 3D Points Anu
12/15/12 Re: Alignment of 3D Points Roger Stafford
12/16/12 Re: Alignment of 3D Points Matt J
12/14/12 Re: Alignment of 3D Points Roger Stafford | {"url":"http://mathforum.org/kb/thread.jspa?threadID=2420469&messageID=7937173","timestamp":"2014-04-17T08:03:01Z","content_type":null,"content_length":"28870","record_id":"<urn:uuid:0cc0180f-34da-4c2a-ab6f-8002f3020f8b>","cc-path":"CC-MAIN-2014-15/segments/1397609538423.10/warc/CC-MAIN-20140416005218-00069-ip-10-147-4-33.ec2.internal.warc.gz"} |
Re: st: merging datasets
Notice: On March 31, it was announced that Statalist is moving from an email list to a forum. The old list will shut down at the end of May, and its replacement, statalist.org is already up and
[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]
Re: st: merging datasets
From Kyleigh Schraeder <kyschraeder@gmail.com>
To statalist@hsphsun2.harvard.edu
Subject Re: st: merging datasets
Date Mon, 20 Feb 2012 09:20:55 -0500
As you said, the 'small sample' was independently collected from the
national sample. The small sample has its own survey structure and no
population weights. Both samples have been matched for the same
Thank you for your help Steve!
On Mon, Feb 20, 2012 at 9:05 AM, Steve Samuels <sjsamuels@gmail.com> wrote:
> Kyleigh Schraeder:
> As a start, I assume that by "small sample", you mean a small survey sample, with its own survey structure. If not, see below. The trick is to combine the two data sets in such a way so that you can -svyset- the combination and apply Stata's survey commands. This is the standard approach for combining two independent samples.
> Suppose the -svyset- statement for large survey data set is:
> ************************
> svyset psu [pw = myweight], strata(stratumvar)
> ************************
> In what follows, I use the prefix "small_" for variables from the small data set. If the small sample was not a survey sample, then for "small_psu" use "_n" and for "small_weight" use "1". It is crucial to assign a stratum number for the small sample that is not present in the large sample.
> **************************************
> use small_data, clear
> gen psu = small_psu
> gen int stratumvar = small_stratum+10000 // a stratum number not in the large sample
> gen myweight = small_weight
> gen samptype = 1
> append using large_data
> replace samptype = 2 if sample==.
> label define samptype 1 "small" 2 "national"
> label values samptype samptype
> svyset psu [pw = myweight], stratum(stratumvar)
> save combo, replace
> **************************************
> Then do any survey command for comparing the two samples, e.g.
> ************************
> svy: reg myoutcome i.samptype
> *************************
> Hypothesis tests are often not appropriate for comparing descriptive statistics of two finite populations, because no specific groups of people can expected to have _identical_ means or other statistics. For references, see: http://www.stata.com/statalist/archive/2011-09/msg01121.html. Confidence intervals provide a satisfying alternative.
> Steve
> sjsamuels@gmail.com
> On Feb 19, 2012, at 6:03 PM, Kyleigh Schraeder wrote:
> I would like to compare means and percentages from a small sample
> dataset to a large population national dataset. The population
> dataset has population weights. I have stset the population dataset
> but I need to merge the two datasets in order to run analyses. I am
> wondering how I can merge the two datasets but still apply the
> population weights to the large dataset beforehand (and not apply the
> population weights to the small sample).
> Thanks for your help,
> KS
> *
> * For searches and help try:
> * http://www.stata.com/help.cgi?search
> * http://www.stata.com/support/statalist/faq
> * http://www.ats.ucla.edu/stat/stata/
> *
> * For searches and help try:
> * http://www.stata.com/help.cgi?search
> * http://www.stata.com/support/statalist/faq
> * http://www.ats.ucla.edu/stat/stata/
Kyleigh Schraeder, BSc (Hons)
M.Sc. Candidate
Clinical Psychology Program
Department of Psychology
University of Western Ontario
* For searches and help try:
* http://www.stata.com/help.cgi?search
* http://www.stata.com/support/statalist/faq
* http://www.ats.ucla.edu/stat/stata/ | {"url":"http://www.stata.com/statalist/archive/2012-02/msg00896.html","timestamp":"2014-04-19T12:17:43Z","content_type":null,"content_length":"11544","record_id":"<urn:uuid:cba065e6-410c-40fc-85d4-f9195ace93fb>","cc-path":"CC-MAIN-2014-15/segments/1398223206118.10/warc/CC-MAIN-20140423032006-00118-ip-10-147-4-33.ec2.internal.warc.gz"} |
188 helpers are online right now
75% of questions are answered within 5 minutes.
is replying to Can someone tell me what button the professor is hitting...
• Teamwork 19 Teammate
• Problem Solving 19 Hero
• Engagement 19 Mad Hatter
• You have blocked this person.
• ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.
This is the testimonial you wrote.
You haven't written a testimonial for Owlfred. | {"url":"http://openstudy.com/users/cleavland*kidd/asked","timestamp":"2014-04-17T22:01:28Z","content_type":null,"content_length":"105957","record_id":"<urn:uuid:519bd6a0-2237-456b-8dc2-26af0c6b77f8>","cc-path":"CC-MAIN-2014-15/segments/1397609532128.44/warc/CC-MAIN-20140416005212-00586-ip-10-147-4-33.ec2.internal.warc.gz"} |
Kidtoons December Movie: Curious George: A Very Monkey Christmas Giveaway–Closed - "Deal"icious Mom
This month Kidtoons is happy to announce their December feature movie is:
Curious George: A Very Monkey Christmas
George and The Man with The Yellow Hat are having a very merry time counting down the days until Christmas. There’s only one puzzle: neither of them can figure out what to give the other for a
present. The Man is having trouble reading George’s wish list and George doesn’t have a clue about what to get for The Man who has everything. Will they be able to find the answers before
Christmas morning?
As always, Kidtoons is committed to providing safe, affordable, fun family matinees. Check out where you can see Curious George: A Very Monkey Christmas in a theater near you through the month of
Also, print out a fun Curious George coloring sheet to go along with the movie here!
On to the Giveaway!
I have a fun prize pack to giveaway to 1 lucky winner!
The prize pack includes:
* 1 Curious George Book
* 1 Curious George DVD
* 1 Curious George poster
Enter Here
Just enter your info in the form by December 10th. I will choose the winner by random number generator then. I will email the winner and the winner will have 48 hours to get back to me or I will
choose a new winner(s).
Open to U.S. residents only. No P.O Boxes and One entry daily per household.
***As always for extra entries you can do any of the following.
Please leave a separate comment for each extra entry you earn.
• “Like” Dealicious Mom and Kidtoons on Facebook
• Follow “Deal”icious Mom on Twitter and send out a tweet about the giveaway. Leave a link to the tweet below.
• Follow Kidtoons on twitter as well.
• Blog about my giveaway on your own personal blog/website.
• Follow me publicly on Google Friend Connect (on my right sidebar below my button)
• Enter this giveaway into another giveaway linky on another blog or website. Then leave me the link to the where you posted in the comments
• Put up my button on your blog (see button code on my right hand sidebar).
• Put up a link to DealiciousMom.com on your sidebar of your own site. If you already have my link on your site please make sure it is current.
• Sign up for my RSS feed or email here
Comments on this post saying: “Enter me” or “I would love to win” or anything of that manor will not be counted. You must enter through the method outlined above.
Thanks for reading,
Deal”icious Mom’s Giveaway Disclosure: This is a sponsored post and I was provided the prize pack to giveaway. The opinions in this post are entirely my own. This post has not been reviewed or
edited by anyone. I was not compensated for this post in any other way. The sponsor of this giveaway is responsible for prize fulfillment and shipping the winner(s) their prize.
i like u both on fb. amy bolda pugmire
i follow your blog.
3. Karen says:
I subscribe to your rss feed
follow on twitter and tweeted
email subscriber.
6. Cristalle says:
I follow your blog and would love to win this for my daughter. She is having a Curious George birthday party in January!
7. Shannon Foster says:
Follow kid toons and deal on Facebook
8. Shannon Foster says:
Follow you on twiter adn tweeted
9. Shannon Foster says:
Now following Kidtoons on twitter @sfoster71
10. Shannon Foster says:
Follow you publicly GFC
11. Danelle says:
I follow/like you both on FB-DanelleJohns
danellejohns at gmail dot com
12. Danelle says:
I follow/like Kidtoons on Twitter-DanelleJohns(Danelle)
danellejohns at gmail dot com
13. Danelle says:
I follow you publicly via GFC-DanelleJohnson
danellejohns at gmail dot com
14. Danelle says:
I follow via google Reader
danellejohns at gmail dot com
15. JoeyfromSC says:
I love Curious George & so does my 6 yr. old Godson!
I am a GFC follower as JoeyfromSC
Thank you for the chance to win!
16. JoeyfromSC says:
have your button on my blog
17. JoeyfromSC says:
email subscriber
18. JoeyfromSC says:
Following you on twitter @JoeyfromSC and tweeted:
twitter follower
google follower
email subscriber
email subscriber
follow kidtoons on twitter
like both of you on facebook
noelle davis
25. SGuzman says:
Follow you on GFC
26. SGuzman says:
I’m an email subscriber
27. Linda B says:
I like you and Kidtoons on facebook (Linda Bradley). Thanks for the chance to win!
28. Linda B says:
I’m an email subscriber.
29. Chelsei Ryan says:
I like Dealicious Mom and Kidtoons on FB
Chelsei Ryan
30. Chelsei Ryan says:
I follow via GFC
31. Chelsei Ryan says:
I subscribe to email
32. Joyce Mlinek says:
I like Dealicious Mom and Kidtoon on fb.
33. Joyce Mlinek says:
I followed Dealicious Mom on twitter and retweeted @joycemlinek
34. Joyce Mlinek says:
I get your e-mails.
35. Joyce Mlinek says:
I am a follower on Google Friend Connect.
36. ReggieMann says:
RSS feed subscriber via Google Reader
ReggieM1961 [at] gmail [dot] com
37. deb c says:
email subscriber
38. deb c says:
follow GFC-missdeb1
“Like” Dealicious Mom and Kidtoons on Facebook
got your button
i tweeted this
i subscribe via email
Follow Kidtoons on twitter-gabbylowe
i follow on google
45. Jennifer says:
I follow you via gFC
46. Marla Y says:
I follow you on Kidtoons on Facebook (marla yuhas)
47. Marla Y says:
I follow you on Twitter (nanatide)
48. Marla Y says:
I fol Kidtoons on Twitter (nanatide)
49. Marla Y says:
Email subscriber
50. Marla Y says:
On my post that I follow on Twitter I forgot to also say I tweeted:
51. LISA BLUMENSTEIN says:
I AM AN EMAIL SUBSCRIBER
52. LISA BLUMENSTEIN says:
I am a google friend
53. Addison KAT says:
following you via GFC as Addison K.A.T.
anita [dot] truck [at] gmail [dot] com
54. Addison KAT says:
RSS feed subscriber
anita [dot] truck [at] gmail [dot] com
“Like” Dealicious mom on FB
“Like” Kidtoons on FB
I follow Dealicious Mom on Twitter: TheWorthys
I tweeted about this GIVEAWAY!
I follow Kidtoons on Twitter: TheWorthys
I follow you through GFC
I have your button on my blog
I have your link on my sidebar on my blog
63. Aleksandra Nearing says:
I like you on FB already
64. Crystal Sanchez says:
Love your site!
65. Ashley says:
I like Dealicious Mom on facebook!
i “Like” Dealicious Mom and Kidtoons on Facebook
I am a GFC follower
Your button is on my blog
I follow your RSS feed via Google Reader
I follow you on Twitter and tweeted here: https://twitter.com/#!/LifeContentment/status/13068491418509313
I am following Kidtoons on Twitter.
72. Shannon Foster says:
73. Shannon Foster says:
74. kelly west says:
follow you both on facebook
75. kelly west says:
tweeted giveaway
76. kelly west says:
follow kidtoons on twitter
77. kelly west says:
google follower
78. Ashley says:
I like dealicious mom on FB
79. Ashley says:
I follow dealicious mom on twitter @shuggysmommy
discuss antiochene buttonbush says:
otherwise they will grow weary of you….
being creative in terms of presentation will keep you in the public limelight. nevertheless, you must be vigilant to know what is happening in order to beat the competition.if you are considering how
to become famous for free, you can try… | {"url":"http://www.dealiciousmom.com/kidtoons-december-movie-curious-george-a-very-monkey-christmas-giveaway/","timestamp":"2014-04-18T15:38:39Z","content_type":null,"content_length":"126095","record_id":"<urn:uuid:36555f64-c2dc-488f-9f60-632b77c28b57>","cc-path":"CC-MAIN-2014-15/segments/1397609533957.14/warc/CC-MAIN-20140416005213-00615-ip-10-147-4-33.ec2.internal.warc.gz"} |
Unibooks - Mathematics
by: Ralph P. Grimaldi
$180.00 $200.00 inc GST $163.64 $181.82 ex GST
Edition: 5 ISE
Publication Date: 01/07/2003
ISBN: 9780321211033
Published In: United States
Offers a flexible organization, enabling instructors to adapt the book to their particular courses. This book gives emphasis on algorithms and applications. Including exercises, it features numerous
computer science applications. | {"url":"http://www.unibooks.com.au/Pages/Category.aspx?cat=Catalog&category=U89908&page=16","timestamp":"2014-04-17T21:35:21Z","content_type":null,"content_length":"64565","record_id":"<urn:uuid:013beccf-b73a-4111-8c5f-e6bb459fe75e>","cc-path":"CC-MAIN-2014-15/segments/1398223211700.16/warc/CC-MAIN-20140423032011-00001-ip-10-147-4-33.ec2.internal.warc.gz"} |
topological ring
topological ring
Basic concepts
Higher algebra
Algebraic theories
Algebras and modules
Higher algebras
Model category presentations
Geometry on formal duals of algebras
A topological ring is a ring internal to Top, a ring object in Top:
a topological space $R$ equipped with the structure of a ring on its underlying set, such that addition and multiplication are continuous functions.
Similarly a topological field is a topological ring whose underlying ring is in fact a field and a topological algebra is a topological ring under a base topological ring (a topological associative
Revised on April 6, 2014 22:51:26 by
Tim Porter | {"url":"http://www.ncatlab.org/nlab/show/topological+ring","timestamp":"2014-04-20T03:30:20Z","content_type":null,"content_length":"25783","record_id":"<urn:uuid:b26a5e7a-2699-467a-a26d-6334b9e81b8b>","cc-path":"CC-MAIN-2014-15/segments/1397609537864.21/warc/CC-MAIN-20140416005217-00170-ip-10-147-4-33.ec2.internal.warc.gz"} |
Paraquaternionic projective space and pseudo-Riemannian geometry
Novica Bla\v zi\'c
Matemati\v cki fakultet, Beograd, Yugoslavia
Abstract: A natural and geometrical definition of projective space $(P_n(\Bbb B),g_0)$, based on the algebra of paraquaternionic numbers $\Bbb B$, is given. Using the technique of pseudo-Riemannian
submersions, we determine the curvature of the paraquaternionic space $(P_n(\Bbb B),g_0)$. Moreover, the properties of this curvatures are studied.
Classification (MSC2000): 53C15; 53C50
Full text of the article:
Electronic fulltext finalized on: 1 Nov 2001. This page was last modified: 16 Nov 2001.
© 2001 Mathematical Institute of the Serbian Academy of Science and Arts
© 2001 ELibM for the EMIS Electronic Edition | {"url":"http://www.emis.de/journals/PIMB/074/11.html","timestamp":"2014-04-18T13:47:47Z","content_type":null,"content_length":"3307","record_id":"<urn:uuid:b2b5d068-ddba-4658-aae7-41bdcf868d82>","cc-path":"CC-MAIN-2014-15/segments/1398223203422.8/warc/CC-MAIN-20140423032003-00159-ip-10-147-4-33.ec2.internal.warc.gz"} |
Math Help
February 4th 2006, 05:54 PM #11
Oct 2005
Right, I can solve this, but the solution is does not qualify as high school
maths. Are you sure that you don't already have a short cut for this problem
in your notes or textbook?
Also its a lot of typing, I will start typing the solution in about 3 hours.
I saw the first problem in a magazine not in my textbook,so you can work it out in any ways.And thank you for your later typing.
The second one is from Cambridge College Math Institute and the answer to this problem will not be given untill several months later. Anyone who works it out can send email to
puzzlemaster@cambridgecollege.edu with your solution.
Thank you , thank you for your thinking and typing,
and words fail me to say anything others.
Last edited by yiyayiyayo; February 4th 2006 at 06:25 PM.
The problems were very nice problems.
I was further thinking about the second problem you gave. I believe I have a simplified version other than I posted previously. I think (not completely proven but close to it) that all number
which CANNOT be expressed as the sum of consecutives is of the form $2^n$.
I will not post my solution now, but later on in a few hours, I do not have enough time now.
Last edited by ThePerfectHacker; February 5th 2006 at 12:51 PM.
Let me show my proof to problem 2.
Notice that a number expressed, as $m$ consecutives (odd number), then we have,
Now $m-1$ is even, thus,
where $j$ is an integer thus,
Thus, if a number can be expressed as a sum of $m$ (odd) consecutives, then it is divisible by $m$.
Now we prove, the converse (not exactly a converse you will see). That if a number is divisible by $m$ then, we can express it as a sum of consecutives (I did not say $m$ consecutives rather I
said it can be expressed as consecutives!). If $m|n$ then there exists $k$ such as $mk=n$. Thus, instead of $k$ write $m(j+s)=n$ where $j=(m-1)/2$ (as before), thus we can find such an $s$. The
problem is that $s$ can be a negative number. Thus, the number can be expressed as:
The following is the foundation of the proof; observe that if a number is expressed as a sum of consecutives starting from a negative number then it still can be expressed as a sum of
consecutives! Because they cancel each other out. Observe,
Now follow with me. A number is expressed as a sum of consecutives from a negative number. Then they cancel each other out, and you are left with,
still a sum of consecutives.
The problem is of course if they cancel each other out in such a way then you a left with a single number. For example,
(-1)+0+1+2, becomes,
But 2 is not expressing 2 as a sum of consecutives by just 2 (that is trivial).
But to show this does not happen over here is because since $m$ is an odd number, and zero is part of this expansion, thus there are a total of even numbers. Thus, either the number of negatives
is more than positives (which is not possible). They are equal (which is not possible). Thus, the number of positives must overtake the number of negatives by and even amount! Thus at least two
which is considered a sum of consecutives.
Now we have that ANY number divisible by any odd number CAN be expressed as a sum of consecutives. Thus, if a number IS NOT expressable as a sum of consecutives it must have the form $2^n$.
Finally, we prove the converse, that if a number has the form $2^n$ then it cannot be expressed as a sum of consecutives, then we have that,
Since of equality and the fact we are using integers we have that $b$ cannot have odd factors thus,
But the right factor of the LHS is odd,
Thus an impossibility.
Thus, all and only thus of the form $2^n$. Cannot be expressed as a sum of consecutives.
I hope I did not make a mistake in proof. I think this is a nice problem and I had fun solving it.
Last edited by ThePerfectHacker; December 18th 2007 at 01:13 PM.
You're very kind,and I really hope too much typing didn't trouble you. Though I want to say something,my poor English frustrated me, sorry.
In one word, your proof is wonderfull.Thank you.
You're very kind,and I really hope too much typing didn't trouble you. Though I want to say something,my poor English frustrated me, sorry.
In one word, your proof is wonderfull.Thank you.
It took me a quick time to type that, besides I had fun solving this problem. Where are you from?
I am from China and I'm a student studying in Senior Middle School.
February 4th 2006, 06:24 PM #12
Global Moderator
Nov 2005
New York City
February 5th 2006, 09:48 AM #13
Global Moderator
Nov 2005
New York City
February 6th 2006, 02:47 PM #14
Global Moderator
Nov 2005
New York City
February 6th 2006, 06:48 PM #15
Oct 2005
February 6th 2006, 06:53 PM #16
Global Moderator
Nov 2005
New York City
February 6th 2006, 07:17 PM #17
Oct 2005 | {"url":"http://mathhelpforum.com/algebra/1799-help-plz-2.html?pp=10","timestamp":"2014-04-19T22:06:02Z","content_type":null,"content_length":"56265","record_id":"<urn:uuid:7f660c37-a596-4783-8cb9-33a4f9599e57>","cc-path":"CC-MAIN-2014-15/segments/1398223205137.4/warc/CC-MAIN-20140423032005-00252-ip-10-147-4-33.ec2.internal.warc.gz"} |
Alpine, CA Algebra 1 Tutor
Find an Alpine, CA Algebra 1 Tutor
...I have taught prealgebra in a classroom and thoroughly enjoyed it. This is the point when the kids can really start sinking their teeth into some pretty complex math problems and seeing how
you can use their skills to do some important things. They also get introduced to the very basic concepts of algebra and that is where they can get a bit frustrated.
11 Subjects: including algebra 1, calculus, algebra 2, geometry
...During those four years, I became an honors member after completing over 600 cumulative hours of involvement in the theater. I used to be a theater student in high school, and would regularly
get on stage for my performances. I have given several presentations for large groups of people about the research I have done.
42 Subjects: including algebra 1, reading, Spanish, writing
...In other words, I have take on an approach to math that makes it easy to understand and NOT stressful. For each lesson, I will create a lesson agenda, preview the work ahead of time, and
enhance the skills/concepts with worksheets to make sure gaps in learning are filled. With my methods of tea...
21 Subjects: including algebra 1, reading, geometry, Chinese
...I studied mathematics for my undergraduate. In those courses, I especially enjoyed linear algebra, calculus, and abstract algebra. After my undergrad I studied computer science, which has
always been a passion for me.
26 Subjects: including algebra 1, physics, calculus, statistics
Hello my name is Sean and I am a graduating student at UCSD in the field of Mathematics. I have taken a number of educational studies courses to better prepare myself for a future in education,
specifically high school math. I have over twenty hours of in-class tutoring experience at Montgomery Middle School.
10 Subjects: including algebra 1, calculus, public speaking, cooking
Related Alpine, CA Tutors
Alpine, CA Accounting Tutors
Alpine, CA ACT Tutors
Alpine, CA Algebra Tutors
Alpine, CA Algebra 2 Tutors
Alpine, CA Calculus Tutors
Alpine, CA Geometry Tutors
Alpine, CA Math Tutors
Alpine, CA Prealgebra Tutors
Alpine, CA Precalculus Tutors
Alpine, CA SAT Tutors
Alpine, CA SAT Math Tutors
Alpine, CA Science Tutors
Alpine, CA Statistics Tutors
Alpine, CA Trigonometry Tutors | {"url":"http://www.purplemath.com/alpine_ca_algebra_1_tutors.php","timestamp":"2014-04-21T07:38:22Z","content_type":null,"content_length":"24074","record_id":"<urn:uuid:ff988361-febc-4e19-94e5-2c40fee5be30>","cc-path":"CC-MAIN-2014-15/segments/1397609539665.16/warc/CC-MAIN-20140416005219-00577-ip-10-147-4-33.ec2.internal.warc.gz"} |
[Numpy-discussion] Numpy and PEP 343
Travis Oliphant oliphant at ee.byu.edu
Fri Mar 3 14:42:05 CST 2006
Tim Hochberg wrote:
> We may want to reconsider this at least partially. I tried
> implementing a few 1-argument functions two way. First as a table
> lookup and second using a dedicated opcode. The first gave me a
> speedup of almost 60%, but the latter gave me a speedup of 100%. The
> difference suprised me, but I suspect it's do to the fact that the x86
> supports some functions directly, so the function call gets optimized
> away for sin and cos just as it does for +-*/. That implies that some
> functions should get there own opcodes, while others are not worthy.
> This little quote from wikipedia lists the functions we would want to
> give there own opcodes to:
> x86 (since the 80486DX processor) assembly language includes a stack
> based floating point unit which can perform addition, subtraction,
> negation, multiplication, division, remainder, square roots, integer
> truncation, fraction truncation, and scale by power of two. The
> operations also include conversion instructions which can load or
> store a value from memory in any of the following formats: Binary
> coded decimal, 32-bit integer, 64-bit integer, 32-bit floating
> point, 64-bit floating point or 80-bit floating point (upon loading,
> the value is converted to the currently floating point mode). The
> x86 also includes a number of transcendental functions including
> sine, cosine, tangent, arctangent, exponentiation with the base 2
> and logarithms to bases 2, 10, or e
> <http://www.answers.com/main/ntquery;jsessionid=aal3fk2ck8cuc?method=4&dsid=2222&dekey=E+%28mathematical+constant%29&gwp=8&curtab=2222_1&sbid=lc04b>.
> So, that's my new proposal: some functions get there own opcodes (sin,
> cos, ln, log10, etc), while others get shunted to table lookup (not
> sure what's in that list yet, but I'm sure there's lots).
For the same reason, I think these same functions should get their own
ufunc loops instead of using the default loop with function pointers.
Thanks for providing this link. It's a useful list.
More information about the Numpy-discussion mailing list | {"url":"http://mail.scipy.org/pipermail/numpy-discussion/2006-March/019124.html","timestamp":"2014-04-20T16:04:22Z","content_type":null,"content_length":"5051","record_id":"<urn:uuid:ef9182a1-d43a-439a-8c19-81500e63b58b>","cc-path":"CC-MAIN-2014-15/segments/1397609540626.47/warc/CC-MAIN-20140416005220-00049-ip-10-147-4-33.ec2.internal.warc.gz"} |
Re: Is Point inside Polygon or Block's Area?
Auto-suggest helps you quickly narrow down your search results by suggesting possible matches as you type.
Anyone come across a good method or the algebraic formula for a funtion to tell me if a point is inside a polygon or block's area?
Or if a two blocks or polygons are overlapping area?
if you can convert Polylines to MPOLYGON-objects you do have the calculation of isPointInside as a function of the object itself.
Public Overridable Function IsPointInsideMPolygon(worldPoint As Autodesk.AutoCAD.Geometry.Point3d, tolerance As Double) As Autodesk.AutoCAD.Geometry.IntegerCollection Member von
Found a formula, link listed below and produced this, appears to work, but you may want to test to ensure it suits your needs.
//Point inside a polyline came from the Solution 2 (2d) section of this website http://paulbourke.net/geometry/insidepoly/ /// <summary> /// Check if the point is within the polyline /// </summary> /
// <param name="polygon"></param> /// <param name="pt"></param> /// <returns></returns> public static bool InsidePolygon(Polyline polygon, Point3d pt) { int n = polygon.NumberOfVertices; double angle
=0; Point pt1 , pt2 ; for (int i = 0; i < n; i++) { pt1.X = polygon.GetPoint2dAt(i).X - pt.X; pt1.Y = polygon.GetPoint2dAt(i).Y - pt.Y; pt2.X = polygon.GetPoint2dAt((i+1)%n).X - pt.X; pt2.Y =
polygon.GetPoint2dAt((i+1)%n).Y - pt.Y; angle += Angle2D(pt1.X,pt1.Y,pt2.X,pt2.Y); } if (Math.Abs(angle) < Math.PI) return false; else return true; } /// <summary> /// Point structure to add
InsidePolygon function /// </summary> public struct Point { public double X, Y; }; /* */ /// <summary> /// Return the angle between two vectors on a plane /// The angle is from vector 1 to vector 2,
positive anticlockwise /// The result is between -pi -> pi /// </summary> /// <param name="x1"></param> /// <param name="y1"></param> /// <param name="x2"></param> /// <param name="y2"></param> ///
<returns></returns> public static double Angle2D(double x1, double y1, double x2, double y2) { double dtheta,theta1,theta2; theta1 = Math.Atan2(y1,x1); theta2 = Math.Atan2(y2, x2); dtheta = theta2 -
theta1; while (dtheta > Math.PI) dtheta -= (Math.PI * 2); while (dtheta < -Math.PI) dtheta += (Math.PI * 2); return(dtheta); }
This method use a Ray to get the intersection with a polyline.
You get a error-message when yo use a 64 bit Windows but there is a workaround for that problem.
Attention! Both versions do have problems you should be aware of:
a) the version that summarizes the angles does only work on polylines with no arcs in it, that are not curved and not splined.
b) the version using ray and count the intersections will have two critical situations
Important: I don't want to critism the above suggestions, I just want to inform about situations you should be prepared before start development.
Good point, my implementation is timber components which never have curves, so works well for me.
Hi Alfred, FYI Point3dCollections do not require the contents to be distinct. There are several functions in my code where I am taking the points of a polyline that is required to be a closed loop,
in order to standardize the way the polylines were drawn, I test distance from the last point to the first, and if it is not 0 then I add the first point in the collection onto the end of the
collection so that the first and last points in the collection are equal.
If your intersection example with the bad return is something you have experienced, then there is another reason for it which I am not sure of.
>> Point3dCollections do not require the contents to be distinct
Maybe, I have not tested it creating it by myself (as I'm using my own type of PointLists if I need it).
However, AutoCAD does not return 2 Intersections in the above sample (where the ray crosses two segments on the same point). And if I remember right, there are more Curve-functions also avoiding
double/same points (neighboring) in the return collection.
For details I would have to search now, sorry to have no time at the moment, next time I get an example I hope to remember to this thread!
Log into access your profile, ask and answer questions, share ideas and more. Haven't signed up yet? Register | {"url":"http://forums.autodesk.com/t5/NET/Is-Point-inside-Polygon-or-Block-s-Area/m-p/3164952","timestamp":"2014-04-16T09:55:59Z","content_type":null,"content_length":"352044","record_id":"<urn:uuid:59d0e35c-81ee-4731-8280-5825882a8c4e>","cc-path":"CC-MAIN-2014-15/segments/1397609521558.37/warc/CC-MAIN-20140416005201-00466-ip-10-147-4-33.ec2.internal.warc.gz"} |
Re: st: Grid lines on top of shaded time series graph
Notice: On March 31, it was announced that Statalist is moving from an email list to a forum. The old list will shut down at the end of May, and its replacement, statalist.org is already up and
[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]
Re: st: Grid lines on top of shaded time series graph
From Maarten Buis <maartenlbuis@gmail.com>
To statalist@hsphsun2.harvard.edu
Subject Re: st: Grid lines on top of shaded time series graph
Date Mon, 31 Oct 2011 11:18:09 +0100
2011/10/30 Jorge Eduardo Pérez Pérez:
> I have been creating time series graphs for several countries with
> recession shading, <snip> I would like the horizontal and vertical
> grid lines on the graph to be on top of the shading. Does anyone
> know how to do this?
In Stata gridlines are always in the background, which fits its logic:
they are the grid on top of which the graphs are drawn. Personally, I
would not try to draw the gridlines on top, but you can with the help
of new calls to -twoway function- to draw horizontal or vertical lines
where the grid lines are. I adapted your example so I need to add both
horizontal and one vertical grid line:
*--------------------------------- begin example
ssc install freduse, replace
freduse MPRIME, clear
gen ym = mofd(daten)
tsset ym, monthly
twoway ///
function y=20.705,range(119 130) recast(area) color(gs12) base(4.7025) || ///
function y=20.705,range(166 182) recast(area) color(gs12) base(4.7025) || ///
function y=20.705,range(240 274) recast(area) color(gs12) base(4.7025) || ///
function y= 5 ,range(119 274) lstyle(grid) || ///
function y=10 ,range(119 274) lstyle(grid) || ///
function y=15 ,range(119 274) lstyle(grid) || ///
function y=20 ,range(119 274) lstyle(grid) || ///
function y=ym(1980,11), range(4.7025 20.705) horizontal lstyle(grid) || ///
tsline MPRIME if tin(1970m1,1990m1), xlabel(,format(%tm)) lstyle(p1) ///
legend(order(5 1 "Recession")) tlabel(,grid) scheme(s2color)
*---------------------------------- end example
(For more on examples I sent to the Statalist see:
http://www.maartenbuis.nl/example_faq )
Hope this helps,
Maarten L. Buis
Institut fuer Soziologie
Universitaet Tuebingen
Wilhelmstrasse 36
72074 Tuebingen
* For searches and help try:
* http://www.stata.com/help.cgi?search
* http://www.stata.com/support/statalist/faq
* http://www.ats.ucla.edu/stat/stata/ | {"url":"http://www.stata.com/statalist/archive/2011-10/msg01500.html","timestamp":"2014-04-20T13:56:00Z","content_type":null,"content_length":"9645","record_id":"<urn:uuid:f1b14260-8f7f-4cc4-9f63-6c47dd3582b4>","cc-path":"CC-MAIN-2014-15/segments/1397609538787.31/warc/CC-MAIN-20140416005218-00061-ip-10-147-4-33.ec2.internal.warc.gz"} |
Binomial and Poisson Distribution.
October 17th 2008, 01:04 PM
Binomial and Poisson Distribution.
Hi, I understand both the poisson distribution and binomial distribution relatively well. However, the way I see it, for any question requiring the use of a poisson distribution, it makes sense
that a binomial distribution could be used. For example:
"A hockey team has a shut out at a rate of 1 of every 20 games. calculate the probability of having 2 shutouts in the next 10 games."
The reason I believe binomial applies is: the probability of success is 0.05%, the number of trials is 10, and the desired number of shutouts is 2.
October 17th 2008, 01:27 PM
Hello !
Actually, the binomial distribution can be approximated into a Poisson distribution if :
n>30 and p<0.1 and npq<10
the new $\lambda$ will be np.
Basically, I think it is easier to compute values of a Poisson distribution than a binomial distribution. | {"url":"http://mathhelpforum.com/statistics/54252-binomial-poisson-distribution-print.html","timestamp":"2014-04-18T16:32:28Z","content_type":null,"content_length":"4292","record_id":"<urn:uuid:8289e540-f025-4ecf-a5b6-97e4ff48f2fd>","cc-path":"CC-MAIN-2014-15/segments/1397609533957.14/warc/CC-MAIN-20140416005213-00615-ip-10-147-4-33.ec2.internal.warc.gz"} |
Limits cont (x-2/x-3) = 1 + 1/(x-3)
Thank you to those who replied to my previous post(I had a problem repling on that post). What I was after was a formal definition
as in
I have the algebraic definition of division as a/b = a * 1/b. Division being defined as multiplication by the reciprocal.
I know that when I get to intergration, I will have to resolve the following. I wish to identify the full dynamic Zeta function as being the product of the Geometric Zeta and the Diffractive. The
geometric should be obtainable from the elliptic.In as much as I have a outside double helix(electromagnetic) inside a spiral(low frequency amplification). The spiral if taken to be Ulam, has
vertical and horizontal lines as being Non Prime.I know there is a correlation between Energy levels, primes and element nuclei with the Zeta function. Higher elements have increasing diffraction,
the distribution of the primes also increases. So if I take say Platinium I should have two different rates of change. Or intervals in the case of Intergration. As this process includes, molecular
dissasociation there are Partial charges, ie the sum of the charges is greater than whole. So, simplistically, I need limits like (x-2/x-3) = 1 + 1/(x-3) as the prime correlations are products. Of
course, I could take Eulers spiral in which case, I would have Cubics intersecting and something like the squeeze theorem Method of images(electromagnetic) and Spiral (Euler Triconi). and the limit
as above is >=1, I still have to identify the diffractive, which seems to be Harmonic, and I think I will run into Ramfied Primes and cubic reciprocy. I would still have the same requirement of the
division as in limits.
My fluency to deal creativly with this advanced maths require revising. So I have gone back to basics to identify what should be a simple process. It would be great to identify this type of division
as I will need to set limits with this process when I start Intergrating | {"url":"http://www.physicsforums.com/showthread.php?p=3547561","timestamp":"2014-04-18T03:05:20Z","content_type":null,"content_length":"20695","record_id":"<urn:uuid:b5fd741f-1e34-4915-8ebb-a06da6ad44f7>","cc-path":"CC-MAIN-2014-15/segments/1397609532480.36/warc/CC-MAIN-20140416005212-00043-ip-10-147-4-33.ec2.internal.warc.gz"} |
Réunion d'été 2002 de la SMC
Multiple zeta values are values of multiple polylogarithms at positive integer arguments. They can also be viewed as a multiply nested sum extension of the Riemann zeta function. As noted by
Pierre Cartier in his recent Bull. Amer. Math. Soc. article commemorating the 40th anniversary of the IHES, classifying the relations amongst multiple zeta values connects with some of the
deepest problems in transcendental number theory. It is well-known that multiple zeta values satisfy certain ``shuffle'' relations. We describe here a new technique for proving certain shuffle
convolution formulae. Applications include a short proof of a former conjecture of Zagier and some new results for multiple zeta values as well.
We are interested in studying the norm of Littlewood polynomials, i.e., polynomials with coefficients +1 or -1. The problem is to find polynomials having small L[4] norms over the unit circle.
The best known polynomials are Turyn polynomials whose coefficients are the shifted legendre symbols. Some old and new results about this problem will be discussed in this talk, especially for
polynomials constructed by cyclic difference sets (Turyn polynomial is one of the examples).
Let E be an elliptic curve defined over Q and without complex multiplication. We consider the problem of determining an effective asymptotic formula for the number of primes p < x of good
reduction for E and such that the group of points of E modulo p has square-free order. This problem is related to the one regarding the cyclicity of E modulo p, but more challenging. The
situation of an elliptic curve with complex multiplication can also be considered, however it is very different from the non-complex multiplication case and so has to be discussed on a different
It has been observed in a number of cases that the number of points on certain hyper elliptic curves over a finite field may be recovered as the values of depth zero representations of p-adic
groups, but the nature of this relationship remains a mystery. In this talk I will describe a new geometric approach to these representations which promises to shed light on this and other
related problems.
Suppose (u[n])[n ³ 1] is a bounded sequence of positive integers and a = [0,u[1],u[2],...,u[n]¼] is the corresponding continued fraction with convergents ([(p[n])/(q[n])])[n ³ 0]. If the infinite
word u = u[1],u[2],... has the property that any finite subword of u occurs with a frequency, then we prove that lim[n®¥][1/(n)]lnq[n] exists. An application of this result is given.
Let p[1](n) < p[2](n) < ¼ be the distinct prime factors of an integer n ³ 2. Given a positive integer k, we investigate the distribution function of the arithmetic function n® p[k](n). As an
application of our result, we prove the estimate loglogp^*[k] = k-c + O(1/Ök), where p^*[k] stands for the median value of the k-th prime factor of an integer and where c=[1/3] +g-å[n ³ 2] å[p]
[1/(np^n )] » 0.59483. This is joint work with Professor Gérald Tenenbaum.
On considère trois extensions ab\' eliennes réelles finies de Q, k[1], k[2] et k[3] de conducteurs respectifs p[1]^e[1], p[2]^e[2] et p[3]^e[3], avec p[1], p[2] et p[3] des nombres premiers
distinsts deux à deux et e[1], e[2] et e[3] des entiers naturels non nuls. L'objet de cette communication est de déterminer une base du groupe des unités cyclotomiques du composé k=k[1]k[2]k[3].
Ceci est un travail conjoint avec Hugo Chapdelaine.
For a positive integer k, let r[k](n) denote the number of representations of the positive integer n as the sum of k squares. In 1987, using the theory of modular functions, Ewell proved a
formula for r[16](n) in terms of real-divisor functions and established a result for r[12](n). In 1996, Milne obtained formulas for r[k](n) where k is any integer of the form 4m^2 or 4m(m+1).
Milne combined methods from the theory of elliptic functions, continued fractions, hypergeometric functions, Schur functions, and Hankel and Tur án determinants. Using a recent elementary
arithmetic identity of Huard, Ou, Spearman and Williams, we give elementary proofs of Ewell s formulae and of Milne s formula for k=16. This is joint work with K. S. Williams.
We classify orders over surfaces up to birational and Morita equivalence. We use the geometric ramification data of a maximal order on a surface to define a class of terminal orders. We compute
all possible étale local structures of terminal orders. We use the ideas of Mori's minimal model program for log surfaces to show that terminal orders with non-negative Kodaira dimension have
unique minimal models up to Morita equivalence. We describe the possible centres and ramification divisors of the minimal models of orders of negative Kodaira dimension.
Let H(n) denote the (weighted) number of positive definite binary quadratic forms of discriminant -n. It is well-known that H(n) can be expressed in terms of the class number h(n) of the field Q
(Ö[(-n)]). For an integer D ³ 1, let
æ ö
H[D](n) = å H è 4n-x^2D ø ,
x Î S[D](n)
where S[D](n) = {x Î Z : x^2 £ 4n, x^2 º 4n mod D. In 1857 Kroecker found a closed expression for H[1](n), and this was generalized by Gierster(1880) and Hurwitz(1883) to H[p^2](n), where p is a
prime. In this lecture I will explain how to sharpen the Gierster/Hurwitz results and also how to generalize them to arbitrary D = N^2.
Let p be a prime ¹ 2 and let q[1],¼,q[n] be primes º 1 mod p. Let S={q[1],¼,q[n],p,¥} and let G[S] be the galois group of the maximal p-extension of Q which is unramified outside of S. Under
certain congruence conditions on the the finite primes in S, we give an explicit description in terms of generators and relations of the Lie algebra associated to the lower central series and the
p-central series of the group G[S].
We will discuss generalizations of the classical Hurwitz zeta functions, obtain analytic continuations for them and show that certain special values (namely at negative integers) are given by
generalized Bernoulli polynomials. (This is joint work with Kaneenika Sinha.)
This talk will consider the distribution of nontrivial zeros close to the real axis of the family of all Dedekind Zeta functions of quadratic extensions of a given imaginary quadratic number
field. The main focus will the case where the ground field has class number one.
In their 1968 seminal paper, Davenport and Schmidt studied the approximation of a given real number by algebraic integers of a fixed degree d. They did so by resorting to the dual problem of
approximating the d-1 consecutive powers of this number by rational numbers with the same denominator. In this talk, we show that, for d=3, their exponent of approximation for the dual problem is
optimal, against natural heuristics, and we discuss consequences on the original problem.
For an even Dirichlet character y, we obtain a formula for L(1,y) in terms of a sum of Dirichlet L-series evaluated at s=2 and s=3 and a rapidly convergent numerical series involving the central
binomial coefficients. We then derive a class number formula for real quadratic number fields by taking L(s,y) to be the quadratic L-series associated with these fields.
Let V denote the set of positive integers which are k-th powers of a positive integer for some integer k larger than one. We shall discuss the problem of estimating the size of a set A of
positive integers with the property that ab+1 is in V whenever a and b are distinct elements of A.
Let D be an integrally closed, characteristic zero domain, K its field of fractions, m ³ 2 an integer and P(x)=å[k=0]^m-1c[k]x^k = Õ[i=0]^m-1(x-q[i]) Î D[x] a cyclic polynomial. Let t be a
generator of Gal(K(q[0])/K) and suppose the q[i] are labeled so that t(q[i])=q[i+1] (indices mod m). Suppose that the discriminant discr[K(q[0])/K] (q[0],q[1],...,q[m-1]) is nonzero. For 0 £ i, j
£ m-1, define the elements a[i,j] Î K by q[0]q[i] = å[j=0]^m-1 a[i,j]q[j]. Let A=[a[i,j]][0 £ i,j < m]. We call A the multiplication matrix of the q[i]. We have that P(x) is the characteristic
polynomial of A. We study the relations between P(x) and A. We show how to factor P(x) in the field K[A] and how to construct A in terms of the coefficients c[i]. We give methods to construct
matrices A, with entries in K, such that the characteristic polynomial of A belongs to D[x], is cyclic, and has A as the multiplication matrix of its roots. One of these methods derives from a
natural composition of multiplication matrices. The other method gives matrices A, that are generalizations of matrices of cyclotomic numbers of order m, whose characteristic polynomials have
roots that are generalizations of Gaussian periods of degree m.
We will discuss Baker's method for solving certain related cubic families of Thue equations. First we will give details for solving a first equation and then use changes of variables to obtain
the solutions to the other equations.
In recent work, Corvaja and Zannier have used the subspace theorem to prove an upper bound for gcd(a^k-1,b^k-1) for a fixed pair of positive integers a,b. Also, it has recently been conjectured
by Rudnick that this gcd is 1 infinitely often provided that a and b are multiplicatively independent. In joint work with Florian Luca, we use the methods of Corvaja and Zannier to prove that for
fixed a,b, the equation (a^k-1)(b^k-1)=z^n has finitely many integer solutions k,x and n > 1. We further describe a computational method to determine all integer solutions (k,x) to the equation (
a^k-1)(b^k-1)=x^2, and solve this equation for all 1 < a < b < 100 provided that (a-1)(b-1) is not a square. | {"url":"http://cms.math.ca/Events/summer02/abs/nt-f.html","timestamp":"2014-04-20T03:15:21Z","content_type":null,"content_length":"27593","record_id":"<urn:uuid:5c76ac45-fd71-408a-a04b-c8e1bcd20711>","cc-path":"CC-MAIN-2014-15/segments/1398223201753.19/warc/CC-MAIN-20140423032001-00428-ip-10-147-4-33.ec2.internal.warc.gz"} |
FIELDS INSTITUTE - Ontario Combinatorics Workshop
Andrea Burgess (Ryerson University)
Near-factorizations of the complete graph
A $w$-near $k$-factor of a graph $G$ on $n$ vertices is a spanning subgraph of $G$ with $w$ vertices of degree 0 and $n-w$ vertices of degree $k$. In this talk, we introduce the concept of a
$w$-near $k$-factorization of a graph $G$, which is a decomposition of $G$ into $w$-near $k$-factors. Thus, for example, a $k$-factorization is equivalent to a 0-near $k$-factorization, and a
near 1-factorization is equivalent to a 1-near 1-factorization. We focus on $w$-near 2-factorizations of $K_n$ and $K_n-I$; in the case that the partial 2-factors are required to be pairwise
isomorphic, this may be viewed as a generalization of the Oberwolfach problem. We discuss some constructions of $w$-near 2-factorizations in which all cycles in the near-factors have the same
length. This is joint work with Peter Danziger.
Xiaoxia (Fiona) Fan, University of Waterloo
Quantum State Transfer on Double Star Graphs
Given a graph X with adjacency matrix A, we define the transition
matrix U(t) =exp(iAt). This function determines what is called a continuous quantum walk.
We say there is perfect state transfer if the uv-entry of U(t) has norm 1.
Similarly, we say there is pretty good state transfer if the uv-entry gets arbitrarly close to 1.
In this talk, we characterize pretty good state transfer and strong copectral vertices. In particular, we show that perfect state transfer does not occur on double star graphs.
Finally, we give a sufficient condition for pretty good state transfer on double star graphs.
This is joint work with Chris Godsil.
Jan Foniok (Queen's University and Swiss National Science Foundation Research Fellow)
Homomorphism Dualities
I will talk about homomorphisms of digraphs, or more generally, relational structures. They have very natural uses in category theory, order theory, constraint satisfaction (artificial
intelligence), etc. A homomorphism duality is a situation where the nonexistence of a homomorphism from some F is equivalent to the existence of a homomorphism to some D (vaguely said; I'll make
it precise in the talk). I will show how (surprisingly) they correspond (1) to finite maximal antichains in some partial order, (2) to first-order definable constraint satisfaction problems. If
time permits, I will also show an application of adjoint functors.
Nevena Francetic, University of Toronto
Covering Arrays with Row Limit: bounds and constructions
Covering arrays with row limit, $CARL$s for short, are a natural generalization of covering arrays which have a new parameter row limit, $w$, representing the number of non-empty cells in a row.
When $w$ equals the number of columns $k$, then a $CARL$ is a covering array. We present some upper and lower bounds on the size of $CARL$s which have the
row limit $w(k)$ as a function of $k$. We show that the nature of the problem splits into at least two subcases: $w(k)={\rm o}(k)$ and $w(k)={\rm \Theta}(k)$, for which
the asymptotic growth of $CARL$s differs. We also discuss two construction methods of
$CARL$s which we apply to obtain a number of families of objects for which the size is
within the bounds.
Zoltán Füredi (University of Illinois at Urbana-Champaign)
Huge Superimposed codes (.pdf of abstract)
There are many instances in Coding Theory when codewords must be restored from partial information, like defected data (error correcting codes), or some superposition of the strings. These lead
to superimposed codes, a close relative of group testing problems. There are lots of versions and related problems, like Sidon sets, sum-free sets, union-free families, locally thin families,
cover-free codes and families, etc. We discuss two cases cancellative and union-free codes.
A family of sets $\mathcal F$ (and the corresponding code of 0-1 vectors) is called {\bf union-free} if $A\cup B\neq C\cup D$ and $A,B,C,D\in \mathcal F$ imply $\{ A,B\}=\{ C, D \}$.$\mathcal F$
is called $t$-{\bf cancellative} if for all distict $t+2$ members $A_1, \dots, A_t$ and $B,C\in \mathcal F$$$A_1\cup\dots \cup A_t\cup B \neq A_1\cup \dots A_t \cup C.$$Let $c_t(n)$ be the size
of the largest $t$-cancellative code on $n$ elements. We significantly improve the previous upper bounds of K\"orner and Sinaimeri, e.g., we show $c_2(n)\leq 2^{0.322n}$ (for $n> n_0$).
Majid Karimi, Brock University
Graph Powers and Graph Roots
Graph $G$ is the square ($k^{\mbox{th}}$ power) of graph $H$, if two vertices $x, y$ have an edge in $G$ if and only if $x, y$ are of distance at most two ($k$) in $H$. Given $H$ it is easy to
compute its square $H^2$ . Determining if a given graph $G$ is the square of some graph is NP-complete in general.
{\em Root} and {\em root finding} are concepts familiar to most branches of mathematics. Graph power is a basic operation with a number of results about its properties in the literature.
The main motivation for studying the complexity of checking if a given graph is a certain power (square specifically) of another graph comes from distributed computing. The $r^{\mbox{th}}$ power
of graph $H$ represents the possible flow of information in $r$ round of communication in a distributed network of processors organized according to $G$.
We are interested in the characterization and recognition problems of square root graphs. This recognition problem has an almost complete di- chotomy theorem in terms of the girth of square root
graph. Indeed when girth of graph is at most 4 the recognition problem is NP-Complete and when girth is at least 6 there are algorithms to find the unique (up to iso-
morphism) square root. However this problem is still open in square root of graphs with girth five.
We present partial structures that by excluding them, the recognition prob- lem has a polynomial-time answer. We also present graphs with exponential number of non-isomorphic square roots.
Avery Miller (University of Toronto)
Thick Cover-Free Families with Applications to Wireless Radio Networks
An r-cover-free family is a family of sets such that no set in the family is contained in the union of at most r other sets in the family. We introduce a new generalization of such families that
takes into account how many times a set is covered. Namely, an r-cover-free family of thickness b is a family of sets such that no set in the family is contained b times in the multiset union of
at most r other sets in the family. Extending a result by Füredi (1996), we are able to prove an upper bound on the size of these families. Finally, we show how this upper bound leads to new
lower bounds for neighbourhood discovery algorithms in wireless radio networks.
Natalie Mullin, University of Waterloo
Uniform Mixing and Association Schemes
Continuous-time quantum walks on graphs are quantum analogues of classical random walks on graphs. In recent years quantum walks have been studied for their potential applications in quantum
algorithms. We say that a graph admits uniform mixing if the probability distribution visited by the continuous-time quantum walk is uniform at a particular time. In this talk we use the
framework of association schemes to determine whether certain graphs admit uniform mixing
David Roberson, University of Waterloo
Cores of Vertex Transitive Graphs
A graph homomorphism is an adjacency preserving map between the vertex sets of two graphs. An endomorphism is a homomorphism from a graph to itself. The core of a graph is its smallest
endomorphic image. If $Y$ is the core of a vertex transitive graph $X$, then any homomorphism from $X$ to $Y$ maps the same number of vertices to every vertex of $Y$ and therefore $|V(Y)|$
divides $V(X)$. Using this result we will describe the structure of vertex transitive graphs which have cores of half their size. We will see that this description does not generalize to
vertex transitive graphs with cores of less than half their size, but that it can be partially extended to Normal Cayley graphs
Mateja Sajna (University of Ottawa)
Cycle Systems: A Neverending Fascination
This talk begins with an account of the fascinating history of combinatorial designs and cycle systems. We then introduce some of the basic problems involving cycle systems: cycle
decomposition of complete (and nearly complete) graphs, and the Oberwolfach problem, both in its directed and undirected variant. We briefly sketch some of the proofs of the solved problems,
and give an update on the status of the open ones. Finally, we discuss the author s progress (joint work with Andrea Burgess and Patrick Niesink) on the directed Oberwolfach problem with
constant cycle lengths.
Yoshio Sano (National Institute of Informatics, Japan) (abstract.pdf)
Fat Hoffman graphs with smallest eigenvalue at least $-1-\tau$
In the field of Spectral Graph Theory, one of the important research problem is to characterize graphs with bounded smallest eigenvalue. P. J. Cameron, J. M. Goethals, J. J. Seidel, and E. E.
Shult (1976) characterized graphs whose adjacency matrices have smallest eigenvalue at least $-2$ by using root systems. Their results revealed that graphs with smallest eigenvalue at least
$-2$ are generalized line graphs, except a finite number of graphs represented by the root system $E_8$. A. J. Hoffman (1977) studied graphs whose adjacency matrices have smallest eigenvalue
at least $-1-\sqrt{2}$ by using a technique of adding cliques to graphs. R. Woo and A. Neumaier (1995) formulated Hoffman's idea
by introducing the notion of Hoffman graphs and generalizations of line graphs.
In this talk, we show that all fat Hoffman graphs with smallest eigenvalue at least $-1-\tau$, where $\tau$ is the golden ratio, can be described by a finite set of fat $(-1-\tau)
$-irreducible Hoffman graphs. In the terminology of Woo and Neumaier, we mean that every fat Hoffman graph with smallest eigenvalue at least $-1-\tau$ is an $\mathcal{H}$-line graph, where $\
mathcal{H}$ is the set of isomorphism classes of maximal fat $(-1-\tau)$-irreducible Hoffman graphs. It turns out that there are $37$ fat $(-1-\tau)$-irreducible Hoffman graphs, up to
(This is joint work with Akihiro Munemasa and Tetsuji Taniguchi.)
Jihyeon Jessie Yang (University of Toronto)
Parameter space of curves constructed from a polygon
Given a lattice polygon, we construct a parameter space of algebraic curves. Some attributes of this parameter space are purely combinatorial, such as dimension and degree. This idea can be
generalized to many directions. For example, we can consider a subdivision of the polygon into subpolygons which appear naturally in tropical geometry and is related to a very classical
object in algebraic geometry called Severi variety.
Also, instead of a polygon we can consider higher dimensional polytope and construct a parameter space of hypersurfaces. I will present the combinatorial aspect of this idea. | {"url":"http://www.fields.utoronto.ca/programs/scientific/11-12/OCW/abstracts.html","timestamp":"2014-04-18T11:12:12Z","content_type":null,"content_length":"26163","record_id":"<urn:uuid:ae4f609f-0aac-4df2-9ca5-b520d72a4afe>","cc-path":"CC-MAIN-2014-15/segments/1397609533308.11/warc/CC-MAIN-20140416005213-00239-ip-10-147-4-33.ec2.internal.warc.gz"} |
Mathematics Problems And Solutions
CATEGORIES TOP DOWNLOADS NEW DOWNLOADS Related Downloads Popular Topics
Mathematics Problems And Solutions
Tools for Solving Mathematics problems. Tools for Solving Mathematics problems. Mathematics Tools is a tools that help people in solving Mathematical problems such as: Solving quadratic equation and
cubic equationSolving System of equations (2 or 3 unknowns)Working in the Base Number...
Magic Problems Creator for Mathematics has a powerful Wizard to help you Create your own custom problems collections. Magic Problems Creator for Mathematics has a powerful Wizard to help you Create
your own custom problems collections.ALGEBRA: - Matrices, determinants - Matricial equations - Study of system of equations- Easy and fast to use.- User's manual in...
OS: Windows
1.9 MB |
Shareware |
US$45 |
Category: Mathematics
Visual Mathematics is a highly interactive visualization software (containing -at least- 67 modules) addressed to High school, College and University students. This is a very powerful tool that
helps to learn and solve problems by the hundreds in a very short time. Included areas: Arithmetic, Algebra, Geometry, Trigonometry, Analytic Geometry and miscellaneous.Visual Mathematics, a member
of the Virtual Dynamics Mathematics Virtual Laboratory,...
OS: Windows
1.2 MB |
Freeware |
Category: Mathematics
Numerical Mathematics is the branch of mathematics that develops, analyzes, and applies methods to compute with finite-precision numbers. Numerical Mathematics is the branch of mathematics that
develops, analyzes, and applies methods to compute with finite-precision numbers. Numerical mathematics is a vast field whose importance cannot be over-emphasized. The solution of real-life...
OS: Windows
2.5 MB |
Shareware |
US$35 |
Category: Mathematics
Interpolation and Regression are fundamental and important calculations in mathematics. Interpolation and Regression are fundamental and important calculations in mathematics. Mr. Newton and Mr.
Gauss were engaged in-depth with numerical solutions for these problems. Today, there are improved algorithms, that can solve such tasks....
OS: Windows
10.3 MB |
Demo |
US$68 |
Category: Mathematics
An game that teaches mathematics whilst being fun and rewarding. The interactive content of the computer game teaches the student to really see how mathematic skills can help to solve daily
problems and how it helps to play along in the game. The game mix the classic platform genre with interactive problems and practice sessions. The software contains simulations of a calculator,
sketch pad, graphs and adds the ability to construct objects.
OS: Windows
Software Terms: Education, Edutainment Game, Game, High School, Junior, Mathematics
20.4 MB |
Demo |
US$25 |
Category: Mathematics
Mathtopper brings you a first of its kind Maths Learning Course that meets all your Mathematics requirements from the comfort of your home. With Detailed Conceptual lectures of each chapter in the
curriculum, NCERT Solutions to each and every question in the text book, self-evaluatory practice tests with detailed solutions, games and more of our unique features ensure that you learn while
having fun! Mathtopper is a unique Computer based...
OS: Windows
Software Terms: Arithmetic, Cbse Maths, Geometry, Linear Equationsm Mensuration, Math, Math Coaching, Mathematics, Maths Online, Natural Numbers, Polynomial
30.7 MB |
Demo |
US$25 |
Category: Mathematics
Mathtopper brings you a first of its kind Maths Learning Course that meets all your Mathematics requirements from the comfort of your home. With Detailed Conceptual lectures of each chapter in the
curriculum, NCERT Solutions to each and every question in the text book, self-evaluatory practice tests with detailed solutions, games and more of our unique features ensure that you learn while
having fun! Mathtopper is a unique Computer based...
OS: Windows
Software Terms: Algebra, Arithmetic, Cbse Maths, Geometry, Linear Equationsm Mensuration, Math, Math Coaching, Mathematics, Maths Online, Natural Numbers
26.3 MB |
Demo |
US$25 |
Category: Mathematics
Mathtopper brings you a first of its kind Maths Learning Course that meets all your Mathematics requirements from the comfort of your home. With Detailed Conceptual lectures of each chapter in the
curriculum, NCERT Solutions to each and every question in the text book, self-evaluatory practice tests with detailed solutions, games and more of our unique features ensure that you learn while
having fun! Mathtopper is a unique Computer based...
OS: Windows
Software Terms: Algebra, Arithmetic, Cbse Maths, Geometry, Linear Equationsm Mensuration, Math, Math Coaching, Mathematics, Maths Online, Natural Numbers
23.7 MB |
Demo |
US$25 |
Category: Mathematics
Mathtopper brings you a first of its kind Maths Learning Course that meets all your Mathematics requirements from the comfort of your home. With Detailed Conceptual lectures of each chapter in the
curriculum, NCERT Solutions to each and every question in the text book, self-evaluatory practice tests with detailed solutions, games and more of our unique features ensure that you learn while
having fun! Mathtopper is a unique Computer based...
OS: Windows
Software Terms: Algebra, Arithmetic, Cbse Maths, Geometry, Linear Equationsm Mensuration, Math, Math Coaching, Mathematics, Maths Online, Natural Numbers
1.7 MB |
Shareware |
Category: Mathematics
System of Nonlinear Equations numerically solves systems of simultaneous nonlinear equations. System of Nonlinear Equations numerically solves systems of simultaneous nonlinear equations. It can
fully explore defined intervals to search for multiple solutions or quickly find solutions starting with random seeds. You may predefine constants...
OS: Windows
Software Terms: 3d, Advanced Mathematics, Approximation, Calculus, Calculus Education, College, Derivatives, Differential Equations, Downloads, Education
A simple mathematics program for students. A simple mathematics program for students. FMFS stands for FMFS may free students, it is a small collection of programs related to mathematics. It consists
of a 2D graph plotter, a 3D graph plotter, a evaluator for basic mathematics expressions at...
Implementation done in Mathematics for a quadratic sieve. Implementation done in Mathematics for a quadratic sieve. A very basic Quadratic Sieve implementation done for a BSc in Mathematics, using
MPIR. Experienced programmers may groan when seeing the code - however it should give a simple enough...
1.7 MB |
Shareware |
Category: Business
Performs linear regression using the Least Squares method. Performs linear regression using the Least Squares method. Determines the regression coefficients, the generalized correlation coefficient
and the standard error of estimate. Does multivariate regression. Displays 2D and 3D plots.
OS: Windows
Software Terms: 3d, Advanced Mathematics, Approximation, Calculus, Calculus Education, College, Derivatives, Differential Equations, Downloads, Education
1.7 MB |
Shareware |
Category: Business
Approximates tabulated functions in 1 to 4 independent variables by finite power and/or trigonometric series. Approximates tabulated functions in 1 to 4 independent variables by finite power and/or
trigonometric series. The program fits the function exactly at the grid points.
OS: Windows
Software Terms: 3d, Advanced Mathematics, Approximation, Calculus, Calculus Education, College, Derivatives, Differential Equations, Downloads, Education | {"url":"http://www.bluechillies.com/software/mathematics-problems-and-solutions.html","timestamp":"2014-04-21T15:11:07Z","content_type":null,"content_length":"62067","record_id":"<urn:uuid:b9f4c145-5bc0-4195-b9b7-7d44a0e6a658>","cc-path":"CC-MAIN-2014-15/segments/1397609540626.47/warc/CC-MAIN-20140416005220-00614-ip-10-147-4-33.ec2.internal.warc.gz"} |
Experiments with a randomized algorithm for a frequency assignement problem.
Janez Žerovnik
WSEAS Trans. Math. Volume 3, Number 4, , 2004.
The problems of assigning frequencies to transmitters can be naturally modelled by generalizations of graph coloring problems.We start with a randomized graph coloring algorithm of Petford and Welsh
and propose a randomized algorithm for minimizing the number of constraints violated when a set of frequencies available is fixed. Experiments on instances of various types relevant to mobile
communication networks are reported.
EPrint Type: Article
Project Keyword: Project Keyword UNSPECIFIED
Subjects: Theory & Algorithms
ID Code: 688
Deposited By: Boris Horvat
Deposited On: 30 December 2004 | {"url":"http://eprints.pascal-network.org/archive/00000688/","timestamp":"2014-04-19T22:11:46Z","content_type":null,"content_length":"5442","record_id":"<urn:uuid:2544914b-db38-4165-9788-44f3ea5cd2c9>","cc-path":"CC-MAIN-2014-15/segments/1398223206672.15/warc/CC-MAIN-20140423032006-00588-ip-10-147-4-33.ec2.internal.warc.gz"} |
Comments on Paul's Pontifications: Anatomy of a new monadanonymous: I've had a look at the pages you refere...As your 2nd exercise for the reader indicates, a M...Could do. I was following in the footsteps of the...Shouldn't your runMonteCarlo function return the g...
tag:blogger.com,1999:blog-5975524006824862804.post5727721235329443774..comments2014-04-18T09:51:35.628-07:00Paul Johnsonhttp://www.blogger.com/profile/
07353083601285449293noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-5975524006824862804.post-88405417413040558142007-08-19T08:54:00.000-07:002007-08-19T08:54:00.000-07:00anonymous: I've had a
look at the pages you referenced. But I'm not that much of a statistician.<BR/><BR/>It sounds like the MonteCarlo monad should be renamed the Markov monad. Am I right?<BR/><BR/>A non-uniform
selection of next states could be done, but it would require a different monad. The type would be something like:<BR/><BR/>newtype Markov a = Markov (StdGen -> (StdGen, [(Int, a)])<BR/><BR/>The
integer components in the returned values would be the relative probabilities of each value. The original monad is then the special case in which all these values are the same.<BR/><BR/>Would this do
the job?Paul Johnsonhttp://www.blogger.com/profile/
07353083601285449293noreply@blogger.comtag:blogger.com,1999:blog-5975524006824862804.post-56556419277866139012007-08-19T08:23:00.000-07:002007-08-19T08:23:00.000-07:00As your 2nd exercise for the
reader indicates, a Monte Carlo monad would be interested in integrating by a large number of random samples. What you appear to have here is a Monad that would help with building uniformly
distributed Markov chain simulations. Monte Carlo integration is often used in combination with a Markov chain to calculate the probabilities of the possible resulting states.<BR/><BR/>See:<BR/><BR/>
http://en.wikipedia.org/wiki/Markov_chain<BR/>http://en.wikipedia.org/wiki/Markov_chain_Monte_Carlo<BR/><BR/>A possible improvement to the presented Monad would be to allow for non-uniformly
distributed selection of the next state at each
step.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-5975524006824862804.post-75469732386873112722007-08-19T07:48:00.000-07:002007-08-19T07:48:00.000-07:00Could do. I was following in the
footsteps of the QuickCheck "Gen" monad, which doesn't.<BR/><BR/>The best thing would probably be to do as you suggest, but then have an "evalMonteCarlo" which throws away the state.<BR/><BR/>I did
wonder about genericising the whole thing by RandomGen, but decided not to bother.Paul Johnsonhttp://www.blogger.com/profile/
07353083601285449293noreply@blogger.comtag:blogger.com,1999:blog-5975524006824862804.post-7105399270648793342007-08-19T06:24:00.000-07:002007-08-19T06:24:00.000-07:00Shouldn't your runMonteCarlo
function return the generator along with the result, so that it can be threaded with other random functions? I.e.:<BR/><BR/>runMonteCarlo :: MonteCarlo a -> StdGen -> (StdGen, Maybe a)<BR/><BR/><BR/>
Or perhaps:<BR/><BR/>runMonteCarlo :: RandomGen g => MonteCarlo a -> g -> (g, Maybe a)Neil Bartletthttp://www.blogger.com/profile/08588098030811273044noreply@blogger.com | {"url":"http://paulspontifications.blogspot.com/feeds/5727721235329443774/comments/default","timestamp":"2014-04-21T04:58:22Z","content_type":null,"content_length":"10228","record_id":"<urn:uuid:f966e25a-0f31-4581-a730-176c76bcea50>","cc-path":"CC-MAIN-2014-15/segments/1397609539493.17/warc/CC-MAIN-20140416005219-00591-ip-10-147-4-33.ec2.internal.warc.gz"} |
[Numpy-discussion] masked ufuncs in C: on github
Charles R Harris charlesr.harris@gmail....
Fri May 15 22:06:31 CDT 2009
On Fri, May 15, 2009 at 7:48 PM, Eric Firing <efiring@hawaii.edu> wrote:
> http://www.mail-archive.com/numpy-discussion@scipy.org/msg17595.html
> Prompted by the thread above, I decided to see what it would take to
> implement ufuncs with masking in C. I described the result here:
> http://www.mail-archive.com/numpy-discussion@scipy.org/msg17698.html
> Now I am starting a new thread. The present state of the work is now in
> github: http://github.com/efiring/numpy-work/tree/cfastma
> I don't want to do any more until I have gotten some feedback from core
> developers. (And I would be delighted if someone wants to help with
> this, or take it over.)
Here the if ... continue needs to follow the declaration:
if (*mp1) continue;
float in1 = *(float *)ip1;
float in2 = *(float *)ip2;
*(float *)op1 = f(in1, in2);
I think this would be better as
if (!(*mp1)) {
float in1 = *(float *)ip1;
float in2 = *(float *)ip2;
*(float *)op1 = f(in1, in2);
But since this is actually a ternary function, you could define new
functions, something like
double npy_add_m(double a, double b, double mask)
if (!mask) {
return a + b;
else {
return a;
And use the currently existing loops. Well, you would have to add one for
ternary functions.
Question, what about reduce? I don't think it is defined defined for ternary
functions. Apart from reduce, why not just add, you already have the mask to
tell you which results are invalid.
-------------- next part --------------
An HTML attachment was scrubbed...
URL: http://mail.scipy.org/pipermail/numpy-discussion/attachments/20090515/64250623/attachment.html
More information about the Numpy-discussion mailing list | {"url":"http://mail.scipy.org/pipermail/numpy-discussion/2009-May/042534.html","timestamp":"2014-04-19T13:00:44Z","content_type":null,"content_length":"4880","record_id":"<urn:uuid:0ffa4d01-ba47-427a-b1d7-346e3088a157>","cc-path":"CC-MAIN-2014-15/segments/1397609537271.8/warc/CC-MAIN-20140416005217-00409-ip-10-147-4-33.ec2.internal.warc.gz"} |
Bonney Lake Precalculus Tutor
Find a Bonney Lake Precalculus Tutor
...I am also the administrator and a volunteer tutor for a tutoring group in Buckley. If you got high C's or solid B's in math and now you're mystified by some of the new stuff in calculus and
precaclulus, or if you're baffled by how much algebra and geometry you forgot during the summer or the yea...
11 Subjects: including precalculus, calculus, statistics, geometry
...From learning shapes, colors, letters and numbers to learning simple addition and subtraction, I have some experience with montessori methods using manipulatives and other objects to help teach
the younger elementary school age all that they need to build on in the upper elementary ages. I also ...
46 Subjects: including precalculus, English, reading, algebra 1
...My primary programming language is currently Java. Regardless of the subject, I would say I am effective at recognizing patterns. I love sharing any shortcuts or tips that I discover.I have
taken 2 quarters of Discrete Structures (Mathematics) at University of Washington, Tacoma.
16 Subjects: including precalculus, chemistry, calculus, algebra 2
...However, looking back, the lessons taught in class carried over into the real world and most of the problems that looked overly complex had very simple solutions. American Sign Language is the
language of the Deaf culture. Some may think it silly when they see people move their fingers about rapidly, but this is hardly the case.
50 Subjects: including precalculus, reading, chemistry, physics
...I have over four years of experience as a tutor, working with students from the elementary through the college level. When I work with students, I am aiming for more than just good test scores
- I will build confidence so that my students know that they know the material. Math is my passion, not just what I majored in.
8 Subjects: including precalculus, calculus, geometry, algebra 1 | {"url":"http://www.purplemath.com/bonney_lake_precalculus_tutors.php","timestamp":"2014-04-19T02:31:37Z","content_type":null,"content_length":"24207","record_id":"<urn:uuid:5a16db8a-365a-42c1-8dd9-2fafab7fc389>","cc-path":"CC-MAIN-2014-15/segments/1397609535745.0/warc/CC-MAIN-20140416005215-00307-ip-10-147-4-33.ec2.internal.warc.gz"} |
Superior, CO Algebra 1 Tutor
Find a Superior, CO Algebra 1 Tutor
...Through this exposure to biology and to Genetics, I am a qualified tutor on this subject. I have a bachelor's degree in Dietetics from UNC. Since then have been tutoring nutrition for the last
2 years.
7 Subjects: including algebra 1, chemistry, physics, biology
...My research requires me to frequently break down complex concepts into layman's terms in order to train new lab members, and medical students completing fellowships. I love teaching and tutor
in a way that pin-points the root cause. If your child is reading at a level a few grades behind, we will start from the level and slowly work up to their expected level.
13 Subjects: including algebra 1, reading, English, grammar
...I played for 6 years in school. I was first chair most of those years. I taught my daughter how to play the flute and to read music.
49 Subjects: including algebra 1, reading, English, biology
...As such, I have a thorough understanding of science, math, physics, and engineering. Through my educational background, I believe that understanding previous material fully and the derivation
of this material are crucial for understanding and remembering new concepts. As a tutor, I reinforce this understanding of the fundamentals to help a student learn difficult concepts.
20 Subjects: including algebra 1, chemistry, calculus, algebra 2
...I have tutored students individually, in small groups, and in large classroom settings. My experience includes tutoring chemistry, biology, anatomy and physiology, and microbiology at a
community college for 8 years, as well as tutoring high school chemistry (general chemistry and AP). I am pas...
7 Subjects: including algebra 1, chemistry, geometry, biology
Related Superior, CO Tutors
Superior, CO Accounting Tutors
Superior, CO ACT Tutors
Superior, CO Algebra Tutors
Superior, CO Algebra 2 Tutors
Superior, CO Calculus Tutors
Superior, CO Geometry Tutors
Superior, CO Math Tutors
Superior, CO Prealgebra Tutors
Superior, CO Precalculus Tutors
Superior, CO SAT Tutors
Superior, CO SAT Math Tutors
Superior, CO Science Tutors
Superior, CO Statistics Tutors
Superior, CO Trigonometry Tutors
Nearby Cities With algebra 1 Tutor
Boulder, CO algebra 1 Tutors
Broomfield algebra 1 Tutors
East Lake, CO algebra 1 Tutors
Eastlake, CO algebra 1 Tutors
Edgewater, CO algebra 1 Tutors
Eldorado Springs algebra 1 Tutors
Erie, CO algebra 1 Tutors
Evergreen, CO algebra 1 Tutors
Federal Heights, CO algebra 1 Tutors
Firestone algebra 1 Tutors
Frederick, CO algebra 1 Tutors
Glendale, CO algebra 1 Tutors
Lafayette, CO algebra 1 Tutors
Louisville, CO algebra 1 Tutors
Westminster, CO algebra 1 Tutors | {"url":"http://www.purplemath.com/Superior_CO_algebra_1_tutors.php","timestamp":"2014-04-21T00:00:07Z","content_type":null,"content_length":"24093","record_id":"<urn:uuid:36dd23a3-9d88-4e5e-8393-022ba5277cf6>","cc-path":"CC-MAIN-2014-15/segments/1397609539337.22/warc/CC-MAIN-20140416005219-00097-ip-10-147-4-33.ec2.internal.warc.gz"} |
Hudson, NH Algebra 2 Tutor
Find a Hudson, NH Algebra 2 Tutor
I am a mother of three young children who is currently in my Junior year at Southern NH University. I am studying to become a Middle School Mathematics Teacher. I am also a cheerleading coach for
girls who range from 6 years old to 13 years old.
3 Subjects: including algebra 2, algebra 1, prealgebra
...I have also taught C at the college level, and I am very comfortable working with students. For several years, my wife and home schooled our daughter, which taught me patience.I am a 25 year
veteran software engineer, and I worked in C++ for the last 15 years, doing projects big and small, and c...
10 Subjects: including algebra 2, algebra 1, elementary math, C
...My most recent student earned a 782. One of the most moving applications for reading skills is for appreciating and learning from literature. Through short stories, plays, and novels, we can
appreciate important questions and lessons that cannot be captured in any other way.
55 Subjects: including algebra 2, English, reading, algebra 1
...I'd love to see students gaining confidence in solving problems. I had chances to reinforce my math skills while I have done research all these years. I have very strong mathematical skills.
5 Subjects: including algebra 2, physics, Chinese, precalculus
...Algebra 2 skills, including factoring, finding roots, solving sets of equations and classifying functions by their properties, are a necessary foundation for trigonometry, pre-calculus,
calculus and linear algebra. Particularly important are operations with exponents and an understanding of the ...
7 Subjects: including algebra 2, calculus, physics, algebra 1
Related Hudson, NH Tutors
Hudson, NH Accounting Tutors
Hudson, NH ACT Tutors
Hudson, NH Algebra Tutors
Hudson, NH Algebra 2 Tutors
Hudson, NH Calculus Tutors
Hudson, NH Geometry Tutors
Hudson, NH Math Tutors
Hudson, NH Prealgebra Tutors
Hudson, NH Precalculus Tutors
Hudson, NH SAT Tutors
Hudson, NH SAT Math Tutors
Hudson, NH Science Tutors
Hudson, NH Statistics Tutors
Hudson, NH Trigonometry Tutors | {"url":"http://www.purplemath.com/Hudson_NH_Algebra_2_tutors.php","timestamp":"2014-04-18T14:13:21Z","content_type":null,"content_length":"23722","record_id":"<urn:uuid:eb9f1d84-e606-4123-a271-358cc6e19a18>","cc-path":"CC-MAIN-2014-15/segments/1398223211700.16/warc/CC-MAIN-20140423032011-00020-ip-10-147-4-33.ec2.internal.warc.gz"} |
New principle sets maximum limit on quantum information communication
Schematic of the quantum information causality game, in which the amount of quantum information communicated among the parties is limited by the principle of quantum information causality. Credit:
Pitalúa-García. ©2013 American Physical Society
(Phys.org) —When two parties use a quantum system to share information, the amount of quantum information that can be communicated is fundamentally limited by quantum properties. Now in a new paper,
Damián Pitalúa-García, a scientist in the University of Cambridge's Centre for Quantum Information and Foundations in the Department of Applied Mathematics and Theoretical Physics, has proposed a
principle that can determine the maximum amount of quantum information that a quantum system can communicate. According to this principle, the maximum amount of information is limited only by the
quantum system's dimension, and does not depend on any physical resources previously shared by the communicating parties.
Pitalúa-García's paper, called "Quantum Information Causality," is published in a recent issue of Physical Review Letters.
Specifically, Pitalúa-García's principle of quantum information causality says that, after a quantum system of m qubits is transmitted from one party to another, the quantum information shared
between the two parties cannot increase by more than 2m. As Pitalúa-García explains, this limit is the maximum amount of information that a quantum system can fundamentally communicate, regardless of
how technologically advanced it may be and how much quantum entanglement the communicating parties share.
"The principle of information causality states that m classical bits can transmit m's worth of information," Pitalúa-García told Phys.org. "On the other hand, quantum information causality states
that m qubits can transmit 2m's worth of information. In this sense, a qubit can communicate twice the amount of information that a classical bit can communicate. This might seem strange because,
after being measured, a qubit reduces to a classical bit. However, a qubit can be entangled with another qubit, while a classical bit cannot. It is entanglement that allows a qubit to communicate
more information than a classical bit."
In his paper, he showed that quantum information causality follows from three mathematical properties satisfied by quantum information. While the maximum amount of information is independent of any
previously shared quantum physical resources, it does depend on the quantum system's dimension.
"The dimension of a quantum system can be understood as the number of different possible outcomes that are obtained when the system is subject to a measurement," Pitalúa-García said. "For example, a
qubit has dimension two, because it gives one of two possible measurement results. Similarly, a system of m qubits has dimension 2^m. It is thus natural to expect that a system with bigger dimension
can communicate more quantum information. This is proved mathematically by quantum information causality."
In order to illustrate the limit imposed by quantum information causality and come as close as possible to reaching this limit, Pitalúa-García presented a new quantum game. He found that an optimal
strategy in this game is a quantum teleportation strategy.
Although this method is not the first for determining the maximum of quantum information that can be communicated by a quantum system, it is different because it does not involve any classical
"Other methods can determine the maximum amount of information that can be transmitted by a quantum system, but in different scenarios," Pitalúa-García said. "For example, [in some scenarios,] the
communicated information is classical, as stated in a theorem by Holevo in 1973, or the transmitted system is classical, as published in 2009 in the principle of information causality. Our approach
considers the scenario in which the transmitted and the communicated information are both quantum and the communicating parties share any quantum physical resources. This scenario is more general
because, fundamentally, every system is quantum, and a classical system is a special class of quantum system."
Overall, the principle of quantum information causality may have implications for the broad field of quantum information, which deals with how information can be fundamentally encoded, processed, and
communicated using quantum systems.
More information: Damián Pitalúa-García. "Quantum Information Causality." PRL 110, 210402 (2013). DOI: 10.1103/PhysRevLett.110.210402
not rated yet Jun 04, 2013
Classical information theory is without physical constraints.
There are countable and uncountable dimensions. Both infinite.
Are possible outcomes limited to this?
3 / 5 (2) Jun 05, 2013
Wouldn't the information carrying properties change if the entangled entities were entangled not only by one property but by several (e.g. entanglement via polarization and spin would leadt to 4m).
But I guess that would no longer be a qbit, as that is defined as a two state QM system.
not rated yet Jun 20, 2013
My response to your curiosity. | {"url":"http://phys.org/news/2013-06-principle-maximum-limit-quantum.html","timestamp":"2014-04-18T06:24:35Z","content_type":null,"content_length":"77063","record_id":"<urn:uuid:d214e47f-f574-4af2-992e-36ff36f2c452>","cc-path":"CC-MAIN-2014-15/segments/1397609539066.13/warc/CC-MAIN-20140416005219-00094-ip-10-147-4-33.ec2.internal.warc.gz"} |
Math Forum: Math Library - Middle
Browse and Search the Library Home : Levels : Middle
Library Home || Search || Full Table of Contents || Suggest a Link || Library Help
component stack: /library/branch.html
code stack: /var/lib/mason/obj/library/branch.html:208
debug info: Debug file is '/var/lib/mason/debug/anon/17'.
error while executing /library/branch.html:
raw error: Server message number=1105 severity=17 state=4 line=1 text=Can't allocate space for object 'syslogs' in database 'catalog' because 'logsegment' segment is full/has no free extents.
If you ran out of space in syslogs, dump the transaction log. Otherwise, use ALTER DATABASE or sp_extendsegment to increase size of the segment.
Statement=INSERT INTO keystorage ( keys ) VALUES ( '41749;7441;8026;63524;2835;7335;75526;62434;2811;62038;74581;18702;6382;7753;7752;7027;10956;7760;73679;18124;18125;41523;61808;
HTML::Mason::Interp::__ANON__('Server message number=1105 severity=17 state=4 line=1 text=Can\'...') called at /usr/lib/perl5/site_perl/5.6.0/Forum/Key.pm line 284
Forum::Key::store('Forum::Key=HASH(0x8f1c860)') called at /var/lib/mason/obj/library/branch.html line 208
HTML::Mason::Commands::__ANON__('passed_args', 'HASH(0x8fa43f4)', 'tree', 'levels', 'branch', 'middle') called at /usr/lib/perl5/site_perl/5.6.0/HTML/Mason/Component.pm line 131
HTML::Mason::Component::run('HTML::Mason::Component::FileBased=HASH(0x8fa0014)', 'passed_args', 'HASH(0x8fa43f4)', 'tree', 'levels', 'branch', 'middle') called at /usr/lib/perl5/
site_perl/5.6.0/HTML/Mason/Request.pm line 653
require 0 called at /usr/lib/perl5/site_perl/5.6.0/HTML/Mason/Request.pm line 653
HTML::Mason::Request::comp('HTML::Mason::Request::ApacheHandler=HASH(0x8f9c41c)', '/library/branch.html', 'passed_args', 'HASH(0x8fa43f4)', 'tree', 'levels', 'branch', 'middle')
called at /usr/lib/perl5/site_perl/5.6.0/HTML/Mason/Commands.pm line 70
HTML::Mason::Commands::mc_comp('/library/branch.html', 'passed_args', 'HASH(0x8fa43f4)', 'tree', 'levels', 'branch', 'middle') called at /var/lib/mason/obj/library/dhandler line 90
HTML::Mason::Commands::__ANON__('start_at', 3601, 'num_to_see', 50, 'keyid', 38645439) called at /usr/lib/perl5/site_perl/5.6.0/HTML/Mason/Component.pm line 131
HTML::Mason::Component::run('HTML::Mason::Component::FileBased=HASH(0x8fa6788)', 'start_at', 3601, 'num_to_see', 50, 'keyid', 38645439) called at /usr/lib/perl5/site_perl/5.6.0/HTML/
Mason/Request.pm line 653
require 0 called at /usr/lib/perl5/site_perl/5.6.0/HTML/Mason/Request.pm line 653
HTML::Mason::Request::comp('HTML::Mason::Request::ApacheHandler=HASH(0x8f9c41c)', 'HASH(0x8faf41c)', 'HTML::Mason::Component::FileBased=HASH(0x8fa6788)', 'start_at', 3601,
'num_to_see', 50, 'keyid', ...) called at /usr/lib/perl5/site_perl/5.6.0/HTML/Mason/Request.pm line 159
require 0 called at /usr/lib/perl5/site_perl/5.6.0/HTML/Mason/Request.pm line 159
HTML::Mason::Request::exec('HTML::Mason::Request::ApacheHandler=HASH(0x8f9c41c)', '/library/levels/middle', 'start_at', 3601, 'num_to_see', 50, 'keyid', 38645439) called at /usr/lib/
perl5/site_perl/5.6.0/HTML/Mason/ApacheHandler.pm line 914
HTML::Mason::ApacheHandler::handle_request_1('HTML::Mason::ApacheHandler=HASH(0x8de2bfc)', 'Apache=SCALAR(0x8e0004c)', 'HTML::Mason::Request::ApacheHandler=HASH(0x8f9c41c)', 'HASH
(0x8fa2358)') called at /usr/lib/perl5/site_perl/5.6.0/HTML/Mason/ApacheHandler.pm line 560
require 0 called at /usr/lib/perl5/site_perl/5.6.0/HTML/Mason/ApacheHandler.pm line 560
HTML::Mason::ApacheHandler::handle_request('HTML::Mason::ApacheHandler=HASH(0x8de2bfc)', 'Apache=SCALAR(0x8e0004c)') called at /etc/httpd/conf/handler.pl line 97
HTML::Mason::handler('Apache=SCALAR(0x8e0004c)') called at /dev/null line 0
require 0 called at /dev/null line 0 | {"url":"http://mathforum.org/library/levels/middle/?keyid=38645439&start_at=3601&num_to_see=50","timestamp":"2014-04-18T18:28:15Z","content_type":null,"content_length":"8161","record_id":"<urn:uuid:8386baf5-057b-4d54-a351-80c94a0421ef>","cc-path":"CC-MAIN-2014-15/segments/1398223202774.3/warc/CC-MAIN-20140423032002-00488-ip-10-147-4-33.ec2.internal.warc.gz"} |
Got Homework?
Connect with other students for help. It's a free community.
• across
MIT Grad Student
Online now
• laura*
Helped 1,000 students
Online now
• Hero
College Math Guru
Online now
Here's the question you clicked on:
\[\sqrt[3]{24x^8}\] Simplify by factoring assume all expressions under radicals reprisent nonnegative number
Your question is ready. Sign up for free to start getting answers.
is replying to Can someone tell me what button the professor is hitting...
• Teamwork 19 Teammate
• Problem Solving 19 Hero
• Engagement 19 Mad Hatter
• You have blocked this person.
• ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.
This is the testimonial you wrote.
You haven't written a testimonial for Owlfred. | {"url":"http://openstudy.com/updates/4e4476070b8b3609c71fe004","timestamp":"2014-04-21T10:13:42Z","content_type":null,"content_length":"36921","record_id":"<urn:uuid:15622636-8dd5-4b88-b799-621aceb3557f>","cc-path":"CC-MAIN-2014-15/segments/1397609539705.42/warc/CC-MAIN-20140416005219-00250-ip-10-147-4-33.ec2.internal.warc.gz"} |
The question was mine, but the answer was all his.
I carry a defective teacher gene that makes me intolerant of pacing guides and curriculum guidelines.
I know where we're at: my 6th graders are working on adding and subtracting fractions, algebra kids are solving compound inequalities, geometry group just took a test on chapter 6 (not doing SBG with
this class). And I have no clue what chapter 7 is about.
Yet I'm well aware that the state test is in the first week of May when we still have almost a full quarter left of school. No one has given me an intelligent explanation as to why a multiple-choice
test administered in the name of "Algebra 1 Standards Test" does not allow students to get a full year's worth of algebra and why it takes 3 months to get the results.
They might as well rename the test as "We-Hate-Students-So-Here's-Your-Algebra-1-Standards-Test-Version-A," and "We-Hate-Teachers-Too-So-Let's-See-How-Poorly-Your-Students-Do-On-This-
Anyway, I'm sure I'm a month behind in the pacing guide, and I'm pretty sure no part of today's lesson will appear on any state test.
But I did it anyway.
The algebra kids have been doing a lot of graphing inequalities on the number line, and the geometry kids have been doing a bunch of
-squared for their
Viewmongus lesson
So I'm looking at my geometry kids and thinking: Hmmm... I wonder if you know how to graph an irrational number on the number line.
I ask them to locate sqrt(7) on the number line. Two students pull out their calculators. The rest are scribbling and erasing, doodling too I suppose. They know sqrt(7) is somewhere between 2 and 3.
Five minutes pass quietly.
Another five minutes, their faces grow longer. Gabe brings his journal up to me. He writes:
You could create a right triangle with a vertex at 0 and the side being sqrt(7) going along the number line. The other vertex would be the point where the sqrt(7) is located.
I nod my head but ask, "Want to help me understand what you wrote with a picture?"
He comes back with this sketch. I tell him, "I see. Something to do with right triangles. Okay. But you know that I still don't see how you arrive at sqrt(7) right there, right? I think you're on to
something, Gabemeister."
Enough individual think/stuck time has passed, I put them into random groups of three. I walk around, they're talking about the problem, but I'm not seeing much on the whiteboards. Maia [bottom
right] thinks she's funny. Gabe gets himself a compass.
I'm watching the clock. Jack wonders if he could just make a number line for irrational numbers only. You know, 0 here, then sqrt(1) here, then sqrt(2) here, then oh never mind. Gabe looks busy with
his compass. His group mates are observing him carefully and listening to him mumble.
Time to nudge them along. I ask, "This question that I'm asking you of where is sqrt(7) or sqrt(any irrational number) on the number line came from my watching you in the last activity. What were you
doing in last two days?"
They burst out:
Aspect ratio thingies.
Pythagorean theorems — but this [number line] is not a right triangle!
The diagonal of the TV is the number line!
I say nothing more and continue to walk around. Now I'm seeing more on their whiteboards.
All the groups are working with right triangles, but I'm unable to take more pictures of their work as I'm now with Gabe's group and listening to him explain how he thinks he has the answer.
He goes over his drawing above step-by-step by drawing another similar one. I'm retelling his story using Geometer's Sketchpad.
1. Draw an arc of radius 3 units.
2. Draw an arc of radius 4 units.
3. Draw the line y = -3.
4. Draw a perpendicular line (pink) to the red line where it intersects blue arc.
5. Sharing this final step right now with you makes me tear up.
Tomorrow Gabe will get to share his way of finding sqrt(7) on the number line with his class.
Then maybe I'll ask the class to try finding sqrt(11), sqrt(10), sqrt(bring-it-on-Mrs.Win-we-got-this). Maybe they'll have fun doing this.
I'd posed a question that wasn't lined up with the curriculum. It just came to me as I was watching my kids do math. But the question lined up with my gut, and my heart went along and said, "Do this
because it'll remind you of why you love this job."
• January 11, 2013 5:37 AM Betty M wrote:
I agree with everything you said about state testing. My 7th and 8th graders test in MARCH!!! And I KNOW I'm at least a month behind on the pacing guide. My belief is that they learn the
concepts...radical thought, I know!
Reply to this
1. January 11, 2013 1:48 PM fawnnguyen wrote:
March?? That's criminal. Sorry to hear that, Betty. I'll stop whining then. Thanks for dropping in.
Reply to this
• January 11, 2013 6:28 AM Kate Nowak wrote:
Reply to this
1. January 11, 2013 1:49 PM fawnnguyen wrote:
Thanks, Kate!
Reply to this
• January 11, 2013 7:52 AM Matt Vaudrey wrote:
Boom! Math bomb. Wicked.
Reply to this
1. January 12, 2013 1:30 PM fawnnguyen wrote:
Thanks, Matt aka Mr.MarriedtoHotWifeandDaddyofCutestBaby. (Did I get that right?)
Reply to this
• January 11, 2013 10:53 AM Sue VanHattum wrote:
You got one thing wrong - that gene is not defective. Maybe it's an adaptive mutation?
Reply to this
1. January 12, 2013 1:45 PM fawnnguyen wrote:
True true. Or I'm counting on it being a recessive gene. Thanks, Sue.
Reply to this
• January 11, 2013 12:45 PM Robert Kaplinsky wrote:
I’ve never seen a student approach this type of problem using this method. It got me thinking though, “Will this always work?” Specifically, I mean will this method always produce a leg and
hypotenuse that are integers. If they aren’t integers then you will have to plot the points for two irrational numbers, which is pretty challenging to do accurately on graph paper.
So, I started out by trying sqrt(10) and sqrt(11) as you suggested. sqrt(10) did not seem to work as there would be another leg/hypotenuse that was irrational, but sqrt(11) did produce an integer
leg and hypotenuse. Trying more values, a pattern emerged: this technique only works with the square root of odd numbers. For example:
sqrt(7) gives sides of 3 and 4
sqrt(9) gives sides of 4 and 5
sqrt(11) gives sides of 5 and 6
sqrt(13) gives sides of 6 and 7
I realized the reason why was because you were subtracting one leg from the hypotenuse and the difference between any two consecutive perfect squares was an odd number. This led to a pattern of:
sqrt(x + y) gives sides of x and y
(where x is the length of a leg, y is the length of the hypotenuse, and x and y are consecutive whole numbers)
Thanks for sharing this Fawn.
Reply to this
1. January 11, 2013 12:57 PM fawnnguyen wrote:
Your comment is exactly what I asked the kids today. After Gabe showed his sqrt(7), I asked everyone for sqrt(11). They were able to duplicate the process using 5 and 6 as the other two
sides. Then I asked for sqrt(10) and sure enough they were stuck. (Gabe's group got it though because they went ahead of the class.) Then I asked, "Why did you assume that sqrt(10) had to be
one of the legs? Couldn't it be another side, like the hypotenuse maybe?" So with this hint, it didn't take them long to figure out 1 and 3 for the legs to produce a hypotenuse of sqrt(10).
My next question to them (this afternoon!) would be "How do you know when an irrational number is a leg or a hypotenuse? Is there a way to tell?" We'll see what conjectures they come up with.
Thanks so much, Robert!
Reply to this
• January 11, 2013 12:47 PM Marshall Thompson wrote:
It's like you live in a strange far away Utopia where kids actually care a little bit about math class.
I'm sure your excellence and enthusiasm have something to do with that.
Coolest thing I've seen today.
Reply to this
1. January 11, 2013 1:10 PM fawnnguyen wrote:
Ha! We refer to this campus as the "little school among the lemon orchards," so a bit Utopian in setting at least. I make these kids love math. Dammit, I love it, so will they. It kinda
works. Thanks for the kind words, Marshall.
Reply to this
• January 11, 2013 4:11 PM Dan Goldner wrote:
Beautiful!! You, him, the problem, the solution, all of it....
Reply to this
1. January 12, 2013 1:48 PM fawnnguyen wrote:
So so kind, thanks, Dan. I'm trying to have more of the "yum mantra."
Reply to this
• January 11, 2013 8:45 PM Steve Grossberg wrote:
I can't think of anything new to say, but I just want to agree with all of the commenters above. This is a great story, and paints a nice picture of the Math Atmosphere in your classroom.
Reply to this
1. January 12, 2013 1:51 PM fawnnguyen wrote:
Sometimes I wish I could videotape them. They are a good bunch of kids who have a lot of respect for each other's thinking. We laugh a lot. Thanks, Steve.
Reply to this
• February 20, 2013 5:13 AM tomctutor wrote:
If we make the hypotenuse an even number
say H = (N+1)/2, with the opposite side say Y = (N-1)/2 will get the adjacent side X = sqrt(N) where N is odd.
Note that Y = H -1 so Y will also be odd.
Im not certain that this will be irrational in all cases but interesting!
Reply to this
1. February 28, 2013 8:21 PM fawnnguyen wrote:
Thanks, tomctutor. I think this is what Robert K is saying above?
Reply to this
• March 1, 2013 2:34 AM tomctutor wrote:
If we now make hypotenuse an odd number (H =2N+1 say) and opposite Y =2N (even) so that H =Y+1, we get the interesting fact that adjacent X =sqrt(H+Y)which is a generalisation of Robert K's idea.
If X irrational then H+Y (=4N+1) must be prime, which of course is not always the case. If H+Y not prime,e.g. N =2, X is rational.
Reply to this
1. March 1, 2013 3:07 AM tomctutor wrote:
What I meant to say was if H+Y (=4N+1)is prime then X must be irrational - not the other way about (sorry)!
Reply to this
1. March 3, 2013 4:44 PM fawnnguyen wrote:
So the converse isn't true.
Reply to this
• January 7, 2014 11:42 AM Shecky R wrote:
Wonderful! (I think you just made many tear up!)
Reply to this
1. January 11, 2014 6:26 PM fawnnguyen wrote:
Sweet of you to drop me a note, thank you, Shecky. I always enjoy reading your tidbits and summaries at Math-Frolic!
Reply to this
Recent Comments | {"url":"http://fawnnguyen.com/2013/01/10/20130110.aspx?ref=rss","timestamp":"2014-04-19T20:14:22Z","content_type":null,"content_length":"70083","record_id":"<urn:uuid:75f0e873-81bf-4004-a419-9ba6a4e1c3b6>","cc-path":"CC-MAIN-2014-15/segments/1397609537376.43/warc/CC-MAIN-20140416005217-00099-ip-10-147-4-33.ec2.internal.warc.gz"} |
The Period of 61/97
Date: 01/12/2001 at 08:46:22
From: Celia
Subject: period of 61/97
I need to know the period of 61/97 (if there is one). I've calculated
it to the 31st decimal place, but can't tell if it is a finite or
infinite and periodic... Is there any way I can figure it out?
Thank you!
Date: 01/12/2001 at 15:52:02
From: Doctor Rick
Subject: Re: period of 61/97
Hi, Celia.
I can tell you that the period is finite; more particularly, that it
is no greater than 97 digits. You've done at least 1/3 of the work.
How do I know that? If you've done the calculations by long division,
then you've seen a sequence of remainders:
97 ) 61.000000000...
The partial remainders are 28, 86, 84, 64, 58, 95, 77, 91, 37, ...
The first time you get a remainder that has shown up before, the next
quotient digit will be the same as it was the first time, and the next
remainder will be the same as it was the first time, and so on - in
other words, the decimal begins repeating at that point.
Now we can apply the "pigeonhole principle." How many different
remainders can there be? The remainder must be between 0 and 96. In
fact, if it's 0 then the decimal will terminate, and we know that
won't happen. (If you don't know why, I'd be glad to tell you.) There
are thus only 96 different possible remainders. When we've gotten 97
digits and 97 remainders, we can be sure that one of them has shown up
before. You can imagine 96 "pigeonholes" labeled with the possible
remainders. We have 97 numbers (the actual remainders) to put in them;
at least two of the numbers must go into the same pigeonhole.
Therefore, the decimal must begin repeating by the 97th digit.
If you're doing the calculation by a calculator (such as the
calculator built into Windows) that handles up to 31 digits but no
more, you can use this trick. Calculate 25 digits (so we have some
digits to spare and we won't overtax the calculator in what follows):
61/97 = 0.6288659793814432989690721
Then find the partial remainder after the last digit so far. Here's
how to do it. Multiply the decimal by 97, subtract this from 61, and
multiply by 1E25. I get a partial remainder of 63.
Next, divide the remainder by 97. You will get a continuation of the
decimal expansion of 61/97. I get:
63/97 = 0.64948453608247422680412371134021
When I calculated 61/97, I got 32 digits:
61/97 = 0.62886597938144329896907216494845
Note that the last 7 digits, 6494845, match the first 7 digits of the
continuation. This is a check on the accuracy of my method. The full
decimal expansion so far is thus:
61/97 = 0.62886597938144329896907216494845649484536082474226804
You can continue in this way as far as you need in order to find where
the decimal begins repeating. Have fun!
- Doctor Rick, The Math Forum | {"url":"http://mathforum.org/library/drmath/view/58169.html","timestamp":"2014-04-19T12:28:00Z","content_type":null,"content_length":"8368","record_id":"<urn:uuid:658ba74c-4258-4ee2-8ee4-bc7fd2fd7d76>","cc-path":"CC-MAIN-2014-15/segments/1397609540626.47/warc/CC-MAIN-20140416005220-00494-ip-10-147-4-33.ec2.internal.warc.gz"} |
STEP Maths I, II, III 1993 Solutions
STEP III Number 11 (not quite complete)
Can anyone finish this off please. Just the very last part is missing.
(Original post by brianeverit)
It's a very long while since I've done vector angular momentum, so this is from looking stuff up on Wiki.
I believe you can simply dot the vector moment (call it V_m) we previously calculated with the direction vector (1, 1, 1)/sqrt(3) to get the torque about the axis OO'. (I didn't find a direct
statement that this is the case, but if the cube wasn't constrained to rotate on the OO' axis, then it's certainly true that . On the assumption that the constraint effectively acts as to remove
any resultant torque NOT parallel to OO', then I think you can simply dot with the OO' axis to get the behaviour).
From which point it's simply a standard "acceleration = moment / MI" calculation.
[I don't consider this terribly satisfactory since I have no real idea if it's right. Sorry.]
STEP 1 Q16
Taking the question's advice and letting we see that:
and so
as required.
Now, if X=x, consider the case when the pin has fallen in such a way that it's end only just touches the line. From a diagram it can be seen that a right angled triangle is formed by the pin, the
line and the distance X such that:
. So, the probability tht the pin crosses the line, in this case, is the probability that which, since Y is uniformly distributed, is
Now, for the next part, the probability that the pin will cross the line for a general throw is the sum of the probabilities that X will take a particular value
less than a and that Y will be less than for this particular value of X, i.e:
P(crosses) .
Taking a hint from the first part we let which is what we calculated in the first part so P(crosses) as required.
(Original post by Rabite)
I think I did Q2 in the Further Maths A.
But it seems quite easy so I've probably made a mistake. It's still red on the front page, so if no one else has typed it out already, I'll do so~
[edit] Here it is anyway.
By the product/sum formulae that no one remembers.
But if m=±n, one of the fractions explodes. So in that case the question is:
If m=n=0, the integral turns to .
As for the second bit.
Let x = sinh²t
dx = 2sinhtcosht dt
Ignoring the +c for now
Which you can rewrite using the log form of arsinh.
Ignoring the +c for now
(Original post by nota bene)
I'm on to Q1 STEP II (Further Pure A)
Is it just me or is it pure brute force?
Okay, if B knows A's numbers and they are of the form B can always chose so that he wins; the possible numbers are:
3+3+3 (and of course in other order as well...)
So here it is quite convincing B can always beat A if B knows A's numbers and the order of them.
edit: To make this clearer I'll list the possibilities explicitly like David told (so the person typing out these markschemes won't have to fill in half the answers themselves!)
A ------B
Furthermore, if A choses 1+1+7 (or some other order of those numbers) it is impossible for A to win no matter what B choses (they can tie).
If now A gets to chose two triples and B are to find one triple that beats both it is quite clear from looking at the possible combinations that A shall not chose any of the combinations with few
rearrangements (like 333 and 117 can easily be counteracted by 441). Many combinations leads to tied situations. From trial and error it is possible to eliminate all triples but some of the 531s.
Testing these we can see 135/153 (by 171),135/531 (by 441), 135/513 (by 144), 135/351 (by 441), 135/315 (by 441), 153/531 (by 261), 153/513 (by 126), 153/351 (by 261), 153/315 (by 414), 531/513
(by 144), 531/351 (by 441), 531/315 (by NONE), 351/315 (by 414)
Conclusion: A shall chose 5+3+1 and 3+1+5 as his triples to always be sure of winning.
(okay and I am masochistic, here are all the stupid possible combinations:
117 (beats neither 531 nor 315)
711 (beats neither 531 nor 315)
171 (beats neither 531 nor 315)
144 (beats 531, not 315)
141 (beats neither 531 nor 315)
441 (beats 315, not 531)
135 (ties with both 315 and 531)
153 (beats 531, not 315)
531 (beats 315, ties with 531)
513 (ties with both 531 and 315)
351 (ties with both 531 and 315)
315 (beats neither 315 nor 531)
225 (beats neither 531 nor 315)
252 (beats 531, not 315)
522 (beats 315, ties with 531)
333 (ties with both 531 and 315)
234 (beats neither 531 nor 315)
243 (beats neither 531 nor 315)
432 (beats 315, ties with 531)
423 (beats 315, not 531)
342 (beats 531, ties with 315)
324 (beats neither 315 nor 531)
126 (beats 315, not 531)
162 (beats 531, not 315)
216 (beats neither 531 nor 315)
261 (beats neither 531 nor 315)
612 (beats 531, ties with 315)
621 (beats 315, ties with 531)
Firstly, as a1, a2, a3 are non negative numbers, so I think they can take the zero value as well.
For the first part, I first let A choose the numbers a1<a2<a3, then I let B choose b1=a1+1; b2=a2+1;b3= 7-a1-a2. Then I can prove that 7- a1-a2 is always non-negative so B can always find the
valid b1,b2,b3 in this way.
For the second part I let A choose 0,0,9. Notice that A can never win the first two rounds and lose the last round. then it can be deduced that A can never win more rounds then the rounds he
loses (if we say there are 3 rounds)
For the last bit, first condiser 5,3,1, then we can find the range of b1,b2,b3. Then we try to use b1,b2,b3 in these ranges to beat 3,1,5. But finally I proved that I can never beat it.
But I think brute force is quick indeed, at least for the first part.
(Original post by generalebriety)
Done II/4, but I'm ****ed if I'm LaTeXing it. I swear TSR's LaTeX is messed up somehow. Written and scanned.
I agree with the first two parts but not the last one. The first part gives the perpendicular distance between the two lines, but this is not necessary the shortest distance between the two
planes. This is because the position vector of the two planes is determined by the parameter t so they may not be able to just be at the two ends of the common perpendicular at the same tome.
My method is to express the distance in terms of v2 and treat all other things as constants. Then differentiate the expression with respect to v2 to get a minimum point. But my answer is ugly so
I may have made some mistakes. Any one has an idea for this?
(Original post by khaixiang)
I've done STEP II (paper A), question 2, 3, 8 and STEP III (paper B), question 1, 2, 4, 9 awhile ago. So I won't do them again and will try other questions. Here's question 9 of STEP II:
Sorry, I know this is very ugly, if it's too much of an eyesore I will remove it for conformity's sake.
This question seems way too easy compared to others, so perhaps I've overlooked something.
May be we need to notice that we only take 0 < =arg z < 2 pi, so arg(z1z2z3) = arg z1 + arg z2 + arg z3 > arg z3 is not necessary true. When arg z1 + arg z2 + arg z3 > 2 pi, we need to take 2 pi
away from it to give a arg(z1z2z3) between 0 and 2 pi. And we need to prove that this value for arg(z1z2z3) is less than arg z1. But this is in fact no hard as well. I did it by some
straightforward inequalities.
(Original post by SimonM)
(Updated as far as #213) SimonM - 11.05.2009
If you see any mistakes please point them out.
There's nothing wrong with Brian's solution as such - he has got the required answer in exactly the way the examiners expected. But unfortunately, the required answer is wrong. It should be ,
not .
This is the only STEP question I've ever found with a mistake in it. It's particularly bad that it indicates that the examiner misunderstood Newton's Law.
I've got a document that proves the correct result four different ways, but I'll let people think about it a while before posting it.
EDIT This is being discussed at http://www.thestudentroom.co.uk/show...4#post43561514 . Unless that discussion is long finished, it's probably best to post there rather than here.
(Original post by MAD Phil)
There's nothing wrong with Brian's solution as such - he has got the required answer in exactly the way the examiners expected. But unfortunately, the required answer is wrong. It should be ,
not .
This is the only STEP question I've ever found with a mistake in it. It's particularly bad that it indicates that the examiner misunderstood Newton's Law.
I've got a document that proves the correct result four different ways, but I'll let people think about it a while before posting it.
EDIT This is being discussed at http://www.thestudentroom.co.uk/show...4#post43561514 . Unless that discussion is long finished, it's probably best to post there rather than here.
We've had a bit of a discussion over there, and the upshot is that the examiners used the wrong "Not Newton theorem" for the part of the chain hanging down. They used force = rate of change of
momentum, which is not correct in this situation, as the parts of the chain joining the hanging section are not at rest just before joining the body. They should have used force = mass times
acceleration, which is the correct theorem in cases where mass joins or leaves the body without changing its velocity. (I prove the theorems, in the appropriate situations, at http://
www.thestudentroom.co.uk/show...4#post43576544 .)
Back in the 90's I wrote the attached document and sent it off to Cambridge; I can't remember what reply, if any, I got back. (That email system is long dead - I had to use a version of the
document that I scanned in 2004.)
The document contains 4 proofs of the correct result. One uses the (correct) Not Newton Theorem and is very short. The next uses energy considerations; the rate of increase of the mechanical
energy of the system is the rate at which (kinetic) energy is being fed into it by the mass joining it, minus the rate at which the system is doing work against the tension. The third finds a
differential equation (with respect to position) satisfied by the tension in the hanging part of the chain, and solves it using boundary conditions derived from the lower end. The fourth uses
rotational Newton for the pulley and the section of the chain in contact with it.
Those four methods all give the same answer, of course. I also give two "proofs" of the "as desired" value, but they both depend on using the incorrect Not Newton Theorem. I wanted to check that
that was the full explanation of the value they asked for. I can't remember why I did it twice.
• Follow
• 8 followers
• Follow
• 1 follower | {"url":"http://www.thestudentroom.co.uk/showthread.php?t=394479&page=13","timestamp":"2014-04-20T02:43:50Z","content_type":null,"content_length":"283201","record_id":"<urn:uuid:90bc812f-5a73-4d92-afd5-073a90e9c875>","cc-path":"CC-MAIN-2014-15/segments/1398223206672.15/warc/CC-MAIN-20140423032006-00449-ip-10-147-4-33.ec2.internal.warc.gz"} |
Shape Tiling
Given a list $1\times 1, 1\times a, 1\times b, \dots, 1\times c$ of rectangles, with $a,b,\dots,c$ non-negative, when can $1\times{t}$ be tiled by positive and negative copies of rectangles which are
similar (uniform scaling) to those in the list? We prove that such a tiling exists iff $t$ is in the field $Q(a,b,\dots,c)$.
Full Text: | {"url":"http://www.combinatorics.org/ojs/index.php/eljc/article/view/v4i2r12/0","timestamp":"2014-04-16T11:08:05Z","content_type":null,"content_length":"13903","record_id":"<urn:uuid:d395e06c-86ef-49fc-8cbf-911c2a268329>","cc-path":"CC-MAIN-2014-15/segments/1397609523265.25/warc/CC-MAIN-20140416005203-00533-ip-10-147-4-33.ec2.internal.warc.gz"} |
Posts by
Posts by brad
Total # Posts: 259
Algebra 2
Yoko threw a stone upward at a speed of 10m/sec while standing on a cliff 40 m above ground. A. What was the height of the stone after 3 seconds? B. Estimate how long it took for the stone to touch
the ground
The speed of light in polythene is 1.99 x 108 m/s What is the index of refraction of polythene
An inductor (L = 405 mH), a capacitor (C = 4.43 µF), and a resistor (R = 400 ) are connected in series. A 50.0 Hz AC generator produces a peak current of 250 mA in the circuit. (a) Calculate the
required peak voltage ΔVmax. V (b) Determine the phase angle by which t...
Rose has a square garden with an area of 49 square feet. She wants to put a fence around her garden. How much fencing does she need to purchase?
using d^2(h/dt^2=−g+k(dh/dt^2, find an expression for the terminal velocity in terms of k and g? g is the acceleration due to gravity, k is a constant, h(t) is the height of the falling object, dh/dt
is its velocity, and d^2(h)dt^2 is its acceleration. And can you e...
Could you explain as to how you got that answer?
using d^2(h)/dt^2=−g+k(dh/dt)^2, find an expression for the terminal velocity in terms of k and g? g is the acceleration due to gravity, k is a constant, h(t) is the height of the falling object, dh/
dt is its velocity, and d^2(h)/dt^2 is its acceleration.
Scientists are experimenting with a kind of gun that may eventually be used to fire payloads directly into orbit. In one test, this gun accelerates a 9.7-kg projectile from rest to a speed of 6.5 ×
103 m/s. The net force accelerating the projectile is 8.0 × 105 N. ...
You are the accountant for Suite Dreams, a retail furniture store. Recently, an order of sofas and chairs was received from the manufacturer with terms of 3/15, n/45. The order amounted to $230,000,
and Suite Dreams can borrow money at 13% ordinary interest. How much can be sa...
Varsity Press, a publisher of college textbooks, received a $70,000 promissory note at 12% ordinary interest for 60 days from one of its customers, Reader s Choice Bookstores. After 20 days, Varsity
Press discounted the note at the Grove Isle Bank at a discount rate of 14...
Euromart Tile Company borrowed $40,000 on April 6 for 66 days. The rate was 14% using the ordinary interest rate method. On day 25 of the loan, Euromart made a partial payment of $15,000, and on day
45 of the loan, Euromart made a second partial payment of $10,000. What was th...
I have a thesis started, I kind of decided on my topic, how Lewis has influenced such writers like JK Rowling, Tolkien and helped them write the novels they are so famous for here is the thesis
statement so far "Modern interpretive Literature has led the way for some of t...
I have read the narnia books, I have another book called "A Life" by Michael White its a biography, the essay is as I said before 1500 word minimum, I am looking at arguing how he was influential and
is influential still today in his writings, I am having issues comi...
Need help on a Research paper, my author is CS Lewis, I am having a major writers block on what to write about, teacher has left it fairly open, need to have an outline and cited works today but he
is pretty slack I could have it in tomorrow and be fine, either way stuck on th...
Corporate Finance
Your firm is looking at 3 projects, each costing $500,000: A is estimated to save $125,000 per year for 5 years; B is estimated to save $75,000 for 6 years plus generate tax savings of $20,000 per
year; C is estimated to save $75,000 per year for 10 years but requires addition...
3. Using Bohr s model of the atom, calculate the energy required to move an electron from a ground state of n = 2 to an excited state of n = 3. Express your answer in both J/photon and kJ/mol.
if u travel 1.5 and the box way 93 she traveled 62 watts I think
When you use the distance formula, you are building a _____ triangle whose hypotenuse goes between two given points. A.right B.equilateral C.acute D.None of these
Life orientation
*Describe ;)
Life orientation
*hazards *crisis *globally ;)
In plants, it can be assumed that NADPH like NADH is energetically equivalent to 2.5 ATP. Calculate the number of ATP and ATP equivalents that are needed to synthesize one molecule 0f
glucose-6-phosphate from CO2 and photosynthetically produced ATP and NADPH.
y3K, Inc., has sales of $5,276, total assets of $3,105, and a debt equity ratio of 1.40. If its return on equity is 15 percent, what is its net income? Can someone help with a formula?
a ladder 6m long is leaning against a wall. if the top of th ladder is slipping down at th rate of 13 m/s, how fast is the bottom moving away from the wall when it is 5m from the wall? (answer in m/
s) Please Help Before 230 pm central time
A planned community has 300 homes, each with an automatic garage door opener. The door opener has eight switches that a homeowner can set to 0 or 1. For example, a door opener code might be 01100101.
Assuming all the homes in the community are sold, what is the probability tha...
A bag contains 44 U.S. quarters and six Canadian quarters. (The coins are identical in size.) If seven quarters are randomly picked from the bag, what is the probability of getting at least one
Canadian quarter? (Round your answer to one decimal place.)
If a person draws two cards from a standard deck (without replacing them), what is the probability that at least one of the cards is a face card? (Round your answer to one decimal place.)
Find the value for W when the limit as x approaches 8 of ((2x^2)-7x + W)/(x-8) = 25
evaluate the following limit... ((1-x)/((1/e)-(e^-x))) as x approaches one
what is the limit of (9x/(9x+5))^(6x) as x approaches infinity?
the total potential difference from point A to point B in a circuit is +5 V. The total potential difference from point A to point C in a circuit is -16 V. What must be hte potential difference from
point B to point C?
7th grade math please help Ms. Sue ASAP
you know Delilah our math teacher looks at this if you are going to connexs
Molarity = moles of solute/ Liter. 5g O2 * (1 mol O2/ 32 g O2)= x moles O2 convert 250 mL to Liters X moles O2/ Liters = molarity
When using the van't Hoff factor, I multiply the number of moles of CaCl2 by the factor right? So when finding the mole fraction of CaCl2 in the solution, it would be 3(1.22 mol CaCl2)/[3(1.22) +
12.2] which equals about .231. So then it would be dP = .231 * 239 = 55.2 mm ...
Okay so I used the equation dP= Xsolute * Psol. I got 32.3 and it was correct. I used the exact same equation for this one, and I got 21.7. For some reason it was incorrect. What am I doing wrong?
The vapor pressure of pure water at 70°C is 239 mm Hg. What is the vapor pre...
What's the difference between Psol and Pvap depression? How would I find the Pvap depression?
The vapor pressure of pure water at 70°C is 231 mm Hg. What is the vapor pressure depression of a solution of 115 g of the antifreeze ethylene glycol, C2H6O2, a nonvolatile compound, in 205 g of
water? Use molar masses with at least as many significant figures as the data ...
i have the words in front of me with the meaning.... so I am lost thats all I can say...
1. poignant 2. contend 4. conversely 7. prevalent 8. contemporary 9. charisma
those r my answers
Many people are surprised to learn how __1__ poverty is __2__ America. Today millions live below the poverty line, and the number seems to escalate daily. Judy and Martin Reed exemplify the old
saying, Opposites attract. A __3__. Judy chooses work that brings her i...
then 5 has to be wrong
4. benefactor 7. speculate 9. alleviate
Shortly before the Russian Revolution, an eccentric man named Rasputin became ___1___as the "mad monk." Because he dressed like a peasant, drank heavily, and rarely bathed, the nobility often felt
__2__during their encounters with him at the palace. Yet despite...
Shortly before the Russian Revolution, an eccentric man named Rasputin became ______as the "mad monk." Because he dressed like a peasant, drank heavily, and rarely bathed, the nobility often felt
____during their encounters with him at the palace. Yet despite h...
thank you it wouldnt surprise me if u didnt get more from these words..... from other class mates.... once again ty
solve the logarithmic equation. log(5x+7)=1+log(x-9)
find the inverse. f(x)=-2+log_4(x-4)
how do you write that in interval notation?
solve the following inequality. (x-3)^2/(x^2-4)is greater than or equal to 0.
find the real solutions using quadratic formula. im sorry.
find the real solutions using the quadratic formula 6-(1/x)-(4/x^2)=0
find the inverse of f(x)=-5+log(base5)(y-5)
Find the accumulated value of a CD of $20000 for 3 years at an interest of 3.1% if the money is compounded continously.
So, 5.9 to be exact?
How long will it take $1400 to double at 12% annual interest compounded quarterly?
Physics HELP!
A simple pendulum consists of a small object of mass 7.40 kg hanging at the end of a 2.10 m long light string that is connected to a pivot point. (a) Calculate the magnitude of the torque (due to the
force of gravity) about this pivot point when the string makes a 3.00° an...
Find the theoretical pH of .01M and .05M benzoic acid buffer when 2ml of .1MNaOH was added to each buffer.
A ball acquires a horizontal speed of 12m/sec when a force is applied for a distance of .50m. If the ball has a mass of 1.0kg what is the force applied? ANSWER: 144N....I'm not sure what formulas I'd
apply. It takes a force of 109N to life a stone straight up. This for...
How many times more energy is associ- ated with a 282 nm ultraviolet photon than a 5494 nm microwave photon?
Statistics: Regression
The June 1997 issue of Management Accounting gave the following rule for predicting your current salary if you are a managerial accountant. Take $31,865. Next, add $20,811 if you are top management,
add $3604 if you are senior management, or subtract $11,419 if you are entry m...
A population is increasing according to the exponential function defined by y = 2e0.02x, where y is in millions and x is the number of years. How large will the population be in 3 years?
the radius of the base of the metallic rod is 2o centimeters and height 15 centimeters what is the volume of a cylinder
the radius of the base of the metallic rod is 2o centimeters and height 15 centimeters what is the volume of a cylinder
Probability and Statistics
A package contains 12 resistors, 3 of which are defective. If four are selected, find the probability of getting the following. No defective resistors One defective resistors 3 defective resistors
Probability and Statistics
A package contains 12 resistors, 3 of which are defective. If four are selected, find the probability of getting the following. No defective resistors One defective resistors 3 defective resistors
In a box of fruit there were 11 oranges and 9 apples. What fraction of the fruit were the oranges?
veterinarians as prescribers
Alteration of the physical form of a drug outside its label is
calculate the pressure when 57 g of flourine at 55 degrees celsius is confined to a 152 liter container.
help...If exactly 5.0 mL of HNO3 will neutralize 15 mL of 2.0 M NaOH, what is the molarity of the HNO3 solution? Have no idea what to do. thank you.
Suppose that the travel time from your home to your office is normally distributed with a mean of 40 minutes and standard deviation of 7 minutes. If you want to be 95% certain that you will not be
late for an office appointment at 1:00pm, what is the latest time that you shoul...
So i found the solubility to be x=0.001296, is this the concentration of I^-? can i multiply this by 30mL to get my moles?
how can i calculate the solubility with the information given ? in class we use concentrations to find solubility
A 30.00mL sample of a clear saturated solution of PbI2 requires 14.7mL of a certain AgNO3 for its titration. I^-(saturated PbI2)+Ag^+(from AgNO3)--> AgI(s) What is the molarity of this AgNO3? I'm not
really sure where to start.
A mixture formed by adding 55.0 mL of a 1.5x10^-2 M HCl to 140 mL of 1.0x10^-2 M HI. How do you calculate the pH for this problem?
Ba(OH)2(aq)+2CH3COOH(aq)=Ba(CH3COO)2(aq)+2(l)H2O what is the net ionic equation with phases?
Ms.Sue,is the ans 3?
4 1/5 divided 1 2/5 21/5 x 7/5 = ?
thanks, I am stuck on this one 4 1/5 divided 1 2/5 21/5 x 7/5 =
1. 2 1/3 x 3 1/2 = 2. 4 2/3 divided 7 =
Thanks! can you please show me how to do these: 2 1/3 x 3 1/2 4 2/3 divided 7
How do I estimate these? 1. 7/8 + 3 1/4 2. 5 1/9 - 2/3 3. 9 5/6 divided 2 1/8 4. 6 divided 1/2
Ms. SUE, Is this correct? 4. 5/8 + 5/6 = 1 11/24 5. 13 1/2 + 7 2/3 = 21 1/6
Ms. SUE, Is this correct? 4. 5/8 + 5/6 = 1 11/24 5. 13 1/2 + 7 2/3 = 21 1/6
1. 9-5 3/4 = 2. 7/8 + 3 1/4 = 3. 5 1/9 -2/3 = 4. 5/8 + 5/6 = 5. 13 1/2 + 7 2/3 =
Statisics Question Help Please
The proportion of students in private schools is around 11%. A random sample of 450 students from a wide geographic area indicated that 55 attended private schools. Estimate the true proportion of
students attending private schools with 95% confidence. How does it estimate com...
If EF = 4x - 19, FG = 3x - 9, and EG = 28, find the values of x, EF, ad FG.
A dart is thrown horizontally with an initial speed of 11 m/s toward point P, the bull's-eye on a dart board. It hits at point Q on the rim, vertically below P, 0.19 s later. (a) What is the distance
PQ? (b) How far away from the dart board is the dart released?
A small lake contains 0.0500 mi3 of water [H2O]. If the density of water is 1.000 g/mL, determine the volume (in gal) of water in the lake.
Math Help
When asked for standard deviation when dealing with grouped data for linear regression, do you give them for each the x and y variable or is there a way to configure for grouped data set? I have a Ti
84 plus calculator
The wildlife department has been feeding a special food to rainbow trout fingerlings in a pond. A sample of the weights of 40 trout revealed that the mean weight is 402.7 grams and the standatd
deviation 8alE8 gr. What is the probability that the mean weight for a sample of 40...
The table didn't turn out 0, goes with 0 underneath. 1 goes with 45.2 3 goes with 96.3 8 goes with 178.2 20 goes with 254.3 40 goes with 380.5
A radar gun was used to record the speed of a racecar during the first 40 seconds while driving on a straight road. Use the chart to calculate the car's distance after 40 seconds using righthand
sums. Is this an over or underestimate? Justify the answer. This is the table ...
social study
what made the hbc and nwc so imortant to this reion
Some firms are too production-oriented and inefficient. That can result in customers who are not satisfied and micro-marketing that can cost too much. Identify and explain at least three reasons for
these marketing inefficiencies.
Basic Marketing
so much for trying to get a little help on which direction to go. I didn't want a full answer just sometips of where to do some research.
Basic Marketing
A large number of forces shape the marketing environment. The technological environment is one of the most important today. Discuss the impact of technology on marketing including, the opportunities,
challenges and ethical issues technology poses for marketing.
Explain the words element compound and mixture. Identify which substances ara element compound and mixture
Directions: Use the underlined etymology clues to help you choose the correct word that is missing from each of the following sentences. 3. The [underlined](Middle English, from Old French boc, "male
goat")[/underlined] had a physically demanding job. A. son B. barbe...
Pages: 1 | 2 | 3 | Next>> | {"url":"http://www.jiskha.com/members/profile/posts.cgi?name=brad","timestamp":"2014-04-17T19:45:27Z","content_type":null,"content_length":"28104","record_id":"<urn:uuid:949e0c0d-bc70-4bf9-b584-305b89a5c440>","cc-path":"CC-MAIN-2014-15/segments/1397609530895.48/warc/CC-MAIN-20140416005210-00480-ip-10-147-4-33.ec2.internal.warc.gz"} |
integrate cos^3(x)
July 6th 2009, 12:22 AM #1
Junior Member
Jan 2009
integrate cos^3(x)
Hi, how do I integrate cos^3(x)?
I split it into cos(x)[1/2(1+cos(2x)] and then removed the constant of a 1/2 from the integration. Then I mutilpied through by cos(x) and got cos(x)+cos^2(2x), which didn't really help.
Then I split cos^3(x) into cos(x).cos^2(x) tried substituting cos^2(x) with 1-sin^2(x) and that didn't help either.
What am I missing?
Thank you.
Hi, how do I integrate cos^3(x)?
I split it into cos(x)[1/2(1+cos(2x)] and then removed the constant of a 1/2 from the integration. Then I mutilpied through by cos(x) and got cos(x)+cos^2(2x), which didn't really help.
Then I split cos^3(x) into cos(x).cos^2(x) tried substituting cos^2(x) with 1-sin^2(x) and that didn't help either.
What am I missing?
Thank you.
Note that $\int\cos^3x\,dx=\int\cos^2x\cos x\,dx=\int\left(1-\sin^2x\right)\cos x\,dx$$=\int\cos x\,dx-\int\sin^2x\cos x\,dx$
In the second integral, make the substitution $u=\sin x$.
Can you continue?
Hi, how do I integrate cos^3(x)?
I split it into cos(x)[1/2(1+cos(2x)] and then removed the constant of a 1/2 from the integration. Then I mutilpied through by cos(x) and got cos(x)+cos^2(2x), which didn't really help.
Then I split cos^3(x) into cos(x).cos^2(x) tried substituting cos^2(x) with 1-sin^2(x) and that didn't help either.
What am I missing?
Thank you.
Use the identity
$\cos^3{x} = \frac{3}{4}\cos{x} + \frac{1}{4}\cos{(3x)}$.
$\int{\cos^3{x}\,dx} = \int{\frac{3}{4}\cos{x} + \frac{1}{4}\cos{(3x)}\,dx}$
$= \frac{3}{4}\sin{x} + \frac{1}{12}\sin{(3x)} + C$.
Out of curiosity, is there a method of solving this problem without using substitution. In the cousre I am doing substitution has already been covered so I am fine with that, but I am trying to
get the big picture of integration and get a feel for as many techniques I can. Cheers
Yes, use the identity I've given you. There's no $u$ substitution there...
July 6th 2009, 12:29 AM #2
July 6th 2009, 12:34 AM #3
Junior Member
Jan 2009
July 6th 2009, 12:35 AM #4
July 6th 2009, 12:39 AM #5
Junior Member
Jan 2009
July 6th 2009, 01:12 AM #6 | {"url":"http://mathhelpforum.com/calculus/94494-integrate-cos-3-x.html","timestamp":"2014-04-18T11:24:43Z","content_type":null,"content_length":"50666","record_id":"<urn:uuid:23c2cccf-d58e-45cf-afa9-265e07d4cfa9>","cc-path":"CC-MAIN-2014-15/segments/1397609537308.32/warc/CC-MAIN-20140416005217-00438-ip-10-147-4-33.ec2.internal.warc.gz"} |
La Marque Statistics Tutor
Find a La Marque Statistics Tutor
Hi, my name's Brian, I have a lot of experience tutoring and I'm fun and easy to work with. I can guarantee that I will help you get an A in your course or ace that big test you're preparing for.
I am a Trinity University graduate and I have over 4 years of tutoring experience.
38 Subjects: including statistics, English, calculus, reading
I am currently a CRLA certified level 3. I have been tutoring for close to 5 years now on most math subjects from Pre-Algebra up through Calculus 3. I have done TA jobs where I hold sessions for
groups of students to give them extra practice on their course material and help to answer any question...
7 Subjects: including statistics, calculus, algebra 2, algebra 1
I have taught math and science as a tutor since 1989. I am a retired state certified teacher in Texas both in composite high school science and mathematics. I offer a no-fail guarantee (contact
me via WyzAnt for details). I am available at any time of the day; I try to be as flexible as possible.
35 Subjects: including statistics, chemistry, physics, calculus
I am an experienced Information technology professional with more than 13 years of experience. I have extensive experience in developing and managing IT Systems and large teams in corporate
environment. My expertise is in Microsoft Technologies.
14 Subjects: including statistics, writing, algebra 1, ACT Math
...I have taught statistics, experimental design, technical writing and various subjects and levels in college psychology, including introduction, personality theory, research methods and
psychological measurement (i.e. testing). My specialty is statistics, and in addition to teaching I have served ...
20 Subjects: including statistics, writing, algebra 1, algebra 2
Nearby Cities With statistics Tutor
Alvin, TX statistics Tutors
Bacliff statistics Tutors
Bayou Vista, TX statistics Tutors
Beach City, TX statistics Tutors
Clute statistics Tutors
Dickinson, TX statistics Tutors
Hitchcock, TX statistics Tutors
Hunters Creek Village, TX statistics Tutors
Manvel, TX statistics Tutors
Nassau Bay, TX statistics Tutors
Santa Fe, TX statistics Tutors
Seabrook, TX statistics Tutors
Texas City statistics Tutors
Tiki Island, TX statistics Tutors
Webster, TX statistics Tutors | {"url":"http://www.purplemath.com/la_marque_statistics_tutors.php","timestamp":"2014-04-21T15:22:30Z","content_type":null,"content_length":"24017","record_id":"<urn:uuid:423d39e2-52cc-4f16-9fc7-97928f142d4b>","cc-path":"CC-MAIN-2014-15/segments/1398223205137.4/warc/CC-MAIN-20140423032005-00321-ip-10-147-4-33.ec2.internal.warc.gz"} |
Gaussian Process Training with Input Noise
Andrew McHutchon and Carl Edward Rasmussen
In: NIPS 2011, 12-17th December 2011, Granada, Spain.
In standard Gaussian Process regression input locations are assumed to be noise free. We present a simple yet effective GP model for training on input points corrupted by i.i.d. Gaussian noise. To
make computations tractable we use a local linear expansion about each input point. This allows the input noise to be recast as output noise proportional to the squared gradient of the GP posterior
mean. The input noise variances are inferred from the data as extra hyperparameters. They are trained alongside other hyperparameters by the usual method of maximisation of the marginal likelihood.
Training uses an iterative scheme, which alternates between optimising the hyperparameters and calculating the posterior gradient. Analytic predictive moments can then be found for Gaussian
distributed test points. We compare our model to others over a range of different regression problems and show that it improves over current methods.
PDF - Requires Adobe Acrobat Reader or other PDF viewer. | {"url":"http://eprints.pascal-network.org/archive/00008456/","timestamp":"2014-04-18T08:07:47Z","content_type":null,"content_length":"7436","record_id":"<urn:uuid:9a0511ca-2bfc-4668-a883-78198e032e63>","cc-path":"CC-MAIN-2014-15/segments/1397609533121.28/warc/CC-MAIN-20140416005213-00317-ip-10-147-4-33.ec2.internal.warc.gz"} |
MathGroup Archive: February 2005 [00321]
[Date Index] [Thread Index] [Author Index]
Re: Algebraic Symbol Manipulation
• To: mathgroup at smc.vnet.net
• Subject: [mg54160] Re: [mg54125] Algebraic Symbol Manipulation
• From: "David Park" <djmp at earthlink.net>
• Date: Sat, 12 Feb 2005 01:57:10 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com
The Mathematica syntax and commands for solving this problem would be as
follows. First, let's define the equation.
eqn = V == 1/3 Pi r^2h;
Notice that eqn is a symbol that stands for the entire equation. It is Set
with =. But in the equation itself we use == for the equal symbol. Then to
solve the equation we write...
hsol = Solve[eqn, h][[1,1]]
h -> (3*V)/(Pi*r^2)
The '[[1,1]]' was added to the Solve statement because there was only a
single solution and it was returned as a List within a List. Generally there
are multiple solutions and multiple variables and that is why Mathematica
returns Lists of solutions. In this case we just picked off the inner
The solution was returned as a rule with an arrow. It is stored under the
name hsol. You can use hsol to substitute into any expression that contains
h. The substitution is done using '/.'. For example...
3h + h^2 /. hsol
(9*V)/(Pi*r^2) + (9*V^2)/(Pi^2*r^4)
But you might want to define h as a function of V and r. You can do this
with the following...
h[V_, r_] = h /. hsol
Then for example, if you wanted an expression for the height of right
circular cones with a radius of 2, you could write...
h[V, 2]
If you are a beginner at Mathematica it is worthwhile to work through most
of Part I of The Mathematica Book, actually typing in expressions and making
certain they work.
David Park
djmp at earthlink.net
From: mattisbusy at gmail.com [mailto:mattisbusy at gmail.com]
To: mathgroup at smc.vnet.net
I was wondering how to manipulate Mathematica into solving a problem
such as this:
Solve for h:
V = 1/3(pie)r^2h
I would think you would do:
Solve[{1/3(pie)r^2h},{h}] - although it does not compute the expected
answer. Am I doing this right? Thanks! | {"url":"http://forums.wolfram.com/mathgroup/archive/2005/Feb/msg00321.html","timestamp":"2014-04-18T00:58:26Z","content_type":null,"content_length":"36010","record_id":"<urn:uuid:a1ce478f-c0b1-4e5b-869e-44af61fd36ee>","cc-path":"CC-MAIN-2014-15/segments/1397609532374.24/warc/CC-MAIN-20140416005212-00072-ip-10-147-4-33.ec2.internal.warc.gz"} |
finitary monad
Higher algebra
Algebraic theories
Algebras and modules
Higher algebras
Model category presentations
Geometry on formal duals of algebras
A monad $(T,\mu,i)$ on the category Set of sets, is finitary (also called algebraic, although some people consider any monad to be an algebraic notion) if the underlying endofunctor $T:\mathrm{Set}\
to\mathrm{Set}$ commutes with filtered colimits.
In other words, an algebraic monad is a monoid in the category of algebraic endofunctors on $\mathrm{Set}$.
A finitary monad $(T,\mu,i)$ is completely determined by its value on all finite ordinals $n\in\mathbb{N}_0$ considered as standard finite sets. $T(n)$ is then the set of $n$-ary operations. The
notion of algebraic monad is hence similar to the notion of a nonsymmetric operad in $\mathrm{Set}$, but it is not equivalent, because of the possibility of duplicating or discarding inputs.
More precisely, each finitary monad $T$ defines a Lawvere theory $Th_T$, namely $Th_T = Free_{fin}^{op}$ where $Free_{fin}$ is the category of free algebras $T(n)$ on finite sets (as a full
subcategory of $Alg_T$). In fact, the two notions are equivalent: the assignment
$T \mapsto Th_T$
defines an equivalence between the category of finitary monads on $Set$ and the category of Lawvere theories. Moreover, the category of $T$-algebras is equivalent to the category of models of $Th_T$.
However, a technical advantage of Lawvere theories is that they can be interpreted in categories other than Set: a model of a Lawvere theory $\mathcal{T}$ in a category with cartesian products $C$ is
just a product-preserving functor $\mathcal{T} \to C$.
There is an interesting commutativity condition singling out the subclass of commutative algebraic/finitary monads, cf. commutative algebraic theory; they are useful to establish a theory of
generalized commutative schemes.
For a proof of the equivalence between finitary monads and Lawvere theories, see
Durov’s application of finitary monads to the “field with one element” may be found in
This discussion appeared when the page was at algebraic monad.
Mike: Does anyone besides Durov use this terminology? In category theory these already have two standard names: “finitary monads” and “(Lawvere) theories.”
Zoran Škoda Lawvere theories are equivalent to algebraic monads, but not in standard exposition literally a type of monad, but one says algebraic monad when one really talks about a condition on
monads. Algebraic monad is just a monoid in the category of algebraic endofunctors. Lawvere and others studied few variants of notion of algebraic functor, but in all of them algebraic functor
commutes with filtered colimits, isn’t it ? I heard the term certainly in a number of algebra talks before Nikolai Durov’s thesis (I can say some names but I may misremeber sources). Definitely the
term is getting much more influential after the Durov’s work, and reused by algebraic geometers now. He is quite familiar with Lawvere’s work so I hope the related expression “algebraic endofunctor”
is not chosen incompatibly. Also there is some parallel with terminology cartesian monad. But what do you think ? In any case, one should also list term finitary monad, both synonyms should be
Toby: Whether these are ‘algebraic’ or ‘finitary’ (I'd be more inclined to the latter, but not through any familiarity with the literature), they're not obviously the same as Lawvere theories. I've
tried to indicate the connection, although (vague as my statement is) I'm not even sure that it's correct!
Zoran Škoda added below redirect finitary monad.
Toby: I moved this to finitary monad now, after Zoran made a link to it using that name from an article on Durov's work. | {"url":"http://ncatlab.org/nlab/show/finitary+monad","timestamp":"2014-04-17T15:30:51Z","content_type":null,"content_length":"29726","record_id":"<urn:uuid:2a712f43-f22a-4404-b27b-da239779d32e>","cc-path":"CC-MAIN-2014-15/segments/1398223202774.3/warc/CC-MAIN-20140423032002-00413-ip-10-147-4-33.ec2.internal.warc.gz"} |
[ir′i do̵̅o̅s′ə bəl, -dyo̵̅o̅s′-]
that cannot be reduced
Impossible to reduce to a desired, simpler, or smaller form or amount: irreducible burdens.
Related Forms:
• ir′re·duc′i·bil′i·ty, ir′re·duc′i·ble·ness
(comparative more irreducible, superlative most irreducible)
1. Not able to be reduced or lessened.
2. Not able to be brought to a simpler or reduced form.
3. (mathematics, of a polynomial) Unable to be factorized into polynomials of lower degree, as (x^2 + 1).
4. (mathematics, of an integer) Unable to be factored into smaller integers; prime.
5. (topology, of a manifold) Not containing a sphere of codimension 1 that is not the boundary of a ball.
6. (group theory, of a representation) impossible to divide further into representations of lower dimension by means of any similarity transformation
• reducible
• (unable to be reduced): unincreasable
(plural irreducibles)
1. (mathematics) Such a polynomial | {"url":"http://www.yourdictionary.com/irreducible","timestamp":"2014-04-16T22:16:32Z","content_type":null,"content_length":"45840","record_id":"<urn:uuid:6860254c-b5ca-40b7-9900-cf72d9c609c7>","cc-path":"CC-MAIN-2014-15/segments/1397609525991.2/warc/CC-MAIN-20140416005205-00421-ip-10-147-4-33.ec2.internal.warc.gz"} |
Let K be a field & Let K be a subfield of L
November 26th 2012, 02:35 PM #1
Junior Member
Oct 2012
Let K be a field & Let K be a subfield of L
1.) Let K be a field. If f(x) is a polynomial in K[x] of positive degree and K[x]/(f) is a field, prove that f(x) is irreducible in K[x]
2.)Let K be a subfield of a field L. Let f(x) and g(x) be polynomials in K[x].
(a) If f(x) is a factor of g(x) in L[x], prove that f(x) is also a factor of g(x) in K[x].
(b) If f(x) and g(x) have a common factor of positive degree in L[x], prove that they also have a common factor of positive degree in K[x].
Any help please! Be a lifesaver!
Follow Math Help Forum on Facebook and Google+ | {"url":"http://mathhelpforum.com/advanced-algebra/208484-let-k-field-let-k-subfield-l.html","timestamp":"2014-04-18T16:17:27Z","content_type":null,"content_length":"29011","record_id":"<urn:uuid:bb16c112-f35f-4c18-b02f-fc3e344249a0>","cc-path":"CC-MAIN-2014-15/segments/1397609533957.14/warc/CC-MAIN-20140416005213-00395-ip-10-147-4-33.ec2.internal.warc.gz"} |
The Energy Return on Investment threshold
Hall and Day (2009) report that the EROI for coal might be as high as 80 and that for hydropower, EROI is 40. Does this mean that coal is twice as ‘good’ as hydro? The answer is no, and in this post
I will discuss how this relates to the idea of an EROI Threshold.
This post is based on a presentation that I gave at the recent ASPO conference on November 4th, 2011.
We must first realize that EROI is a somewhat theoretical concept; it is a unitless ratio that does not describe actual flows of energy. What society really cares about, and what is really used to
grow economies around the world, are actual flows of energy. More precisely, the economy utilizes flows of net energy. What, if anything, can EROI tell us about the flow of net energy?
To understand how EROI influences the flow of net energy, we must first look at the equation for both net energy and EROI, which are:
Net Energy = Eout – Ein
EROI = Eout/Ein
If we solve the EROI equation for Ein and substitute it into the Net Energy equation, we get:
Net Energy = Eout*((EROI-1)/EROI)
From this equation Mearns (2008) created the “Net Energy Cliff” graph. The net energy cliff figure relates the percent of energy delivered as net energy (y-axis, dark grey) and the percent of energy
used to procure energy (y-axis, light grey) as a function of EROI (x-axis).
The exponential relation between net energy and EROI creates what I am calling an EROI Threshold at roughly 8. Due to the asymptotic nature of the curve at high EROIs, there is little difference in
the actual flow of net energy delivered from technologies that have EROIs above 8. The corollary is that extraction/conversion processes with EROIs below 8 result in vastly different flows of net
For example, a drop in the EROI of oil extraction from 50 to 10 would result in a change in net energy flow from 98% (of the gross energy flow) to 90%. Yet, a drop in EROI from 10 to 2 would result
in a net energy change from 90% to 50% of the gross energy flow.
This means that the relevance of EROI as a meaningful comparison of extraction/conversion technologies decreases as EROI increases. This is also the reason why I stated in the beginning of the
article that coal, with an EROI of 80, is not twice as good as hydro, with an EROI of 40, because the actual difference in the flow of net energy between these two is very small. The truth is that
they both deliver well over 90% net energy. What this threshold effect means is that, when substituting renewables for fossil fuels, it is less important to match EROIs (i.e. substituting coal for a
renewable that also has an EROI of 80), and more important to focus simply on avoiding very low EROI technologies (EROI < 8).
Major Caveat to the EROI Threshold
There is one major caveat to this discussion. The logic behind the EROI Threshold only applies if the EROIs being compared are actually commensurable: i.e. that the EROI analyses utilize the same set
of assumptions. This is often, however, not the case.
One significant difference between the EROIs calculated for fossil fuels and that for renewable technologies results from the intermittent nature of renewable energy. It is commonly thought that
scaling renewable energy will require the adoption of some sort of storage system to account for times of over- and under-production. The EROI of wind or solar PV will surely decrease if we allocate
the energy costs of those storage systems to the solar PV or wind conversion process. The question is whether this added energy cost will decrease the EROI of these systems below the EROI threshold,
but to my knowledge, there are no peer-reviewed papers reporting EROI numbers that included these costs.
EROI is a useful metric for comparing across energy extraction/conversion technologies, or for comparing the extraction/conversion process of one resource over time. But as EROI increases, and
especially as it increases much beyond 8, its relevance, as it pertains to net energy flows, fades. Furthermore, due to the aggregated nature of the EROI statistic, every analysis involves
assumptions. It is important that those who use these EROI statistics understand what those assumptions are and what they indicate about the utility of the EROI statistic produced.
1.Hall, C.A.S.; Day, J.W., Revisiting the limits to growth after peak oil. American Scientist 2009, 97, 230-237.
2.Mearns, E. In The global energy crises and its role in the pending collapse of the global economy, Royal Society of Chemists, Aberdeen, Scotland, October 29th, 2008; Aberdeen, Scotland, 2008.
This work is licensed under a Creative Commons Attribution-Share Alike 3.0 United States License.
What do you think? Leave a comment below.
Sign up for regular Resilience bulletins direct to your email.
Take action!
Make connections via our GROUPS page.
Start your own projects. See our RESOURCES page.
Help build resilience. DONATE NOW. | {"url":"http://www.resilience.org/stories/2011-11-26/energy-return-investment-threshold","timestamp":"2014-04-18T20:48:40Z","content_type":null,"content_length":"49272","record_id":"<urn:uuid:f79c69d9-5e1f-4e6f-8d57-693bf6f25eef>","cc-path":"CC-MAIN-2014-15/segments/1397609537271.8/warc/CC-MAIN-20140416005217-00258-ip-10-147-4-33.ec2.internal.warc.gz"} |
Six Sigma – Bell Curve
Dear Eric – Thanks for your note. I think I understand using Sigma as representing process capability and standard deviation explaining variation in the process. The question that I had was that if
we look at the bell curve having the mean equivalent to the target, how many standard deviations on either side needs to be fit to depict a Six Sigma process. I understand from Dr. Scott reply that
it has to be six standard deviations on both sides (ie, a total of 12 standard deviations). Put another way, if I have the classical bell curve with mean=target, with 3 standard deviations on either
side of the mean with Z=-3 coinciding with the LSL and Z=3 coinciding with the USL, explains a 3 Sigma process and not a Six Sigma process.
Thanks and Regards,
PS: The reason for posting this question was that I had somebody looking at this classical bell curve and telling me that it represents a 6 Sigma process and my argument was that it represents a 3
Sigma process. I hope with the answers that I got from you and Dr. Scott, my understanding is right! | {"url":"http://www.isixsigma.com/topic/six-sigma-bell-curve/","timestamp":"2014-04-21T07:33:58Z","content_type":null,"content_length":"95437","record_id":"<urn:uuid:39bf45a7-d56b-4c5e-8f12-2eb2d18283d4>","cc-path":"CC-MAIN-2014-15/segments/1397609539665.16/warc/CC-MAIN-20140416005219-00271-ip-10-147-4-33.ec2.internal.warc.gz"} |
The University of Montana
Department of Mathematical Sciences
Technical report #6/2014
Exploring Creativity: From the mathematics classroom to the mathematician's mind
Ann Kajander, Dominic Manuel, Bharath Sriraman
Learners of mathematics do not typically experience mathematics as a creative subject, yet research mathematicians often describe their field as a highly creative endeavour (Burton, 2004). The term
creativity has sometimes come to imply eminent acts/products/achievements, yet research suggests that creative thinking is an everyday occurrence (Craft, 2002). In this working group we sought to
capture the essence of mathematical creativity as seen through the eyes of mathematicians and described by current research, and express it in ways that might also be applicable to learners of
mathematics including, but not restricted to, students described as highly able. Our initial questions for consideration included: What is mathematical creativity? Does it differ from other kinds of
creativity? How can we observe it in learners? Is creativity necessary for mathematics research? How can creativity be enhanced in classroom mathematics learning? Are some students more
mathematically creative than others? Time was allowed during the working group meetings for those participants who wished to be generative; in particular, the construction or sharing of classroom
tasks that had potential for occasioning creative behaviour was a focus for some participants. Such tasks could be illustrative to teachers who wish to provide potentially rich learning environments
to students, and samples are included in this report.
Keywords: Mathematical Proof; Algorithms; Visual proofs
AMS Subject Classification: 97
Preprint of Proceedings of the 2013 Annual Canadian Mathematics Education Study Group, Working Group on Creativity Pdf (318 KB) | {"url":"http://cas.umt.edu/math/reports/sriraman/2014_abstract_06.html","timestamp":"2014-04-17T16:03:16Z","content_type":null,"content_length":"2876","record_id":"<urn:uuid:70a575bf-4f70-4a4c-8b8b-bac723507ea9>","cc-path":"CC-MAIN-2014-15/segments/1397609530136.5/warc/CC-MAIN-20140416005210-00432-ip-10-147-4-33.ec2.internal.warc.gz"} |
Computational Power of Infinite Quantum Parallelism
- in the School of Mathematics at the University of Leeds, U.K. © 2012 ACM 0001-0782/12/03 $10.00 march 2012 | vol. 55 | no. 3 | communications of the acm 83
"... Abstract. We turn ‘the ’ Church-Turing Hypothesis from an ambiguous source of sensational speculations into a (collection of) sound and well-defined scientific problem(s): Examining recent
controversies, and causes for misunderstanding, concerning the state of the Church-Turing Hypothesis (CTH), sug ..."
Cited by 3 (0 self)
Add to MetaCart
Abstract. We turn ‘the ’ Church-Turing Hypothesis from an ambiguous source of sensational speculations into a (collection of) sound and well-defined scientific problem(s): Examining recent
controversies, and causes for misunderstanding, concerning the state of the Church-Turing Hypothesis (CTH), suggests to study the CTH relative to an arbitrary but specific physical theory—rather than
vaguely referring to “nature ” in general. To this end we combine (and compare) physical structuralism with (models of computation in) complexity theory. The benefit of this formal framework is
illustrated by reporting on some previous, and giving one new, example result(s) of computability
, 2008
"... In the 1940s, two different views of the brain and the computer were equally important. One was the analog technology and theory that had emerged before the war. The other was the digital
technology and theory that was to become the main paradigm of computation. 1 The outcome of the contest between ..."
Add to MetaCart
In the 1940s, two different views of the brain and the computer were equally important. One was the analog technology and theory that had emerged before the war. The other was the digital technology
and theory that was to become the main paradigm of computation. 1 The outcome of the contest between these two competing views derived from technological and epistemological arguments. While digital
technology was improving dramatically, the technology of analog machines had already reached a significant level of development. In particular, digital technology offered a more effective way to
control the precision of calculations. But the epistemological discussion was, at the time, equally relevant. For the supporters of the analog computer, the digital model — which can only process
information transformed and coded in binary — wouldn’t be suitable to represent certain kinds of continuous variation that help determine brain functions. With analog machines, on the contrary, there
would be few or no layers between natural objects and the work and structure of computation (cf. [4, 1]). The 1942–52 Macy Conferences in cybernetics helped to validate digital theory and logic as
legitimate ways to think about the brain and the machine [4]. In particular, those conferences helped made McCulloch-Pitts ’ digital model | {"url":"http://citeseerx.ist.psu.edu/showciting?cid=3978946","timestamp":"2014-04-23T09:36:32Z","content_type":null,"content_length":"16094","record_id":"<urn:uuid:0a9211ca-7e40-4797-b9a7-ba39d196b8fe>","cc-path":"CC-MAIN-2014-15/segments/1398223202457.0/warc/CC-MAIN-20140423032002-00109-ip-10-147-4-33.ec2.internal.warc.gz"} |
188 helpers are online right now
75% of questions are answered within 5 minutes.
is replying to Can someone tell me what button the professor is hitting...
• Teamwork 19 Teammate
• Problem Solving 19 Hero
• Engagement 19 Mad Hatter
• You have blocked this person.
• ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.
This is the testimonial you wrote.
You haven't written a testimonial for Owlfred. | {"url":"http://openstudy.com/users/deldrickg/answered","timestamp":"2014-04-20T03:45:12Z","content_type":null,"content_length":"110963","record_id":"<urn:uuid:dade81e7-9094-4c2a-82b5-8c8f6caf0e6e>","cc-path":"CC-MAIN-2014-15/segments/1398223206120.9/warc/CC-MAIN-20140423032006-00650-ip-10-147-4-33.ec2.internal.warc.gz"} |
Illinois Learning Standards
Illinois Learning Standards
Stage F - Math
6A —
Students who meet the standard can demonstrate knowledge and use of numbers and their many representations in a broad range of theoretical and practical settings. (Representations)
1. Represent place values from units through billions using powers of ten.
2. Represent, order, compare, and graph integers.
3. Identify fractional pieces that have the same value but different shapes.
4. Compare and order fractions and decimals efficiently and find their approximate position on a number line. **
5. Represent repeated factors using exponents.
6B —
Students who meet the standard can investigate, represent and solve problems using number facts, operations, and their properties, algorithms, and relationships. (Operations and properties)
1. Write prime factorizations of numbers.
2. Determine the least common multiple and the greatest common factor of a set of numbers.
3. Demonstrate the meaning of multiplication of fractions (e.g.,1/2 x 3 is 1/2 of a group of three objects).
4. Simplify simple arithmetic expressions with rational numbers using the field properties and the order of operations.
5. Recognize and use the inverse relationships of addition and subtraction, multiplication and division to simplify computations and solve problems. **
6. Solve multiplication number sentences and word problems with whole numbers and familiar fractions.
6C —
Students who meet the standard can compute and estimate using mental mathematics, paper-and-pencil methods, calculators, and computers. (Choice of method)
1. Select and use appropriate operations, methods, and tools to compute or estimate using whole numbers with natural number exponents. **
2. Analyze algorithms for computing with whole numbers, familiar fractions, and decimals and develop fluency in their use. **
6D —
Students who meet the standard can solve problems using comparison of quantities, ratios, proportions, and percents.
1. Solve number sentences and word problems using percents.
2. Demonstrate and explain the meaning of percents, including greater than 100 and less than 1. **
3. Create and explain a pattern that shows a constant ratio.
4. Analyze situations to determine whether ratios are appropriate to solve problems.
5. Determine equivalent ratios.
7A —
Students who meet the standard can measure and compare quantities using appropriate units, instruments, and methods. (Performance and conversion of measurements)
1. Investigate the history of the U.S. customary and metric systems of measurement.
2. Measure, with a greater degree of accuracy, any angle using a protractor or angle ruler.
7B —
Students who meet the standard can estimate measurements and determine acceptable levels of accuracy. (Estimation)
1. Estimate distance, weight, temperature, and elapsed time using reasonable units and with acceptable levels of accuracy.
7C —
Students who meet the standard can select and use appropriate technology, instruments, and formulas to solve problems, interpret results, and communicate findings. (Progression from selection of
appropriate tools and methods to application of measurements to solve problems)
1. Select and justify an appropriate formula to find the area of triangles, parallelograms, and trapezoids. **
2. Select an appropriate formula or strategy to find the surface area and volume of rectangular and triangular prisms. **
3. Develop and use formulas for determining the area of triangles, parallelograms, and trapezoids.
4. Develop and use the formula for determining the volume of a rectangular and triangular prism.
5. Calculate the surface area of a cube, rectangular prism, and triangular prism.
6. Develop and use formulas for determining the circumference and arc of circles.
Students who meet the standard can describe numerical relationships using variables and patterns. (Representations and algebraic manipulations)
1. Investigate, extend, and describe arithmetic and geometric sequences of numbers whether presented in numeric or pictorial form. **
2. Evaluate algebraic expressions for given values.
3. Express properties of numbers and operations using variables (e.g., the commutative property is m + n = n + m).
4. Simplify algebraic expressions involving like terms.
Students who meet the standard can interpret and describe numerical relationships using tables, graphs, and symbols. (Connections of representations including the rate of change)
1. Graph simple inequalities on a number line.
2. Create a table of values that satisfy a simple linear equation and plot the points on the Cartesian plane.
3. Describe, verbally, symbolically, and graphically, a simple relationship presented by a set of ordered pairs of numbers.
Students who meet the standard can solve problems using systems of numbers and their properties. (Problem solving; number systems, systems of equations, inequalities, algebraic functions)
1. Identify and explain incorrect uses of the commutative, associative, and distributive properties.
2. Identify and provide examples of the identity property of addition and multiplication.
3. Identify and provide examples of inverse operations.
4. Explain why division by zero is undefined.
Students who meet the standard can use algebraic concepts and procedures to represent and solve problems. (Connection of 8A, 8B, and 8C to solve problems)
1. Create, model, and solve algebraic equations using concrete materials.
2. Solve linear equations, including direct variation, with whole number coefficients and solutions using algebraic or graphical representations.
Students who meet the standard can demonstrate and apply geometric concepts involving points, lines, planes, and space. (Properties of single figures, coordinate geometry and constructions)
1. Plot and read ordered pairs of numbers in all four quadrants.
2. Describe sizes, positions, and orientations of shapes under transformations, including dilations.
3. Perform simple constructions (e.g., equal segments, angle and segment bisectors, or perpendicular lines, inscribing a hexagon in a circle) with a compass and straightedge or a mira.
4. Determine and describe the relationship between pi, the diameter, the radius, and the circumference of a circle.
5. Determine unknown angle measures using angle relationships and properties of a triangle or a quadrilateral.
Students who meet the standard can identify, describe, classify and compare relationships using points, lines, planes, and solids. (Connections between and among multiple geometric figures)
1. Determine the relationships between the number of vertices or sides in a polygon, the number of diagonals, and the sum of its angles.
2. Solve problems that involve vertical, complementary, and supplementary angles.
3. Analyze quadrilaterals for defining characteristics.
4. Create a three-dimensional object from any two-dimensional representation of the object, including multiple views, nets, or technological representations.
Students who meet the standard can construct convincing arguments and proofs to solve problems. (Justifications of conjectures and conclusions)
1. Make, test, and justify conjectures about various quadrilateral and triangle relationships, including the triangle inequality.
2. Justify the relationship between vertical angles.
3. Justify that the sum of the angles of a triangle is 180 degrees.
9D is Not Applicable for Stages A - F.
Students who meet the standard can organize, describe and make predictions from existing data. (Data analysis)
1. Construct, read, interpret, infer, predict, draw conclusions, and evaluate data from various displays, including circle graphs. **
2. Recognize and explain misleading displays of data due to inappropriate intervals on a scale.
Students who meet the standard can formulate questions, design data collection methods, gather and analyze data and communicate findings. (Data Collection)
1. Gather data by conducting simple simulations.
2. Collect data over time with or without technology.
Students who meet the standard can determine, describe and apply the probabilities of events. (Probability including counting techniques)
1. Record probabilities as fractions, decimals, or percents.
2. Demonstrate that the sum of all probabilities equals one.
3. Determine empirical probabilities from a set of data provided.
4. Set up a simulation to model the probability of a single event.
5. Discuss the effect of sample size on the empirical probability compared to the theoretical probability.
6. List outcomes by a variety of methods (e.g., tree diagram).
7. Determine theoretical probabilities of simple events.
* National Council of Teachers of Mathematics. Principles and Standards for School Mathematics. Reston, Va: National Council of Teachers of Mathematics, 2000.
** Adapted from: National Council of Teachers of Mathematics. Principles and Standards for School Mathematics. Reston, Va: National Council of Teachers of Mathematics, 2000.
Return to Math Classroom Assessments and Performance Descriptors | {"url":"http://www.isbe.state.il.us/ils/math/stage_F/descriptor.htm","timestamp":"2014-04-18T13:36:45Z","content_type":null,"content_length":"25292","record_id":"<urn:uuid:02cb3c64-c858-41c8-aa69-64e87522015c>","cc-path":"CC-MAIN-2014-15/segments/1397609533689.29/warc/CC-MAIN-20140416005213-00576-ip-10-147-4-33.ec2.internal.warc.gz"} |
[R] Markov Switching with TVTP - problems with convergence
Houge jb.houge at gmail.com
Tue Oct 26 10:13:27 CEST 2010
Greetings fellow R entusiasts!
We have some problems converting a computer routine written initially for
Gauss to estimate a Markov Regime Switching analysis with Time Varying
Transition Probability. The source code in Gauss is here:
We have converted the code to R, and it's running without errors, but we
have some convergence problems. According to the authors of the Gauss code,
the initial guess for the Transition Matrix (probability of going from one
regime to the other) could be chosen arbitrary, but unfortunately this is
not the case for our R code. Also, we do not have Gauss available to test
the original source code.
A function used in Gauss is called "optmum", while R has a function called
"optim". Are these the same? If not, this might be the cause of our
convergence problems.
I would be glad to share the R program with anyone interested, as well as
the panel data used in the analysis.
Jørgen Blystad Houge
jorgehou at stud.ntnu.no
View this message in context: http://r.789695.n4.nabble.com/Markov-Switching-with-TVTP-problems-with-convergence-tp3013292p3013292.html
Sent from the R help mailing list archive at Nabble.com.
More information about the R-help mailing list | {"url":"https://stat.ethz.ch/pipermail/r-help/2010-October/257521.html","timestamp":"2014-04-19T22:09:09Z","content_type":null,"content_length":"4332","record_id":"<urn:uuid:2ac3a6fe-1831-4899-9bed-0cf5b6b99a0c>","cc-path":"CC-MAIN-2014-15/segments/1397609537754.12/warc/CC-MAIN-20140416005217-00178-ip-10-147-4-33.ec2.internal.warc.gz"} |
Supermodularity on chains and complexity of maximum constraint satisfaction
Supermodularity on chains and complexity of maximum constraint satisfaction
Vladimir Deineko, Peter Jonsson, Mikael Klasson, Andrei Krokhin
In the maximum constraint satisfaction problem (Max CSP), one is given a finite collection of (possibly weighted) constraints on overlapping sets of variables, and the goal is to assign values from a
given finite domain to the variables so as to maximise the number (or the total weight) of satisfied constraints. This problem is NP-hard in general so it is natural to study how restricting the
allowed types of constraints affects the complexity of the problem. In this paper, we show that any Max CSP problem with a finite set of allowed constraint types, which includes all constants (i.e.
constraints of the form x=a), is either solvable in polynomial time or is NP-complete. Moreover, we present a simple description of all polynomial-time solvable cases of our problem. This description
uses the well-known combinatorial property of supermodularity.
Full Text:
GZIP Compressed PostScript PostScript PDF original HTML abstract page | {"url":"http://www.dmtcs.org/dmtcs-ojs/index.php/proceedings/article/viewArticle/dmAE0111","timestamp":"2014-04-18T03:15:16Z","content_type":null,"content_length":"11585","record_id":"<urn:uuid:e6070a10-91a1-4ce2-a09e-dcd35fb12ae3>","cc-path":"CC-MAIN-2014-15/segments/1397609532480.36/warc/CC-MAIN-20140416005212-00103-ip-10-147-4-33.ec2.internal.warc.gz"} |
Janardhan, S and Rajagopal, KS (1975) Lapeqs: A Fortran programme to solve laplaces equation. Technical Report. National Aeronautical Laboratory, Bangalore,India.
Full text available as:
Restricted to Archive staff only
Download (4017Kb)
The curves PQ and RS lie in the closed interval (a,b) and. they are given as a set of ordinates.The problem is to solve in the region PQRS. The subroutine contructs a grid in the region PQRS, numbers
the grid points alonG the grid lines and sets up the Laplace difference equation at each grid point using 3-point finite difference fcrmulae for the derivatives.The set of these difference equations
is banded and is solved by Liebmann's iterative technique. Successive over-relaxation is employed to speed up the convergence of the iteration if invoked the user and if he provides the SOR factor.
The subroutine provijes good starting approximations for the potentials at each grid point by assuming linear variation along each vertical grid lineo In most cases this is found to result in fast
convergence and consequently considerable saving of computer time.
Item Type: Proj.Doc/Technical Report (Technical Report)
Uncontrolled Keywords: Laplace equation;Fortran programme;LAPEQS
Subjects: MATHEMATICAL AND COMPUTER SCIENCES > Mathematical and Computer Scienes(General)
Division/Department: Computer Support and Services Division, Computer Support and Services Division
Depositing User: M/S ICAST NAL
Date Deposited: 21 Sep 2006
Last Modified: 24 May 2010 09:50
URI: http://nal-ir.nal.res.in/id/eprint/2740
Actions (login required) | {"url":"http://nal-ir.nal.res.in/2740/","timestamp":"2014-04-20T13:38:54Z","content_type":null,"content_length":"15321","record_id":"<urn:uuid:68181bb5-5bf4-4894-a026-3f8a1681d95d>","cc-path":"CC-MAIN-2014-15/segments/1397609538787.31/warc/CC-MAIN-20140416005218-00367-ip-10-147-4-33.ec2.internal.warc.gz"} |
Obama and Earth-Moon L2 Lagrange point base
Some media
spread rumors about a possible imminent Branco Bamma's plan to announce a new space station.
Yellow is the Earth, blue is the Moon. And 1,2,3,4,5 are the Lx Lagrange points.
Instead of resembling the International Space Station that orbits the Earth just 400+ km above the surface (see
current location
to check whether you may see the dot above you), it would be placed in a more exotic place – the Earth-Moon
L2 Lagrange point
The point is located about 60,000 km behind the Moon so you can't see it from the Earth. I said "it is located". When is it located? The funny feature of the Lagrange points is that if you place
something at a Lagrange point – defined by its position relatively to two celestial bodies that orbit each other – it stays there. It stays there from the viewpoint of the rotating reference frame
which keeps the orbiting plane as well as the locations of the two celestial bodies fixed.
You see that there are five Lagrange points for each pair; L4 and L5 form a mirror pair. L2 is behind the Moon and has the same angular frequency as the Moon – so it has a higher velocity.
Consequently, the centifugal acceleration \(v\omega\) is greater than the Moon's, but that's OK because the attractive acceleration is also greater than the acceleration that attaches the Moon to the
Earth: the Moon itself adds its own force.
Note that the L2's distance from the Earth is about \(7/6\) times the distance of the Moon, so the centrifugal acceleration \(v\omega\) is about \(7/6\) times greater than it is for the Moon. The
Earth's attractive acceleration is \((7/6)^2\) times smaller than for the Moon, because of the inverse square law, but\[
\zav{\frac 67}^2 + \frac{1}{81}\cdot 6^2\sim 1.18\sim \frac 76
\] which gives approximately the right enhancement, with the help of the term from the Moon which is suppressed by Moon's \(81\) times smaller mass but enhanced by the \(6\) times shorter distance
from the Moon.
An Orion capsule
(picture above) could be sent over there by the
Space Launch System
between 2017 and the 2020s so don't change your dinner plans yet. A particular plan suggests the first people at L2 around 2021. They would be the first people who would have the privilege of seeing
no Earth around them for extended periods of time. :-) Instead, they would be watching the other side of the (six times larger than usual) Moon than almost all other mortals. Note that the Earth's
radius is just \(3.66\) times larger than Moon's but the Earth is six times further from L2 than the Moon, so it's too small to be seen behind the Moon.
Solar activity from planetary tidal forces
Incidentally, I am kind of fascinated by the
new paper
) showing a rather remarkable agreement in the Fourier transformation of two charts.
One of them is the solar activity, as reconstructed from some cosmogenic radionuclides (geology), and the other one is a theoretical model calculating the tidal forces of all the planets on the Sun's
. The agreement in the precise frequencies of the peaks looks totally remarkable. A priori, I would think that the tides are too weak. On the other hand, many things may be strengthened by various
effects and because it's a real measurable effect now, tides scaling as the justifiable, measurable yet modest \(1/r^3\), and not a hypothetical effect of the
relative position of the barycenter and the Sun
which would contradict the equivalence principle, none of my criticisms against the "barycenter theories" apply.
Even if this planetary influence on the solar activity is genuine, it doesn't imply that either of these curves is a good proxy to the Earth's climate. But the picture looks rather intriguing...
Needless to say, it's rather compatible with the 30 years of warming in the recent era and it predicts some cooling for the following decades (see e.g. Figure 3 in the paper).
6 comments:
1. Three years ago I found this video from Bad Astronomy, Phil Plait, on the Lagrangian points which I knew nothing about (of course). I like it.
If they miss seeing the Earth from their capsule why don't we put a huge mirror on L4 or L5 ? ;-)
2. You're so creative, Shannon! Maybe not the cheapest idea for replacing a photograph but it could be great for signal transmission in general.
3. Thanks for the compliment, Humble servant ;-)
4. Lubos,
I am doubtful of planetry influence on solar activity; the tidal forces are so very tiny. One has to be very cautious about such correlations, remarkable as they may be. Feynman warned about
this; it is so very easy to fool one’s self.
Small effects can have cumulative results but they seem to always involve resonances. For instance, two pendulum clocks hung on the same wall have a strong tendency to (slowly) become
synchronized but in the turbulence of the inner sun I don’t think anything can be so finely tuned. Call me skeptical.
5. Dear Gene, I am also skeptical, of course, 95+ percent against it. Remarkable claims need remarkable evidence. But this claim seems plausible times remarkable enough so that it's pretty
interesting to me...
Right, the Fourier modes are results of resonances. They're not the most elementary frequencies you get from the planets but some more complicated ones and the hypothetical effect is accumulated
over 1 century or centuries.
6. Sören FNov 12, 2012, 6:30:00 AM
Somebody must have misunderstood something as this source http://www.3news.co.nz/Obama-win-puts-NASA-over-the-moon---and-beyond/tabid/1160/articleID/276105/Default.aspx puts it "The 'L2' point
NASA wants to investigate lies about 1,500,000km further away from the Sun than the Earth." as if it'd be about the sun-earth L2 point. The graphic also has earth sun-yellow. | {"url":"http://motls.blogspot.com/2012/11/obama-and-earth-moon-l2-lagrange-point.html?m=1","timestamp":"2014-04-20T08:40:29Z","content_type":null,"content_length":"92121","record_id":"<urn:uuid:9bf709b6-ae97-4298-81c2-a068e89d9302>","cc-path":"CC-MAIN-2014-15/segments/1397609538110.1/warc/CC-MAIN-20140416005218-00389-ip-10-147-4-33.ec2.internal.warc.gz"} |
Hyperboloid of One Sheet
The hyperboloid of one sheet is possibly the most complicated of all the quadric surfaces. For one thing, its equation is very similar to that of a hyperboloid of two sheets, which is
confusing. (See the section on the two-sheeted hyperboloid for some tips on telling them apart.) For another, its cross sections are quite complex.
Gridlines: Having said all that, this is a shape familiar to any fan of the Simpsons, or even anybody who has only seen the beginning of the show. A hyperboloid of one sheet looks an awful lot like a
cooling tower at the Springfield Nuclear Power Plant.
On the left you can see the cross sections of a simple one-sheeted hyperboloid with A=B=C=1. The horizontal cross sections are ellipses -- circles, even, in this case -- while the vertical
cross sections are hyperbolas. The reason I said they are so complex is that these hyperbolas can open up and down or sideways, depending on what values you choose for x and y. Check the
example and see for yourself. Yikes! If you do these cross sections by hand, you have to check an awful lot of special cases.
The constants A, B, and C once again affect how much the hyperboloid stretches in the x-, y-, and z-directions. You can see this for yourself in the second picture. Notice how quickly the
hyperboloid grows, particularly in the z-direction. When C=2, a relatively small number, the surface already stretches from -8 to +8 on the z-axis.
One caveat: the picture only shows a small portion of the hyperboloid, but it continues on forever. So adjusting the value of C doesn't really make the surface taller -- it's already
"infinitely" tall -- but it certainly does affect the shape and slope of the surface. If you know something about partial derivatives, you could investigate how quickly z changes with
respect to x and y for different values of C. You could also explore why adjusting C seems to have a more dramatic effect than changing A and B.
Here are a few more points for you to consider.
• Once again, the sliders don't go all the way to 0. Why not? Make all of them as small as possible and zoom in to see the resulting hyperboloid.
• Look at the equation. What should happen when x=A or x=-A? Check this in the first picture; recall that A=1 there.
• Does there always have to be a "hole" through the hyperboloid, or could the sides touch at the origin? In other words, could the cross section given by z=0 ever be a point instead of
an ellipse? Experiment with the second picture; be sure to look directly from the top and zoom in before just assuming that the hole is gone. | {"url":"http://www.math.umn.edu/~rogness/quadrics/hyper1.shtml","timestamp":"2014-04-17T09:44:45Z","content_type":null,"content_length":"6613","record_id":"<urn:uuid:1138fa41-635a-4a22-9071-7035015b6517>","cc-path":"CC-MAIN-2014-15/segments/1398223207046.13/warc/CC-MAIN-20140423032007-00209-ip-10-147-4-33.ec2.internal.warc.gz"} |
Problems with adding double.
04-26-2012, 11:24 AM
Problems with adding double.
I got a really strange problem about adding 2 doubles.
double a = 2.3 + 3.4;
the result will be 5.699999999999.
Can anybody explain it for me!!!!!
04-26-2012, 11:33 AM
Re: Problems with adding double.
Read Goldberg's article and you know all.
kind regards,
04-26-2012, 11:36 AM
Re: Problems with adding double.
U have to determine the number of digits after the decimal point, this problem is related to the binary representation of doubles and intgers, it usually happens that's why it is better to
determine the number of digit after the decimal point u want to represent, this will force the rounding of the result and fix this calculation error
04-26-2012, 12:16 PM
Re: Problems with adding double.
U have to determine the number of digits after the decimal point, this problem is related to the binary representation of doubles and intgers, it usually happens that's why it is better to
determine the number of digit after the decimal point u want to represent, this will force the rounding of the result and fix this calculation error
Determining the representation of IEEE754 floaing point numbers doesn't fix any calculation errors. Read the link I supplied in my previous reply.
kind regards, | {"url":"http://www.java-forums.org/new-java/58902-problems-adding-double-print.html","timestamp":"2014-04-21T00:01:38Z","content_type":null,"content_length":"6832","record_id":"<urn:uuid:e0700826-3e4a-4773-9606-e81c44448caa>","cc-path":"CC-MAIN-2014-15/segments/1397609539337.22/warc/CC-MAIN-20140416005219-00132-ip-10-147-4-33.ec2.internal.warc.gz"} |
Modeling Information Diffusion in Implicit Networks
Download Links
by Jaewon Yang , Jure Leskovec
author = {Jaewon Yang and Jure Leskovec},
title = {Modeling Information Diffusion in Implicit Networks},
year = {}
Abstract—Social media forms a central domain for the production and dissemination of real-time information. Even though such flows of information have traditionally been thought of as diffusion
processes over social networks, the underlying phenomena are the result of a complex web of interactions among numerous participants. Here we develop a Linear Influence Model where rather than
requiring the knowledge of the social network and then modeling the diffusion by predicting which node will influence which other nodes in the network, we focus on modeling the global influence of a
node on the rate of diffusion through the (implicit) network. We model the number of newly infected nodes as a function of which other nodes got infected in the past. For each node we estimate an
influence function that quantifies how many subsequent infections can be attributed to the influence of that node over time. A nonparametric formulation of the model leads to a simple least squares
problem that can be solved on large datasets. We validate our model on a set of 500 million tweets and a set of 170 million news articles and blog posts. We show that the Linear Influence Model
accurately models influences of nodes and reliably predicts the temporal dynamics of information diffusion. We find that patterns of influence of individual participants differ significantly
depending on the type of the node and the topic of the information. I.
1583 Time Series Analysis: Forecasting and Control - Box, Jenkins - 1970
1182 Diffusion of Innovations - Rogers - 2003
490 Ridge regression : biased estimation for nonorthogonal problems - Hoerl, Kennard - 1970
316 Threshold models of collective behavior - Granovetter - 1978
237 The Mathematical Theory of Infectious Diseases and Its Applications - Bailey - 1975
233 The dynamics of viral marketing - Leskovec, Adamic, et al. - 2006
150 Measuring User Influence in Twitter: The Million Follower Fallacy - Cha, Haddadi, et al.
147 Meme-tracking and the dynamics of the news cycle - Leskovec, Backstrom, et al. - 2009
141 A Simple Model of Global Cascades on Random Networks - Watts - 2002
133 Talk of the network: A complex systems look at the underlying process of word-of-mouth - Goldenberg, Libai, et al.
98 Algorithm as 136: A k-means clustering algorithm - Hartigan, Wong - 1979
93 Social ties and word-of-mouth referral behavior - Brown, Reingen - 1987
80 Personal Influence: The Part Played by People in the Flow of Mass Communications - Katz, Lazarsfeld - 1955
77 Tracking information epidemics in blogspace - Adar, Adamic - 2005
77 Cascading behavior in large blog graphs - Leskovec, McGlohon, et al. - 2007
68 Network-based marketing: Identifying likely adopters via consumer networks - Hill, Provost, et al. - 2006
63 A structural theory of social influence - Friedkin - 2006
62 A measurement-driven analysis of information propagation in the flickr social network - Cha, Mislove, et al. - 2009
58 Learning influence probabilities in social networks - Goyal, Bonchi, et al. - 2010
56 Novelty and collective attention - WU, HUBERMAN - 2007
54 Influentials, networks, and public opinion formation - Watts, Dodds
49 A Reflective Newton Method for Minimizing a Quadratic Function Subject to Bounds on Some of the Variables - Coleman, Li - 1996
48 Patterns of temporal variation in online media - Yang, Leskovec - 2011
44 Tracing information flow on a global scale using Internet chainletter data - Liben-Nowell, Kleinberg
33 Modeling blog dynamics - Goetz, Leskovec, et al. - 2009
18 Information flow modeling based on diffusion rate for prediction and ranking - Song, Chi, et al. - 2007
16 2007): “Naïve Learning in Social Networks: Convergence, Influence, and the Wisdom of Crowds,” Forthcoming: Preprint, available at http://www.stanford.edu/~jacksonm/naivelearning.pdf ——— (2011):
“Network Structure and the Speed of Learning: Measuring Homop - Golub, Jackson
9 Wag the blog: How reliance on traditional media and the Internet influence credibility perceptions of weblogs among web users. Journalism and Mass Communication Quarterly - Johnson, Kaye - 2004
2 The rumour bomb: Theorising the convergence of new and old trends in mediated U.S. politics - Harsin
1 How can we measure the influence of the blogosphere? Workshop on the Weblogging Ecosystem - Gill - 2004
1 Solving least squares problems. 3rd edition - Lawson, Hanson - 1995 | {"url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.190.5932","timestamp":"2014-04-18T07:18:05Z","content_type":null,"content_length":"29175","record_id":"<urn:uuid:eebd3a78-f97e-43a2-bb0f-d53f07e17891>","cc-path":"CC-MAIN-2014-15/segments/1397609532573.41/warc/CC-MAIN-20140416005212-00472-ip-10-147-4-33.ec2.internal.warc.gz"} |
The characterization of the integers
Okay, so we’ve seen that the integers form an ordered ring with unit, and that the non-negative elements are well-ordered. It turns out that the integers are an integral domain (thus the name).
Let’s assume we have two integers (still using the definition by pairs of natural numbers) whose product is zero: $(a,b)(c,d)=(ac+bd,ad+bc)=(0,0)$. Since each of $a$, $b$, $c$, and $d$ is a natural
number, the order structure of $\mathbb{N}$ says that for $ac+bd=0$ we must have either $a$ or $c$ be zero and either $b$ or $d$ as well. Similarly, either $a$ or $d$ and either $b$ or $c$ must be
zero. If $a$ is not zero then this means both $c$ and $d$, making $(c,d)=0$. If $b$ is not zero again both $c$ and $d$ are zero. If both $a$ and $b$ are zero, then $(a,b)=0$. That is, if the product
of two integers is zero, one or the other must be zero.
So the integers are an ordered integral domain with unit whose non-negative elements are well-ordered. It turns out that $\mathbb{Z}$ is the only such ring. Any two rings satisfying all these
conditions are isomorphic, justifying our use of “the” integers. In fact, now we can turn around and define the integers to be any of the isomorphic rings satisfying these properties. What we’ve
really been showing in all these posts is that if we have any model of the axioms of the natural numbers, we can use it to build a model of the axioms of the integers. Once we know (or assume) that
some model of the natural numbers exists we know that a model of the integers exists.
Of course, just like we don’t care which model of the natural numbers we use, we don’t really care which model of the integers we use. All we care about is the axioms: those of an ordered integral
domain with unit whose non-negative elements are well-ordered. Everything else we say about the integers will follow from those axioms and not from the incidentals of the pairs-of-natural-numbers
construction, just like everything we say about the natural numbers follows from the Peano axioms and not from incidental properties of the Von Neumann or Zermelo or Church numeral models.
2 Comments »
1. [...] uniqueness of the integers It’s actually not too difficult to see that the integers are the only ordered integral domain with unit whose non-negative elements are well-ordered. So let’s go
ahead and do [...]
Pingback by The uniqueness of the integers « The Unapologetic Mathematician | April 4, 2007 | Reply
2. I’m not quite sure I agree with your argument for Z to be an integral domain, if (ac+bd, ad+bc)= (0,0) that only says that ac+bd=ad+bc, you cannot conclude that the components are equal because
what was meant by the = was an equivalence relation
Sharkasm | December 24, 2010 | Reply
• Recent Posts
• Blogroll
• Art
• Astronomy
• Computer Science
• Education
• Mathematics
• Me
• Philosophy
• Physics
• Politics
• Science
• RSS Feeds
• Feedback
Got something to say? Anonymous questions, comments, and suggestions at
• Subjects
• Archives | {"url":"http://unapologetic.wordpress.com/2007/04/03/the-characterization-of-the-integers/?like=1&_wpnonce=84af3d0b4c","timestamp":"2014-04-18T03:10:30Z","content_type":null,"content_length":"76022","record_id":"<urn:uuid:ce9c3be1-7327-4da7-a9a0-0d91e76fe7ec>","cc-path":"CC-MAIN-2014-15/segments/1398223203841.5/warc/CC-MAIN-20140423032003-00496-ip-10-147-4-33.ec2.internal.warc.gz"} |