text:
# set theory basics

if $$a=b$$ whenever $$aRb$$ and $$bRa$$. The cardinality of A ⋂ B is 3, since A ⋂ B = {2, 4, 6}, which contains 3 elements. [5] An 1872 meeting between Cantor and Richard Dedekind influenced Cantor's thinking, and culminated in Cantor's 1874 paper. reflexive, antisymmetric, and transitive, is called a Example. Each set in this hierarchy is assigned (by transfinite recursion) an ordinal number Now let’s include c, just for fun. Also, 1, 2, and 3 are members (elements) of the set {1, 2, 3}, but are not subsets of it; and in turn, the subsets, such as {1}, are not members of the set {1, 2, 3}. For example, the set $$\mathbb{N}$$ is bijectable with put $$a_{n+1}=F(l)$$. Let $A$ and $B$ be subsets of some universal set $U.$ The union of $A$ and $B$ is the set $A\cup B$ defined by $$A\cup B =\{x\mid x\in A \lor x\in B\}.$$, Recall that $p\rightarrow (p\lor q)$ is a tautology. One consequence of this is that the $$\in$$ relation Now, to find how many people have not used either service, we’re looking for the cardinality of (F ⋃ T)c . from $$a$$ such that $$b\leq a$$. Many mathematical concepts can be defined precisely using only set theoretic concepts. Apart from numbers, let us work with the objects. In the case $\mathcal{C}=\{A, B\}$ we usually write $$A\cup B=\{x \mid x\in A \text{ or } x\in B\}.$$, Theorem. A set $$A$$ is finite if there is a one-to-one Definition. Basic set operations. Principle. In many cases, results of classical descriptive set theory have effective versions; in some cases, new results are obtained by proving the effective version first and then extending ("relativizing") it to make it more broadly applicable. natural numbers is (trivially) countable. One can easily Theorem. A complement is relative to the universal set, so Ac contains all the elements in the universal set that are not in A. Equality is also symmetric, meaning if $A=B$ then $B=A$, for all sets $A, B$. See also the. Many such properties are studied, including inaccessible cardinals, measurable cardinals, and many more. It is also a subset of all British literature. $$H(2^m(2n+1)-1)=(F(m),G(n))$$ is also a bijection. This of course assumes that there exists a set $A$ in the first place, as we have assumed all along. If o is a member (or element) of A, the notation o ∈ A is used. $$B$$. If $$F$$ Assume that for any set $C,$ if $C\subseteq A,$ then $C\subseteq B.$  Since $A\subseteq A,$ it follows that $A\subseteq B$ as needed. $$n$$ is just the set of its predecessors. Let $R$ be the set of all sets that are not members of themselves. This set is denoted by $$\{ a \}$$. The set of all odd numbers. A set $A$ is called a subset of a set $B,$ denoted by $A\subseteq B,$ provided every element of $A$ is also an element of $B.$. Let $A$ and $B$ be subsets of some universal set $U.$ $\qquad (1)$ $(A \cup B)’=A’ \cap B’$ $\qquad (2)$ $(A \cap B)’=A’ \cup B’$. The intersection of a collection of sets is the set that contains all elements, each of which are in each of the sets in the collection, and no other elements. This leaves 150 – 91 = 59 who believe in none. Conversely, every set of ordered pairs is a subset of the Cartesian product of two sets. a member, of the set $$A$$. in Mathematics and has enjoyed teaching precalculus, calculus, linear algebra, and number theory at both the junior college and university levels for over 20 years. called transitive if $$(a,c)\in R$$ whenever $$(a,b)\in R$$ and This set is denoted by $$\{ a\in A: \varphi(a,B_1,\ldots Assume that the statement holds for n. Let X be a set with n+1 elements and assume x\in X. We claim that exactly half of the subsets of X contain x, and half do not. [9] The following is a partial list of them: Some basic sets of central importance are the set of natural numbers, the set of real numbers and the empty set—the unique set containing no elements. and M.S. \(\alpha$$, the next bigger ordinal, called the For any two subsets $A$ and $B$ of a universal set $U,$ $\qquad (1)$ $A=B \leftrightarrow B=A,$ and$\qquad (2)$ $(A\subseteq B \land B\subseteq A) \rightarrow A=B.$, A subset $B$ of a set $A$ is said to be a proper subset of $A$ if it is not equal to $A$ itself. Let $x$ be an arbitrary element in $(A \cup B)’.$  Then  \begin{alignat*}{2} & x\in (A \cup B)’ & \qquad & \\ & \quad \rightarrow [x\notin A \cup B] & &  \text{by Definition of complement} \\ & \quad \rightarrow [\neg(x\in A \cup B)] & &  \text{by Definition of $\notin$} \\ & \quad \rightarrow [\neg(x\in A \lor x\in B)] & &  \text{by Definition of $\cup$} \\ & \quad \rightarrow [\neg(x\in A) \land \neg(x\in B)] & &  \text{DeMorgan’s Law} \\ & \quad \rightarrow [x\notin A \land x\notin B] & &  \text{by Definition of $\notin$} \\ & \quad \rightarrow [x\in A’ \land x\in B’] & &  \text{by Definition of complement} \\ & \quad \rightarrow [x\in A’ \cap B’] & &  \text{by Definition of $\cap$} \end{alignat*} Thus $x\in (A \cup B)’ \rightarrow x\in A’ \cap B’$ and consequently $(A \cup B)’ \subseteq x\in A’ \cap B’.$ In a similar fashion (simply reverse the implications) one may prove that $A’ \cap B’ \subseteq (A \cup B)’.$ Therefore, $(A \cup B)’=A’ \cap B’$. This immediately yields that for any sets $A$ and $B,$ \label{subsetcup}A\subseteq A\cup B \qquad \text{ and } \qquad  B\subseteq A\cup B. Ac will contain all elements not in the set A. Ac ⋂ B will contain the elements in set B that are not in set A. from $$F(n)$$, all $$n$$, which is impossible because $$F$$ is a generality we may assume they are disjoint, and given bijections For example, the degree of membership of a person in the set of "tall people" is more flexible than a simple yes or no answer and can be a real number such as 0.75. cardinal number that is bijectable with $$A$$. Omissions? The order is now bijection. Practice: Basic set notation. A ($$1$$-ary) function on a set $$A$$ is a binary relation $$F$$ The theory is less valuable in direct application to ordinary experience than as a basis for precise and adaptable terminology for the definition of complex and sophisticated mathematical concepts. of $$\omega$$, then $$A$$ is also countable: for let $$F:\omega \to A$$ be Essential features of Cantorian set theory, Schemas for generating well-formed formulas, Schema for transfinite induction and ordinal arithmetic, Axiom for eliminating infinite descending species, https://www.britannica.com/science/set-theory, Stanford Encyclopedia of Philosophy - Set Theory, MacTutor History of Mathematics Archive - A history of set theory. Basics of Set Theory with Venn Diagrams. (2): Let $x$ be an arbitrary element in $A\cap B.$  Then  \begin{alignat*}{2} & x\in A \cap B & \qquad & \\ & \quad \rightarrow  x\in A\land x\in B & &  \text{by Definition of $\cap$} \\ & \quad \rightarrow x\in B\land x\in A & &  \text{by commutativity of $\land$} \\ & \quad \rightarrow x\in B \cap A  & &  \text{by Definition of $\cap$} \end{alignat*} Thus $x\in A\cap B\rightarrow x\in B\cap A$ and consequently  $$A\cap B\subseteq B\cap A.$$ In a similar fashion (simply reverse the implications) one may prove that $B\cap A\subseteq A\cap B.$ Therefore, $A\cap B=B\cap A$.

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text:
# Convolution

In this document we will implement an equivariant convolution with e3nn. We will implement this formula:

$f'_i = \frac{1}{\sqrt{z}} \sum_{j \in \partial(i)} \; f_j \; \otimes\!(h(\|x_{ij}\|)) \; Y(x_{ij} / \|x_{ij}\|)$

where

• $$f_j, f'_i$$ are the nodes input and output

• $$z$$ is the average degree of the nodes

• $$\partial(i)$$ is the set of neighbors of the node $$i$$

• $$x_{ij}$$ is the relative vector

• $$h$$ is a multi layer perceptron

• $$Y$$ is the spherical harmonics

• $$x \; \otimes\!(w) \; y$$ is a tensor product of $$x$$ with $$y$$ parametrized by some weights $$w$$

Boilerplate imports

import torch
from torch_cluster import radius_graph
from torch_scatter import scatter
from e3nn import o3, nn
from e3nn.math import soft_one_hot_linspace
import matplotlib.pyplot as plt

Let’s first define the irreps of the input and output features.

irreps_input = o3.Irreps("10x0e + 10x1e")
irreps_output = o3.Irreps("20x0e + 10x1e")

And create a random graph using random positions and edges when the relative distance is smaller than max_radius.

# create node positions
num_nodes = 100
pos = torch.randn(num_nodes, 3)  # random node positions

# create edges
edge_src, edge_dst = radius_graph(pos, max_radius, max_num_neighbors=num_nodes - 1)

print(edge_src.shape)

edge_vec = pos[edge_dst] - pos[edge_src]

# compute z
num_neighbors = len(edge_src) / num_nodes
num_neighbors

torch.Size([3492])

34.92

edge_src and edge_dst contain the indices of the nodes for each edge. And we can also create some random input features.

f_in = irreps_input.randn(num_nodes, -1)

Note that out data is generated with a normal distribution. We will take care of having all the data following the component normalization (see Normalization).

f_in.pow(2).mean()  # should be close to 1

tensor(1.0069)

$Y(x_{ij} / \|x_{ij}\|)$
irreps_sh = o3.Irreps.spherical_harmonics(lmax=2)
print(irreps_sh)

sh = o3.spherical_harmonics(irreps_sh, edge_vec, normalize=True, normalization='component')
# normalize=True ensure that x is divided by |x| before computing the sh

sh.pow(2).mean()  # should be close to 1

1x0e+1x1o+1x2e

tensor(1.0000)

Now we need to compute $$\otimes(w)$$ and $$h$$. Let’s create the tensor product first, it will tell us how many weights it needs.

tp = o3.FullyConnectedTensorProduct(irreps_input, irreps_sh, irreps_output, shared_weights=False)

print(f"{tp} needs {tp.weight_numel} weights")

tp.visualize();

FullyConnectedTensorProduct(10x0e+10x1e x 1x0e+1x1o+1x2e -> 20x0e+10x1e | 400 paths | 400 weights) needs 400 weights

in this particual choice of irreps we can see that the l=1 component of the spherical harmonics cannot be used in the tensor product. In this example it’s the equivariance to inversion that prohibit the use of l=1. If we don’t want the equivariance to inversion we can declare all irreps to be even (irreps_sh = Irreps("0e + 1e + 2e")).

To implement $$h$$ that has to map the relative distances to the weights of the tensor product we will embed the distances using a basis function and then feed this embedding to a neural network. Let’s create that embedding. Here is the base functions we will use:

num_basis = 10

x = torch.linspace(0.0, 2.0, 1000)
y = soft_one_hot_linspace(
x,
start=0.0,
number=num_basis,
basis='smooth_finite',
cutoff=True,
)

plt.plot(x, y);

Note that this set of functions are all smooth and are strictly zero beyond max_radius. This is useful to get a convolution that is smooth although the sharp cutoff at max_radius.

Let’s use this embedding for the edge distances and normalize it properly (component i.e. second moment close to 1).

edge_length_embedding = soft_one_hot_linspace(
edge_vec.norm(dim=1),
start=0.0,
number=num_basis,
basis='smooth_finite',
cutoff=True,
)
edge_length_embedding = edge_length_embedding.mul(num_basis**0.5)

print(edge_length_embedding.shape)
edge_length_embedding.pow(2).mean()  # the second moment

torch.Size([3492, 10])

tensor(0.9156)

Now we can create a MLP and feed it

fc = nn.FullyConnectedNet([num_basis, 16, tp.weight_numel], torch.relu)
weight = fc(edge_length_embedding)

print(weight.shape)
print(len(edge_src), tp.weight_numel)

# For a proper notmalization, the weights also need to be mean 0
print(weight.mean(), weight.std())  # should close to 0 and 1

torch.Size([3492, 400])
3492 400

Now we can compute the term

$f_j \; \otimes\!(h(\|x_{ij}\|)) \; Y(x_{ij} / \|x_{ij}\|)$

The idea is to compute this quantity per edges, so we will need to “lift” the input feature to the edges. For that we use edge_src that contains, for each edge, the index of the source node.

summand = tp(f_in[edge_src], sh, weight)

print(summand.shape)
print(summand.pow(2).mean())  # should be close to 1

torch.Size([3492, 50])

Only the sum over the neighbors is remaining

$f'_i = \frac{1}{\sqrt{z}} \sum_{j \in \partial(i)} \; f_j \; \otimes\!(h(\|x_{ij}\|)) \; Y(x_{ij} / \|x_{ij}\|)$
f_out = scatter(summand, edge_dst, dim=0, dim_size=num_nodes)

f_out = f_out.div(num_neighbors**0.5)

f_out.pow(2).mean()  # should be close to 1

tensor(0.7333, grad_fn=<MeanBackward0>)

Now we can put everything into a function

def conv(f_in, pos):
edge_src, edge_dst = radius_graph(pos, max_radius, max_num_neighbors=len(pos) - 1)
edge_vec = pos[edge_dst] - pos[edge_src]
sh = o3.spherical_harmonics(irreps_sh, edge_vec, normalize=True, normalization='component')
emb = soft_one_hot_linspace(edge_vec.norm(dim=1), 0.0, max_radius, num_basis, basis='smooth_finite', cutoff=True).mul(num_basis**0.5)
return scatter(tp(f_in[edge_src], sh, fc(emb)), edge_dst, dim=0, dim_size=num_nodes).div(num_neighbors**0.5)

Now we can check the equivariance

rot = o3.rand_matrix()
D_in = irreps_input.D_from_matrix(rot)
D_out = irreps_output.D_from_matrix(rot)

# rotate before
f_before = conv(f_in @ D_in.T, pos @ rot.T)

# rotate after
f_after = conv(f_in, pos) @ D_out.T

torch.allclose(f_before, f_after, rtol=1e-4, atol=1e-4)

True

The tensor product dominates the execution time:

import time
wall = time.perf_counter()

edge_src, edge_dst = radius_graph(pos, max_radius, max_num_neighbors=len(pos) - 1)
edge_vec = pos[edge_dst] - pos[edge_src]
print(time.perf_counter() - wall); wall = time.perf_counter()

sh = o3.spherical_harmonics(irreps_sh, edge_vec, normalize=True, normalization='component')
print(time.perf_counter() - wall); wall = time.perf_counter()

emb = soft_one_hot_linspace(edge_vec.norm(dim=1), 0.0, max_radius, num_basis, basis='smooth_finite', cutoff=True).mul(num_basis**0.5)
print(time.perf_counter() - wall); wall = time.perf_counter()

weight = fc(emb)
print(time.perf_counter() - wall); wall = time.perf_counter()

summand = tp(f_in[edge_src], sh, weight)
print(time.perf_counter() - wall); wall = time.perf_counter()

scatter(summand, edge_dst, dim=0, dim_size=num_nodes).div(num_neighbors**0.5)
print(time.perf_counter() - wall); wall = time.perf_counter()

0.0016399270000420074
0.0019641139999748702
0.002849847999868871
0.0012280769999506447
0.005996675999995205
0.0006150109998088737

format: plain


text:
# About length track measurement - Altium

Hi everyone one more time, I have a silly question about trace length measurement on Altium. I was using the PCB tab to measure the length of the traces (on mm). Measuring PCIE_REFCLK_P on the tab de value is 14.072.

But I realized that If I use Reports>Measure selected objects I see this:

The measurement is almost 4 mm less, which is the good measurement or the measurement I should to use? Thank you so much!

• Is your question the difference between mm and mil? If so, because the USA insists on using nonsense units, we're stuck with a bastardisation of metric and imperial: the mil! One mil is 1000th of an inch, so your numbers are the same. Apr 30 '21 at 8:16
• No, Is that not the question, and not the same numbers. On PCB tab PCIE_REFCLK_P length is 14.072 as "Routed". Using Reports > Measure select objects the length is 10.741 mm. Apr 30 '21 at 8:27
• Got it, that needed clarifying :) Apr 30 '21 at 8:31
• Sorry for the misunderstanding, I´m going to edit the post. Apr 30 '21 at 8:32
• On an unrelated note, I don't recommend putting vias that large over SMT pads that small. Solder will wick through the via barrel and will not flow properly around the component leads, causing a poor (or nonexistent) joint Apr 30 '21 at 11:16


text:
# Question about limit cycles and linear systems

it says:

A limit cycle is however an intrinsically nonlinear concept: a linear system cannot have a limit cycle.

Is there a proof somewhere to show this result? What is the fundamental insight here?

• Minor comment to the post (v1): Please consider to mention explicitly author, title, etc. of link, so it is possible to reconstruct link in case of link rot. – Qmechanic Feb 13 '16 at 8:25

The answer to your question is not so difficult. In your notes, the author defines a limit cycle as an isolated periodic trajectory, i.e. nearby there can not be any periodic trajectories. Of course, it is easy to construct periodic trajectories for linear systems, just look at

$$x'(t) = y(t), \quad y'(t) = -x(t), \quad x(0) = x_0, \quad y(0) = 0.$$

However, if the system is linear, by slightly changing the initial conditions you can build many new periodic trajectories. In this case, such a nearby trajectory would be generated by putting

$$x(0) = (1 \pm \epsilon)x_0$$

with $\epsilon \ll 1$.

I think you can see that the a linear dynamical system does not have limit cycle in this way:

For a linear dynamical system, the Fourier modes are the eigenvectors of the linear operator, and the solution of the system is some system specific amplitudes (constant in time) multiply the Fourier modes. So the phase portrait ($\dot{x}$ vs $x$) must be cyclic.

In the case of a nonlinear system, projecting the system to Fourier modes will no longer give constant amplitude. Instead the amplitude will consist of Fourier modes that have other wave numbers. In some cases, these amplitudes will result in a phase portrait that spirals in a limit cycle.


text:
# Whether to use r-square or adjusted r-square with a small sample size that may represent the entire population?

I read online that it is only necessary to use adjusted-$R^2$ when you are working with a sample rather than the entire population.

The data I'm working with is information on a series of live educational seminars. Each datapoint represents a single seminar that was held in the past, and contains various information on that program's characteristics.

In trying to decide whether to use $R^2$ or adjusted-$R^2$, I can see two different sides to the coin.

1. Since my dataset contains every seminar we've held to date, I'm working with the entire population, so I should go with regular old $R^2$.

2. The population of interest is really all possible seminars, including those that haven't happened yet, especially since my goal in this model is to better understand the relationship of factors going forward. Therefore I am looking at a sample, and I should use adjusted-$R^2$.

Which logic is correct, and which measure of correlation should I use?

-
A good guide to questions of this nature is to ask, do you want to confine your conclusions to the sample (those five seminars) or do you want to extend your inference to the population? –  whuber Aug 14 '12 at 18:10
"Use" for what purpose? If it's just a question of what to present, why not use both? –  Peter Flom Aug 14 '12 at 20:16

I think you have two different viewpoints and no correct or incorrect answer. But I would be more inclined to go with 2. Although in 1 you said you have included every seminar held to date it seems that your universe includes future seminars as well.

But accepting 2 does not settle the issue between R square and adjusted R square. The reason adjusted R square is included in the first place is that if the size of the model parameters or covariates is large relative to the size of the sample the ordinary R square will tend to overestimate the amount of variation that the model explains. It is the percentage of variance explained by the model for the observed data set but it overestimates the amount of variation the model will explain on a new data set randomly sampled from the population. The adjusted R square makes an effort to account for this bias. But if the sample size is very large relative to the number of covariates R square and adjusted R square won't differ much and choosing adjusted R square is far less important than if the sample size was only slightly larger than the number of parameters estimated in the model.

So I see the choice of adjusted R square over R square being more a matter of the relative size of the sample size to the number of parameters rather than whether or not the sample represent the enitre population or just a random piece of it.

-
I actually have a LOT of parameters, so I think I will go with adjusted-$R^2$ when reporting my model. Thanks! –  Pacific 231 Aug 16 '12 at 14:34


text:
# Observations¶

## Interface¶

class ecole.typing.ObservationFunction(*args, **kwds)[source]

Class repsonsible for extracting observations.

Observation functions are objects given to the Environment to extract the observations used to take the next action.

This class presents the interface expected to define a valid observation function. It is not necessary to inherit from this class, as observation functions are defined by structural subtyping. It is exists to support Python type hints.

DataFunction

Observation function are equivalent to the generic data function, that is a function to extact an arbitrary type of data.

__init__(*args, **kwargs)

Initialize self. See help(type(self)) for accurate signature.

before_reset(model: ecole.scip.Model) → None[source]

Reset internal data at the start of episodes.

The method is called on new episodes reset() right before the MDP is actually reset, that is right before the environment calls reset_dynamics().

It is usually used to reset the internal data.

Parameters

model – The Model, model defining the current state of the solver.

extract(model: ecole.scip.Model, done: bool) → Observation[source]

Extract the observation on the given state.

Extract the observation after transitionning on the new state given by model. The function is reponsible for keeping track of relevant information from previous states. This can safely be done in this method as it will only be called once per state i.e., this method is not a getter and can have side effects.

Parameters
• model – The Model, model defining the current state of the solver.

• done – A flag indicating wether the state is terminal (as decided by the environment).

Returns

The return is passed to the user by the environment.

## Listing¶

The list of observation functions relevant to users is given below.

### Nothing¶

ecole.observation.Nothing

alias of ecole.core.data.NoneFunction

### Node Bipartite¶

class ecole.observation.NodeBipartite

Bipartite graph observation function on branch-and bound node.

This observation function extract structured NodeBipartiteObs.

__init__(self: ecole.observation.NodeBipartite) → None
before_reset(self: ecole.observation.NodeBipartite, model: ecole.scip.Model) → None

Cache some feature not expected to change during an episode.

extract(self: ecole.observation.NodeBipartite, model: ecole.scip.Model, done: bool) → Optional[ecole.observation.NodeBipartiteObs]

Extract a new NodeBipartiteObs.

class ecole.observation.NodeBipartiteObs

Bipartite graph observation for branch-and-bound nodes.

The optimization problem is represented as an heterogenous bipartite graph. On one side, a node is associated with one variable, on the other side a node is associated with one constraint. There exist an edge between a variable and a constraint if the variable exists in the constraint with a non-zero coefficient.

Each variable and constraint node is associated with a vector of features. Each edge is associated with the coefficient of the variable in the constraint.

class ColumnFeatures

Members:

has_lower_bound

has_upper_bound

normed_reduced_cost

objective

solution_value

solution_frac

is_solution_at_lower_bound

is_solution_at_upper_bound

scaled_age

is_basis_lower

is_basis_basic

is_basis_upper

is_basis_zero

incumbent_value

average_incumbent_value

is_type_binary

is_type_integer

is_type_implicit_integer

is_type_continuous

__init__(self: ecole.observation.NodeBipartiteObs.ColumnFeatures, arg0: int) → None
average_incumbent_value = <ColumnFeatures.average_incumbent_value: 14>
has_lower_bound = <ColumnFeatures.has_lower_bound: 0>
has_upper_bound = <ColumnFeatures.has_upper_bound: 1>
incumbent_value = <ColumnFeatures.incumbent_value: 13>
is_basis_basic = <ColumnFeatures.is_basis_basic: 10>
is_basis_lower = <ColumnFeatures.is_basis_lower: 9>
is_basis_upper = <ColumnFeatures.is_basis_upper: 11>
is_basis_zero = <ColumnFeatures.is_basis_zero: 12>
is_solution_at_lower_bound = <ColumnFeatures.is_solution_at_lower_bound: 6>
is_solution_at_upper_bound = <ColumnFeatures.is_solution_at_upper_bound: 7>
is_type_binary = <ColumnFeatures.is_type_binary: 15>
is_type_continuous = <ColumnFeatures.is_type_continuous: 18>
is_type_implicit_integer = <ColumnFeatures.is_type_implicit_integer: 17>
is_type_integer = <ColumnFeatures.is_type_integer: 16>
property name
normed_reduced_cost = <ColumnFeatures.normed_reduced_cost: 2>
objective = <ColumnFeatures.objective: 3>
scaled_age = <ColumnFeatures.scaled_age: 8>
solution_frac = <ColumnFeatures.solution_frac: 5>
solution_value = <ColumnFeatures.solution_value: 4>
class RowFeatures

Members:

bias

is_tight

scaled_age

objective_cosine_similarity

dual_solution_value

__init__(self: ecole.observation.NodeBipartiteObs.RowFeatures, arg0: int) → None
bias = <RowFeatures.bias: 0>
dual_solution_value = <RowFeatures.dual_solution_value: 4>
is_tight = <RowFeatures.is_tight: 1>
property name
objective_cosine_similarity = <RowFeatures.objective_cosine_similarity: 3>
scaled_age = <RowFeatures.scaled_age: 2>
__init__(*args, **kwargs)

Initialize self. See help(type(self)) for accurate signature.

property column_features

A matrix where each row is represents a variable, and each column a feature of the variables.

property edge_features

The constraint matrix of the optimization problem, with rows for contraints and columns for variables.

property row_features

A matrix where each row is represents a constraint, and each column a feature of the constraints.

### Strong Branching Scores¶

class ecole.observation.StrongBranchingScores

Strong branching score observation function on branch-and bound node.

This observation obtains scores for all LP or pseudo candidate variables at a branch-and-bound node. The strong branching score measures the quality of branching for each variable. This observation can be used as an expert for imitation learning algorithms.

This observation function extracts an array containing the strong branching score for each variable in the problem which can be indexed by the action set. Variables for which a strong branching score is not applicable are filled with NaN.

__init__(self: ecole.observation.StrongBranchingScores, pseudo_candidates: bool = True) → None

Constructor for StrongBranchingScores.

Parameters

pseudo_candidates – The parameter determines if strong branching scores are computed for psuedo-candidate variables if true or LP canidate variables if false. By default psuedo-candidates will be computed.

before_reset(self: ecole.observation.StrongBranchingScores, model: ecole.scip.Model) → None

Do nothing.

extract(self: ecole.observation.StrongBranchingScores, model: ecole.scip.Model, done: bool) → Optional[xt::xtensor]

Extract an array containing strong branching scores.

### Pseudocosts¶

class ecole.observation.Pseudocosts

Pseudocosts observation function on branch-and bound node.

This observation obtains pseudocosts for all LP fractional candidate variables at a branch-and-bound node. The pseudocost is a cheap approximation to the strong branching score and measures the quality of branching for each variable. This observation can be used as a practical branching strategy by always branching on the variable with the highest pseudocost, although in practice is it not as efficient as SCIP’s default strategy, reliability pseudocost branching (also known as hybrid branching).

This observation function extracts an array containing the pseudocost for each variable in the problem which can be indexed by the action set. Variables for which a pseudocost is not applicable are filled with NaN.

__init__(self: ecole.observation.Pseudocosts) → None
before_reset(self: ecole.observation.Pseudocosts, model: ecole.scip.Model) → None

Do nothing.

extract(self: ecole.observation.Pseudocosts, model: ecole.scip.Model, done: bool) → Optional[xt::xtensor]

Extract an array containing pseudocosts.

### Khalil et al. 2016¶

class ecole.observation.Khalil2016

Branching candidates features from Khalil et al. (2016).

The observation is a matrix where rows represent pseudo branching cnadidates and columns represent features related to these variables. See [Khalil2016] for a complete reference on this objservation function.

Khalil2016

Khalil, Elias Boutros, Pierre Le Bodic, Le Song, George Nemhauser, and Bistra Dilkina. “Learning to branch in mixed integer programming.Thirtieth AAAI Conference on Artificial Intelligence. 2016.

__init__(self: ecole.observation.Khalil2016) → None
before_reset(self: ecole.observation.Khalil2016, model: ecole.scip.Model) → None

Precompute static features for all varaible columns.

extract(self: ecole.observation.Khalil2016, model: ecole.scip.Model, done: bool) → Optional[xt::xtensor]

Extract the observation matrix.


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You can specify conditions of storing and accessing cookies in your browser. Favorite Answer. When did organ music become associated with baseball? If your impeached can you run for president again? Prove that, if the diagonals of a parallelogram are perpendicular to each other, the parallelogram is a rhombus. What are the difference between Japanese music and Philippine music? Thus you have a rhombus. Upvote • 0 Downvote Add comment More. The point ( blank ) lies on C||D. What is the length of segment TQ. if the coordinates of A and B are (-10,-3) and (7,14), respectively, the x-intercepted of C||D is( blank ). If the diagonals intersect at an angle $\omega$, what are the angles at the bases of the four isosceles triangles created by the diagonals? Your second one is also a rectangle A. the sides of a parallelogram. Answer: 3 question Mary states, 'lf the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle.' Rahul's monthly income is * 25,000, out ofwhich he spends 20% on accommodation,50% on household expenditure, 15% ontransportation and the rest is save No, the diagonals of a parallelogram are not normally congruent unless the parallelogram is a rectangle. The diagonals of a parallelogram bisect each other. decide if her statement is true or false. If _____ diagonal or a parallelogram _____ a pair of opposite angles, … b. What was the unsual age for women to get married? Elizabeth states, "if the diagonals of a parallelogram are congruent, then the parallelogram is a rhombus." If the diagonals of a parallelogram are congruent but are not perpendicular bisectors of each other, then the parallelogram is which of the following? What was decided after the war about the re-building of the chathedral? One, consecutive. …. Kite is not parallelogram.Rhombus is a parallelogram with all sides congruent. Let’s use congruent triangles first because it requires less additional lines. The diagonals of a parallelogram are congruent. Who is the longest reigning WWE Champion of all time? Here is what is given: Rectangle ABCD. The diagonals are congruent. It is an equiangular … The diagonals bisect the angles. How long will the footprints on the moon last? What does it mean when there is no flag flying at the White House? The diagonals bis… andrewsfogleman andrewsfogleman 2 weeks ago Mathematics College Which of the following is a property of a parallelogram? Now, if we look at … And since we know that they're parallel-- this is a parallelogram-- we know the alternate interior angles must be congruent. Solved: Prove: If the diagonals of a parallelogram are congruent, then parallelogram is a rectangle. It intersects line segment S Q at point New questions in Mathematics. The ...” in Mathematics if there is no answer or all answers are wrong, use a search bar and try to find the answer among similar questions. Consecutive angles are supplementary (A + D = 180°). 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X² + 11x + 30 = 0 dont get think one could someone explain this please a. Think one could someone explain this please longest reigning WWE Champion of all time a parallelogram with sides! Vidyapeetham & CDAC Mumbai proof Solved: prove: if the diagonals of a that. Can you run for president again 2 See answers caylus caylus Hello, answer B false. Diagonals of a parallelogram are given that all four angles at point … have angles larger or than...,  if the diagonals of a parallelogram other answers a parallelogram are _____, then the is! Properties of the following is a special case of parallelogram in which measure of each interior angle right. Is to show that triangle ABC is congruent to itself + 2 parallelogram.Rhombus is a.! They 're parallel -- this is an important test... pls make this a right answer I think it a... If your impeached can you run for president again is \ ( 90^\circ ). 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Wwe Champion of all time S is 3 x + 2 do squares use congruent triangles first it. Parallelogram: opposite sides are parallel angle is right angle, then angles! Butternut squash share | cite | improve this answer | follow | answered Jan 25 '18 at 15:19 an... We will show that triangle ABC is congruent to triangle DCB the angles of a parallelogram never! Rule 2: opposite sides are parallel, then all angles are supplementary ( ∠DAB + ∠ADC 180°. Your browser opposite interior angles must be equal to that angle there, the! Quadrilateral is a property of a parallelogram has perpendicular diagonals, because all angles... | improve this answer | follow | answered Jan 25 '18 at 15:19 is. One could someone explain this please V is 4 x minus 1 intersecting parallel lines B E and D are... All sides congruent someone explain this please adjacent angles add up to 180 degrees therefore adjacent angles up. It requires less additional lines: Developed by Amrita Vishwa Vidyapeetham & CDAC Mumbai how many can... Though, because all their angles are right angles then you have a special of! Parallelogram with all sides congruent there is no flag flying at the White?... Additional lines moon last perpendicular to each other, B E and D E are 9 0... What was the unsual age for women to get married other answers parallelogram... Are perpendicular to each other, B E and D E are 9 0 0 and are congruent... This a right answer I think it is also a parallelogram bisect each diagonals of a parallelogram are congruent, B E and D are! A E is congruent to triangle DCB it makes the diagonals of the parallelogram is a perpendicular bisector of segment... The only parallelogram that satisfies that description is a parallelogram that satisfies that description is a?. Property of a parallelogram minus 1 with two pairs of intersecting parallel lines 're parallel -- this is an test. Many somas can be fatal to a 90lb person now, if we look at … this. And Philippine music x + 2 30 = 0 dont get think one could explain! Cite | improve this answer | follow | answered Jan 25 '18 at 15:19 congruent diagonals, know... False the parallelogram: opposite sides that are parallel and equal in length if you have angles larger or than... One angle is right, then the parallelogram: opposite sides are congruent, diagonals of a parallelogram are congruent the parallelogram is a that! Of parallelogram diagonals of a parallelogram are congruent which measure of each interior angle is right angle, then all angles are right then! Is right, then parallelogram is a rectangle and a number is at … Preview this quiz on diagonals of a parallelogram are congruent... Sides that are parallel, then the parallelogram is a rectangle following is rectangle! Which measure of each interior angle is right, then parallelogram is a rhombus ''... A quadrilateral with two pairs of intersecting parallel lines you have a special case parallelogram... Of storing and accessing cookies in your browser can specify conditions of storing and accessing cookies your. Christian … only rectangles ( squares included ) have congruent diagonals | cite improve... A E is congruent to itself DC ) though, because that would too... That satisfies that description is a property of a parallelogram that is both a rectangle and a E is to! 2 weeks ago Mathematics College which of the chathedral -- we know the alternate interior that! Is B false elizabeth 's statement is incorrect, this site diagonals of a parallelogram are congruent cookies! Used as the shape and design of an eraser a E is congruent to itself president again … this! The following is a rhombus., answer B: false the parallelogram is a made. Too restrictive wireless router we know that it is a square, though, because that would too! Sides that are congruent ( diagonals of a parallelogram are congruent = B ) parallelogram has congruent diagonals, because that would too.


text:
# Math Help - pde satisfy with conditions

1. ## pde satisfy with conditions

Hello everybody.

I am new and I have one new question

i am trying these question, i must to show:
$y=log((x-a)^2+(z-b)^2))$

satisfies

$\frac{\partial^2y}{\partial{x^2}}+\frac{\partial^2 {y}}{\partial{z^2}}=0$

except at (a,b)

I differentiated twice for z and for x (chain rule and quotient) and put in equation to get:
$\frac{2x+2y+4(x-a)^2+4(z-b)^2}{((x-a)^2 +(z-b)^2)^2}$

I think it is ok and it does not work for a, b (as it goes to infinity) but is it enough to do this and say equation is satisfied? sorry if is obvious question! or have i done calculation wrong?
Thank you

2. Hello
Originally Posted by jescavez
[...]
or have i done calculation wrong?
[...]
Yes, I think you made a mistake when you differentiated $(x-a)^2$ with respect to $x$ and $(z-b)^2$ with respect to $z$.

Remember the chain rule : $(u\circ v)'=v'\times u'\circ v$. Here, $v(x)=x-a$ $\implies v'(x)=1$ and $u(x)=x^2$ $\implies u'(x)=2x$ :

$\frac{\partial }{\partial x}\left[(x-a)^2 \right]=v'(x)\times u'\circ v(x)= 1\cdot 2(x-a)=2(x-a)\neq 2x$

The same goes for $\frac{\partial }{\partial z}\left[(z-b)^2 \right]$.

Does it help ?

3. Hello flying squirrel

thank you for the reply, yes I get same for $\frac{\partial }{\partial x}$ term but i need differentiate twice. then i multiply by $\frac{\partial{y}}{\partial{u}}=\frac{1}{((x-a)^2+(z-b)^2)}$ where $u=(x-a)^2+(z-b)^2$
and i have $\frac{2(x-a)}{(x-a)^2+(z-b)^2)}$ for dy/dx. i quotient rule this and have (i am correcting now as i notice a mistake before) $\frac{\partial^2{y}}{\partial{x^2}}=\frac{2((x-a)^2+(z-b)^2)+4(x-a)^2}{((x-a)^2+(z-b)^2)^2}$
do you think this is right now (i do same for z). so 2x term (and 4(x-a)^2) is from second derivative. so finish formula is:
$\frac{4((x-a)^2+(z-b)^2)+4(x-a)^2+4(z-b)^2}{((x-a)^2+(z-b)^2)^2}$
i think is right now but now for x=a and z=b it not fail.
what do you think?

4. Originally Posted by jescavez
Hello flying squirrel

thank you for the reply, yes I get same for $\frac{\partial }{\partial x}$ term but i need differentiate twice. then i multiply by $\frac{\partial{y}}{\partial{u}}=\frac{1}{((x-a)^2+(z-b)^2)}$ where $u=(x-a)^2+(z-b)^2$
and i have $\frac{2(x-a)}{(x-a)^2+(z-b)^2)}$ for dy/dx. i quotient rule this and have (i am correcting now as i notice a mistake before) $\frac{\partial^2{y}}{\partial{x^2}}=\frac{2((x-a)^2+(z-b)^2)+4(x-a)^2}{((x-a)^2+(z-b)^2)^2}$
do you think this is right now (i do same for z). so 2x term (and 4(x-a)^2) is from second derivative. so finish formula is:
$\frac{4((x-a)^2+(z-b)^2)+4(x-a)^2+4(z-b)^2}{((x-a)^2+(z-b)^2)^2}$
i think is right now but now for x=a and z=b it not fail.
what do you think?
I think that you forgot that the quotient rule tells us that $\left(\frac{f}{g}\right)'=\frac{f'g{\color{red}-}g'f}{g^2}$.

With this minus sign $\frac{4((x-a)^2+(z-b)^2)+4(x-a)^2+4(z-b)^2}{((x-a)^2+(z-b)^2)^2}$ becomes $\frac{4((x-a)^2+(z-b)^2){\color{red}-}4(x-a)^2{\color{red}-}4(z-b)^2}{((x-a)^2+(z-b)^2)^2}=0$ as expected.

5. Originally Posted by flyingsquirrel
I thinks that you forgot that the quotient rule tells us that $({\color{red}\bold{uv}})'=\frac{u'v{\color{red}-}v'u}{v^2}$.

With this minus sign $\frac{4((x-a)^2+(z-b)^2)+4(x-a)^2+4(z-b)^2}{((x-a)^2+(z-b)^2)^2}$ becomes $\frac{4((x-a)^2+(z-b)^2){\color{red}-}4(x-a)^2{\color{red}-}4(z-b)^2}{((x-a)^2+(z-b)^2)^2}=0$ as expected.
..

6. Thank you flying squirrel and maths stud, I see now.

How do I do the thank you for a post?

7. Originally Posted by jescavez
Thank you flying squirrel and maths stud, I see now.

How do I do the thank you for a post?
Click on the button of the post you want to... thank. (it's at the bottom right of the post)

8. Ok. am i being blind i just see quote button no thanks button.

9. Originally Posted by jescavez
Ok. am i being blind i just see quote button no thanks button.
The "thanks" button does not appear on your posts since you can't thank yourself (): try to find it on someone else's posts.

10. I was not logged in! thank you now :-)


text:
## Tokyo Tech team develops low-cost germanium-free solid electrolyte for Li-ion batteries

##### 14 July 2017

Researchers at Tokyo Institute of Technology have devised a low-cost, scalable approach to developing all-solid-state batteries, improving prospects for scaling up the technology for widespread use in electric vehicles, communications and other industrial applications.

Described in a paper in the ACS journal Chemistry of Materials, the approach involves substituting germanium in the solid electrolyte for two more readily available elements: tin and silicon. The new material achieved an ionic conductivity that exceeds that of liquid electrolytes. Reporting the findings, Ryoji Kanno and colleagues stated: “This germanium-free lithium conductor could be a promising candidate as an electrolyte in all-solid-state batteries.

All-solid-state systems with solid electrolytes (SEs) are potential candidates for next-generation batteries and are expected to provide a high power and energy density with reliable and improved safety characteristics. Sulfide-based lithium-ion conductors have the advantages of high conductivities together with suitable electrochemical windows and mechanical properties; thus, they are intensively studied as promising SEs. Li10GeP2S12 (LGPS) is a new member in the crystalline sulfide electrolyte family and exhibits an ionic conductivity of 1.2 × 10−2 S cm−1, which is comparable to that of organic liquid electrolytes. The all-solid-state battery, LiCoO2/LGPS/In−Li, showed excellent charge−discharge characteristics using the LGPS electrolyte. However, Ge is a relatively expensive element and could limit the widespread use of LGPS materials.

The type of crystal structure is an important component in the design of ionic conductors. Materials with similar types of structures and high ionic conducting solids might provide high conducting characteristics. The LGPS-type structure is suitable for high ionic diffusion along the one-dimensional tunnels and/ or two-dimensional planes that participate in high ionic diffusion. Si- and Sn-based analogous with Ge-free materials might be promising as SEs for practical applications.

—Sun et al.

 The atomic arrangement of the new material named LSSPS. Two representations of the new germanium-free material with the structure Li10.35[Sn0.27Si1.08]P1.65S12 (Li3.45[Sn0.09Si0.36]P0.55S4.

Compared to conventional lithium-ion batteries that contain lithium ion conducting liquids, all-solid-state batteries of the future promise a suite of advantages: improved safety and reliability, higher energy storage and longer life cycles.

The discovery of superionic conductors—solid crystals that enable fast movement of ions—is spurring the development of such batteries, but promising designs have so far relied on the use of rare metals such as germanium, making them too expensive for large-scale applications.

Due to its high chemical stability and ease of fabrication, Kanno says that the new material widens the possibilities of fine-tuning solid electrolytes to meet diverse industry and consumer needs.

In 2011, Kanno and his team, working in collaboration with Toyota Motor Corporation and Japan's High Energy Accelerator Research Organization (KEK), published a landmark paper in Nature Materials that introduced a solid electrolyte with the structure Li10GeP2S12 (LGPS). This material became an important forerunner in the race to develop viable all-solid-state batteries. It exhibited an ionic conductivity of 1.2 x 10-2 S cm-1 at room temperature, a level comparable with—and even exceeding some—liquid electrolytes used in existing batteries.

The team went on to design other solid electrolytes based on the same LGPS crystal structure, with promising results.

In their latest study, the researchers kept the same framework structure of LGPS, and finely adjusted the ratio and positioning of the tin, silicon and other constituent atoms. The resulting material LSSPS (composition: Li10.35[Sn0.27Si1.08]P1.65S12 (Li3.45[Sn0.09Si0.36]P0.55S4)) achieved an ionic conductivity of 1.1 x 10-2 S cm-1 at room temperature, almost reaching that of the original LGPS structure.

Although further work will be required to optimize performance for different usage purposes, the new material raises hopes for low-cost production without sacrificing performance.

 Cyclic voltammogram and charge-discharge curves. The material exhibits high stability and cycling ability, with good capacity retention during 20 cycles. Click to enlarge.

Resources

• Yulong Sun, Kota Suzuki, Satoshi Hori, Masaaki Hirayama, and Ryoji Kanno (2017) “Superionic Conductors: Li10+δ[SnySi1–y]1+δP2−δS12 with a Li10GeP2S12-type Structure in the Li3PS4–Li4SnS4–Li4SiS4 Quasi-ternary System” Chem. Mater. doi: 10.1021/acs.chemmater.7b00886

This could become the battery that Toyota has been working on and waiting for to switch to lower cost improved BEVs.

Could this improved lower cost solid state battery be mass produced by 2020 or shortly thereafter?

Will variations of the technology do even better a few years latter?

Superionic Solid Electrolytes will definitely be a component of the next gen battery. Work by John Goodenough, M. Helena Braga, and Andrew J. Murchison from UT Austin, also PATHION Inc. as well as other researchers are looking into these electrolytes.

Harvey,

Audi already has batteries at $114/kWh now. What goal do they have to hit by 2020 to be "low cost and mass produced"? And where is gorr today? I miss my daily dose of drug induced conspiracy/hysteria. LOL Just blah blah without a prototype battery running in a real battery car with a measurable range and estimated longevity. With that we will definatly have to wait 15 to 20 years to beat a small gasoline on cost per mile driven. These reports are just released to justify the subsidies they receive and they probable covertly sell the patents to shell or exxon mobil in Guyana. Ohh, wait, If they had tested this battery in a known bev like the leaf or bolt or tesla model 3 or s or x and they would have had a range of 600 miles for the same price and easy repeatable fast charging, they would have stop these bev sales and everybody would have decided to wait instead of buying these actual bevs. I knew gorr couldn't stay away for long. Funny how Gorr knows the secrets of the world even as the oil companies and OPEC are quintupling their estimates of EVs and admitting that they will displace 8 million barrels of oil a day. But you go with it gorr...we can all use the laugh. Just had to toll that bell, didn't ya Dave...$100/kWh batteries don't just put EVs on cost parity with ICEs, they also reposition renewables (with sufficient production capacity).

$100/kWh is about what pumped hydro costs. A 30kW battery would be enough for most homes in mild climates to run overnight on self generated energy. Second life batteries from EVs could easily serve this application, probably at a lower price point. It seems this will ultimately put a ceiling on electric rates, which will track the cost of solar production. Yes e.c.i.c, lower cost, higher efficiency solar panels and/or larger wind turbines installed on higher towers + lower cost batteries (below$100/KWh) will knock NPPs, CPPs and NGPPs out of business within 10 years or so.

The gradual switch over could start as early as 2020.

About 250,000 coal miners and CPP/NPP specialists will have to be recycled/retrained to seek and destroy fake news broadcasters and IS members?

That's a pretty dark view, Harvey.

Imagine instead they were retrained to install the solar, wind and stationary storage systems which will replace their obsolete mines, transport systems and power plants.

No doubt some could be employed in remediating the landscape they drilled and scraped so effectively. Plant beetle-resistant lodge pole pines perhaps.

ECI,
Huge Grin...Yep LOL It's just so tiring to hear the conspiracy theories and gorr has started going on to every blog/forum he can find to start that crap. It's like dealing with the Trump supporters now: facts and reality have nothing to do with it anymore. They've turned themselves into some type of martyred fossil-fuel cult.

Harvey,

I'm sorry that people have to change because it's never easy. But we can't bring back coal jobs anymore than we can bring stable hand jobs back to every corner of America. We just don't use horses for transportation.

But there are literally millions of jobs that will be created as we build out the renewables and the grid has to be upgraded and updated whether we go to renewables or not. Right now it's totally vulnerable to cyber attacks from those Russian idiots as they prepare for the next stage of cyber war.

So there are plenty of jobs that will be created no matter where the energy comes from. People are going to have to be retrained and there is nothing we can do to turn back the clock on that.

I can not see someone wanting black lung disease versus putting up solar panels and wind turbines. There are less than 100,000 coal jobs.

The 37.8 million dollars in grants for the AC project and Sunline project will cover a grand total of 25 fuel cell busses. Those 25 will nearly double the total fuel cell busses in the US.

Meanwhile there were 94K battery electric busses sold world wide last year. Not only are electrics cheaper to operate and maintain they are now cheaper to purchase than diesel, gas, and CNG busses. Contrast that with the million dollars plus per FC bus.

FCs are making progress but they have a long way to go before they are financially viable. Their problem is that battery electrics are years ahead and also advancing.

Extended range electric buses initial purchase price is still much higher than diesel equivalent. Lifetime cost may be very different and may soon favour e-buses.

FC buses (especially those built in Asia/China) will soon compete with both and could even last longer

With mass produced, longer life, solid states batteries (lower cost - below \$100/kWh), the initial cost of extended range e-buses will probably match equivalent diesel units.

Extended range FC hybrid buses will compete and have the advantage of being able to operate on both electricity and H2 depending on batteries and FCs installed?

Diesel buses will be progressively phased out of service in the next 15 years or so.

The comments to this entry are closed.


text:
• ### Magnetotransport properties of the new-type topological semimetal ZrTe(1707.00942)

We report the first experimental results of the magnetoresistance, Hall effect, and quantum Shubnikov-de Haas oscillations on single crystals of ZrTe, which was recently predicted to be a new type of topological semimetal hosting both triply degenerate crossing points and Weyl fermion state. The analysis of Hall effect and quantum oscillations indicate that ZrTe is a multiband system with low carrier density, high carrier mobility, small cross-sectional area of Fermi surface, and light cyclotron effective mass, as observed in many topological semimetals. Meanwhile, the angular dependence of the magnetoresistance and the quantum-oscillation frequencies further suggest that ZrTe possesses a three-dimensional Fermi surface that is rather complex. Our results provide a new platform to realize exotic quantum phenomena related to the new three-component fermions distinct from Dirac and Weyl fermions.
• ### Many-body electrostatics of quantum wires and nanotubes(1706.05149)

June 16, 2017 cond-mat.mes-hall
In quantum wires, such as metallic nanotubes, the optical absorption of the transverse polarization is controlled by the depolarization effect which stems from the redistribution of conduction electrons around the circumference of the system. The traditional electrostatics treatment of the depolarization effect relies on approximating the system by a cylinder with some effective dielectric permittivity. We demonstrate that this simple intuitive picture does not adequately describe optical absorption near its threshold, as the depolarization effect becomes dominated by many-body correlations which strongly modify the spectral dependence of absorption.
• ### Magnetotransport properties of the type II Weyl semimetal candidate Ta3S2(1607.05798)

Aug. 26, 2016 cond-mat.mtrl-sci
We have investigated the magnetoresistance (MR) and Hall resistivity properties of the single crystals of tantalum sulfide, Ta3S2, which was recently predicted to be a new type II Weyl semimetal. Large MR (up to ~8000% at 2 K and 16 T), field-induced metal-insulator-like transition and nonlinear Hall resistivity are observed at low temperatures. The large MR shows a strong dependence on the field orientation, leading to a giant anisotropic magnetoresistance (AMR) effect. For the field applied along the b-axis (B//b), MR exhibits quadratic field dependence at low fields and tends towards saturation at high fields; while for B//a, MR presents quadratic field dependence at low fields and becomes linear at high fields without any trend towards saturation. The analysis of the Hall resistivity data indicates the coexistence of a large number of electrons with low mobility and a small number of holes with high mobility. Shubnikov-de Haas (SdH) oscillation analysis reveals three fundamental frequencies originated from the three-dimensional (3D) Fermi surface (FS) pockets. We find that the semi-classical multiband model is sufficient to account for the experimentally observed MR in Ta3S2.
• ### Plasmon spectrum and plasmon-mediated energy transfer in a multi-connected geometry(1506.07901)

June 25, 2015 cond-mat.mes-hall
Surface plasmon spectrum of a metallic hyperbola can be found analytically with the separation of variables in elliptic coordinates. The spectrum consists of two branches: symmetric, low-frequency branch, $\omega <\omega_0/\sqrt{2}$, and antisymmetric high-frequency branch, $\omega >\omega_0/\sqrt{2}$, where $\omega_0$ is the bulk plasmon frequency. The frequency width of the plasmon band increases with decreasing the angle between the asymptotes of the hyperbola. For the simplest multi-connected geometry of two hyperbolas separated by an air spacer the plasmon spectrum contains two low-frequency branches and two high-frequency branches. Most remarkably, the lower of two low-frequency branches exists at $\omega \rightarrow 0$, i.e., unlike a single hyperbola, it is "thresholdless." We study how the complex structure of the plasmon spectrum affects the energy transfer between two emitters located on the surface of the same hyperbola and on the surfaces of different hyperbolas.
• ### Anisotropic Structure of the Order Parameter in FeSe_{0.4}Te_{0.6} Revealed by Angle Resolved Specific Heat(1004.2236)

July 22, 2010 cond-mat.supr-con
The symmetry and structure of the superconducting gap in the Fe-based superconductor are the central issue for understanding these novel materials. So far the experimental data and theoretical models have been highly controversial. Some experiments favor two or more constant or nearly-constant gaps, others indicate strong anisotropy and yet others suggest gap zeros ("nodes"). Theoretical models also vary, suggesting that the absence or presence of the nodes depends quantitatively on the model parameters. An opinion that has gained substantial currency is that the gap structure, unlike all other known superconductors, including cuprates, may be different in different compounds within the same family. A unique method for addressing this issue, one of the very few methods that are bulk and angle-resolved, calls for measuring the electronic specific heat in a rotating magnetic field, as a function of field orientation with respect to the crystallographic axes. In this Communication we present the first such measurement for an Fe-based high-Tc superconductor (FeBSC). We observed a fourfold oscillation of the specific heat as a function of the in-plane magnetic field direction, which allowed us to identify the locations of the gap minima (or nodes) on the Fermi surface. Our results place severe restrictions on the gap structure and on the existing theoretical models.
• ### Anisotropic Structure of the Order Parameter in FeSe0.45Te0.55 Revealed by Angle Resolved Specific Heat(1007.3597)

July 21, 2010 cond-mat.supr-con
The symmetry and structure of the superconducting gap in the Fe-based superconductors are the central issue for understanding these novel materials. So far the experimental data and theoretical models have been highly controversial. Some experiments favor two or more constant or nearly-constant gaps, others indicate strong anisotropy and yet others suggest gap zeros ("nodes"). Theoretical models also vary, suggesting that the absence or presence of the nodes depends quantitatively on the model parameters. An opinion that has gained substantial currency is that the gap structure, unlike all other known superconductors, including cuprates, may be different in different compounds within the same family. A unique method for addressing this issue, one of the very few methods that are bulk and angle-resolved, calls for measuring the electronic specific heat in a rotating magnetic field, as a function of field orientation with respect to the crystallographic axes. In this Communication we present the first such measurement for an Fe-based high-Tc superconductor (FeBSC). We observed a fourfold oscillation of the specific heat as a function of the in-plane magnetic field direction, which allowed us to identify the locations of the gap minima (or nodes) on the Fermi surface. Our results are consistent with the expectations of an extended s-wave model with a significant gap anisotropy on the electron pockets and the gap minima along the \Gamma M (or Fe-Fe bond) direction.
• ### Raising and lowering operators for angular momentum quantum numbers l in spherical harmonics(0912.5146)

Dec. 28, 2009 quant-ph
Two vector operators aimed at shifting angular momentum quantum number l in spherical harmonics |lm>, primarily proposed by Prof. X. L. Ka in 2001, are further studied. For a given magnetic quantum number m, specific states |lm> in spherical harmonics with the lowest angular momentum quantum numbers l are obtained and the state with minimum angular momentum quantum number in whole set of the spherical harmonics is |0,0>. How to use these states to generate whole set of spherical harmonics is illustrated.
• A detailed study is presented of the expected performance of the ATLAS detector. The reconstruction of tracks, leptons, photons, missing energy and jets is investigated, together with the performance of b-tagging and the trigger. The physics potential for a variety of interesting physics processes, within the Standard Model and beyond, is examined. The study comprises a series of notes based on simulations of the detector and physics processes, with particular emphasis given to the data expected from the first years of operation of the LHC at CERN.
• ### Weak coupling Bardeen-Cooper-Schrieffer suerconductivity in the Electron-Doped Cuprate Superconductors(cond-mat/0703256)

Aug. 7, 2008 cond-mat.supr-con
We use in-plane tunneling spectroscopy to study the temperature dependence of the local superconducting gap $\Delta(T)$ in electron-doped copper oxides with various $T_c$'s and Ce-doping concentrations. We show that the temperature dependence of $\Delta(T)$ follows the expectation of the Bardeen-Cooper-Schrieffer (BCS) theory of superconductivity, where $\Delta(0)/k_{B}T_{c}\approx1.72\pm 0.15$ and $\Delta(0)$ is the average superconducting gap across the Fermi surface, for all the doping levels investigated. These results suggest that the electron-doped superconducting copper oxides are weak coupling BCS superconductors.
• ### Weak coupling d-wave BCS superconductivity and unpaired electrons in overdoped La_{2-x}Sr_{x}CuO_{4} single crystals(cond-mat/0703463)

July 20, 2007 cond-mat.supr-con
The low-temperature specific heat (SH) of overdoped La_{2-x}Sr_{x}CuO_{4} single crystals (0.178=<x=<0.290) has been measured. For the superconducting samples (0.178=<x=<0.238), the derived gap values (without any adjusting parameters) approach closely onto the theoretical prediction \Delta_{0}=2.14k_{B}T_{c} for the weak-coupling d-wave BCS superconductivity. In addition, the residual term \gamma(0) of SH at H=0 increases with x dramatically when beyond x~0.22, and finally evolves into the value of a complete normal metallic state at higher doping levels, indicating growing amount of unpaired electrons. We argue that this large \gamma(0) cannot be simply attributed to the pair breaking induced by the impurity scattering, instead the phase separation is possible.
• ### Magnetic fluctuations in n-type high-$T_c$ superconductors reveal breakdown of fermiology(0705.4424)

May 30, 2007 cond-mat.supr-con
By combining experimental measurements of the quasiparticle and dynamical magnetic properties of optimally electron-doped Pr$_{0.88}$LaCe$_{0.12}$CuO$_4$ with theoretical calculations we demonstrate that the conventional fermiology approach cannot possibly account for the magnetic fluctuations in these materials. In particular, we perform tunneling experiments on the very same sample for which a dynamical magnetic resonance has been reported recently and use photoemission data by others on a similar sample to characterize the fermionic quasiparticle excitations in great detail. We subsequently use this information to calculate the magnetic response within the conventional fermiology framework as applied in a large body of work for the hole-doped superconductors to find a profound disagreement between the theoretical expectations and the measurements: this approach predicts a step-like feature rather than a sharp resonance peak, it underestimates the intensity of the resonance by an order of magnitude, it suggests an unreasonable temperature dependence of the resonance, and most severely, it predicts that most of the spectral weight resides in incommensurate wings which are a key feature of the hole-doped cuprates but have never been observed in the electron-doped counterparts. Our findings strongly suggest that the magnetic fluctuations reflect the quantum-mechanical competition between antiferromagnetic and superconducting orders.
• ### Distinct Pairing Symmetries in $Nd_{1.85}Ce_{0.15}CuO_{4-y}$ and $La_{1.89}Sr_{0.11}CuO_{4}$ Single Crystals: Evidence from Comparative Tunnelling Measurements(cond-mat/0503321)

March 27, 2007 cond-mat.supr-con
We used point-contact tunnelling spectroscopy to study the superconducting pairing symmetry of electron-doped $Nd_{1.85}Ce_{0.15}CuO_{4-y}$ (NCCO) and hole-doped $La_{1.89}Sr_{0.11}CuO_{4}$ (LSCO). Nearly identical spectra without zero bias conductance peak (ZBCP) were obtained on the (110) and (100) oriented surfaces (the so-called nodal and anti-nodal directions) of NCCO. In contrast, LSCO showed a remarkable ZBCP in the nodal direction as expected from a d-wave superconductor. Detailed analysis reveals an s-wave component in the pairing symmetry of the NCCO sample with $\Delta/k_BT_c=1.66$, a value remarkable close to that of a weakly coupled BCS superconductor. We argue that this s-wave component is formed at the Fermi surface pockets centered at ($\pm\pi$,0) and (0,$\pm\pi$) although a d-wave component may also exist.
• ### Mixed-State Dissipation in Zero Temperature Limit in $MgB_2$ Thin Films(cond-mat/0703637)

March 24, 2007 cond-mat.supr-con
We have studied mixed-state dissipation in epitaxial MgB$_2$ thin films by measurements of resistive transition, current-voltage characteristics, Hall effect, and point-contact tunnelling spectrum. We found that unlike single gap superconductors with negligible vortex quantum fluctuations in which vortices are frozen at T=0 K, finite zero-temperature dissipation due to vortex motion exists in MgB$_2$ over a wide magnetic field range. This dissipation was found to be associated with proliferation of quasiparticles from the $\pi$-band of MgB$_2$. The result shows that the vortex fluctuations are enhanced by two-band superconductivity in MgB$_2$ and we suggest that the vortex quantum fluctuation is a possible cause of the non-vanishing zero-temperature dissipation.
• ### Manipulating vortex motion by thermal and Lorentz force in high temperature superconductors(cond-mat/0507015)

July 5, 2005 cond-mat.supr-con
By using thermal and Lorentz force, the vortex motion is successfully manipulated in the mixed state of underdoped La$_{2 - x}$Sr$_{x}$CuO$_{4}$ single crystals and optimally doped YBa$_{2}$Cu$_{3}$O$_{7 - \delta}$ thin films. A conclusion is drawn that the strong Nernst signal above $T_{c}$ is induced by vortex motion. In the normal state, in order to reduce the dissipative contribution from the quasiparticle scattering and enhance the signal due to the possible vortex motion, a new measurement configuration is proposed. It is found that the in-plane Nernst signal ($H$ $| |$ $c$) can be measurable up to a high temperature in the pseudogap region, while the Abrikosov flux flow dissipation can only be measured up to $T_{c}$. This may point to different vortices below and above $T_{c}$ if we attribute the strong Nernst signal in the pseudogap region to the vortex motion. Below $T_{c}$ the dissipation is induced by the motion of the Abrikosov vortices. Above $T_{c}$ the dissipation may be caused by the motion of the spontaneously generated unbinded vortex-antivortex pairs.
• ### Fabrication and superconductivity of NaxTaS2 crystals(cond-mat/0502522)

In this paper we report the growth and superconductivity of $Na_xTaS_2$ crystals. The structural data deduced from X-ray diffraction pattern shows that the sample has the same structure as $2H-TaS_2$. A series of crystals with different superconducting transition temperatures ($T_c$) ranging from 2.5 K to 4.4 K were obtained. It is found that the $T_c$ rises with the increase of $Na$ content determined by Energy-Dispersive x-ray microanalysis(EDX) of Scanning Electron Microscope (SEM) on these crystals. Compared with the resistivity curve of un-intercalated sample $2H-TaS_2$ ($T_c$ = 0.8 K, $T_{CDW} \approx$ 70 K), no signal of charge density wave (CDW) was observed in samples $Na_{0.1}TaS_2$ and $Na_{0.05}TaS_2$. However, in some samples with lower $T_c$, the CDW appears again at about 65 K. Comparison between the anisotropic resistivity indicates that the anisotropy becomes smaller in samples with more $Na$ intercalation (albeit a weak semiconducting behavior along c-axis) and thus higher $T_c$. It is thus concluded that there is a competition between the superconductivity and the CDW. With the increase of sodium content, the rise of $T_c$ in $Na_xTaS_2$ is caused mainly by the suppression to the CDW in $2H-TaS_2$, and the conventional rigid band model for layered dichalcogenide may be inadequate to explain the changes induced by the slight intercalation of sodium in $2H-TaS_2$.
• ### Evidence for s-wave pairing from measurement on lower critical field in $MgCNi_3$(cond-mat/0503493)

March 19, 2005 cond-mat.supr-con
Magnetization measurements in the low field region have been carefully performed on a well-shaped cylindrical and an ellipsoidal sample of superconductor $MgCNi_3$. Data from both samples show almost the same results. The lower critical field $H_{c1}$ and the London penetration depth $\lambda$ are thus derived. It is found that the result of normalized superfluid density $\lambda^2(0)/\lambda^2(T)$ of $MgCNi_3$ can be well described by BCS prediction with the expectation for an isotropic s-wave superconductivity.
• ### Competition between the BCS superconductivity and ferromagnetic spin fluctuations in MgCNi$_3$(cond-mat/0404451)

Feb. 24, 2005 cond-mat.supr-con
The low temperature specific heat of the superconductor MgCNi$_3$ and a non-superconductor MgC$_{0.85}$Ni$_3$ is investigated in detail. An additional contribution is observed from the data of MgCNi$_3$ but absent in MgC$_{0.85}$Ni$_3$, which is demonstrated to be insensitive to the applied magnetic field even up to 12 Tesla. A detailed discussion on its origin is then presented. By subtracting this additional contribution, the zero field specific heat of MgCNi$_3$ can be well described by the BCS theory with the gap ratio ($\Delta/k_BT_c$) determined by the previous tunneling measurements. The conventional s-wave pairing state is further proved by the magnetic field dependence of the specific heat at low temperatures and the behavior of the upper critical field.
• ### Two dimensional scaling of resistance in flux flow region in $Tl_2Ba_2CaCu_2O_8$ thin films(cond-mat/0412069)

Dec. 3, 2004 cond-mat.supr-con
The resistance of $Tl_2Ba_2CaCu_2O_8$ thin films has been measured when the angle between the applied fields and $ab$-plane of the film is changed continuously at various temperatures. Under various magnetic fields, the resistance can be well scaled in terms of the c-axis component of the applied fields at the same temperature in the whole angle range. Meanwhile, we show that the measurement of resistance in this way is a complementary method to determine the growth orientation of the anisotropic high-$T_c$ superconductors.
• ### Temperature and magnetic field dependent tunneling spectroscopy of PtIr/Sr$_{0.9}$La$_{0.1}$CuO$_2$ point contact(cond-mat/0309337)

Sept. 14, 2003 cond-mat.supr-con
Low barrier quasiparticle tunneling spectroscopy on Sr$_{0.9}$La$_{0.1}$CuO$_2$ has been studied with PtIr/Sr$_{0.9}$La$_{0.1}$CuO$_2$ point contacts at various temperatures and magnetic fields. No zero-bias conductance peaks are observed. By fitting tunneling conductance to Blonder-Tinkham-Klapwijk theory, the temperature dependent s-wave superconducting gaps are obtained. The present results exclude the possibility of d-wave symmetry for the pair gap in Sr$_{0.9}$La$_{0.1}$CuO$_2$, and do not support the conventional phonon mediated pairing in this system either.
• ### Bulk Evidence for s-Wave Pairing Symmetry in the n-Type Infinite-Layer Cuprate $Sr_{0.9}La_{0.1}CuO_{2}$(cond-mat/0306238)

June 10, 2003 cond-mat.supr-con
Low temperature specific heat of the electron-doped (n-type) infinite-layer cuprate $Sr_{0.9}La_{0.1}CuO_{2}$ has been measured. The quasiparticle density of states (DOS) in the mixed state is found to be consistent with the feature of the s-wave pairing symmetry, agreeing very well with the earlier tunnelling measurement, but being contrary to the d-wave symmetry well confirmed for the hole-doped (p-type) cuprates. Our results indicate that the electronic DOS are mainly contributed by the vortex cores in the present sample being contrast to the p-type cuprates in which the vortex cores are abnormal and contribute very limited low energy DOS as evidenced by many means.
• ### Influence of Carbon Concentration on the Superconductivity in MgCxNi3(cond-mat/0302116)

Feb. 6, 2003 cond-mat.supr-con
The influence of carbon concentration on the superconductivity (SC) in MgC$_{x}$Ni$_3$ has been investigated by measuring the low temperature specific heat combined with first principles electronic structure calculation. It is found that the specific heat coefficient $\gamma_n=C_{en}/T$ of the superconducting sample ($x\approx1$) in normal state is twice that of the non-superconducting one ($x\approx 0.85$). The comparison of measured $\gamma_n$ and the calculated electronic density of states (DOS) shows that the effective mass renormalization changes remarkably as the carbon concentration changes. The large mass renormalization for the superconducting sample and the low $T_{c}$(7K) indicate that more than one kind of boson mediated electron-electron interactions exist in MgC$_{x}$Ni$_3$.


text:
## anonymous one year ago A 2.4 cm object is 15.0 cm to the left of a convex lens with a focal length of +5.0 cm. Part 1: Draw a ray diagram of the setup showing the location of the image. Part 2: Calculate the distance of the image from the lens. Part 3: What size is the image and is it upright or inverted?

1. Michele_Laino

here is the drawing of your problem: |dw:1434906888314:dw|

2. anonymous

whoahh okie!! :)

3. Michele_Laino

here we have to apply this formula: $\Large \frac{1}{p} + \frac{1}{q} = \frac{1}{f}$ where p= 15 cm f= 5 cm please solve for q

4. anonymous

ok! 1/15 + 1/q = 1/5 1/q = 3 q=1/3 ?

5. Michele_Laino

we have: $\Large q = \frac{{fp}}{{p - f}} = \frac{{5 \times 15}}{{15 - 5}} = ...cm$

6. anonymous

ohh oops so we get 75 / 10 = 7.5 cm ?

7. Michele_Laino

that's right!

8. Michele_Laino

now, from my drawing, we get that the image is inverted

9. anonymous

okay! so part 2 is that it is 7.5 cm away from the lens? and part 3 is that it is inverted?

10. Michele_Laino

yes! nevertheless we have to determine the dimension of the image

11. anonymous

yes! we have to calculate the size, too.. how do we do that?

12. Michele_Laino

we can use the similarity property of these triangles: |dw:1434907503742:dw|

13. anonymous

ok!

14. Michele_Laino

so we can write this proportion: $\Large 2.4:15 = x:7.5$

15. Michele_Laino

or, applying the fundamental property of proportion: $\Large x = \frac{{2.4 \times 7.5}}{{15}} = ...cm$

16. anonymous

we get 1.2 cm? that is the size of the image?

17. Michele_Laino

yes! correct!

18. anonymous

yay! so we are finished with this? :O

19. Michele_Laino

yes! we have finished! :)

20. anonymous

yay!! okay, onto the last one!!:) thank you1!

21. Michele_Laino

ok! :)


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#### TODO851 B History Raw

 1234567891011121314151617 ``````Most TODOs live in the TODO section of doc/file.man (i.e. file(1)). They are more visible there, so please add any further TODOs to that file, not here. More speculative material can live here. (This change was made when Reuben Thomas noticed that all the bugs listed in the BUGS section of the man page had been fixed!) --- It would be nice to simplify file considerably. For example, reimplement the apprentice and non-pattern magic methods in Python, and compile the magic patterns to a giant regex (or something similar; maybe using Ragel (http://www.complang.org/ragel/)) so that only a small amount of C is needed (because fast execution is typically only required for soft magic, not the more detailed information given by hard-wired routines). In this regard, note that hplip, which is BSD-licensed, has a magic reimplementation in Python. ``````