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# How can I show that the interior of the set of interior points is an interior set? $(X^\circ)^\circ = X^\circ$

I am trying to show that the interior of a set of interior points is an interior point, that is, if $X$ is a subset of a metric space $M$, that $(X^\circ)^\circ = X^\circ$ for $X \subset M$. My approach is to show that each is a subset of the other. It is quite obvious that $(X^\circ)^\circ \subset X^\circ$. However, I am bogged down when trying to have an intuitive understanding how to show the other direction. Can anyone give me help? It would be greatly appreciated!

• You can see $X^\circ=\bigcup_{U\subset X\text{ open}} U$. It should be clear from there. – Ian Coley Apr 22 '14 at 2:40
• Hint Prove $A=A^\circ\iff A$ is open. Then prove $A^\circ$ is open. – Pedro Tamaroff Apr 22 '14 at 2:41
• Thanks! Was able to solve it, just one thing, how did we know that the set of interior points equals the union of open sets on $X$? – user123276 Apr 22 '14 at 3:28
• What does it mean to be in the interior of a set? Just check the definitions. – Andrés E. Caicedo Apr 22 '14 at 6:02

One way to see this for a metric space, is to use that every point of an open ball $B(x,r) = \{y: d(x,y) < r \}$ is indeed an interior point of that open ball (justifying the name "open ball", one could say).
(Proof: if $y \in B(x,r)$, define $s = r - d(x,y) > 0$, and for any $z$, if $d(y,z) < s$, we know that $d(x,z) <= d(x,y) + d(y,z) < d(x,y) + s = d(x,y) + (r - d(x,y)) = r$, so indeed $B(y, s) \subset B(x,r)$. This $s$ shows that $y$ is an interior point of $B(x,r)$.)
Now, if $x \in X^\circ$, this means that there is some $r>0$ such that $B(x,r) \subset X$. For any $y \in B(x,r)$, there exists $s>0$ such that $B(y,s) \subset B(x,r) \subset X$, see above. But this just says that every point of $B(x,r)$ is itself an interior point of $X$, i.e. $B(x,r) \subset X^\circ$. And this by definition means $x \in (X^\circ)^\circ$, as required.

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# MPOGraph¶

Inheritance Diagram

Methods

 MPOGraph.__init__(sites[, bc, max_range]) MPOGraph.add(i, keyL, keyR, opname, strength) Insert an edge into the graph. MPOGraph.add_missing_IdL_IdR([insert_all_id]) Add missing identity ('Id') edges connecting 'IdL'->'IdL' and 'IdR'->'IdR'. MPOGraph.add_string_left_to_right(i, j, key) Insert a bunch of edges for an 'operator string' into the graph. MPOGraph.add_string_right_to_left(j, i, key) Insert a bunch of edges for an 'operator string' into the graph. MPOGraph.build_MPO([Ws_qtotal]) Build the MPO represented by the graph (self). MPOGraph.from_term_list(term_list, sites, bc) Initialize from a list of operator terms and prefactors. MPOGraph.from_terms(terms, sites, bc[, ...]) Initialize an MPOGraph from OnsiteTerms and CouplingTerms. MPOGraph.has_edge(i, keyL, keyR) True if there is an edge from keyL on bond (i-1, i) to keyR on bond (i, i+1). Sanity check, raises ValueErrors, if something is wrong.

Class Attributes and Properties

 MPOGraph.L Number of physical sites; for infinite boundaries the length of the unit cell.
class tenpy.networks.mpo.MPOGraph(sites, bc='finite', max_range=None)[source]

Bases: object

Representation of an MPO by a graph, based on a ‘finite state machine’.

This representation is used for building H_MPO from the interactions. The idea is to view the MPO as a kind of ‘finite state machine’. The states or keys of this finite state machine life on the MPO bonds between the Ws. They label the indices of the virtul bonds of the MPOs, i.e., the indices on legs wL and wR. They can be anything hash-able like a str, int or a tuple of them.

The edges of the graph are the entries W[keyL, keyR], which itself are onsite operators on the local Hilbert space. The indices keyL and keyR correspond to the legs 'wL', 'wR' of the MPO. The entry W[keyL, keyR] connects the state keyL on bond (i-1, i) with the state keyR on bond (i, i+1).

The keys 'IdR' (for ‘idenity left’) and 'IdR' (for ‘identity right’) are reserved to represent only 'Id' (=identity) operators to the left and right of the bond, respectively.

Todo

might be useful to add a “cleanup” function which removes operators cancelling each other and/or unused states. Or better use a ‘compress’ of the MPO?

Parameters
• sites (list of Site) – Local sites of the Hilbert space.

• bc ({'finite', 'infinite'}) – MPO boundary conditions.

• max_range (int | np.inf | None) – Maximum range of hopping/interactions (in unit of sites) of the MPO. None for unknown.

sites

Defines the local Hilbert space for each site.

Type

list of Site

chinfo

The nature of the charge.

Type

ChargeInfo

bc

MPO boundary conditions.

Type

{‘finite’, ‘infinite’}

max_range

Maximum range of hopping/interactions (in unit of sites) of the MPO. None for unknown.

Type

int | np.inf | None

states

states[i] gives the possible keys at the virtual bond (i-1, i) of the MPO. L+1 enries.

Type

list of set of keys

graph

For each site i a dictionary {keyL: {keyR: [(opname, strength)]}} with keyL in states[i] and keyR in states[i+1].

Type

list of dict of dict of list of tuples

_grid_legs

The charges for the MPO

Type

None | list of LegCharge

classmethod from_terms(terms, sites, bc, insert_all_id=True)[source]

Initialize an MPOGraph from OnsiteTerms and CouplingTerms.

Parameters
Returns

graph – Initialized with the given terms.

Return type

MPOGraph

from_term_list

equivalent for representation by TermList.

classmethod from_term_list(term_list, sites, bc, insert_all_id=True)[source]

Initialize from a list of operator terms and prefactors.

Parameters
• term_list (TermList) – Terms to be added to the MPOGraph.

• sites (list of Site) – Local sites of the Hilbert space.

• bc ('finite' | 'infinite') – MPO boundary conditions.

• insert_all_id (bool) – Whether to insert identities such that IdL and IdR are defined on each bond. See add_missing_IdL_IdR().

Returns

graph – Initialized with the given terms.

Return type

MPOGraph

from_terms

equivalent for other representation of terms.

test_sanity()[source]

Sanity check, raises ValueErrors, if something is wrong.

property L

Number of physical sites; for infinite boundaries the length of the unit cell.

add(i, keyL, keyR, opname, strength, check_op=True, skip_existing=False)[source]

Insert an edge into the graph.

Parameters
• i (int) – Site index at which the edge of the graph is to be inserted.

• keyL (hashable) – The state at bond (i-1, i) to connect from.

• keyR (hashable) – The state at bond (i, i+1) to connect to.

• opname (str) – Name of the operator.

• strength (str) – Prefactor of the operator to be inserted.

• check_op (bool) – Whether to check that ‘opname’ exists on the given site.

• skip_existing (bool) – If True, skip adding the graph node if it exists (with same keys and opname).

add_string_left_to_right(i, j, key, opname='Id', check_op=True, skip_existing=True)[source]

Insert a bunch of edges for an ‘operator string’ into the graph.

Terms like $$S^z_i S^z_j$$ actually stand for $$S^z_i \otimes \prod_{i < k < j} \mathbb{1}_k \otimes S^z_j$$. This function adds the $$\mathbb{1}$$ terms to the graph.

Parameters
• i (int) – An edge is inserted on all sites between i and j, i < j. j can be larger than L, in which case the operators are supposed to act on different MPS unit cells.

• j (int) – An edge is inserted on all sites between i and j, i < j. j can be larger than L, in which case the operators are supposed to act on different MPS unit cells.

• key (tuple) – The key at bond (i+1, i) to connect from.

• opname (str) – Name of the operator to be used for the string. Useful for the Jordan-Wigner transformation to fermions.

• skip_existing (bool) – Whether existing graph nodes should be skipped.

Returns

key_i – The key on the right of site i we connected to.

Return type

tuple

add_string_right_to_left(j, i, key, opname='Id', check_op=True, skip_existing=True)[source]

Insert a bunch of edges for an ‘operator string’ into the graph.

Similar as add_string_left_to_right(), but in the other direction.

Parameters
• j (int) – An edge is inserted on all sites between i and j, i < j. Note the switched argument order compared to add_string_left_to_right().

• i (int) – An edge is inserted on all sites between i and j, i < j. Note the switched argument order compared to add_string_left_to_right().

• key (tuple) – The key at bond (j-1, j) to connect from.

• opname (str) – Name of the operator to be used for the string. Useful for the Jordan-Wigner transformation to fermions.

• skip_existing (bool) – Whether existing graph nodes should be skipped.

Returns

key_i – The key on the right of site i we connected to.

Return type

hashable

Add missing identity (‘Id’) edges connecting 'IdL'->'IdL' and 'IdR'->'IdR'.

This function should be called after all other operators have been inserted.

Parameters

insert_all_id (bool) – If True, insert ‘Id’ edges on all bonds. If False and boundary conditions are finite, only insert 'IdL'->'IdL' to the left of the rightmost existing ‘IdL’ and 'IdR'->'IdR' to the right of the leftmost existing ‘IdR’. The latter avoid “dead ends” in the MPO, but some functions (like make_WI) expect ‘IdL’/’IdR’ to exist on all bonds.

has_edge(i, keyL, keyR)[source]

True if there is an edge from keyL on bond (i-1, i) to keyR on bond (i, i+1).

build_MPO(Ws_qtotal=None)[source]

Build the MPO represented by the graph (self).

Parameters

Ws_qtotal (None | (list of) charges) – The qtotal for each of the Ws to be generated, default (None) means 0 charge. A single qtotal holds for each site.

Returns

mpo – the MPO which self represents.

Return type

MPO


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# Why is (von Neumann) entropy maximized for an ensemble in thermal equilibrium?

Consider a quantum system in thermal equilibrium with a heat bath. In determining the density operator of the system, the usual procedure is to maximize the von Neumann entropy subject to the constraint that the ensemble average of the Hamiltonian has a fixed value.

What justifies this assumption?

Sakurai, in his QM text, writes

To justify this assumption would involve us in a delicate discussion of how equilibrium is established as a result of interactions with the environment.

I'd appreciate if someone could shed some light on this. References are welcome as well.

I've heard the suggestion that a thermal equilibrium ensemble is simply defined by that density operator which solves the constrained optimization problem above. If this is the case, then why are real physical systems that are in weak contact with heat baths for long periods well described by such mathematical ensembles, and how would one identify the Lagrange multiplier $\beta$ that arises with inverse temperature of the heat bath?

You need to read this paper by Jaynes. I can't explain it as well as him, but I will try to summarise the main points below.

The first thing is to realise that the entropy is observer-dependent: it depends on what information you have access to about the system. A finite temperature means that you don't have access to all the information about the state of the system; in particular, you cannot keep track of the (infinite) degrees of freedom of the bath. However, suppose that some demon could keep track of all the degrees of freedom of the system and bath: he/she sees zero entropy. For the demon, it looks a bit like the total system is at zero temperature (although really it is better to say that temperature is ill-defined for the demon).

Given that you are ignorant (sorry, but at least I'm not calling you a demon), you need to find a consistent prescription for assigning probabilities to the different microstates. The prescription must be 'honest' about what you do or don't know. The entropy is in some sense a unique measure of ignorance, as proved by Shannon. Therefore you should 'maximise your ignorance', subject to the constraint that you do know certain macroscopic observables, e.g. average energy or average particle number if the system is open, etc.

Maximising the entropy of the system is the most logical way to assign probabilities to the microstates of the system, given access only to a limited subset of observables. The same 'MaxEnt' principle is quite general and applies to all statistical analysis, not only physics. The Lagrange multiplier $\beta$ is identified with inverse temperature by comparing the outcome of this abstract procedure to the experimental facts of phenomenological thermodynamics.

If you are interested in the actual dynamics of equilibration, there has been a lot of literature on this recently, especially in mesoscopic systems. Particular focus is laid on the integrability of the system: non-integrable (chaotic) systems do thermalise, whereas there is a fair bit of evidence that integrable systems do not thermalise properly. Intuitively, this is because integrable systems have a maximal set of locally conserved quantities so that, even when in contact with a heat bath, the memory of the initial conditions is never quite lost.

See, for example: Dynamics of thermalisation in small Hubbard-model systems and Thermalization and ergodicity in many-body open quantum systems, if you search 'thermalization' (sic) on arxiv then you will find many more.

• Thanks Mark. Yeah I actually forgot about the information-theoretic viewpoint for some reason when I was asking this question. I guess I was hoping that the MaxEnt principle could somehow be justified not only from the perspective of statistical inference, but that it would emerge in equilibrium ensembles as a consequence of the process of equilibration (or something to that effect). Do you think such an expectation is unreasonable? I'm not really sure what to think on this point. Also, thanks very much for the references at the end. Feb 6, 2013 at 19:22
• I think this is a very good question, and it's the subject of a lot of research at the moment, although it comes with a caveat. In the context of classical physics, it's important to remember that the system is always really in a pure state. So the emergence of the Gibbs ensemble cannot really be separated from the observer's subjective knowledge about the system. I think of it as ignorance/information/entropy being created dynamically each time the system interacts with degrees of freedom that the observer cannot track. Feb 6, 2013 at 19:30
• (contd.) When the energy/particle etc. distribution is uniform over scales longer than the minimal achievable experimental resolution then further interactions do not increase the observer's entropy, i.e. the probability distribution hits the steady state. Feb 6, 2013 at 19:34
• (contd.) However, in quantum mechanics you can't say the system is always really in a pure state, and the uncertainty of the observer is not subjective, it's required by the laws of physics. You can study equilibration of small quantum systems in a heat bath and you find that the system evolves towards a thermal state, basically due to entanglement with the bath. Likewise, it has been shown that almost all bipartite states for systems with a natural system-environment division are locally thermal, see here. Feb 6, 2013 at 19:39
• Wow thank you so much Mark. I couldn't have asked for better responses; I'll definitely look at all of the references you suggested. Feb 6, 2013 at 19:43

Here is an alternate approach to answering this question (which ignores temperature and lagrange multipliers) given to us by the 1st law of thermodynamics and quantum information.

In short, a weakly interacting ensemble at thermal equilibrium maximises the von Neumann entropy because in doing so it minimises the free energy of the system.

Why can we say this? A weakly interacting ensemble at thermal equilibrium corresponds to a Gibbs state, which is nothing more than a quantum version of a canonical ensemble. We can write this out as $$\hat{\rho}_\beta = \frac{e^{-\beta \hat{H}}}{\mathcal{Z}}$$ where $$\mathcal{Z}$$ is the canonical partition function. Canonical ensembles also have a related quantity known as the Gibbs Free energy given by $$F = U - tS$$ where $$U$$ is the internal energy and $$t$$ is the temperature. We can write out a quantum version of this as $$F = \langle \hat{H} \rangle - tS.$$ For a Gibbs state, this will coincide with the Gibbs Free energy but what if we define this quantity for an arbitrary quantum state modeling an open quantum system taking $$S$$ to be the von Neumann entropy $$S = -\text{tr}\{\hat{\rho}\ln\hat{\rho}\}.$$ In general we have $$F(\hat{\rho}) = \text{tr}\{\hat{\rho}\hat{H}\} + \beta^{-1}\text{tr}\{\hat{\rho}\ln\hat{\rho}\} = \beta^{-1}\text{tr}\{\hat{\rho}(\ln\hat{\rho}+\beta\hat{H})\}$$ by linearity of the trace. The Free energy of a Gibbs state is the Gibbs Free energy $$F(\hat{\rho_\beta}) = -\beta \ln \mathcal{Z} = -\beta^{-1}\ln\left(\text{tr}\{e^{-\beta \hat{H}}\}\right).$$ Considering the relative entropy of this arbitrary state $$\hat{\rho}$$ and the Gibbs state $$\hat{\rho}_\beta$$ we have $$D(\hat{\rho}||\hat{\rho}_\beta) = \text{tr}\{\hat{\rho}\ln\hat{\rho}\} - \text{tr}\{\hat{\rho}\ln\hat{\rho}_\beta\}$$ which can be expressed in terms of the Free Energy as $$D(\hat{\rho}||\hat{\rho}_\beta) = \beta \left(F(\hat{\rho}) - F(\hat{\rho}_\beta)\right).$$ But, the relative entropy is known to be nonnegative $$D(\cdot||\cdot)\geq 0.$$ As a result the Gibbs Free energy is the lowest possible free energy or the free energy of the Gibbs state is minimal.

The first law of thermodynamics can be stated in this context as $$dE = tdS +dF$$ so if Gibbs states minimise the free energy, they maximise the von Neumann entropy, which happens to be the Gibbs Entropy.

Beyond this one can also justify the approach to thermal equilibrium on the grounds of quantum information expanding on this argument. Any quantum channel that preserves the Gibbs state cannot increase the free energy. Rather, the free energy of out-of-equilibrium states is monotonically decreasing to the Gibbs Free Energy giving equilibrium, maximimising von Neumann entropy on long times.

This argument is given by Preskill in his notes on Quantum Shannon Theory.


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# NAG Library Routine Document

## 1Purpose

s15aff returns a value for Dawson's Integral, $F\left(x\right)$, via the function name.

## 2Specification

Fortran Interface
 Function s15aff ( x,
 Real (Kind=nag_wp) :: s15aff Integer, Intent (Inout) :: ifail Real (Kind=nag_wp), Intent (In) :: x
#include nagmk26.h
 double s15aff_ (const double *x, Integer *ifail)

## 3Description

s15aff evaluates an approximation for Dawson's Integral
 $Fx=e-x2∫0xet2dt.$
The routine is based on two Chebyshev expansions:
For $0<\left|x\right|\le 4$,
 $Fx=x∑r=0′arTrt, where t=2 x4 2-1.$
For $\left|x\right|>4$,
 $Fx=1x∑r=0′brTrt, where t=2 4x 2-1.$
For $\left|x\right|$ near zero, $F\left(x\right)\simeq x$, and for $\left|x\right|$ large, $F\left(x\right)\simeq \frac{1}{2x}$. These approximations are used for those values of $x$ for which the result is correct to machine precision.

## 4References

Abramowitz M and Stegun I A (1972) Handbook of Mathematical Functions (3rd Edition) Dover Publications

## 5Arguments

1:     $\mathbf{x}$ – Real (Kind=nag_wp)Input
On entry: the argument $x$ of the function.
2:     $\mathbf{ifail}$ – IntegerInput/Output
On entry: ifail must be set to $0$, $-1\text{ or }1$. If you are unfamiliar with this argument you should refer to Section 3.4 in How to Use the NAG Library and its Documentation for details.
For environments where it might be inappropriate to halt program execution when an error is detected, the value $-1\text{ or }1$ is recommended. If the output of error messages is undesirable, then the value $1$ is recommended. Otherwise, if you are not familiar with this argument, the recommended value is $0$. When the value $-\mathbf{1}\text{ or }\mathbf{1}$ is used it is essential to test the value of ifail on exit.
On exit: ${\mathbf{ifail}}={\mathbf{0}}$ unless the routine detects an error or a warning has been flagged (see Section 6).

## 6Error Indicators and Warnings

There are no failure exits from this routine.

## 7Accuracy

Let $\delta$ and $\epsilon$ be the relative errors in the argument and result respectively.
If $\delta$ is considerably greater than the machine precision (i.e., if $\delta$ is due to data errors etc.), then $\epsilon$ and $\delta$ are approximately related by:
 $ε≃ x 1-2xFx Fx δ.$
The following graph shows the behaviour of the error amplification factor $\left|\frac{x\left(1-2xF\left(x\right)\right)}{F\left(x\right)}\right|$:
Figure 1
However if $\delta$ is of the same order as machine precision, then rounding errors could make $\epsilon$ somewhat larger than the above relation indicates. In fact $\epsilon$ will be largely independent of $x$ or $\delta$, but will be of the order of a few times the machine precision.

## 8Parallelism and Performance

s15aff is not threaded in any implementation.

None.

## 10Example

This example reads values of the argument $x$ from a file, evaluates the function at each value of $x$ and prints the results.

### 10.1Program Text

Program Text (s15affe.f90)

### 10.2Program Data

Program Data (s15affe.d)

### 10.3Program Results

Program Results (s15affe.r)

© The Numerical Algorithms Group Ltd, Oxford, UK. 2017


text:
ISSN 0439-755X
CN 11-1911/B

Acta Psychologica Sinica ›› 2016, Vol. 48 ›› Issue (8): 981-988.

Narcissism and adolescents’ prosocial behaviors: The role of public and private situations

DING Ruyi1,3; ZHOU Hui1; ZHANG Bao2; CHEN Xiao2

1. (1 Department of Psychology, Sun Yat-sen University, Guangzhou 510275, China) (2 Faculty of Education, Beijing Normal University Zhuhai Campus, Zhuhai 519085, China) (3 Department of Psychology, The Chinese University of Hongkong, Hong Kong)
• Received:2015-07-02 Published:2016-08-25 Online:2016-08-25
• Contact: ZHOU Hui, E-mail: edszh@mail.sysu.edu.cn

Abstract:

Narcissism was found to be associated with low empathy, insensitive to the need of others and having a tendency to use others for ones’ own gains. That is, narcissists may lay more emphasis on selfish values than prosocial ones. Thus, they may not help with social activities voluntarily unless they are beneficial to enhance their self-worth or self-image. On the other hand, studies have found that help is more likely to occur when one behaves in front of audiences in nonemergency situations. This is because prosocial behaviors can be used for self-enhancement such as gaining good reputation or promoting a positive self-image. Narcissists are good at using interpersonal relationships for self-regulation. They are excessively dependent on others to gain a sense of identity and are motivated to seek continuous external self-affirmation to build or maintain desired selves. From this point of view, narcissists may very likely do prosocial behaviors for seeking continuous external self-affirmation to build or maintain desired selves. In this research, two studies were conducted to explore the relationship between narcissism and prosocial tendencies and actual prosocial behaviors on two different situations---whether there are people watching or not. Study 1 aimed at exploring Chinese narcissistic individuals’ self-reported public and anonymous prosocial tendencies. Public prosocial tendency refers to a tendency to perform prosocial behaviors in front of others while anonymous prosocial tendency refers to a tendency to help without consciousness of being noticed or acknowledged. Participants completed Narcissistic Personality Inventory and Revised Prosocial Tendencies Measure. It revealed that narcissism was positively associated with self reported public but not anonymous prosocial tendency among male participants. Study 2 aimed at exploring whether the prosocial behaviors of narcissists were truly influenced by the publicity of the situations in the real world. Participants were randomly assigned to two conditions according to whether group members know the others’ donation or not. The results showed that male narcissists donated more money to a charity than non-narcissists in a public situation when their contributions were watched by others. However, their prosocial behaviors were not different in a private situation when individuals’ contributions were kept secret. The findings of our studies imply that narcissism may use prosocial behaviors in the service of self-regulation. It increases the knowledge of narcissists’ self regulatory strategies that, besides many maladaptive behaviors, prosocial behaviors can also be used to enhance narcissists’ self-view.


text:
# Slow saving in banks

How long will it take to save € 9,000 by depositing € 200 at the beginning of each year at 2% interest?

Result

y =  32

#### Solution:

$q=2 \%=1 + \dfrac{ 2 }{ 100 }=1.02 \ \\ v=200 \ \text{eur} \ \\ r_{1}=v \cdot \ q=200 \cdot \ 1.02=204 \ \text{eur} \ \\ r_{2}=(r_{1}+v) \cdot \ q=(204+200) \cdot \ 1.02=\dfrac{ 10302 }{ 25 }=412.08 \ \\ r_{3}=(r_{2}+v) \cdot \ q=(412.08+200) \cdot \ 1.02=624.3216 \ \\ r_{4}=(r_{3}+v) \cdot \ q=(624.3216+200) \cdot \ 1.02 \doteq 840.808 \ \\ r_{5}=(r_{4}+v) \cdot \ q=(840.808+200) \cdot \ 1.02 \doteq 1061.6242 \ \\ r_{6}=(r_{5}+v) \cdot \ q=(1061.6242+200) \cdot \ 1.02 \doteq 1286.8567 \ \\ r_{7}=(r_{6}+v) \cdot \ q=(1286.8567+200) \cdot \ 1.02 \doteq 1516.5938 \ \\ r_{8}=(r_{7}+v) \cdot \ q=(1516.5938+200) \cdot \ 1.02 \doteq 1750.9257 \ \\ r_{9}=(r_{8}+v) \cdot \ q=(1750.9257+200) \cdot \ 1.02=1989.9442 \ \\ r_{10}=(r_{9}+v) \cdot \ q=(1989.9442+200) \cdot \ 1.02 \doteq 2233.7431 \ \\ r_{11}=(r_{10}+v) \cdot \ q=(2233.7431+200) \cdot \ 1.02 \doteq 2482.4179 \ \\ r_{12}=(r_{11}+v) \cdot \ q=(2482.4179+200) \cdot \ 1.02 \doteq 2736.0663 \ \\ r_{13}=(r_{12}+v) \cdot \ q=(2736.0663+200) \cdot \ 1.02 \doteq 2994.7876 \ \\ r_{14}=(r_{13}+v) \cdot \ q=(2994.7876+200) \cdot \ 1.02 \doteq 3258.6834 \ \\ r_{15}=(r_{14}+v) \cdot \ q=(3258.6834+200) \cdot \ 1.02 \doteq 3527.8571 \ \\ r_{16}=(r_{15}+v) \cdot \ q=(3527.8571+200) \cdot \ 1.02 \doteq 3802.4142 \ \\ r_{17}=(r_{16}+v) \cdot \ q=(3802.4142+200) \cdot \ 1.02 \doteq 4082.4625 \ \\ r_{18}=(r_{17}+v) \cdot \ q=(4082.4625+200) \cdot \ 1.02 \doteq 4368.1117 \ \\ r_{19}=(r_{18}+v) \cdot \ q=(4368.1117+200) \cdot \ 1.02 \doteq 4659.474 \ \\ r_{20}=(r_{19}+v) \cdot \ q=(4659.474+200) \cdot \ 1.02 \doteq 4956.6634 \ \\ r_{21}=(r_{20}+v) \cdot \ q=(4956.6634+200) \cdot \ 1.02 \doteq 5259.7967 \ \\ r_{22}=(r_{21}+v) \cdot \ q=(5259.7967+200) \cdot \ 1.02 \doteq 5568.9926 \ \\ r_{23}=(r_{22}+v) \cdot \ q=(5568.9926+200) \cdot \ 1.02 \doteq 5884.3725 \ \\ r_{24}=(r_{23}+v) \cdot \ q=(5884.3725+200) \cdot \ 1.02 \doteq 6206.0599 \ \\ r_{25}=(r_{24}+v) \cdot \ q=(6206.0599+200) \cdot \ 1.02 \doteq 6534.1811 \ \\ r_{26}=(r_{25}+v) \cdot \ q=(6534.1811+200) \cdot \ 1.02 \doteq 6868.8648 \ \\ r_{27}=(r_{26}+v) \cdot \ q=(6868.8648+200) \cdot \ 1.02 \doteq 7210.2421 \ \\ r_{28}=(r_{27}+v) \cdot \ q=(7210.2421+200) \cdot \ 1.02 \doteq 7558.4469 \ \\ r_{29}=(r_{28}+v) \cdot \ q=(7558.4469+200) \cdot \ 1.02 \doteq 7913.6158 \ \\ r_{30}=(r_{29}+v) \cdot \ q=(7913.6158+200) \cdot \ 1.02 \doteq 8275.8882 \ \\ r_{31}=(r_{30}+v) \cdot \ q=(8275.8882+200) \cdot \ 1.02 \doteq 8645.4059 \ \\ r_{32}=(r_{31}+v) \cdot \ q=(8645.4059+200) \cdot \ 1.02 \doteq 9022.314 \ \\ r_{33}=(r_{32}+v) \cdot \ q=(9022.314+200) \cdot \ 1.02 \doteq 9406.7603 \ \\ r_{34}=(r_{33}+v) \cdot \ q=(9406.7603+200) \cdot \ 1.02 \doteq 9798.8955 \ \\ r_{35}=(r_{34}+v) \cdot \ q=(9798.8955+200) \cdot \ 1.02 \doteq 10198.8734 \ \\ \ \\ \ \\ y=32$

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# proof that SimpLe is fully expresive

Refering to this paper "SimplE Embedding for Link Prediction in Knowledge Graphs" by Seyed Mehran Kazemi and David Poole in 2018 :

In page 4, about the proof of SimpLE being fully expressive,

I understand that $$h_{e_i} =1 \text{ if }(n \text{ mod }|\mathcal{E}|)=i \text{ and }0 \text{ otherwise }$$, $$v_{r_j}=1 \text{ if }(n \text{ div } |\mathcal{E}|)=j \text{ and }0 \text{ otherwise }.$$ and that the $$(j*|\mathcal{E}|+i$$)-th element of $$t_{e_k}$$ is $$1$$ if $$(e_i,r_j,e_k)$$ holds and $$-1$$ otherwise. From that we get $$\langle h_{e_i},v_r, t_{e_k}\rangle=1$$ But what about $$v_{r^{-1}}$$?


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### Independent Additive Heuristics Reduce Search Multiplicatively

This paper analyzes the performance of IDA* using additive heuristics. We show that the reduction in the number of nodes expanded using multiple independent additive heuristics is the product of the reductions achieved by the individual heuristics. First, we formally state and prove this result on unit edge-cost undirected graphs with a uniform branching factor. Then, we empirically verify it on a model of the 4-peg Towers of Hanoi problem. We also run experiments on the multiple sequence alignment problem showing more general applicability to non-unit edge-cost directed graphs. Then, we extend an existing model to predict the performance of IDA* with a single pattern database to independent additive disjoint pattern databases. This is the first analysis of the performance of independent additive heuristics.

### PDDL+ Planning with Temporal Pattern Databases

The introduction of PDDL+ allowed more accurate representations of complex real-world problems of interest to the scientific community. However, PDDL+ problems are notoriously challenging to planners, requiring more advanced heuristics. We introduce the Temporal Pattern Database (TPDB), a new domain-independent heuristic technique designed for PDDL+ domains with mixed discrete/continuous behaviour, non-linear system dynamics, processes, and events. The pattern in the TPDB is obtained through an abstraction based on time and state discretisation. Our approach combines constraint relaxation and abstraction techniques, and uses solutions to the relaxed problem, as a guide to solving the concrete problem with a discretisation fine enough to satisfy the continuous model's constraints.

### An Improved Search Algorithm for Optimal Multiple-Sequence Alignment

Multiple sequence alignment (MSA) is a ubiquitous problem in computational biology. Although it is NPhard to find an optimal solution for an arbitrary number of sequences, due to the importance of this problem researchers are trying to push the limits of exact algorithms further. Since MSA can be cast as a classical path finding problem, it is attracting a growing number of AI researchers interested in heuristic search algorithms as a challenge with actual practical relevance.

### An Improved Search Algorithm for Optimal Multiple-Sequence Alignment

Multiple sequence alignment (MSA) is a ubiquitous problem in computational biology. Although it is NP-hard to find an optimal solution for an arbitrary number of sequences, due to the importance of this problem researchers are trying to push the limits of exact algorithms further. Since MSA can be cast as a classical path finding problem, it is attracting a growing number of AI researchers interested in heuristic search algorithms as a challenge with actual practical relevance. In this paper, we first review two previous, complementary lines of research. Based on Hirschberg's algorithm, Dynamic Programming needs O(kN^(k-1)) space to store both the search frontier and the nodes needed to reconstruct the solution path, for k sequences of length N. Best first search, on the other hand, has the advantage of bounding the search space that has to be explored using a heuristic. However, it is necessary to maintain all explored nodes up to the final solution in order to prevent the search from re-expanding them at higher cost. Earlier approaches to reduce the Closed list are either incompatible with pruning methods for the Open list, or must retain at least the boundary of the Closed list. In this article, we present an algorithm that attempts at combining the respective advantages; like A* it uses a heuristic for pruning the search space, but reduces both the maximum Open and Closed size to O(kN^(k-1)), as in Dynamic Programming. The underlying idea is to conduct a series of searches with successively increasing upper bounds, but using the DP ordering as the key for the Open priority queue. With a suitable choice of thresholds, in practice, a running time below four times that of A* can be expected. In our experiments we show that our algorithm outperforms one of the currently most successful algorithms for optimal multiple sequence alignments, Partial Expansion A*, both in time and memory. Moreover, we apply a refined heuristic based on optimal alignments not only of pairs of sequences, but of larger subsets. This idea is not new; however, to make it practically relevant we show that it is equally important to bound the heuristic computation appropriately, or the overhead can obliterate any possible gain. Furthermore, we discuss a number of improvements in time and space efficiency with regard to practical implementations. Our algorithm, used in conjunction with higher-dimensional heuristics, is able to calculate for the first time the optimal alignment for almost all of the problems in Reference 1 of the benchmark database BAliBASE.

### Learning Sparse Neural Networks through $L_0$ Regularization

We propose a practical method for $L_0$ norm regularization for neural networks: pruning the network during training by encouraging weights to become exactly zero. Such regularization is interesting since (1) it can greatly speed up training and inference, and (2) it can improve generalization. AIC and BIC, well-known model selection criteria, are special cases of $L_0$ regularization. However, since the $L_0$ norm of weights is non-differentiable, we cannot incorporate it directly as a regularization term in the objective function. We propose a solution through the inclusion of a collection of non-negative stochastic gates, which collectively determine which weights to set to zero. We show that, somewhat surprisingly, for certain distributions over the gates, the expected $L_0$ norm of the resulting gated weights is differentiable with respect to the distribution parameters. We further propose the \emph{hard concrete} distribution for the gates, which is obtained by "stretching" a binary concrete distribution and then transforming its samples with a hard-sigmoid. The parameters of the distribution over the gates can then be jointly optimized with the original network parameters. As a result our method allows for straightforward and efficient learning of model structures with stochastic gradient descent and allows for conditional computation in a principled way. We perform various experiments to demonstrate the effectiveness of the resulting approach and regularizer.


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# Nitrogen and oxygen form a series of oxides with the general formula $\mathrm{N}_{x} \mathrm{O}_{y}$. One of them, a blue solid, contains $36.84 \% N .$ What is the empirical formula of this oxide?

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### Video Transcript

So for this in this problem were given that we are going to be working with a compound that IHS nitrogen and oxygen. But we don't know the ratio of nitrogen into oxygen because there's a variety of ways that nitrogen and oxygen can combine. But we do know that it is 36.84% nitrogen. Um, and we're trying to figure out what formula would work for that. So what, We're going to start off with this, having, assuming we have 100 grams of this substance? And with that, that would mean that we would have 36.84 grams of nitrogen in that substance and then 100 minus. That would give us 63.16 grams of oxygen. And so again, you know, get this. This number comes from taking 100 minus the 36.84 That's how we got that value. Now we have these given numbers of grams, and we're going to go ahead and convert that into moles. So we're take thes 36.84 grams of nitrogen and multiply by one mole divided by 14.1 grant are yes, grams nitrogen and we get that that is 2.63 malls of nature. And we can do the same thing with oxygen's that we're gonna have 63.16 grams of oxygen times one mole divided by 16 grams, and that gives us 3.95 moles of oxygen. Next, we're going to take those, and we're gonna find the ratio by dividing by this smaller value. So obviously 2.63 moles of nitrogen divided by 2.63 is going to be one. We're gonna take this 3.95 moles of oxygen divided by the 2.63 um and that will give us a about approximately 1.5 or three halves. So that tells us that this is going to be three mole of oxygen to two more of nitrogen so that our empirical formula is going to be end to 03

#### Topics

Atoms, Molecules and Ions

Composition

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text:
# Dosage Calculation

Doctors routinely prescribe medications and should, therefore, be comfortable with basic calculations used to determine the optimal dosage. A dosing regimen is the manner in which a drug is administered to an individual, and describes the dose and frequency of the medication to be administered. Accuracy in dosing and the frequency of drug administration is necessary to achieve the desired effect while avoiding side effects and toxicity. In a clinical setting, both the prescribing doctor and pharmacist should review the optimal dose. Several medical conditions, including kidney and liver Liver The liver is the largest gland in the human body. The liver is found in the superior right quadrant of the abdomen and weighs approximately 1.5 kilograms. Its main functions are detoxification, metabolism, nutrient storage (e.g., iron and vitamins), synthesis of coagulation factors, formation of bile, filtration, and storage of blood. Liver diseases and hypersensitivity, require dose adjustments to achieve the desired therapeutic effect.

Last update:

Editorial responsibility: Stanley Oiseth, Lindsay Jones, Evelin Maza

## Overview

It is important for healthcare professionals including doctors, nurses, pharmacists, and pharmacy technicians to know which medications to prescribe and at what dose to prescribe them.

• Dose calculations should be performed before a medication is prescribed so that it is not wasted.
• A dosage calculator should be used if there is any concern about the correct dose.
• Common means of administering a medication:
• Volume infusion: medication given over a set period of time
• Bolus: medication administered quickly or in a short burst
• Continuous infusion: medication administered continuously over an extended period of time
• Dosage regimen is a plan for the administration of a drug for a given time period to achieve the desired physiological and pharmacological effects.
• Loading dose is a specific dose of the medication given, usually when initiating therapy, to achieve the desired plasma drug concentration rapidly.
• Maintenance dose is the amount of medication given, usually repeatedly and at set intervals, to maintain a specific plasma drug concentration over a given time period.

## Therapeutic Window

### Definition

Therapeutic window is the dosage range within which the drug is effective (i.e., the dose at which the drug produces the desired effect) without causing toxicity.

• Minimum effective concentration is the minimum drug level in the blood required to achieve the desired effect.
• Minimum toxic concentration is the minimum drug level in the blood at which toxic side effects occur.

### Therapeutic index

Therapeutic index is a measure similar to therapeutic window and is used for:

• Measurement of the relative safety of a medication
• Comparison between the dose needed for therapeutic effect and the dose that causes toxicity
• Therapeutic index is calculated by dividing the toxic dose for 50% of the population by the minimum effective dose for 50% of the population.
$$Therapeutic~index=\frac{TD_{50}}{ED_{50}}$$
TD50 = toxic dose for 50% of the population
ED50 = effective dose for 50% of the population

### Example

The therapeutic window for digoxin is 0.8–2.0 ng/mL.

• A level lower than this range may not have the desired therapeutic effect.
• A level > 2.4 ng/mL may cause hypokalemia Hypokalemia Hypokalemia is defined as plasma potassium (K+) concentration < 3.5 mEq/L. Homeostatic mechanisms maintain plasma concentration between 3.5-5.2 mEq/L despite marked variation in dietary intake. Hypokalemia can be due to renal losses, GI losses, transcellular shifts, or poor dietary intake. Hypokalemia, hypomagnesemia, and arrhythmia.
• Digoxin is known to have a narrow therapeutic index. Because of its potentially fatal toxicity, digoxin should be administered with caution.
• Elderly individuals are at increased risk for toxicity:
• Impaired renal function
• Decreased muscle mass
• May have comorbidities

## Maintenance Dose

Maintenance dose is the amount of medication given, usually repeatedly and at set intervals, to maintain a specific plasma drug concentration over a given time period of time. Typically, a loading dose is administered before administering the maintenance dose.

• The rate of administration is equal to the rate of elimination at the steady state.
• Maintenance dose is a function of the rate of removal of a drug from circulation (clearance) and its calculation depends on the rate of excretion.
• Administration is repeated at specific intervals to maintain the desired steady-state plasma drug concentration. A maintenance dose administered at least 4 times and 1 half-life (time required for the plasma drug concentration to decrease by 50%) apart will result in steady-state levels.
• The formula typically used to calculate the maintenance dose is:
$$Maintenance~dose =\frac{Clearance \times Desired~peak~concentration}{Bioavailability}$$

• A single or few quick doses administered usually at the onset of therapy
• Often used in an emergency:
• An understanding of the pharmacokinetics Pharmacokinetics Pharmacokinetics is the science that analyzes how the human body interacts with a drug. Pharmacokinetics examines how the drug is absorbed, distributed, metabolized, and excreted by the body. Pharmacokinetics and Pharmacodynamics of the drug is important when prescribing a loading dose.
• Some individuals may need to be monitored on telemetry or may require additional laboratory studies.
$$Loading~dose =\frac{Volume~of~distribution^{^{*}} \times Concentration~at~steady~state}{Bioavailability}$$
*Volume of distribution is the dose of the medication given divided by the concentration in the plasma.

### Example

A 12-year-old boy has pneumonia Pneumonia Pneumonia or pulmonary inflammation is an acute or chronic inflammation of lung tissue. Causes include infection with bacteria, viruses, or fungi. In more rare cases, pneumonia can also be caused through toxic triggers through inhalation of toxic substances, immunological processes, or in the course of radiotherapy. Pneumonia. He receives antibiotic X with a volume of distribution of 31 L and oral bioavailability of 55%. The required plasma concentration is 55 µg/mL. Calculate the loading dose.

$$Loading~dose =\frac{Volume~of~distribution \times Concentration~at~steady~state}{Bioavailability}$$
$$= \frac{31\times 55}{0.55}= 31000\times 100= 3100000~µg= 3.1~g$$

## Correction for Renal Disease

In individuals with renal disease, the drug dosage must be modified to account for reduced clearance.

• The kidney is the primary organ of drug excretion for many medications.
• Kidney function must be accounted for when prescribing a drug.
• Drug clearance is affected by:
• GFR
• Kidney disease
• Renal failure
• Drug dose should be adjusted based on renal function in individuals with renal disease. Given the same dose of medication:
• Increased drug clearance can lead to lower drug concentration.
• Decreased drug clearance can lead to higher drug concentration.
• It is more common for the effect of a drug to be amplified in individuals with renal disease due to drug accumulation. Drug doses should be decreased proportionally with a decrease in kidney function.

### Example

A 68-year-old individual has to be prescribed a drug with a narrow therapeutic index. The drug parameters are as follows:

• Bioavailability = 100%
• Renal excretion = 100%
• Clearance = 1.8 L/hour
• Half-life = 27 hours
• Volume of distribution = 51 L
• Minimum effective concentration = 25 mg/L
• Maximum effective concentration = 63 mg/L
• Creatinine clearance = 66 mL/min

$$Loading~dose =\frac{Volume~of~distribution \times Concentration~at~steady~state}{Bioavailability}$$
$$=\frac{51\times 63}{1}= 3213~mg$$

Dosing interval:

$$Dosing~interval =\frac{Peak~concentration~\text{-}~Trough~concentration}{Clearance}$$
$$= \frac{63~\text{-}~25}{1.8}= 21~hours$$

Maintenance dose:

$$Maintenance~dose = Serum~concentration \times Clearance$$
$$=(\frac{63~\text{-}~25}{2}+25)\times 1.8\times 24 = 44\times 1.8\times 24 =\frac{1900.8~mg}{day}$$

Corrected dose:

$$Corrected~dose = \frac{Original~dose \times Creatinine~clearance~of~the~individual}{100}$$
$$=\frac{1.9\times 66}{100} =\frac{1254~mg}{day} =\frac{1~g}{day}$$

## References

1. Trevor, A.J., et al. (2008). Katzung & Trevor’s Pharmacology: Examination & Board Review. McGraw-Hill.
2. Goodman, L.S., et al., (Eds.) (2011). Goodman & Gilman’s Pharmacological Basis of Therapeutics, 12th ed. McGraw-Hill.
3. Rang, H.P., Dale, M.M. (Eds.) (2016). Rang and Dale’s Pharmacology, 8th Ed. Elsevier, Churchill Livingstone.
4. Miniaci, A., Gupta, V. (2021). Loading Dose. StatPearls. Treasure Island (FL): StatPearls Publishing. Retrieved November 25, 2021, from https://www.ncbi.nlm.nih.gov/books/NBK557418/
5. Kyriakopoulos, C., Gupta, V. (2021). Renal Failure Drug Dose Adjustments. StatPearls. Treasure Island (FL): StatPearls Publishing. Retrieved November 25, 2021, from https://www.ncbi.nlm.nih.gov/books/NBK560512/

#### Resources

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text:
Urbit

Pragrammatic critique of Urbit

I really like the Urbit project. I don't know how long I've been following it now. It was definitely earlier than 2016 when I discovered it, probably even 2014.

I think #Urbit is fundamentally trying to address the right set of problems in a comprehensive, holistic way. The fact that the Internet is broken for anything but centralized silos. I am deeply enthusiastic and cheering for Urbit. I do want it to succeed!

But in this post, I'm going to focus on an honest critique. I've actually read a lot of interesting critique of Urbit over the years – all that I could get my hands on. Mine is going to be less ambitious, and mostly down to earth and pragmatic. I hope it won't come out to harsh.


text:
You're reading the documentation for a development version. For the latest released version, please have a look at v4.3.0.

# Output Group¶

## Group /output¶

LAST_STATE_Y

Full state vector at the last time point of the time integrator if $$\texttt{WRITE_SOLUTION_LAST}$$ in $$\texttt{/input/return}$$ is enabled

Type: double

LAST_STATE_YDOT

Full time derivative state vector at the last time point of the time integrator if $$\texttt{WRITE_SOLUTION_LAST}$$ in $$\texttt{/input/return}$$ is enabled

Type: double

LAST_STATE_SENSY_XXX

Full state vector of the XXX th sensitivity system at the last time point of the time integrator if $$\texttt{WRITE_SENS_LAST}$$ in $$\texttt{/input/return}$$ is enabled

Type: double

LAST_STATE_SENSYDOT_XXX

Full time derivative state vector of the XXX th sensitivity system at the last time point of the time integrator if $$\texttt{WRITE_SENS_LAST}$$ in $$\texttt{/input/return}$$ is enabled

Type: double

## Group /output/solution¶

SOLUTION_TIMES

Time points at which the solution is written if $$\texttt{WRITE_SOLUTION_TIMES}$$ in $$\texttt{/input/return}$$ is enabled

Unit: $$\mathrm{s}$$

Type: double

## Group /output/solution/unit_XXX¶

SOLUTION_BULK

Interstitial solution as $$n_{\text{Time}} \times \texttt{UNITOPORDERING}$$ tensor in row-major storage

Unit: $$\mathrm{mol}\,\mathrm{m}_{\mathrm{IV}}^{-3}$$

Type: double

SOLUTION_PARTICLE

Mobile phase solution inside the particles as $$n_{\text{Time}} \times \texttt{UNITOPORDERING}$$ tensor in row-major storage. Only present if just one particle type is defined.

Unit: $$\mathrm{mol}\,\mathrm{m}_{\mathrm{MP}}^{-3}$$

Type: double

SOLUTION_PARTICLE_PARTYPE_XXX

Mobile phase solution inside the particles of type XXX as $$n_{\text{Time}} \times \texttt{UNITOPORDERING}$$ tensor in row-major storage. Only present if more than one particle type is defined.

Unit: $$\mathrm{mol}\,\mathrm{m}_{\mathrm{MP}}^{-3}$$

Type: double

SOLUTION_SOLID

Solid phase solution inside the particles as $$n_{\text{Time}} \times \texttt{UNITOPORDERING}$$ tensor in row-major storage. Only present if just one particle type is defined.

Unit: $$\mathrm{mol}\,\mathrm{m}_{\mathrm{MP}}^{-3}$$

Type: double

SOLUTION_SOLID_PARTYPE_XXX

Solid phase solution inside the particles of type XXX as $$n_{\text{Time}} \times \texttt{UNITOPORDERING}$$ tensor in row-major storage. Only present if more than one particle type is defined.

Unit: $$\mathrm{mol}\,\mathrm{m}_{\mathrm{SP}}^{-3}$$

Type: double

SOLUTION_FLUX

Flux solution as $$n_{\text{Time}} \times \texttt{UNITOPORDERING}$$ tensor in row-major storage

Unit: $$\mathrm{mol}\,\mathrm{m}^{-2}\,\mathrm{s}^{-1}$$

Type: double

SOLUTION_VOLUME

Volume solution

Unit: $$\mathrm{m}^{3}$$

Type: double

SOLUTION_OUTLET

Tensor of solutions at the unit operation outlet with components as columns in time-port-major storage. Only present if $$\texttt{SPLIT_COMPONENTS_DATA}$$ and $$\texttt{SPLIT_PORTS_DATA}$$ are both disabled. If the unit operation only has a single port, the port-dimension is removed if $$\texttt{SINGLE_AS_MULTI_PORT}$$ is disabled.

Unit: $$\mathrm{mol}\,\mathrm{m}_{\mathrm{IV}}^{-3}$$

Type: double

SOLUTION_INLET

Tensor of solutions at the unit operation inlet with components as columns in time-port-major storage. Only present if $$\texttt{SPLIT_COMPONENTS_DATA}$$ and $$\texttt{SPLIT_PORTS_DATA}$$ are both disabled. If the unit operation only has a single port, the port-dimension is removed if $$\texttt{SINGLE_AS_MULTI_PORT}$$ is disabled.

Unit: $$\mathrm{mol}\,\mathrm{m}_{\mathrm{IV}}^{-3}$$

Type: double

SOLUTION_OUTLET_COMP_XXX

Component XXX of the solution at all outlet ports of the unit operation as matrix in time-major storage. Only present if $$\texttt{SPLIT_COMPONENTS_DATA}$$ is enabled and $$\texttt{SPLIT_PORTS_DATA}$$ is disabled. If the unit operation only has a single port, a vector (1D array) is returned instead of a matrix if $$\texttt{SINGLE_AS_MULTI_PORT}$$ is disabled.

Unit: $$\mathrm{mol}\,\mathrm{m}_{\mathrm{IV}}^{-3}$$

Type: double

SOLUTION_INLET_COMP_XXX

Component XXX of the solution at all inlet ports of the unit operation inlet as matrix in time-major storage. Only present if $$\texttt{SPLIT_COMPONENTS_DATA}$$ is enabled and $$\texttt{SPLIT_PORTS_DATA}$$ is disabled. If the unit operation only has a single port, a vector (1D array) is returned instead of a matrix if $$\texttt{SINGLE_AS_MULTI_PORT}$$ is disabled.

Unit: $$\mathrm{mol}\,\mathrm{m}_{\mathrm{IV}}^{-3}$$

Type: double

SOLUTION_OUTLET_PORT_XXX

All components at outlet port XXX of the solution of the unit operation as matrix in time-major storage. Only present if $$\texttt{SPLIT_COMPONENTS_DATA}$$ is disabled and $$\texttt{SPLIT_PORTS_DATA}$$ is enabled.

Unit: $$\mathrm{mol}\,\mathrm{m}_{\mathrm{IV}}^{-3}$$

Type: double

SOLUTION_INLET_PORT_XXX

All components at inlet port XXX of the solution of the unit operation inlet as matrix in time-major storage. Only present if $$\texttt{SPLIT_COMPONENTS_DATA}$$ is disabled and $$\texttt{SPLIT_PORTS_DATA}$$ is enabled.

Unit: $$\mathrm{mol}\,\mathrm{m}_{\mathrm{IV}}^{-3}$$

Type: double

SOLUTION_OUTLET_PORT_XXX_COMP_YYY

Component YYY at outlet port XXX of the solution of the unit operation. Only present if $$\texttt{SPLIT_COMPONENTS_DATA}$$ and $$\texttt{SPLIT_PORTS_DATA}$$ are enabled, and the unit operation has multiple outlet ports. If the unit operation only has a single port, the field is created if $$\texttt{SINGLE_AS_MULTI_PORT}$$ is enabled.

Unit: $$\mathrm{mol}\,\mathrm{m}_{\mathrm{IV}}^{-3}$$

Type: double

SOLUTION_INLET_PORT_XXX_COMP_YYY

Component YYY at inlet port XXX of the solution of the unit operation. Only present if $$\texttt{SPLIT_COMPONENTS_DATA}$$ and $$\texttt{SPLIT_PORTS_DATA}$$ are enabled, and the unit operation has multiple inlet ports. If the unit operation only has a single port, the field is created if $$\texttt{SINGLE_AS_MULTI_PORT}$$ is enabled.

Unit: $$\mathrm{mol}\,\mathrm{m}_{\mathrm{IV}}^{-3}$$

Type: double

SOLDOT_BULK

Interstitial solution time derivative as $$n_{\text{Time}} \times \texttt{UNITOPORDERING}$$ tensor in row-major storage

Unit: $$\mathrm{mol}\,\mathrm{m}_{\mathrm{IV}}^{-3}\,\mathrm{s}^{-1}$$

Type: double

SOLDOT_PARTICLE

Mobile phase solution time derivative inside the particles as $$n_{\text{Time}} \times \texttt{UNITOPORDERING}$$ tensor in row-major storage. Only present if just one particle type is defined.

Unit: $$\mathrm{mol}\,\mathrm{m}_{\mathrm{MP}}^{-3}\,\mathrm{s}^{-1}$$

Type: double

SOLDOT_PARTICLE_PARTYPE_XXX

Mobile phase solution time derivative inside the particles of type XXX as $$n_{\text{Time}} \times \texttt{UNITOPORDERING}$$ tensor in row-major storage. Only present if more than one particle type is defined.

Unit: $$\mathrm{mol}\,\mathrm{m}_{\mathrm{MP}}^{-3}\,\mathrm{s}^{-1}$$

Type: double

SOLDOT_SOLID

Solid phase solution time derivative inside the particles as $$n_{\text{Time}} \times \texttt{UNITOPORDERING}$$ tensor in row-major storage. Only present if just one particle type is defined.

Unit: $$\mathrm{mol}\,\mathrm{m}_{\mathrm{MP}}^{-3}\,\mathrm{s}^{-1}$$

Type: double

SOLDOT_SOLID_PARTYPE_XXX

Solid phase solution time derivative inside the particles of type XXX as $$n_{\text{Time}} \times \texttt{UNITOPORDERING}$$ tensor in row-major storage. Only present if more than one particle type is defined.

Unit: $$\mathrm{mol}\,\mathrm{m}_{\mathrm{SP}}^{-3}\,\mathrm{s}^{-1}$$

Type: double

SOLDOT_FLUX

Flux solution time derivative as $$n_{\text{Time}} \times \texttt{UNITOPORDERING}$$ tensor in row-major storage

Unit: $$\mathrm{mol}\,\mathrm{m}^{-2}\,\mathrm{s}^{-2}$$

Type: double

SOLDOT_VOLUME

Volume solution time derivative

Unit: $$\mathrm{m}^{3}\,\mathrm{s}^{-1}$$

Type: double

SOLDOT_OUTLET

Tensor of solution time derivatives at the unit operation outlet with components as columns in time-port-major storage. Only present if $$\texttt{SPLIT_COMPONENTS_DATA}$$ and $$\texttt{SPLIT_PORTS_DATA}$$ are both disabled. If the unit operation only has a single port, the port-dimension is removed if $$\texttt{SINGLE_AS_MULTI_PORT}$$ is disabled.

Unit: $$\mathrm{mol}\,\mathrm{m}_{\mathrm{IV}}^{-3}\,\mathrm{s}^{-1}$$

Type: double

SOLDOT_INLET

Tensor of solution time derivatives at the unit operation inlet with components as columns in time-port-major storage. Only present if $$\texttt{SPLIT_COMPONENTS_DATA}$$ and $$\texttt{SPLIT_PORTS_DATA}$$ are both disabled. If the unit operation only has a single port, the port-dimension is removed if $$\texttt{SINGLE_AS_MULTI_PORT}$$ is disabled.

Unit: $$\mathrm{mol}\,\mathrm{m}_{\mathrm{IV}}^{-3}\,\mathrm{s}^{-1}$$

Type: double

SOLDOT_OUTLET_COMP_XXX

Component XXX of the solution time derivative at all outlet ports of the unit operation as matrix in time-major storage. Only present if $$\texttt{SPLIT_COMPONENTS_DATA}$$ is enabled and $$\texttt{SPLIT_PORTS_DATA}$$ is disabled. If the unit operation only has a single port, a vector (1D array) is returned instead of a matrix if $$\texttt{SINGLE_AS_MULTI_PORT}$$ is disabled.

Unit: $$\mathrm{mol}\,\mathrm{m}_{\mathrm{IV}}^{-3}\,\mathrm{s}^{-1}$$

Type: double

SOLDOT_INLET_COMP_XXX

Component XXX of the solution time derivative at all inlet ports of the unit operation inlet as matrix in time-major storage. Only present if $$\texttt{SPLIT_COMPONENTS_DATA}$$ is enabled and $$\texttt{SPLIT_PORTS_DATA}$$ is disabled. If the unit operation only has a single port, a vector (1D array) is returned instead of a matrix if $$\texttt{SINGLE_AS_MULTI_PORT}$$ is disabled.

Unit: $$\mathrm{mol}\,\mathrm{m}_{\mathrm{IV}}^{-3}\,\mathrm{s}^{-1}$$

Type: double

SOLDOT_OUTLET_PORT_XXX

All components at outlet port XXX of the solution time derivative of the unit operation as matrix in time-major storage. Only present if $$\texttt{SPLIT_COMPONENTS_DATA}$$ is disabled and $$\texttt{SPLIT_PORTS_DATA}$$ is enabled.

Unit: $$\mathrm{mol}\,\mathrm{m}_{\mathrm{IV}}^{-3}\,\mathrm{s}^{-1}$$

Type: double

SOLDOT_INLET_PORT_XXX

All components at inlet port XXX of the solution time derivative of the unit operation inlet as matrix in time-major storage. Only present if $$\texttt{SPLIT_COMPONENTS_DATA}$$ is disabled and $$\texttt{SPLIT_PORTS_DATA}$$ is enabled.

Unit: $$\mathrm{mol}\,\mathrm{m}_{\mathrm{IV}}^{-3}\,\mathrm{s}^{-1}$$

Type: double

SOLDOT_OUTLET_PORT_XXX_COMP_YYY

Component YYY at outlet port XXX of the solution time derivative of the unit operation. Only present if $$\texttt{SPLIT_COMPONENTS_DATA}$$ and $$\texttt{SPLIT_PORTS_DATA}$$ are enabled, and the unit operation has multiple outlet ports. If the unit operation only has a single port, the field is created if $$\texttt{SINGLE_AS_MULTI_PORT}$$ is enabled.

Unit: $$\mathrm{mol}\,\mathrm{m}_{\mathrm{IV}}^{-3}\,\mathrm{s}^{-1}$$

Type: double

SOLDOT_INLET_PORT_XXX_COMP_YYY

Component YYY at inlet port XXX of the solution time derivative of the unit operation. Only present if $$\texttt{SPLIT_COMPONENTS_DATA}$$ and $$\texttt{SPLIT_PORTS_DATA}$$ are enabled, and the unit operation has multiple inlet ports. If the unit operation only has a single port, the field is created if $$\texttt{SINGLE_AS_MULTI_PORT}$$ is enabled.

Unit: $$\mathrm{mol}\,\mathrm{m}_{\mathrm{IV}}^{-3}\,\mathrm{s}^{-1}$$

Type: double

LAST_STATE_Y

State vector of this unit at the last time point of the time integrator if $$\texttt{WRITE_SOLUTION_LAST_UNIT}$$ in $$\texttt{/input/return/unit_XXX}$$ is enabled. Note that the vector includes the dedicated inlet DOFs at the beginning (length: $$\texttt{NCOMP} \cdot \texttt{NPORT}$$).

Type: double

LAST_STATE_YDOT

Time derivative state vector of this unit at the last time point of the time integrator if $$\texttt{WRITE_SOLUTION_LAST_UNIT}$$ in $$\texttt{/input/return/unit_XXX}$$ is enabled. Note that the vector includes the dedicated inlet DOFs at the beginning (length: $$\texttt{NCOMP} \cdot \texttt{NPORT}$$).

Type: double

## Group /output/sensitivity/param_XXX/unit_YYY¶

SENS_BULK

Interstitial sensitivity as $$n_{\text{Time}} \times \texttt{UNITOPORDERING}$$ tensor in row-major storage

Unit: $$\mathrm{mol}\,\mathrm{m}_{\mathrm{IV}}^{-3}\,[\mathrm{Param}]^{-1}$$

Type: double

SENS_PARTICLE

Mobile phase sensitivity inside the particles as $$n_{\text{Time}} \times \texttt{UNITOPORDERING}$$ tensor in row-major storage. Only present if just one particle type is defined.

Unit: $$\mathrm{mol}\,\mathrm{m}_{\mathrm{MP}}^{-3}\,[\mathrm{Param}]^{-1}$$

Type: double

SENS_PARTICLE_PARTYPE_XXX

Mobile phase sensitivity inside the particles of type XXX as $$n_{\text{Time}} \times \texttt{UNITOPORDERING}$$ tensor in row-major storage. Only present if more than one particle type is defined.

Unit: $$\mathrm{mol}\,\mathrm{m}_{\mathrm{MP}}^{-3}\,[\mathrm{Param}]^{-1}$$

Type: double

SENS_SOLID

Solid phase sensitivity inside the particles as $$n_{\text{Time}} \times \texttt{UNITOPORDERING}$$ tensor in row-major storage. Only present if just one particle type is defined.

Unit: $$\mathrm{mol}\,\mathrm{m}_{\mathrm{MP}}^{-3}\,[\mathrm{Param}]^{-1}$$

Type: double

SENS_SOLID_PARTYPE_XXX

Solid phase sensitivity inside the particles of type XXX as $$n_{\text{Time}} \times \texttt{UNITOPORDERING}$$ tensor in row-major storage. Only present if more than one particle type is defined.

Unit: $$\mathrm{mol}\,\mathrm{m}_{\mathrm{SP}}^{-3}\,[\mathrm{Param}]^{-1}$$

Type: double

SENS_FLUX

Flux sensitivity as $$n_{\text{Time}} \times \texttt{UNITOPORDERING}$$ tensor in row-major storage

Unit: $$\mathrm{mol}\,\mathrm{m}^{-2}\,\mathrm{s}^{-1}\,[\mathrm{Param}]^{-1}$$

Type: double

SENS_VOLUME

Volume sensitivity

Unit: $$\mathrm{m}^{3}\,[\mathrm{Param}]^{-1}$$

Type: double

SENS_OUTLET

Tensor of sensitivities at the unit operation outlet with components as columns in time-port-major storage. Only present if $$\texttt{SPLIT_COMPONENTS_DATA}$$ and $$\texttt{SPLIT_PORTS_DATA}$$ are both disabled. If the unit operation only has a single port, the port-dimension is removed if $$\texttt{SINGLE_AS_MULTI_PORT}$$ is disabled.

Unit: $$\mathrm{mol}\,\mathrm{m}_{\mathrm{IV}}^{-3}\,[\mathrm{Param}]^{-1}$$

Type: double

SENS_INLET

Tensor of sensitivities at the unit operation inlet with components as columns in time-port-major storage. Only present if $$\texttt{SPLIT_COMPONENTS_DATA}$$ and $$\texttt{SPLIT_PORTS_DATA}$$ are both disabled. If the unit operation only has a single port, the port-dimension is removed if $$\texttt{SINGLE_AS_MULTI_PORT}$$ is disabled.

Unit: $$\mathrm{mol}\,\mathrm{m}_{\mathrm{IV}}^{-3}\,[\mathrm{Param}]^{-1}$$

Type: double

SENS_OUTLET_COMP_XXX

Component XXX of the sensitivity at all outlet ports of the unit operation as matrix in time-major storage. Only present if $$\texttt{SPLIT_COMPONENTS_DATA}$$ is enabled and $$\texttt{SPLIT_PORTS_DATA}$$ is disabled. If the unit operation only has a single port, a vector (1D array) is returned instead of a matrix if $$\texttt{SINGLE_AS_MULTI_PORT}$$ is disabled.

Unit: $$\mathrm{mol}\,\mathrm{m}_{\mathrm{IV}}^{-3}\,[\mathrm{Param}]^{-1}$$

Type: double

SENS_INLET_COMP_XXX

Component XXX of the sensitivity at all inlet ports of the unit operation inlet as matrix in time-major storage. Only present if $$\texttt{SPLIT_COMPONENTS_DATA}$$ is enabled and $$\texttt{SPLIT_PORTS_DATA}$$ is disabled. If the unit operation only has a single port, a vector (1D array) is returned instead of a matrix if $$\texttt{SINGLE_AS_MULTI_PORT}$$ is disabled.

Unit: $$\mathrm{mol}\,\mathrm{m}_{\mathrm{IV}}^{-3}\,[\mathrm{Param}]^{-1}$$

Type: double

SENS_OUTLET_PORT_XXX

All components at outlet port XXX of the sensitivity of the unit operation as matrix in time-major storage. Only present if $$\texttt{SPLIT_COMPONENTS_DATA}$$ is disabled and $$\texttt{SPLIT_PORTS_DATA}$$ is enabled.

Unit: $$\mathrm{mol}\,\mathrm{m}_{\mathrm{IV}}^{-3}\,[\mathrm{Param}]^{-1}$$

Type: double

SENS_INLET_PORT_XXX

All components at inlet port XXX of the sensitivity of the unit operation inlet as matrix in time-major storage. Only present if $$\texttt{SPLIT_COMPONENTS_DATA}$$ is disabled and $$\texttt{SPLIT_PORTS_DATA}$$ is enabled.

Unit: $$\mathrm{mol}\,\mathrm{m}_{\mathrm{IV}}^{-3}\,[\mathrm{Param}]^{-1}$$

Type: double

SENS_OUTLET_PORT_XXX_COMP_YYY

Component YYY at outlet port XXX of the sensitivity of the unit operation. Only present if $$\texttt{SPLIT_COMPONENTS_DATA}$$ and $$\texttt{SPLIT_PORTS_DATA}$$ are enabled, and the unit operation has multiple outlet ports. If the unit operation only has a single port, the field is created if $$\texttt{SINGLE_AS_MULTI_PORT}$$ is enabled.

Unit: $$\mathrm{mol}\,\mathrm{m}_{\mathrm{IV}}^{-3}\,[\mathrm{Param}]^{-1}$$

Type: double

SENS_INLET_PORT_XXX_COMP_YYY

Component YYY at inlet port XXX of the sensitivity of the unit operation. Only present if $$\texttt{SPLIT_COMPONENTS_DATA}$$ and $$\texttt{SPLIT_PORTS_DATA}$$ are enabled, and the unit operation has multiple inlet ports. If the unit operation only has a single port, the field is created if $$\texttt{SINGLE_AS_MULTI_PORT}$$ is enabled.

Unit: $$\mathrm{mol}\,\mathrm{m}_{\mathrm{IV}}^{-3}\,[\mathrm{Param}]^{-1}$$

Type: double

SENSDOT_BULK

Interstitial sensitivity time derivative as $$n_{\text{Time}} \times \texttt{UNITOPORDERING}$$ tensor in row-major storage

Unit: $$\mathrm{mol}\,\mathrm{m}_{\mathrm{IV}}^{-3}\,\mathrm{s}^{-1}\,[\mathrm{Param}]^{-1}$$

Type: double

SENSDOT_PARTICLE

Mobile phase sensitivity time derivative inside the particles as $$n_{\text{Time}} \times \texttt{UNITOPORDERING}$$ tensor in row-major storage. Only present if just one particle type is defined.

Unit: $$\mathrm{mol}\,\mathrm{m}_{\mathrm{MP}}^{-3}\,\mathrm{s}^{-1}\,[\mathrm{Param}]^{-1}$$

Type: double

SENSDOT_PARTICLE_PARTYPE_XXX

Mobile phase sensitivity time derivative inside the particles of type XXX as $$n_{\text{Time}} \times \texttt{UNITOPORDERING}$$ tensor in row-major storage. Only present if more than one particle type is defined.

Unit: $$\mathrm{mol}\,\mathrm{m}_{\mathrm{MP}}^{-3}\,\mathrm{s}^{-1}\,[\mathrm{Param}]^{-1}$$

Type: double

SENSDOT_SOLID

Solid phase sensitivity time derivative inside the particles as $$n_{\text{Time}} \times \texttt{UNITOPORDERING}$$ tensor in row-major storage. Only present if just one particle type is defined.

Unit: $$\mathrm{mol}\,\mathrm{m}_{\mathrm{MP}}^{-3}\,\mathrm{s}^{-1}\,[\mathrm{Param}]^{-1}$$

Type: double

SENSDOT_SOLID_PARTYPE_XXX

Solid phase sensitivity time derivative inside the particles of type XXX as $$n_{\text{Time}} \times \texttt{UNITOPORDERING}$$ tensor in row-major storage. Only present if more than one particle type is defined.

Unit: $$\mathrm{mol}\,\mathrm{m}_{\mathrm{SP}}^{-3}\,\mathrm{s}^{-1}\,[\mathrm{Param}]^{-1}$$

Type: double

SENSDOT_FLUX

Flux sensitivity time derivative as $$n_{\text{Time}} \times \texttt{UNITOPORDERING}$$ tensor in row-major storage

Unit: $$\mathrm{mol}\,\mathrm{m}^{-2}\,\mathrm{s}^{-2}\,[\mathrm{Param}]^{-1}$$

Type: double

SENSDOT_VOLUME

Volume sensitivity time derivative

Unit: $$^{3}\,\mathrm{s}\mathrm{m}^{-1}\,[\mathrm{Param}]^{-1}$$

Type: double

SENSDOT_OUTLET

Tensor of sensitivity time derivatives at the unit operation outlet with components as columns in time-port-major storage. Only present if $$\texttt{SPLIT_COMPONENTS_DATA}$$ and $$\texttt{SPLIT_PORTS_DATA}$$ are both disabled. If the unit operation only has a single port, the port-dimension is removed if $$\texttt{SINGLE_AS_MULTI_PORT}$$ is disabled.

Unit: $$\mathrm{mol}\,\mathrm{m}_{\mathrm{IV}}^{-3}\,\mathrm{s}^{-1}\,[\mathrm{Param}]^{-1}$$

Type: double

SENSDOT_INLET

Tensor of sensitivity time derivatives at the unit operation inlet with components as columns in time-port-major storage. Only present if $$\texttt{SPLIT_COMPONENTS_DATA}$$ and $$\texttt{SPLIT_PORTS_DATA}$$ are both disabled. If the unit operation only has a single port, the port-dimension is removed if $$\texttt{SINGLE_AS_MULTI_PORT}$$ is disabled.

Unit: $$\mathrm{mol}\,\mathrm{m}_{\mathrm{IV}}^{-3}\,\mathrm{s}^{-1}\,[\mathrm{Param}]^{-1}$$

Type: double

SENSDOT_OUTLET_COMP_XXX

Component XXX of the sensitivity time derivative at all outlet ports of the unit operation as matrix in time-major storage. Only present if $$\texttt{SPLIT_COMPONENTS_DATA}$$ is enabled and $$\texttt{SPLIT_PORTS_DATA}$$ is disabled. If the unit operation only has a single port, a vector (1D array) is returned instead of a matrix if $$\texttt{SINGLE_AS_MULTI_PORT}$$ is disabled.

Unit: $$\mathrm{mol}\,\mathrm{m}_{\mathrm{IV}}^{-3}\,\mathrm{s}^{-1}\,[\mathrm{Param}]^{-1}$$

Type: double

SENSDOT_INLET_COMP_XXX

Component XXX of the sensitivity time derivative at all inlet ports of the unit operation inlet as matrix in time-major storage. Only present if $$\texttt{SPLIT_COMPONENTS_DATA}$$ is enabled and $$\texttt{SPLIT_PORTS_DATA}$$ is disabled. If the unit operation only has a single port, a vector (1D array) is returned instead of a matrix if $$\texttt{SINGLE_AS_MULTI_PORT}$$ is disabled.

Unit: $$\mathrm{mol}\,\mathrm{m}_{\mathrm{IV}}^{-3}\,\mathrm{s}^{-1}\,[\mathrm{Param}]^{-1}$$

Type: double

SENSDOT_OUTLET_PORT_XXX

All components at outlet port XXX of the sensitivity time derivative of the unit operation as matrix in time-major storage. Only present if $$\texttt{SPLIT_COMPONENTS_DATA}$$ is disabled and $$\texttt{SPLIT_PORTS_DATA}$$ is enabled.

Unit: $$\mathrm{mol}\,\mathrm{m}_{\mathrm{IV}}^{-3}\,\mathrm{s}^{-1}\,[\mathrm{Param}]^{-1}$$

Type: double

SENSDOT_INLET_PORT_XXX

All components at inlet port XXX of the sensitivity time derivative of the unit operation inlet as matrix in time-major storage. Only present if $$\texttt{SPLIT_COMPONENTS_DATA}$$ is disabled and $$\texttt{SPLIT_PORTS_DATA}$$ is enabled.

Unit: $$\mathrm{mol}\,\mathrm{m}_{\mathrm{IV}}^{-3}\,\mathrm{s}^{-1}\,[\mathrm{Param}]^{-1}$$

Type: double

SENSDOT_OUTLET_PORT_XXX_COMP_YYY

Component YYY at outlet port XXX of the sensitivity time derivative of the unit operation. Only present if $$\texttt{SPLIT_COMPONENTS_DATA}$$ and $$\texttt{SPLIT_PORTS_DATA}$$ are enabled, and the unit operation has multiple outlet ports. If the unit operation only has a single port, the field is created if $$\texttt{SINGLE_AS_MULTI_PORT}$$ is enabled.

Unit: $$\mathrm{mol}\,\mathrm{m}_{\mathrm{IV}}^{-3}\,\mathrm{s}^{-1}\,[\mathrm{Param}]^{-1}$$

Type: double

SENSDOT_INLET_PORT_XXX_COMP_YYY

Component YYY at inlet port XXX of the sensitivity time derivative of the unit operation. Only present if $$\texttt{SPLIT_COMPONENTS_DATA}$$ and $$\texttt{SPLIT_PORTS_DATA}$$ are enabled, and the unit operation has multiple inlet ports. If the unit operation only has a single port, the field is created if $$\texttt{SINGLE_AS_MULTI_PORT}$$ is enabled.

Unit: $$\mathrm{mol}\,\mathrm{m}_{\mathrm{IV}}^{-3}\,\mathrm{s}^{-1}\,[\mathrm{Param}]^{-1}$$

Type: double

## /output/coordinates/unit_XXX¶

AXIAL_COORDINATES

Axial coordinates of the bulk discretization nodes

Unit: $$\mathrm{m}$$

 Type: double Length: $$\texttt{NCOL}$$

RADIAL_COORDINATES

Radial coordinates of the bulk discretization nodes (only for 2D unit operations)

Unit: $$\mathrm{m}$$

 Type: double Length: $$\texttt{NRAD}$$

PARTICLE_COORDINATES_XXX

Coordinates of the particle discretization nodes in particles of type XXX

Unit: $$\mathrm{m}$$

 Type: double Length: $$\texttt{NPAR}$$


text:
Why the layer must be created from my class and not from layer class

I am confused about something. I have the following example:

class mainMenu : public Node {
public:
static Scene* createScene();
virtual bool init();
void GoToGameScene(Ref *pSender);

private:

};

Scene* mainScene::createScene(){
auto scene = Scene::create();
auto layer = mainScene::create();

return scene;
}

Focus on this part.

auto scene = Scene::create();
auto layer = mainScene::create();

Why do we create layer from mainScene not from Layer

For example: Why we do this:

auto layer = mainScene::create();

If we can do it, like creating a scene

auto layer = Layer::create();

First of all, it's very uncommon to start classnames with a lowercase letter. It makes the code harder to understand.

Second, I'm not sure if I got your question right, but it seems like you're asking: Why call a create() method on the mainScene class instead of just using a simple Layer::create()?

If that's the case then the answer is quite simply: Because in this way we can customize how the mainScene should be initialized. Perhaps it needs several layers, like a HUD layer, a game layer, a controls layer, etc. By calling its create() method we make sure the constructor of mainScene is called, but also it's created as a Ref object, meaning that it'll be reference counted and therefore the memory management will be done automagically (for the most part).

If that wasn't the question feel free to explain it to me a bit further.

• C++ Has no common conventions. He can write however he wants. This is also the main reason why C++ is such a terrible language. – Krythic Mar 3 '17 at 3:27


text:
# POLARIZATION OF ATOMIC POTASSIUM FLUORESCENCE EXCITED BY LASER PHOTODISSOCIATION OF K2

Please use this identifier to cite or link to this item: http://hdl.handle.net/1811/17546

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 Title: POLARIZATION OF ATOMIC POTASSIUM FLUORESCENCE EXCITED BY LASER PHOTODISSOCIATION OF K2 Creators: Zafiropulos, V.; Zeng, X.; Lyyra, A. M.; Kleiber, P. D.; Sando, K. M.; Stwalley, W. C. Issue Date: 1988 Publisher: Ohio State University Abstract: A tunable dye laser was used to excite $K_{2}$ from the ground $X(^{1}\Sigma^{+}_{g})$ state into the continuum of the $B(^{1}\Sigma_{u})$ state. This results in dissociation of the molecule producing an excited $K {^{2}}P_{3/2}$ atom which fluoresces. By monitoring the atomic $D_{2}$ fluorescence under these molecular beam (collision-free) conditions, we were able to measure the pure bound-free absorption profile. At the same time, the polarization of the atomic fluorescence was measured for different laser excitation frequencies. We believe this to be the first observation of a large variation in the polarization, ranging from $15 \pm 2\%$ to $-6.3 \pm 0.4\%$ as a function of laser excitation wave-length. The results are explained a) using the theory of Van Brunt and Zare1, which predicts a maximum polarization of 14.3\% (axial recoil) and a minimum of -7.7\% (transverse recoil) and b) the Rotating molecule $theory^{2}$ where the polarization is a function of the angle of rotation of a half collision. Classical, semiclassical and quantum-mechanical calculations in the $K_{2}$ case were also performed and a comparison with the experimental results is given. Description: $^{1}$ R. J. Van Brunt and R. N. Zare, J. Chem. Phys. 48, 4304 (1968). $^{2}$ J. Vigue, J. A. Beswick and M. Broyer, J. de Physique 44, 1225 (1983). Author Institution: Iowa Laser Facility, University of Iowa URI: http://hdl.handle.net/1811/17546 Other Identifiers: 1988-RB-11


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# making terrain's connect together

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ok, ive reached my end! ive got a terrain, here''s the process huge ass map was created, its 256 blocks of 256x256 arranged in a square (128 blocks by 128 blocks, each 256x256pixels). Each block is then taken into photoshop, resized to 1024x1024, and saved as a .raw file. That .raw file is then loaded into the application, and rendered 10''s bigger (glScalef(10,10,10)). Alright, everything is great, except the maps dont want to connect together exactley right. I know each image lines up EXACTLEY cuz it was compiled in a HUGE map then cut up. why dont the terrains line up in the program? Is it because we''re guestimating by using a step size of 16, and that very slight short cut is making it so that they dont line up? if so, whats a really inexpensive way of conneting terrains... also, for future question i know i will have, how could i dynamically load and unload terrains as the player is walking around, i cant render 256 10240x10240 terrains all at once i also plan on adding dynamic dynamic detail textures (double dynamic intended). Im not sure how i will do this, but i want to, visually, have the detail texture decrease in detail as landscape moves farther from the camera, so that it doesnt appear so (plain). Yes less detail, farther away, will make it look better cuz its scaled across the terrain less, and from far away that looks better.

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What does each pixel in the heightmap represent? The quad or the vertex?

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When you cut the large image apart, did you overlap the border? Let''s just say for now that you are cutting the image into 2 halves. It seems to me that there needs to be a row of pixels that both halves share in order to get a smooth transition between one terrain section to the other. Otherwise you''ll be missing a strip between each section or it might appear to take a jump instead of lining up smoothly. If that''s not clear, let me know and I''ll try to explain what I mean more clearly.

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hey mr. grinch...

i decided to do some more work with this quesiton, and now ill post some images of what im talking about

just for ya info, i used photoshop to do everything, and im cutting the image up into slices, so that every block is exactley 256 x 256

Here is a link to the entire image, beware, its quite large...

entire world image, in low quality jpeg format

Here is images 85,86,and 101. They connect together like so:

here are the images

im am pretty sure that these should line up exactley!

also, if you dont mind, please explain in better detail what you were talking about, and thanks!

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hey ostol, im not sure what each pixel represents, but if i show you my rendering routine, im sure you can figure that out... im guessing each pixel determines one of the verticies

int ix;	int iz;	for(iz=0;iz < MAP_SIZE-1;iz+= STEP_SIZE)	{		glBegin(GL_TRIANGLE_STRIP);		for(ix=0;ix < MAP_SIZE-1;ix+= STEP_SIZE)		{			SetTextureCoord((float)ix,(float)iz);			glNormal3f((float)ix,(float)Height(pHeightMap,ix,iz),iz);			//glNormal3f(0.0f,1.0f,0.0f);			glVertex3f(ix,Height(pHeightMap,ix,iz),iz);			SetTextureCoord((float)ix,(float)iz+STEP_SIZE);			glNormal3f((float)ix,(float)Height(pHeightMap,ix,iz+STEP_SIZE),iz+STEP_SIZE);			//glNormal3f(0.0f,1.0f,0.0f);			glVertex3f(ix,Height(pHeightMap,ix,iz+STEP_SIZE),iz+STEP_SIZE);		}		glEnd();	}

the Height() function returns the current value (we use it as y) at that location (specified by x,z) in the array of the .raw file.

[edited by - fireking on October 20, 2003 9:21:50 PM]

[edited by - fireking on October 20, 2003 9:22:47 PM]

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i think wat mr grinch meant is this.. take the following grid for example:

. . x .. . x .. . x .. . x .

assume all points (x or .) are pixels on the raw image. if u cut the image along ''x'' u will have two images like the following:

   (1)      (2). . x        .. . x        .. . x        .. . x        .

now THAT is a bit wrong to store them coz the columns 1 and 2 are two diff values but they represetn edges of a sub-grid. what they SHUD look like is as follows (i think):

. . x       x .. . x       x .. . x       x .. . x       x .

the images shud have one common column so that the rendered vertices coincide.

another note, do NOT resize the images AFTER splitting them up unless u use nearest neighbour filtering in photoshop. Any other filters will cause slight mismatch in the value on the edges of adjacent grids. BUT even using nearest neighbour, u''re overall grid might end up looking rough. Think about it.

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im hoping the nearest neighbor thing works...

i do not want to end up programming some sort of (fill in the gaps) algorithm, cuz thats just too costly and really a cop out job... i want the terrains to fit together without hassle.

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nearest neighbor not working... grrr

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I think the other responders got what I was saying, but I'll try to illustrate it a bit here. For this example, I'm just going to talk about a 1D array, but it works the same for 2D. Ok, let's say you have an array of floats for the heightmap:

float heightmap[4]; // Small terrain for this example

Ok, now let's say the values of those array elements are:
{1.0, 2.0, 3.0, 4.0}

Picture it as a steadily increasing terrain (height goes from 1 to 4). Ok, so now you split that into 2 terrain sections right down the middle. When you draw the sections, you draw polygons (triangles, quads, whatever you do) between 1.0-2.0 in your first section of terrain. Then, your next section of terrain draws the polygons between 3.0-4.0. However, when you split it, you basically lost the drawing between 2.0-3.0.

So my suggestion is to re-split your image so that each section shares it's borders with the sections around it. In the example above, instead of making two sections of 1-2 and 3-4, you would make two of 1-2 and 2-4. That way when you draw your sections, you draw 1.0-2.0 in your first section, and 2.0-3.0-4.0 in your next section, given you a smooth border. I expect that may get a little more complicated if you add LOD, but it should be pretty similar to other crack fixes. Is that more helpful? I'm afraid this didn't come out as clearly as I hoped, so let me know if I can explain something more clearly.

One more thing: if you stuck the 1-2 and 3-4 sections together, they would seem to make a complete image. However, when drawing vertices of the heightmaps, remember that it is the polygons between the vertices that make it seem continuous. The sections need shared vertices.

[edited by - Mr Grinch on October 20, 2003 11:10:17 PM]

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i understand what your talking about, but how to i split my images so that they share a border? this is a huge map, so whatever process would hopefully be batchable (new word of the day) cuz whatever that process is, i have to do it 256 times...

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Rutin
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JoeJ
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