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SpECTRE  v2022.05.05
Burgers::AnalyticData::Sinusoid Class Reference

Analytic data (with an "exact" solution known) that is periodic over the interval $$[0,2\pi]$$. More...

#include <Sinusoid.hpp>

## Public Types

using options = tmpl::list<>

## Public Member Functions

Sinusoid (const Sinusoid &)=default

Sinusoidoperator= (const Sinusoid &)=default

Sinusoid (Sinusoid &&)=default

Sinusoidoperator= (Sinusoid &&)=default

template<typename T >
Scalar< T > u (const tnsr::I< T, 1 > &x) const

tuples::TaggedTuple< Tags::Uvariables (const tnsr::I< DataVector, 1 > &x, tmpl::list< Tags::U >) const

void pup (PUP::er &p)

## Static Public Attributes

static constexpr Options::String help

## Detailed Description

Analytic data (with an "exact" solution known) that is periodic over the interval $$[0,2\pi]$$.

The initial data is given by:

\begin{align} u(x, 0) = \sin(x) \end{align}

At future times the analytic solution can be found by solving the transcendental equation [61]

\begin{align} \label{eq:transcendental burgers periodic} \mathcal{F}=\sin\left(x-\mathcal{F}t\right) \end{align}

on the interval $$x\in(0,\pi)$$. The solution from $$x\in(\pi,2\pi)$$ is given by $$\mathcal{F}(x, t)=-\mathcal{F}(2\pi-x,t)$$. The transcendental equation $$(\ref{eq:transcendental burgers periodic})$$ can be solved with a Newton-Raphson iterative scheme. Since this can be quite sensitive to the initial guess we implement this solution as analytic data. The python code below can be used to compute the analytic solution if desired.

At time $$1$$ the solution develops a discontinuity at $$x=\pi$$ followed by the amplitude of the solution decaying over time.

Note
We have rescaled $$x$$ and $$t$$ by $$\pi$$ compared to [61].
import numpy as np
from scipy.optimize import newton
# x_grid is a np.array of positions at which to evaluate the solution
def burgers_periodic(x_grid, time):
def opt_fun(F, x, t):
return np.sin((x - F * t)) - F
results = []
for i in range(len(x_grid)):
x = x_grid[i]
greater_than_pi = False
if x > np.pi:
x = x - np.pi
x = -x
x = x + np.pi
greater_than_pi = True
guess = 0.0
if len(results) > 0:
if results[-1] < 0.0:
guess = -results[-1]
else:
guess = results[-1]
res = newton(lambda F: opt_fun(F, x, time), x0=guess)
if greater_than_pi:
results.append(-res)
else:
results.append(res)
return np.asarray(results)

## ◆ help

 constexpr Options::String Burgers::AnalyticData::Sinusoid::help
staticconstexpr
Initial value:
{
"A solution that is periodic over the interval [0,2pi]. The solution "
"starts as a sinusoid: u(x,0) = sin(x) and develops a "
"discontinuity at x=pi and t=1."}

The documentation for this class was generated from the following file:
• src/PointwiseFunctions/AnalyticData/Burgers/Sinusoid.hpp


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# In a reciprocating compressor, the clearance ratio is generally between:

Free Practice With Testbook Mock Tests

## Options:

1. 10% and 30%

2.  8% and 20%

3. 5% and 12%

4. 4% and 10%

### Correct Answer: Option 4 (Solution Below)

This question was previously asked in

SSC JE ME Previous Paper 7 (Held on: 27 October 2020 Morning)

SSC JE ME Previous Paper (Held on: 27 October 2020 Morning)

## Solution:

Explanation:

Clearance ratio:

• It is the ratio of clearance volume to the swept volume C = $$\frac {V_c}{V_s}$$
• This ratio has value in general between 4% to 10%
• The clearance volume is that volume which remains in the cylinder after the piston has reached the end of its inward stroke.

• The figure shows the P-V diagram of the reciprocating engine.

• Because of the presence of clearance ratio, volumetric efficiency is always less than unity and varies between 60% to 85%.
• Volumetric efficiency ηvol = 1 + C - C$$(\frac{P_2}{P_1})^{\frac{1}{n}}$$

format: plain


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# Tag

Sort by:

### Successive square method

The successive square method is an algorithm to compute in a finite field . The first step is to decompose in successive powers of two,(1)where , which gives in base 2. can then be represented as(2)(3)This term can be computed by successive steps as(4)(5)(6)(7)For example, to compute in the finite field , first decompose into , then follow the above steps: (8)(9)(10)(11)(12)From there, the final answer can be computed as(13)The successive square method is implemented in the Wolfram Language as PowerMod[a, b, n].

Check the price


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# Matrix trace minimization and zeros

I would like to minimize and find the zeros of the function

$$F(S,P) = trace(S-SP^{T}(A+ PSP^{T})^{-1}PS)$$

in respect to $S$ and $P$.

$S$ is symmetric square matrix.

$P$ is a rectangular matrix

Could you help me? Thank you very much

All the best

GoodSpirit

-
You have an implicit constraint that P and S should be such that $A+PSP^T$ is invertible. This will follow easily if A and S are assumed to be positive definite. IS it OK to make such additional assumptions? –  ACARCHAU Jan 23 '13 at 17:33
I really thank you for your answer.:) The fact is that A is positive definite and symmetric. I forgot to mention that... But S and P might might be positive semi-definite. I also would like to tell that the aim is to minimize an error metric and preferentially drive it to zero. Many thanks GoodSpirit –  GoodSpirit Jan 24 '13 at 12:13
Hello everybody, I've been using derivatives like this $dF/dS=0$ and $dF/dP=0$ What do you think? GoodSpirit –  GoodSpirit Jan 25 '13 at 12:06


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# zbMATH — the first resource for mathematics

Perfect matchings and Hamiltonian cycles in the preferential attachment model. (English) Zbl 1417.05188
This paper deals with B. Bollobás and O. Riordan’s [Combinatorica 24, No. 1, 5–34 (2004; Zbl 1047.05038)] generative preferential attachment model of random graphs where new nodes are added to the graph successively and every new node is connected to $$m$$ existing nodes, more likely to those with higher degree than to those with lower degree. Here, the value of $$m$$ is considered the only parameter of the model. The following two are the main results of the paper under review:
(1)
If $$m \geqslant 1\,253$$, then asymptotically almost surely the random graph contains a perfect matching.
(2)
If $$m \geqslant 29\,500$$, then asymptotically almost surely the random graph contains a Hamiltonian cycle.
The main difficulty in obtaining these results is due to the lack of independence in generating new edges in the preferential attachment model. To overcome this difficulty, the authors first consider the uniform attachment model where new nodes are added to the graph successively but are uniformly likely to be connected to $$m$$ existing nodes chosen independently. The authors first establish the almost sure existence of a perfect matching and a Hamiltonian cycle in the uniform attachment model, and then adjust the construction to the preferential attachment model.

##### MSC:
 05C80 Random graphs (graph-theoretic aspects) 05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) 05C45 Eulerian and Hamiltonian graphs
Full Text:


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A recently developed method to study brain function is to produce a rapidly changing magnetic field within the brain. When this technique, known as transcranial magnetic stimulation (TMS), is applied to the prefrontal cortex, for example, it can reduce a person's ability to conjugate verbs, though other thought processes are unaffected. The rapidly varying magnetic field is produced with a circular coil of 21 turns and a radius of 6.0 {\rm cm} placed directly on the head. The current in this loop increases at the rate of 1.2 \times 10^7 {\rm{A/s}} (by discharging a capacitor).

Part A
At what rate does the magnetic field at the center of the coil increase?

Part B
Suppose a second coil with half the area of the first coil is used instead. Would your answer to part A increase, decrease, or stay the same? By what factor?


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# Software Engineering Institute

## 10 Types of Application Security Testing Tools: When and How to Use Them

##### SHARE

Bugs and weaknesses in software are common: 84 percent of software breaches exploit vulnerabilities at the application layer. The prevalence of software-related problems is a key motivation for using application security testing (AST) tools. With a growing number of application security testing tools available, it can be confusing for information technology (IT) leaders, developers, and engineers to know which tools address which issues. This blog post, the first in a series on application security testing tools, will help to navigate the sea of offerings by categorizing the different types of AST tools available and providing guidance on how and when to use each class of tool.

See the second post in this series, Decision-Making Factors for Selecting Application Security Testing Tools.

Application security is not a simple binary choice, whereby you either have security or you don't. Application security is more of a sliding scale where providing additional security layers helps reduce the risk of an incident, hopefully to an acceptable level of risk for the organization. Thus, application-security testing reduces risk in applications, but cannot completely eliminate it. Steps can be taken, however, to remove those risks that are easiest to remove and to harden the software in use.

The major motivation for using AST tools is that manual code reviews and traditional test plans are time consuming, and new vulnerabilities are continually being introduced or discovered. In many domains, there are regulatory and compliance directives that mandate the use of AST tools. Moreover--and perhaps most importantly--individuals and groups intent on compromising systems use tools too, and those charged with protecting those systems must keep pace with their adversaries.

There are many benefits to using AST tools, which increase the speed, efficiency, and coverage paths for testing applications. The tests they conduct are repeatable and scale well--once a test case is developed in a tool, it can be executed against many lines of code with little incremental cost. AST tools are effective at finding known vulnerabilities, issues, and weaknesses, and they enable users to triage and classify their findings. They can also be used in the remediation workflow, particularly in verification, and they can be used to correlate and identify trends and patterns.

Guide to Application Security Testing Tools

This graphic depicts classes or categories of application security testing tools. The boundaries are blurred at times, as particular products can perform elements of multiple categories, but these are roughly the classes of tools within this domain. There is a rough hierarchy in that the tools at the bottom of the pyramid are foundational and as proficiency is gained with them, organizations may look to use some of the more progressive methods higher in the pyramid.

Static Application Security Testing (SAST)

SAST tools can be thought of as white-hat or white-box testing, where the tester knows information about the system or software being tested, including an architecture diagram, access to source code, etc. SAST tools examine source code (at rest) to detect and report weaknesses that can lead to security vulnerabilities.

Source-code analyzers can run on non-compiled code to check for defects such as numerical errors, input validation, race conditions, path traversals, pointers and references, and more. Binary and byte-code analyzers do the same on built and compiled code. Some tools run on source code only, some on compiled code only, and some on both.

Dynamic Application Security Testing (DAST)

In contrast to SAST tools, DAST tools can be thought of as black-hat or black-box testing, where the tester has no prior knowledge of the system. They detect conditions that indicate a security vulnerability in an application in its running state. DAST tools run on operating code to detect issues with interfaces, requests, responses, scripting (i.e. JavaScript), data injection, sessions, authentication, and more.

DAST tools employ fuzzing: throwing known invalid and unexpected test cases at an application, often in large volume.

Origin Analysis/Software Composition Analysis (SCA)

Software-governance processes that depend on manual inspection are prone to failure. SCA tools examine software to determine the origins of all components and libraries within the software. These tools are highly effective at identifying and finding vulnerabilities in common and popular components, particularly open-source components. They do not, however, detect vulnerabilities for in-house custom developed components.

SCA tools are most effective in finding common and popular libraries and components, particularly open-source pieces. They work by comparing known modules found in code to a list of known vulnerabilities. The SCA tools find components that have known and documented vulnerabilities and will often advise if components are out of date or have patches available.

To make this comparison, almost all SCA tools use the NIST National Vulnerability Database Common Vulnerabilities and Exposures (CVEs) as a source for known vulnerabilities. Many commercial SCA products also use the VulnDB commercial vulnerability database as a source, as well as some other public and proprietary sources. SCA tools can run on source code, byte code, binary code, or some combination.

Database Security Scanning

The SQL Slammer worm of 2003 exploited a known vulnerability in a database-management system that had a patch released more than one year before the attack. Although databases are not always considered part of an application, application developers often rely heavily on the database, and applications can often heavily affect databases. Database-security-scanning tools check for updated patches and versions, weak passwords, configuration errors, access control list (ACL) issues, and more. Some tools can mine logs looking for irregular patterns or actions, such as excessive administrative actions.

Database scanners generally run on the static data that is at rest while the database-management system is operating. Some scanners can monitor data that is in transit.

Interactive Application Security Testing (IAST) and Hybrid Tools

Hybrid approaches have been available for a long time, but more recently have been categorized and discussed using the term IAST. IAST tools use a combination of static and dynamic analysis techniques. They can test whether known vulnerabilities in code are actually exploitable in the running application.

IAST tools use knowledge of application flow and data flow to create advanced attack scenarios and use dynamic analysis results recursively: as a dynamic scan is being performed, the tool will learn things about the application based on how it responds to test cases. Some tools will use this knowledge to create additional test cases, which then could yield more knowledge for more test cases and so on. IAST tools are adept at reducing the number of false positives, and work well in Agile and DevOps environments where traditional stand-alone DAST and SAST tools can be too time intensive for the development cycle.

Mobile Application Security Testing (MAST)

The Open Web Application Security Project (OWASP) listed the top 10 mobile risks in 2016 as

1. improper platform usage
2. insecure data storage
3. insecure communication
4. insecure authentication
5. insufficient cryptography
6. insecure authorization
7. client code quality
8. code tampering
9. reverse engineering
10. extraneous functionality

MAST Tools are a blend of static, dynamic, and forensics analysis. They perform some of the same functions as traditional static and dynamic analyzers but enable mobile code to be run through many of those analyzers as well. MAST tools have specialized features that focus on issues specific to mobile applications, such as jail-breaking or rooting of the device, spoofed WI-FI connections, handling and validation of certificates, prevention of data leakage, and more.

Application Security Testing as a Service (ASTaaS)

As the name suggests, with ASTaaS, you pay someone to perform security testing on your application. The service will usually be a combination of static and dynamic analysis, penetration testing, testing of application programming interfaces (APIs), risk assessments, and more. ASTaaS can be used on traditional applications, especially mobile and web apps.

Momentum for the use of ASTaaS is coming from use of cloud applications, where resources for testing are easier to marshal. Worldwide spending on public cloud computing is projected to increase from $67B in 2015 to$162B in 2020.

Correlation Tools

Dealing with false positives is a big issue in application security testing. Correlation tools can help reduce some of the noise by providing a central repository for findings from others AST tools.

Different AST tools will have different findings, so correlation tools correlate and analyze results from different AST tools and help with validation and prioritization of findings, including remediation workflows. Whereas some correlation tools include code scanners, they are useful mainly for importing findings from other tools.

Test-Coverage Analyzers

Test-coverage analyzers measure how much of the total program code has been analyzed. The results can be presented in terms of statement coverage (percentage of lines of code tested) or branch coverage (percentage of available paths tested).

For large applications, acceptable levels of coverage can be determined in advance and then compared to the results produced by test-coverage analyzers to accelerate the testing-and-release process. These tools can also detect if particular lines of code or branches of logic are not actually able to be reached during program execution, which is inefficient and a potential security concern. Some SAST tools incorporate this functionality into their products, but standalone products also exist.

Since the functionality of analyzing coverage is being incorporated into some of the other AST tool types, standalone coverage analyzers are mainly for niche use.

Application Security Testing Orchestration (ASTO)

ASTO integrates security tooling across a software development lifecycle (SDLC). While the term ASTO is newly coined by Gartner since this is an emerging field, there are tools that have been doing ASTO already, mainly those created by correlation-tool vendors. The idea of ASTO is to have central, coordinated management and reporting of all the different AST tools running in an ecosystem. It is still too early to know if the term and product lines will endure, but as automated testing becomes more ubiquitous, ASTO does fill a need.

Selecting Testing Tool Types

There are many factors to consider when selecting from among these different types of AST tools. If you are wondering how to begin, the biggest decision you will make is to get started by beginning using the tools. According to a 2013 Microsoft security study, 76 percent of U.S. developers use no secure application-program process and more than 40 percent of software developers globally said that security wasn't a top priority for them. Our strongest recommendation is that you exclude yourself from these percentages.

There are factors that will help you to decide which type of AST tools to use and to determine which products within an AST tool class to use. It is important to note, however, that no single tool will solve all problems. As stated above, security is not binary; the goal is to reduce risk and exposure.

Before looking at specific AST products, the first step is to determine which type of AST tool is appropriate for your application. Until your application software testing grows in sophistication, most tooling will be done using AST tools from the base of the pyramid, shown in blue in the figure below. These are the most mature AST tools that address most common weaknesses.

After you gain proficiency and experience, you can consider adding some of the second-level approaches shown below in blue. For instance, many testing tools for mobile platforms provide frameworks for you to write custom scripts for testing. Having some experience with traditional DAST tools will allow you to write better test scripts. Likewise, if you have experience with all the classes of tools at the base of the pyramid, you will be better positioned to negotiate the terms and features of an ASTaaS contract.

The decision to employ tools in the top three boxes in the pyramid is dictated as much by management and resource concerns as by technical considerations.

If you are able to implement only one AST tool, here are some guidelines for which type of tool to choose:

• If the application is written in-house or you have access to the source code, a good starting point is to run a static application security tool (SAST) and check for coding issues and adherence to coding standards. In fact, SAST is the most common starting point for initial code analysis.
• If the application is not written in house or you otherwise don't have access to the source code, dynamic application security testing (DAST) is the best choice.
• Whether you have access to the source code or not, if a lot of third-party and open-source components are known to be used in the application, then origin analysis/software composition analysis (SCA) tools are the best choice. Ideally, SCA tools are run alongside SAST and/or DAST tools, but if resources only allow for implementation of one tool, SCA tools are imperative for applications with 3rd party components because they will check for vulnerabilities that are already widely known.

In the long run, incorporating AST tools into the development process should save time and effort on re-work by catching issues earlier. In practice, however, implementing AST tools requires some initial investment of time and resources. Our guidance presented above is intended to help you select an appropriate starting point. After you begin using AST tools, they can produce lots of results, and someone must manage and act on them.

These tools also have many knobs and buttons for calibrating the output, but it takes time to set them at a desirable level. Both false positives and false negatives can be troublesome if the tools are not set correctly.

In the next post in this series, I will consider these decision factors in greater detail and present guidance in the form of lists that can easily be scanned and used as checklists by those responsible for application security testing.

Read the second post in this series, Decision-Making Factors for Selecting Application Security Testing Tools.

Learn about the National Institute of Standards and Technology (NIST) Software Assurance Metrics And Tool Evaluation (SAMATE) Project.

Learn about the Open Web Application Security Project (OWASP).

Access and download the software, tools, and methods that the SEI creates, tests, refines, and disseminates.

Review the Department of Homeland Security (DHS) Build Security In website.

### Thomas Scanlon

#### Vulnerabilities: Everybody’s Got One!

##### SHARE

This post has been shared 8 times.

## Get updates on our latest work.

Each week, our researchers write about the latest in software engineering, cybersecurity and artificial intelligence. Sign up to get the latest post sent to your inbox the day it's published.


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Preprint Hypothesis Version 1 Preserved in Portico This version is not peer-reviewed

# A Direct Approach for the Lindelöf Conjecture Related to Theory of the Riemann Zeta Function

Version 1 : Received: 26 April 2021 / Approved: 27 April 2021 / Online: 27 April 2021 (09:46:32 CEST)

How to cite: Yang, X. A Direct Approach for the Lindelöf Conjecture Related to Theory of the Riemann Zeta Function. Preprints 2021, 2021040698 (doi: 10.20944/preprints202104.0698.v1). Yang, X. A Direct Approach for the Lindelöf Conjecture Related to Theory of the Riemann Zeta Function. Preprints 2021, 2021040698 (doi: 10.20944/preprints202104.0698.v1).

## Abstract

It is due to Littlewood that the truth of the Riemann theorem implies that of the Lindel\"{o}f conjecture. This paper aims to use the idea of Littlewood to prove the Lindel\"{o}f conjecture for the Riemann zeta function. The Lindel\"{o}f $\mu$ function at the critical line is zero, with use of the Riemann theorem for the entire Riemann zeta function, proved based on the work of Heath-Brown. Our result is given to show that the Lindel\"{o}f conjecture, connected with the proof of the moment conjecture, is true.

## Subject Areas

Lindelöf conjecture; Riemann zeta function; nontrivial zeros; Riemann theorem; moment conjecture

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## Reference Numbers

There is a problem for the reference numbers in the body of the book.  Specifically, a reference number [i] should be

i+1    for    105  <=  i  <=  198

and

i+2    for     199  <=  i  <=  238

For example, Shannon [180] on p. 39 should be Shannon [181], and Yeung and Zhang [232] on p. 325 should be Yeung and Zhang [234].

## Chapter 2

p. 12, Definition 2.15.  "$X$ given $Y$" should be "$Y$ given $X$".

p. 35.  In (2.201), $\lim_{k \rightarrow \infty}$ should be $\lim_{n \rightarrow \infty}$.

p. 36, Problem 6.  The lower limit of $n$ should be 2 instead of 1, i.e., $C_\alpha = \sum_{n=2}^\infty$ and $n = 2, 3, \cdots$.

p. 36, Problem 7.  Define $\overline{\lambda} = 1 - \lambda$, where $0 \le \lambda \le 1$.

## Chapter 3

p. 56, the 4th line above Theorem 3.20.  $\tilde{p}_{k,j}$ should be $\tilde{p}_{k,j} / q_j$.

p. 57.  The equation (3.72) should read

(p_{m-1} + p_m) \left[ 1 - H_2 \left( \left\{ {p_{m-1} \over p_{m-1}+p_m}, {p_m \over p_{m-1}+p_m} \right\} \right) ,

p. 58, Problem 6.  $p_1 \ge 0.4$ should be $p_1 > 0.4$.

## Chapter 4

p. 69.  Eqn (4.52) should read

- {1 \over n} \log {\rm Pr} \{ {\bf X} \} \approx H.

p. 70, Problems 2 and 3.  $P_e \rightarrow 0$ should be $P_e \rightarrow 1$.

p. 70, Problem 5.  $n \rightarrow 0$ should be $n \rightarrow \infty$.

p. 71, Problem 7.  Part a), $A_\epsilon({\cal S})$ should be $A_\epsilon^n({\cal S})$.  Part b), add "for sufficiently large $n$" at the end.

p. 71, Problem 8.  In the definition of $Z_n$, $H(X)$ should be $\sqrt{n} H(X)$.

## Chapter 5

p. 73.  In Definition 5.1, after "such that", add "$N(x;{\bf x}) = 0$ for $x \not\in {\cal S}_X$, and".

p. 81.  In (5.75) - (5.80), $\delta$ should be ${\delta \over | {\cal X} |}$.  In (5.81), $\varphi_x(\delta)$ should be $\varphi_x({\delta \over | {\cal X} |})$.

p. 82.  The example at the end of the section is incorrect.  Here is a correct example.

p. 83.  In Definition 5.6, after "such that", add "$N(x,y;{\bf x},{\bf y}) = 0$ for $(x,y) \not\in {\cal S}_{XY}$, and".

## Chapter 6

p. 114.  Figures 6.13 and 6.14 should refer to Example 6.13 instead of 6.14.

p. 121, Eqn (6.A.8).  All $X$ should be $\tilde{X}$.

p. 121, Problem 3.  In part a), change $p(0,0,1)$ to 0.0772 and $p(1,1,1)$ to 0.375.  And part b) should read:

Verify that the distribution in part a) does not satisfy the conditions in Problem 2.

## Chapter 7

p. 147, Historial Notes: In Yeung et al. [230], they also obtained a hypergraph characterization of a Markov random field based on the I-Measure  characterization.

Chapter 8

p. 183, line 1.  $n \rightarrow 0$ should be $n \rightarrow \infty$.

p. 184, Problem 3.  The sentence before part a) should read:

We assume that $\{ X_i \}$ and $\{ Z_i \}$ are independent, but we make no assumption that $Z_i$ are i.i.d. so that the channel may have memory.

Chapter 9

p. 203, Eqn (9.115).  All $X$ should be $\tilde{X}$ and all $\tilde{X}$ should be $X$.

Chapter 11

p. 244, Eqn (11.45).  $\le$ should be $=$.

Chapter 15

p. 344, 345.  In (15.82) to (15.88), all $i,i’$ should be $i’,i$.

p. 360, below Eqn (15.A.4).  $k \rightarrow \infty$ should be $m \rightarrow \infty$.

## Other Minor Problems/Errors

Last update by Raymond W. Yeung on February 6, 2006.


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# I'm in Radio Shack again!

75 views

Interestingly, I got no responses from yesterday's entry. Usually when I'm on a tear, I get lots of responses from folks telling me they agree or that I ate too many lead paint chips as a child. Oh well.

Anyway, I've finally come full-circle. Yes, for the first time since DeskMate was dropped around 1993, I'm back in Radio Shack. The following ad appears in that big Radio Shack tabloid that will likely be appearing in your mailbox this week.

That's Fifty Big Bad Blazin' Baddass Buttkickin' Games for Windows 95/98/NT up there in the upper-right corner. I headed down to our corner Radio Shack to check. Unfortunately, though, they weren't participating in the deal. They did get on the phone and found out that one of the other three Radio Shacks within a mile radius of my house did indeed have 'em (Fort Worth is the only place I know where Radio Shacks outnumber McDonald's). Upon arriving at the other Radio Shack, Shelly and I came upon a tiny rotating display rack full of Cosmi stuff, including my games!

Unfortunately (for them), this Radio Shack seemed to be staffed by people who rode the little bus to school. They had four copies of every title, and they had taped 'em together in twos. When I asked if I could mix-n-match which products I wanted, they insisted that the deal only counted if you bought two of the same title, and the price was $9.99 for a pair, not$9.99 each. Shelly and I simultaneously rolled our eyes and said "O. . .kay", then proceeded to buy all four copies of my games for $20. Holidays are coming up, and it's a perfect stocking-stuffer. Is it just me? I thought that the ad was pretty obvious. To me, it appears that the CD's are$9.99 each, and if you buy any two titles, you can get three free by mail. They interpreted that as meaning that you must buy two of the same title, pay $9.99 for the pair, and then you'll get your freebies by mail. Weird. Anyway, it's still quite a good deal. The freebie-deal is a bit of a pain, though. They want$2.99 P&H, they want you to pop open the case to retrieve the original UPC symbol, and you can't choose from all 30 titles for your freebies. The titles you can get free are Board Games, Brochure Magic, Business Card Maker, Card Games, Desktop Publisher, Talking Flash Cards, Greeting Card Magic, Guide to the Galaxy, Label Publisher, PC Attorney, Professional Resume, and 10,000 Recipes. It's too bad, because they had a couple of titles I was interested in getting, like Battle-gammon and a 3D Frogger clone. I'll probably pay the cash and pick 'em up later.

FWIW, the fine print says "Details in store. Offer good 10/1/99 to 1/31/00. Limit 1 request per name/family/address". Just being honest.

Also interesting is that this stuff was the only software in the entire store. Looks like Radio Shack pulled out of computers in a big way, because there was very little computer-related stuff there. They had the usual supplies, like floppy disks, CD-R's, and mouse pads, but little else. The little rack was the only software in the store. I guess that's a good thing, because I won't be shoved into a dusty corner behind the top-shelf titles.

I guess it's a bit of forced irony, me being back in Radio Shack. I bailed out of Tandy in early 1992 when I saw that the DeskMate for Windows project was going south. Looks like I've finally returned :)

Anyway, if you're one of those folks who just can't seem to find my games no matter where you look, you might print up the ad above, drag it down to your local Radio Shack, and get 'em to call around for a participating store.

There are no comments to display.


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# Dissemin API¶

Dissemin provides an API to query the availability of arbitrary papers. Please do not assume the interface will not change in the future as it is still being improved.

## Querying by DOI¶

You can retrieve Dissemin’s metadata for a specific paper by DOI:

## Searching for papers¶

The search interface is also exposed as an API. The parameters it understands are the same as the human-readable version at http://dissem.in/search . Statistics about the results are also returned as well.

http://dissem.in/api/search/?q=pregroup

## Understanding the results¶

{

"status": "ok",
"paper": {
"classification": "UNK",
"title": "Refining the Conceptualization of an Important
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"abstract": "Proactive coping, directed at an upcoming as
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Most fields are self-explanatory, here is a quick description of the other ones:

• *classification* is the code for the self-archiving policy of the publisher “OA” (available from the publisher), “OK” (some version can be shared), “UNK” (unknown/unclear sharing policy), “NOK” (restrictive sharing policy).
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text:
Definitions

# Tidewater glacier cycle

The tidewater glacier cycle is the typically centuries-long behavior of tidewater glaciers that consists of recurring periods of advance alternating with rapid retreat and punctuated by periods of stability. During portions of its cycle, a tidewater glacier is relatively insensitive to climate change.

## Calving rate of tidewater glaciers

While climate is the main factor affecting the behavior of all glaciers, additional factors affect calving (iceberg producing) tidewater glaciers. These glaciers terminate abruptly at the ocean interface, with large pieces of the glacier fracturing and separating, or calving, from the ice front as icebergs.

A climate change causes a shift in the equilibrium line altitude (ELA) of a glacier. This is the imaginary line on a glacier, above which snow accumulates faster than it ablates, and below which, the reverse is the case. This altitude shift, in turn, prompts a retreat or advance of the terminus toward a new steady-state position. However, this change in terminus behavior for calving glaciers is also a function of resulting changes in fjord geometry, and calving rate at the glacier terminus as it changes position.

Calving glaciers are different than land terminating glaciers in the variation in velocity along their length. Land terminating glacier velocities decline as the terminus is approached. Calving glaciers accelerate at the terminus. A declining velocity near the terminus slows the glacier response to climate. An accelerating velocity at the front enhances the speed of the glaciers response to climate or glacier dynamic changes. This is observed in Svalbard, Patagonia and Alaska. A calving glacier requires more accumulation area than a land terminating glacier to offset this higher loss from calving.

The calving rate is largely controlled by the depth of the water and the glacier velocity at the calving front. The process of calving provides an imbalance in forces at the front of the glaciers, that raises velocity. The depth of the water at the glacier front is a simple measure that allows estimation of calving rate, but is the amount of flotation of the glacier at the front that is the specific physical characteristic that is important.

Water depth at the glacier terminus is the key variable in predicting calving of a tidewater glacier. Long term sedimentation and sediment recycling at the glacier terminus can alter this depth with time and is also important (Powell, 1991). This effect contributes to the insensitivity of a glacier to climate when its terminus is either retreating or advancing in deep water.

Austin Post was one of the first to propose that water depth at the calving margin strongly affects the rate of iceberg calving. Glaciers that terminate on a morainal shoal are generally stable, but once a glacier retreats into water that deepens as the ice front recedes, calving rate increases rapidly and results in drastic retreat of the terminus. Using data collected from 13 Alaskan tidewater calving glaciers, Brown et al. (1982) derived the following relationship between calving speed and water depth: $V_C = CH_w + D$, where $V_C$ is the mean calving speed (ma-1), $C$ is a calving coefficient (27.1±2 a-1), $H_w$ is the mean water depth at glacier front (m) and $D$ is a constant (0 m⋅a-1). Pelto and Warren (1991) found a similar calving relationship with tidewater glaciers observed over longer time periods, with slightly reduced calving rate to the mainly summer rates noted by Brown et al. (1982).

Calving is an important form of ablation for glaciers that terminate in freshwater, also. Funk and Röthlisberger determined a relationship between calving speed and water depth based on analysis of six glaciers that calve into lakes. They found that the same basic calving relationship developed for tidewater calving glaciers was true for freshwater calving glaciers, only the calving coefficients lead to calving rates 10% of that for tidewater glaciers.

## Tidewater glacier phases

Observations of Alaskan tidewater calving glaciers prompted Austin Post to describe the tidewater calving glacier advance/retreat cycle: (1) advancing, (2) stable-extended, (3) drastically retreating, or (4) stable-retracted. The following is a detailed review of the tidewater glacier cycle derived by Post, with numerous cited examples, the cycle is based on observations of temperate tidewater glaciers in Alaska, not outlet glaciers from large ice sheets or polar glaciers.

The accumulation area ratio of a glacier, AAR, is the percentage of a glacier that is a snow-covered accumulation zone at the end of the summer melt season. This percentage for large Alaskan glaciers is between 60 and 70 for non-calving glaciers, 70-80 for moderately calving glaciers and up to 90 for very high calving rate glaciers. By using accumulation area ratio (AAR) data for Alaskan tidewater calving glaciers, Pelto (1987) and Viens (1995) produced models showing that climate acts as a first-order control on the advance/retreat cycle of calving glaciers during most of the advance retreat cycle, but there are climate insensitive periods as well. Pelto (1987) examined the terminus behavior of 90 Alaskan glaciers and found that the terminus behavior of all 90 were correctly predicted based on the AAR and calving rate.

If we begin at the stable retracted position at the end of a tidewater glacier cycle the glacier will have a moderate calving rate and a high AAR, above 70. The glacier will build a terminus shoal of sediment further reducing the calving rate. This will improve the glacier mass balance and the glacier can begin to advance due to this change or an increase in ice flux to the terminus due to increasing snowfall or reduced snow melt. As the advance proceeds the terminus shoal will be pushed in front of the glacier and continue to build, keeping the calving rate low. In the case of the most glaciers such as the Taku Glacier the glacier will eventually build a terminus shoal that is above water and calving will essentially cease. This will eliminate this loss of ice from the glacier and the glacier can continue to advance. Taku Glacier and Hubbard Glacier have been in this phase of the cycle. Taku Glacier which has been advancing for 120 years no longer calves. Hubbard Glacier still has a calving front. The glacier will then expand until the AAR is between 60 and 70 and equilibrium of the non-calving glacier is achieved. The glacier is not very sensitive to climate during the advance as its AAR is quite high, when the terminus shoal is limiting calving.

### Stable-extended

At the maximum extended position the glacier is once again sensitive to changing climate. Brady Glacier and Baird Glacier are examples of glaciers currently at this point. Brady Glacier has been thinning during the last two decades due to the higher equilibrium line altitudes accompanying warmer conditions in the region, and its secondary termini have begun to retreat. A glacier can remain at this position for sometime, a century at least in the case of Brady Glacier. Usually substantial thinning occurs before retreat from the shoal commences. This allowed the prediction in 1980, by the United States Geological Survey (USGS), of the retreat of the Columbia Glacier from its terminus shoal. The glacier had remained on this shoal throughout the entire 20th century. The USGS was monitoring the glacier due to its proximity to Valdez, Alaska, the port for crude oil export from the Alaskan Pipeline. At some point a decline in mass balance will trigger a retreat from the shoal into deeper water at which point calving will ensue. Based on the recent thinning it is suggested that Brady Glacier is poised to begin retreat.

### Drastically retreating

The calving rate will increase as the glacier retreats from the shoal into the deeper fjord just cleared by the glacier during advance. The water depth initially increases as the glacier retreats from the shoal, causing every more rapid glacier flow, calving and retreat. A glacier is comparatively insensitive to climate during this calving retreat. However, in the case of San Rafael Glacier, Chile, a switch from retreat (1945-1990) to advance (1990-1997) was noted. Current examples of this retreat are Columbia Glacier and Guyot Glacier. The most famous recent example of this is the large retreat of Glacier Bay and Icy Bay glaciers in Alaska that occurred rapidly via this process. Muir Glacier retreated 33 km from 1886 to 1968 featuring extensive calving the entire time. It reversed its retreat briefly 1890—1892. In 1968, Muir Glacier was still 27 km long, less than half of its length in 1886. The retreat continued an additional 6.5 km by 2001. Today, the glacier is near the head of its fjord and with minimal calving the glacier may be stable at this retracted position.

The best current example is illustrated by the United States Geological Survey study of Columbia Glacier. They noted that the average calving rate from Columbia Glacier increased from 3 km3⋅a-1 in the second half of 1983 to 4 km3⋅a-1 during the first nine months of 1984. This rate was four times greater than that measured at the end of 1977 and increased again in 1985. The glacier flow, i.e., the movement of the ice toward the sea, also increased, it was inadequate to keep pace with the break-up and expulsion of icebergs. The increase in speed instead seemed to just feed the ever faster conveyor to the terminus for iceberg production. This prompted the USGS to predict that the glacier would retreat 32 km before stabilizing. By 2006, it has retreated 16 km. The water remains deep and the calving rate and glacier velocity very high, indicating retreat will continue. At this point, just like having a balloon payment in an adjustable rate mortgage, the glacier has to pay a whole new portion of its balance via icebergs. The glacier accelerates as flow is enhanced by the calving process; this increases the export of icebergs from the glacier. Large calving retreats are initiated by warming conditions causing ice thinning. The resulting retreat to a new equilibrium conditions can be far more extensive than will be regained during the next advance stage. A good example of this is Muir Glacier.

Next to Glacier Bay, Icy Bay has had the most extensive retreat. At the beginning of the 20th century, the coastline was nearly straight and the bay non-existent. The entrance of the bay was filled by a tidewater glacier face that calved icebergs directly into the Gulf of Alaska. A century later glacier retreat has opened a multi-armed bay more than 30 miles long. The tidewater glacier has divided into three independent glaciers, Yahtse, Tsaa and Guyot Glacier. Other examples of glaciers currently in the retreat phase are South Sawyer and Sawyer Glaciers in Alaska, retreating 2.1 and 2.3 km respectively from 1961 to 2005.

In Patagonia an example of a rapidly retreating glacier is the Jorge Montt Glacier which drains into Baja Jorge Montt in the Pacific Ocean. The glacier’s ice thinning, at low elevations, from 1975 to 2000 reached 18 m⋅a-1 at the lowest elevations. The glacier calving front experienced a major retreat of 8.5 km in those 25 years as a result of rapid thinning

### Stable-retracted

At some point the glacier reaches a pinning point where calving is reduced due to a fjord narrowing or shoaling and the glacier’s AAR is near 10000. This is occurring with LeConte Glacier and Yathse Glacier. Le Conte Glacier currently has an AAR of 90, is at a retracted position and seems likely to be set to advance after building a terminus shoal. The drop in calving rate allows the glacier to reestablish equilibrium.

## Examples of tidewater glacier behavior

### Taku Glacier

The Taku Glacier provides a good example of this cycle. It was at its maximum extent near 1750. At this point it had closed off Taku Inlet. Subsequently, calving retreat commenced. By the time John Muir saw the glacier in 1890, it was near its minimum extent, at a location where the fjord narrowed, with deep water in front. About 1900, its AAR of 90 led to the Taku Glacier onset of advance, at the same time that the remaining Juneau Icefield glaciers continued receding. This advance continued at a rate of 88 m⋅a-1, advancing 5.3 km from the 1900 minimum until 1948, all the while building and then riding up on a substantial outwash plain beneath its calving face. After 1948, the now non-calving Taku Glacier, possessed an AAR only slightly reduced (86 and 63). This drove 1.5 km of further advance at a reduced rate of 37 m⋅a-1. In 1990, the Taku Glacier’s AAR was 82 high enough, to prompt Pelto and Miller to conclude that the Taku Glacier would continue to advance for the remaining decade of the 20th century. From 1986 to 2005, the equilibrium line altitude on the glacier rose without a significant terminus shift causing the AAR to decline to about 72. Pelto and Miller concluded that the current reduction in rate of advance is since 1970 is attributable to the laterally expanding terminal lobe as opposed to declining mass balance and that the primary force behind the Taku Glacier’s advance since about 1900 is due to positive mass balance. The recent lack of positive mass balance will eventually slow the retreat if it persists.

## Effects of climate change

The size of tidewater glaciers is such that the tidewater glacier cycle is several hundred years in length. A tidewater glacier is not sensitive to climate during the advancing and drastically retreating phases of its cycle. In the same region, disparate terminus responses are observed amongst tidewater calving glaciers, but not land terminating glaciers. This is exemplified by the 17 major glaciers of the Juneau Icefield, 5 have retreated more than 500 m since 1948, 11 more than 1000 m, and one glacier the Taku has advanced. This difference highlights the unique impacts on terminus behavior of the tidewater glacier cycle, which has caused the Taku Glacier to be insensitive to climate change in the last 60 years. Concurrently, in both Patagonia and Alaska, there are tidewater glaciers that have advanced for a considerable period, tidewater glaciers undergoing rapid retreat and stable tidewater glaciers.

## References

### Other references

• Viens, R. 2001. Late Holocene Climate Change and Calving Glacier Fluctuations Along the Southwestern Margin of the Stikine Icefield, U. ALASKA, U. Washington Ph.D dissertation.
• Post, A., and Motyka, R. J. (1995). "Taku and Le Conte glaciers, Alaska: Calving-speed control of late-Holocene asynchronous advances and retreats." Physical Geography 16, 59-82.
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text:
# DAVIDSTUTZ

20thMARCH2020

Li et al. evaluate adversarial training using both $L_2$ and $L_\infty$ attacks and proposes a second-order attack. The main motivation of the paper is to show that adversarial training cannot increase robustness against both $L_2$ and $L_\infty$ attacks. To this end, they propose a second-order adversarial attack and experimentally show that ensemble adversarial training can partly solve the problem.


text:
Chinese Journal of Chemical Physics  2020, Vol. 33 Issue (1): 114-118

#### The article information

Jian-jun Zhou, Run-xia Li, Donghui Quan, Jarken Esimbek, Yu-xin He, Da-lei Li, Xin-di Tang, Gang Wu, Wei-guang Ji, Zheng-xue Chang, Xia Zhang

Effect of Optical Depth on Study of Chemical Properties of Massive Star Forming Clumps

Chinese Journal of Chemical Physics, 2020, 33(1): 114-118

http://dx.doi.org/10.1063/1674-0068/cjcp1911212

### Article history

Accepted on: December 13, 2019
Effect of Optical Depth on Study of Chemical Properties of Massive Star Forming Clumps
Jian-jun Zhoua,c , Run-xia Lia,b , Donghui Quana,d , Jarken Esimbeka,c , Yu-xin Hea,c , Da-lei Lia,c , Xin-di Tanga,c , Gang Wua,c , Wei-guang Jia,c , Zheng-xue Changa,b , Xia Zhanga,b
Dated: Received on November 23, 2019; Accepted on December 13, 2019
a. Xinjiang Astronomical Observatory, Chinese Academy of Sciences, Urumqi 830011, China;
b. University of the Chinese Academy of Sciences, Beijing 100080, China;
c. Key Laboratory of Radio Astronomy, Chinese Academy of Sciences, Urumqi 830011, China;
d. Department of Chemistry, Eastern Kentucky University, Richmond KY 40475, USA
Abstract: Here we present the study on chemical properties of massive star forming clumps using N$_2$H$^+$(1-0), H$^{13}$CO$^+$(1-0), HCN(1-0) and HN$^{13}$C(1-0) data from the literature [Astron. Astrophys. 563, A97 (2014)]. We found that abundances of H$^{13}$CO$^+$ and HN$^{13}$C are affected by H$_2$ column densities. As the median values of these two abundances increase by nearly 10 times from stages A to B, H$^{13}$CO$^+$ and HN$^{13}$C are suitable for tracing the evolution of massive star forming clumps. The order of rapidity in growth of abundances of all the four studied molecules from stages A to B, is H$^{13}$CO$^+$, HCN, HN$^{13}$C, and N$_2$H$^+$, from the highest to the lowest. Our results suggest that the observing optically thin molecular lines with high angular resolution are necessary to study the chemical evolution of massive star forming clumps.
Key words: Stars formation    Clumps    Molecules    Radio lines
Ⅰ. INTRODUCTION

Past observations have shown that CN, HCN, HNC, N$_2$H$^+$ and HCO$^+$ could be used to study the chemical evolution of massive star forming clumps [1-3]. However, these studies did not always yield fully consistent results. Sanhueza et al. [2] suggested that N$_2$H$^+$/HCO$^+$ abundance ratio could serve as a chemical clock for massive star formation, whereas Hoq et al. [1] found that the N$_2$H$^+$/HCO$^+$ abundance ratio shows no discernable trend from quiescent to protostellar, or to HII/PDR stage.

Because these previous studies usually use the molecular data from single point observations, their results may be affected by the distance. The massive stars are believed to be formed in clusters. Newly formed OB stars may affect the chemical properties of nearby star forming clumps. In addition, the chemical properties of star forming regions may have obvious spatial variations [4, 5].

We studied the global chemical properties of massive star forming clumps at different stages using CN(1-0), HCN(1-0), HNC(1-0), HCO$^+$(1-0) and N$_2$H$^+$(1-0) lines, and obtained improved results [6, 7]. Abundances of these four molecules are mainly dominated by H$_2$ column density and thus they cannot be used to trace the evolution of massive star forming clumps [8]. Further studies are necessary to find more appropriate tracers.

Gerner et al. studied the chemical evolution of 59 massive star forming clumps by observing N$_2$H$^+$(1-0), H$^{13}$CO$^+$(1-0), HCN(1-0) and HN$^{13}$C(1-0) with the IRAM 30m millimeter telescope [9]. H$^{13}$CO$^+$(1-0) and HN$^{13}$C(1-0) lines are considered to be optically thin [2], and high sensitivity also improves N$_2$H$^+$(1-0) and HCN(1-0) data. Here we study the data from Gerner et al. [9].

Ⅱ. METHOD

Gerner et al. [9] observed N$_2$H$^+$(1-0), H$^{13}$CO$^+$(1-0), HCN(1-0) and HN$^{13}$C(1-0) toward 59 massive star forming clumps with the IRAM 30m millimeter telescope. The corresponding beam size is 29 arcsecond, the sensitivity is $\sim$0.03 K, and the spectral resolution is $\sim$0.6 km/s. The sample of Gerner et al. [9] includes 19 IRDCs (infrared dark clouds) and 20 HMPOs (high-mass protostellar objects) as well as 11 HMCs (hot molecular cores) and 9 UCHIIs (ultra-compact regions). Following Zhang et al. [7], we classify IRDCs as stage A, and classify HMPO, HMC and UCHII clumps as stage B. We obtained the integrated intensities of N$_2$H$^+$, H$^{13}$CO$^+$, HCN and HN$^{13}$C from Table A.1 of Gerner et al. [9], and plotted the histogram of the integral intensity and the ratios of four kinds of molecules in FIG. 1 and FIG. 2. We obtained the column densities of N$_2$H$^+$, H$^{13}$CO$^+$, HCN and HN$^{13}$C from Table A.3 of Gerner et al. [9], which were derived with several assumptions such as local thermodynamic equilibrium, optical thinness and the initially chosen typical temperatures (see Section 4.3 of Gerner et al. [9]). We estimated their abundances with the beam averaged H$_2$ column densities which were also listed in their Table A.3, which were derived with several assumptions such as local thermodynamic equilibrium, optical. The H$_2$ column densities were derived from their radio fluxes at 850 $\mathtt{μ}$m, or 870 $\mathtt{μ}$m, or 1.2 mm. We plotted the histograms of abundances of these four molecules for stages A and B in FIG. 3, and abundance ratios between them in FIG. 4. We plotted the abundances of N$_2$H$^+$, H$^{13}$CO$^+$, HCN and HN$^{13}$C versus H$_2$ column densities to study the relationship between molecular abundance and H$_2$ column density. Whether observing optically thin molecular lines with high angular resolution is necessary to study the chemical evolution of massive star forming clumps.

 FIG. 1 The histograms of the beam averaged integrated intensities of N$_2$H$^+$(1-0), H$^{13}$CO$^+$(1-0), HCN(1-0) and HN$^{13}$C(1-0) for the stages A and B. The name of the evolutionary stage is given on the top right corner of each panel. The vertical solid lines indicate the median values of the integrated intensities for each evolutionary stage
 FIG. 2 The histograms of the beam averaged integrated intensity ratios of N$_2$H$^+$/H$^{13}$CO$^+$, N$_2$H$^+$/HCN, N$_2$H$^+$/HN$^{13}$C, HCO$^+$/HCN, HCO$^+$/HN$^{13}$C and HCN/HN$^{13}$C for the stages A and B. The name of the evolutionary stage is given on the top right corner of each panel. The vertical solid lines indicate the median values of the integrate intensity ratios for each evolutionary stage
 FIG. 3 The histograms of the beam averaged abundances of N$_2$H$^+$, H$^{13}$CO$^+$, HCN and HN$^{13}$C for the stages A and B (in logarithm). The name of the evolutionary stage is given on the top right corner of each panel. The vertical solid lines indicate the median values of the abundance for each evolutionary stage
 FIG. 4 The histograms of the beam averaged abundance ratios (in logarithm) of N$_2$H$^+$/H$^{13}$CO$^+$, N$_2$H$^+$/HCN, N$_2$H$^+$/HN$^{13}$C, H$^{13}$CO$^+$/HCN, H$^{13}$CO$^+$/HNC and HCN/HN$^{13}$C for the stages A and B. The name of the evolutionary stage is given on the top right corner of each panel. The vertical solid lines indicate the median values of the abundance ratios for each evolutionary stage
Ⅲ. RESULTS AND DISCUSSION

The sample of Gerner et al. [9] includes 19 IRDCs (infrared dark clouds) and 20 HMPOs (high-mass protostellar objects) as well as 11 HMCs (hot molecular cores) and 9 UCHIIs (ultra-compact regions). IRDCs are the objects reaching densities of 10$^4$ cm$^{-3}$ and thus become detectable as cold dense molecular clouds. HMPOs host actively accreting protostars with mass $\geq$8M, which show internal emission sources at mid-infrared wavelengths. In the HMC stage, the central sources heat the surrounding environments, evaporating molecular-rich ices and raising the molecular complexity in the gas. Finally, the UV-radiation from the embedded protostars ionizes the surrounding gas and ultra-compact HII regions are formed (UCHII stage). Gerner et al. [9] observed N$_2$H$^+$(1-0), H$^{13}$CO$^+$(1-0), HCN(1-0) and HN$^{13}$C(1-0) toward these 59 sources with the IRAM 30 m millimeter telescope. The corresponding beam size is 29 arcsecond, the sensitivity is $\sim$ 0.03 K, and the spectral resolution is $\sim$0.6 km/s.

A. Integrated intensities and ratios

We obtained the integrated intensities of N$_2$H$^+$(1-0), H$^{13}$CO$^+$(1-0), HCN(1-0) and HN$^{13}$C(1-0) from Table A.1 of Gerner et al. [9]. Following Zhang et al. [7], we classify IRDCs as stage A, and classify HMPO, HMC and UCHII clumps as stage B. We found that all integrated intensities of N$_2$H$^+$(1-0), H$^{13}$CO$^+$(1-0), HCN(1-0) and HN$^{13}$C(1-0) show an increasing trend from stage A to stage B (see FIG. 1). This is similar to the conclusion of Zhang et al. [7]. We noted that the median values of the integrated intensities of N$_2$H$^+$, H$^{13}$CO$^+$, and HN$^{13}$C for stage B are nearly twice of the corresponding values of stage A. The median value of the integrated intensity of HCN for stage B is nearly four times of that at stage A. This is probably because that the integrated intensities of Gerner et al. [9] come from single point observations, which could better trace the chemical properties of occurring star formation. Meanwhile, the integrated intensities of Zhang et al. [7] come from mapping observation, which is the globally averaged values of the whole star forming clumps. It should be noted that such differences may also be caused by different excitation temperatures used for estimating column densities of these four molecules [9].

We plotted the histograms of integrated intensity ratios between these four molecules for stages A and B in FIG. 2. The integrated intensity ratios of N$_2$H$^+$/H$^{13}$CO$^+$, N$_2$H$^+$/HCN, N$_2$H$^+$/H$^{13}$CO$^+$, N$_2$H$^+$/HN$^{13}$C, and H$^{13}$CO$^+$/HN$^{13}$C show similar trends of variations from stage A to B to those in Zhang et al. [7].

B. Abundances and abundance ratios

We obtained the column densities of N$_2$H$^+$, H$^{13}$CO$^+$, HCN and HN$^{13}$C from Table A.3 of Gerner et al. [9], which were derived with several assumptions such as local thermodynamic equilibrium, optical thinness and the initially chosen typical temperatures (see Section 4.3 of Gerner et al. [9]). We estimated their abundances with the beam averaged H$_2$ column densities which were also listed in their Table A.3. The H$_2$ column densities were derived from their radio fluxes at 850 $\mathtt{μ}$m, or 870 $\mathtt{μ}$m, or 1.2 mm. We plotted the histograms of abundances of these four molecules for stages A and B in FIG. 3. The abundances of HCN, HN$^{13}$C, H$^{13}$CO$^+$ and N$_2$H$^+$ display an increasing trend from stage A to stage B. This is similar to the result from Zhang et al. [7]. Median values of the abundances of HN$^{13}$C, H$^{13}$CO$^+$ increase nearly 10 times from stage A to stage B. This suggests that these two molecules are more sensitive to star formation activities than the previous four molecules/ions, and therefore they are suitable for tracing the evolutionary stage of star formation. As we mentioned above, such difference may also be attributed to the different excitation temperatures used for estimating column densities of these four molecules [9].

We plotted the histograms of abundance ratios between these four molecules for stages A and B in FIG. 4. Abundance ratios of HCN/HN$^{13}$C, H$^{13}$CO$^+$/HCN, H$^{13}$CO$^+$/HN$^{13}$C show an increasing trend from stage A to stage B, while N$_2$H$^+$/H$^{13}$CO$^+$ ratio shows a decreasing trend from stage A to stage B. This is also similar to the conclusion of Zhang et al. [7]. However, abundance ratios of N$_2$H$^+$/HCN and N$_2$H$^+$/HN$^{13}$C display decreasing trends which are contrary to the results of Zhang et al. [7]. The reason is that the data of Gerner et al. [9] were obtained by single point observations, which focused on where star formation is taking place, and is strongly associated with star formation activities. These results suggest that abundances of HCN and HN$^{13}$C in star forming regions increase faster from stage A to stage B than that of N$_2$H$^+$. We further arrange the growth of abundances of these four molecules from stage A to stage B in the order of rapidity from the highest to the lowest to be H$^{13}$CO$^+$$>$HCN$>$HN$^{13}$C$>$N$_2$H$^+$.

C. The relation between abundances and H$_\mathbf{2}$ column densities

We plotted the abundances of N$_2$H$^+$, H$^{13}$CO$^+$, HCN and HN$^{13}$C versus H$_2$ column densities in FIG. 5. The abundance of HCN shows a clear decreasing trend with increasing H$_2$ column density. This is similar to the result from Li et al. [8]. The abundances of H$^{13}$CO$^+$ and HN$^{13}$C display a relatively weak decreasing trend with increasing H$_2$ column density, so optically thinner molecules are barely affected by H$_2$ column density. Abundance of N$_2$H$^+$ shows no obvious trend with the variation of H$_2$ column density. This is consistent with the result of Li et al. [8]. On the other hand, abundance ratios of N$_2$H$^+$/H$^{13}$CO$^+$, N$_2$H$^+$/HCN, N$_2$H$^+$/HN$^{13}$C, H$^{13}$CO$^+$/HCN, H$^{13}$CO$^+$/HNC and HCN/HN$^{13}$C as a function of H$_2$ column density show obvious variations (see FIG. 6). All these supports the idea that optically thinner lines could better trace the chemical properties of massive star forming clumps.

 FIG. 5 The abundances of N$_2$H$^+$, H$^{13}$CO$^+$, HCN, and HN$^{13}$C as a function of H$_2$ column density
 FIG. 6 The beam averaged abundance ratios of N$_2$H$^+$/H$^{13}$CO$^+$, N$_2$H$^+$/HCN, N$_2$H$^+$/HN$^{13}$C, H$^{13}$CO$^+$/HCN, H$^{13}$CO$^+$/HNC and HCN/HN$^{13}$C as a function of H$_2$ column density
Ⅳ. CONCLUSION

We present the chemical properties of massive star forming clumps derived from H$^{13}$CO$^+$(1-0), HN$^{13}$C(1-0), N$_2$H$^+$(1-0) and HCN(1-0) data from Gerner et al. [9], compared with our previous results derived from N$_2$H$^+$(1-0), HCO$^+$(1-0), HCN(1-0) and HNC(1-0) data [7, 8]. Our main conclusions are listed in the following. (i) Compared with our previous results, the integrated intensities of H$^{13}$CO$^+$(1-0), HN$^{13}$C (1-0), N$_2$H$^+$(1-0) and HCN(1-0) and the ratios between them increase much faster from stage A to stage B. This may be because these molecular lines were observed by single point observations, and therefore they are strongly associated with star forming activities. (ii) For the same reason as the above, the increasing trend of the abundances of these four molecules from stage A to stage B, in the order of the fastest to lowest, is H$^{13}$CO$^+$, HCN, HN$^{13}$C and N$_2$H$^+$. This is different from the conclusion from Zhang et al. [7]. (iii) The abundances of H$^{13}$CO$^+$ and HN$^{13}$C display a weak decreasing trend with increasing H$_2$ column density. We suggest these two molecules may not be very optically thin. Abundance ratios of N$_2$H$^+$/H$^{13}$CO$^+$, N$_2$H$^+$/HCN, N$_2$H$^+$/HN$^{13}$C, H$^{13}$CO$^+$/HCN, H$^{13}$CO$^+$/HNC and HCN/HN$^{13}$C as a function of H$_2$ column density show no obvious variations, either. (iv) Higher angular resolution observations of optically thin molecular lines are necessary to study the chemical evolution of massive star forming clumps.

Ⅴ. ACKNOWLEDGMENTS

This work was supported by the Open Program of the Key Laboratory of Xinjiang Uygur Autonomous Region (No.2019D04023) and the National Natural Science foundation of China (No.11973076). It was also partially funded by the National Natural Science foundation of China (No.11433008, No.11603063, No.11703074 and No.11703073), and the CAS "Light of West China" Program (No.2018-XBQNXZ-B-024, No.2016-QNXZ-B-23, and No.2016-QNXZ-B-22).

Reference
 [1] S. Hoq, J. M. Jackson, J. B. Foster, P. Sanhueza, A. Guzmán, J. S. W. C. Claysmith, J. M. Rathborne, T. Vasyunina, and A. Vasyunin, Astrophys. J. 777, 157(2013). DOI:10.1088/0004-637X/777/2/157 [2] P. Sanhueza, J. M. Jackson, J. B. Foster, G. Garay, A. Silva, and S. C. Finn, Astrophsical J. 756, 60(2012). DOI:10.1088/0004-637X/756/1/60 [3] T. Vasyunina, H. Linz, T. Henning, I. Zinchenko, H. Beuther, and M. Voronkov, Astrophys. J. 527, A88 (2011). [4] P. Schilke, C. M. Walmsley, G. P. des Forets, E. Roueff, D. R. Flower, and S. Guilloteau, Astron. Astrophys. 256, 595(1992). [5] M. Tafalla, P. C. Myers, P. Caselli, C. M. Walmsley, and A. Crapsi, Astron. Astrophys. 455, 577(2006). DOI:10.1051/0004-6361:20065311 [6] X. H. Han, J. J. Zhou, J. Z. Wang, J. Esimbek, J. S. Zhang, and N. Wang, Astron. Astrophys. 576, A131 (2015). [7] Y. Zhang, J. Zhou, Y. He, D. Li, W. Ji, Y. Yuan, and W. H. Guo, Astrophys. Space Sci. 361, 191(2016). DOI:10.1007/s10509-016-2773-5 [8] M. Li, J. Zhou, J. Esimbek, D. Quan, Y. He, Q. Li, and C. Zhu, Astrophys. J. Suppl. Ser. 243, 13(2019). DOI:10.3847/1538-4365/ab2465 [9] T. Gerner, H. Beuther, D. Semenov, H. Linz, T. Vasyunina, S. Bihr, Y. L. Shirley, and T. Henning, Astron. Astrophys. 563, A97 (2014).

a. 中国科学院新疆天文台，乌鲁木齐 830011;
b. 中国科学院大学，北京 100049;
c. 中国科学院射电重点实验室，乌鲁木齐 830011;
d. 美国东肯塔基大学化学系，里士满 KY 40475


text:
# KSEEB Solutions for Class 8 Maths Chapter 15 Quadrilaterals Ex 15.3

Students can Download Maths Chapter 15 Quadrilaterals Ex 15.3 Questions and Answers, Notes Pdf, KSEEB Solutions for Class 8 Maths helps you to revise the complete Karnataka State Board Syllabus and score more marks in your examinations.

## Karnataka Board Class 8 Maths Chapter 15 Quadrilaterals Ex 15.3

Question 1.
The adjacent angles of a parallelogram are in the ratio 2 : 1. Find the measures of all the angles.
The adjacent angles are in the ratio 2 : 1.
Let the angles be 2x and x
2x + x = 180°
[adjacent angles of a parallelogram are supplementary]
3x = 180° .
x = $\frac { 180 }{ 3 }$ = 60°
2x = 2 × 60° = 120°
∴The angles of the parallelogram are 60°, 120°. 60° and 120°

Question 2.
A field is in the form of a parallelogram whose perimeter is 450m and one of its sides is larger than the other by 75m. Find the lengths of all the sides.
Let one side be x, then the other side is x + 75

Perimeter = 450
x + (x + 75) + x + (x + 75) = 450
4x + 150 = 450
4x = 450 – 150
4x = 300
x = $$\frac { 300 }{ 4 }$$ = 75
x = 75m
x + 75 = 75 + 75 = 150 m
∴ The four sides are 75m, 150m, 75m, 150m.

Question 3.
In the figure ABCD is a parallelogram. The diagonals AC and BD intersect at 0; and ∠DAC = 40°, ∠CAB = 35° and ∠DOC = 110° calculate the measure ∠ABO, ∠ADC, ∠ACB and ∠CBD

∠AOB = ∠DOC = 110°
[Vertically opposite angles]
In ΔAOB,
∠AOB + ∠OAB + ∠OBA = 180°
110 + 55 +∠OBA = 180°
∠OBA = 180 – 165
∠ABO = 15°
[adjacent angles of a parallelogram , are supplementary]
∠ACB = ∠DAC = 40°
∠ACB = 40°
∠ABC = ∠ ADC = 85°
[Opposite angles pf a parallelogram]
[∠ABC = ∠ABO + ∠CBO]
15 + ∠CBO = 85°
∠CBO = 85 – 15
∠CBO = 70
∴ ∠CBO = ∠CBD = 70°
∴ ∠CBD = 70°

Question 4.
In a parallelogram ABCD, the side DC is produced to E and ∠BCE = 105° calculate ∠A, ∠E, ∠C, and∠D.

∠DCB + ∠DCE = 180° [Linear pair] ∠DCB + 1050 = 180°
∠DCB = 180 – 105
∠DCB = 75°
∠A = ∠DCB = 75°
∠A = ∠C = 75°
[Opposite angles of a parallelogram]
∠A +∠B = 180°
75° + ∠B = 180°
∠B = 180 + 75
∠B = 105°
∠B = ∠D = 105°
[Opposite angles of a parallelogram]

Question 5.
In a parallelogram KLMN, ∠K = 60 °. Find the measures of all the angles.


text:
#52 | Other possibilities of Resonance
(Chemistry) > Organic Chemistry - Some Basic Principles And Techniques


text:
# Given the following formulas

## Homework Statement

Suppose that the position vector for a particle is given as a function of time by (t) = x(t) + y(t), with x(t) = at + b and y(t) = ct2 + d,where a = 1.70 m/s, b = 1.20 m, c = 0.122 m/s2, and d = 1.18 m.
(a) Calculate the average velocity during the time interval from t = 2.05 s to t = 4.05 s.
(b)Determine the velocity at t = 2.05 s.
(c)Determine the speed at t = 2.05 s.

## Homework Equations

for a.) I used Vavg=delta r/delta t

## The Attempt at a Solution

for a.) for rf i got x(t)=8.05
y(t)=3.181

for ri i got x(t)=4.685
y(t)=1.69

and delta t=4.05-2.05=2

Last edited:

Related Introductory Physics Homework Help News on Phys.org
rl.bhat
Homework Helper
Post the complete problem.

listing the variables as a,b,c,d does us no good. We can assume what they are with the units but i don't know what b and d are.

Basically, use the standard symbols.

Simon Bridge
Homework Helper
Do I take it that: $$\vec{r}(t)=x(t)\hat{\imath}+y(t)\hat{\jmath}$$... where: ##x(t)=v_xt+x_0## and ##y(t)=a_yt^2+y_0##

These are position-time functions - I changed the variable names to reflect their roles.
From these you can find ##v_x(t)##, and ##v_y(t)##

(a) average velocity is change in position over change in time - you have two position vectors - what is the distance between their end-points?

(b) ##v_x(t)=\dot{x}(t)##

(c) how is the speed and the velocity related?

SammyS
Staff Emeritus
Homework Helper
Gold Member

## Homework Statement

Suppose that the position vector for a particle is given as a function of time by (t) = x(t) + y(t), with x(t) = at + b and y(t) = ct2 + d,where a = 1.70 m/s, b = 1.20 m, c = 0.122 m/s2, and d = 1.18 m.
(a) Calculate the average velocity during the time interval from t = 2.05 s to t = 4.05 s.
(b)Determine the velocity at t = 2.05 s.
(c)Determine the speed at t = 2.05 s.

## Homework Equations

for a.) I used Vavg=delta r/delta t

## The Attempt at a Solution

for a.) for rf i got x(t)=8.05
y(t)=3.181

for ri i got x(t)=4.685
y(t)=1.69

and delta t=4.05-2.05=2

Do you know Calculus?

Simon Bridge
Homework Helper
Gudduy cobber;
Does not need calculus if kinematics is available
... anyway, piercegirl got stuck on average velocity. The calc is in the next bit.

I know - calculus is fun and we want to spread the Word... ;)

I like Serena
Homework Helper
Hi piercegirl!

You're on the right track.
I guess you need to be aware of the fact that an average "velocity" is a vector.

You have position vectors at both locations.
Can you subtract those position vectors, yielding a change in position vector?
And divide that by the change in time?

In other words, can you calculate:
$$\mathbf{\vec v}_{avg} = {\mathbf{\vec{Δr}} \over Δt}$$


text:
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# Superdense coding

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