text:
# Work with PostgreSQL in MATLAB Using the psycopg2 Python Module

Part 5 of the Python Is The Ultimate MATLAB Toolbox series.

In Read and write SQLite databases in MATLAB with Python I showed how MATLAB can work with SQLite database files using the sqlite3 module from the Python standard library. Here I’ll demonstrate CRUD—create, read, update, delete—operations using the PostgreSQL database engine and the psycopg2 Python module. The best way to work with PostgreSQL in MATLAB is to use the MathWorks' Database Toolbox. This post may only interest you if you lack access to the Database Toolbox and you’re willing to include Python in your MATLAB workflow.

## Install psycopg2

Unlike sqlite3, psycopg2 is not in the standard Python library. Check your Python installation to see if it has psycopg2 by starting the Python command line REPL and importing the module. If it imports successfully you can also check the version number:

> python
>>> import psycopg2
>>> psycopg2.__version__
'2.9.3 (dt dec pq3 ext lo64)'

If you get a ModuleNotFoundError, you’ll need to install it. That can be done on an Anaconda Python installation with

> conda install psycopg2

or with

> python -m pip install psycopg2

using other Python distributions.

## Connecting to a PostgreSQL Database

The most challenging step in this post is setting up, configuring, and making an initial connection to a PostgreSQL database service—all of which are beyond the scope of this post. Ideally you are already familiar with the process, or have access to an existing database service, or know someone who can get you set up. If not, follow the PostgreSQL getting started documentation. The rest of this post assumes you have

• permission to create and delete databases
• network access

on or to a PostgreSQL server. Briefly, a PostgreSQL server administrator on a Linux computer might issue commands such as

> sudo -u postgres psql
postgres=# create database deliveries;
postgres=# grant all privileges on database deliveries to Al;
postgres=# quit
to set me up.

Run this small Python program to check if you can connect to your PostgreSQL server:

#!/usr/bin/env python
# test_pg_connection.py
import psycopg2
conn = psycopg2.connect(host="big_db_server", port=5432, # default port
database="deliveries")
conn.close()

Of course change the hostname, username, password, and/or port number as appropriate for your setup. All is well if the program runs without errors. If there are errors, they’ll likely be one of these:

• psycopg2.OperationalError: could not connect to server: Connection refused
• psycopg2.OperationalError: FATAL: password authentication failed for user Al
• psycopg2.OperationalError: FATAL: database deliveries does not exist

The first means either the database service is down, or a network issue (such as a firewall) is preventing access. The second and third errors show the database service is reachable, but the account or database you want to use either does not exist or is not configured properly. You or your database administrator will need to reexamine the setup.

## Create (and delete)

As hinted by the deliveries database in the SQL commands above, I’ll repeat the package delivery example from the MATLAB+SQLite article. To start, I’ll run the fake_data.m program in MATLAB to create a text file, orders.txt, containing 100,000 lines of data to insert into the database.

MATLAB:

>> fake_data
>>

A Python program that reads orders.txt, creates and inserts the values into the orders table in batches of 10,000 rows at a time looks like this:

File: make_pg_db.py

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47  #!/usr/bin/env python # make_pg_db.py import time import psycopg2 import pathlib conn = psycopg2.connect(host="localhost", port=5432, user="Al", password="SuperSecret", database="deliveries") cursor = conn.cursor() # delete/create cursor.execute("drop table if exists orders;") cursor.execute("drop table if exists rates;") cursor.execute("""create table rates(item varchar primary key, cost_by_weight float);""") create_orders_table = """create table orders ( origin varchar, item varchar, weight float, dest varchar);""" cursor.execute(create_orders_table) rows = [ ['tube' , 0.46], ['package', 0.65], ['letter' , 0.16], ['card' , 0.05] ] insert = "insert into rates (item,cost_by_weight) values(%s,%s)" cursor.executemany(insert, rows) # load orders data from the text file T_s = time.time() P = pathlib.Path('orders.txt') rows = [_.split() for _ in P.read_text().split('\n') if _] print(f'Data read time = {time.time() - T_s:.3f} seconds') insert = "insert into orders (origin,item,weight,dest) values(%s,%s,%s,%s)" T_s = time.time() batch_size = 10_000 # insert this many rows at a time for i in range(0, len(rows), batch_size): rows_subset = rows[i:i+batch_size] cursor.executemany(insert, rows_subset) print(f'inserted {i+1} to {i+batch_size}') conn.commit() print(f'Data insert time = {time.time() - T_s:.3f} seconds') conn.close()

I’m connecting to a PostgreSQL instance running on the same computer (2015 Dell XPS 13 laptop running Ubuntu 20.04) where I run make_pg_db.py. Insert performance is about 8,000 rows per second, 50x slower that SQLite inserts. I’m sure there are PostgreSQL configuration optimizations I could make to increase insert performance if I knew more about this database engine.

As with inserts to a SQLite database, MATLAB needs to store its insertion data row-major. We already saw that reading and reshuffling orders.txt from column-major to row-major in MATLAB is slow so our MATLAB implementation of the PostgreSQL insert program will use the same load_orders.py Python module used to speed up MATLAB in the SQLite example.

Two equivalent MATLAB insertion program appear below. The first relies on the Python function keyword argument enhancements in 2022a.

File: make_pg_db.m

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46  % MATLAB 2022a and newer % make_pg_db.m psycopg2 = py.importlib.import_module('psycopg2'); conn = psycopg2.connect(host="localhost", port=int64(5432), ... user="Al", password="SuperSecret", ... database="deliveries"); cursor = conn.cursor(); % delete/create cursor.execute("drop table if exists rates"); cursor.execute("drop table if exists orders"); cursor.execute("create table rates(item varchar primary key, " + ... "cost_by_weight float);"); create_orders_table = "create table orders (" + ... "origin varchar," + ... "item varchar," + ... "weight float," + ... "dest varchar);"; cursor.execute(create_orders_table); % populate the rates table rows = { {'tube' , 0.46}, ... {'package', 0.65}, ... {'letter' , 0.16}, ... {'card' , 0.05} }; insert = "insert into rates (item,cost_by_weight) values(%s,%s)"; cursor.executemany(insert, rows); % load orders data from the text file and insert to orders table tic; rows = py.load_orders.readfile('orders.txt'); fprintf('Data read time = %.6f seconds\n', toc) insert = "insert into orders (origin,item,weight,dest) values(%s,%s,%s,%s)"; tic batch_size = 10000; % insert this many rows at a time n_rows = length(rows); for i = 1: batch_size:n_rows i_end = min(i+batch_size-1, n_rows); rows_subset = rows(i:i_end); cursor.executemany(insert, rows_subset) fprintf('inserted %d to %d\n', i, i_end); end conn.commit(); fprintf('Data insert time = %.6f seconds\n', toc) conn.close();

while the version below uses the older pyargs() function to wrap Python keyword arguments. It works with MATLAB 2020b and newer. The two versions of this program differ only at lines 4, 5 and 6.

File: make_pg_db_2020b.m

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46  % MATLAB 2020b and newer % make_pg_db_2020b.m psycopg2 = py.importlib.import_module('psycopg2'); conn = psycopg2.connect(pyargs("host","localhost","port",int64(5432), ... "user","Al","password","SuperSecret", ... "database","deliveries")); cursor = conn.cursor(); % delete/create cursor.execute("drop table if exists rates"); cursor.execute("drop table if exists orders"); cursor.execute("create table rates(item varchar primary key, " + ... "cost_by_weight float);"); create_orders_table = "create table orders (" + ... "origin varchar," + ... "item varchar," + ... "weight float," + ... "dest varchar);"; cursor.execute(create_orders_table); % populate the rates table rows = { {'tube' , 0.46}, ... {'package', 0.65}, ... {'letter' , 0.16}, ... {'card' , 0.05} }; insert = "insert into rates (item,cost_by_weight) values(%s,%s)"; cursor.executemany(insert, rows); % load orders data from the text file and insert to orders table tic; rows = py.load_orders.readfile('orders.txt'); fprintf('Data read time = %.6f seconds\n', toc) insert = "insert into orders (origin,item,weight,dest) values(%s,%s,%s,%s)"; tic batch_size = 10000; % insert this many rows at a time n_rows = length(rows); for i = 1: batch_size:n_rows i_end = min(i+batch_size-1, n_rows); rows_subset = rows(i:i_end); cursor.executemany(insert, rows_subset) fprintf('inserted %d to %d\n', i, i_end); end conn.commit(); fprintf('Data insert time = %.6f seconds\n', toc) conn.close();

MATLAB insert performance matches Python’s, about 8,000 rows per second—in other words, not great compared to SQLite inserts.

This query computes the cummulative cost of shipments by originating office.

select origin,sum(weight*cost_by_weight) from orders O, rates R
where O.item = R.item group by origin;

Programmatic implementations of the query in Python and MATLAB resemble those in the SQLite select example:

File: select_pg.py

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15  #!/usr/bin/env python # select_pg.py import psycopg2 conn = psycopg2.connect(host="localhost", port=5432, user="Al", password="SuperSecret", database="deliveries") cursor = conn.cursor() query = "select origin,sum(weight*cost_by_weight) from orders O, rates R" \ " where O.item = R.item group by origin order by origin;" cursor.execute(query) for row in cursor.fetchall(): print(f'{row[0]} {row[1]:7.2f}') conn.close()

and equivalently in MATLAB 2022a+ with

File: select_pg.m

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16  % MATLAB 2022a and newer % select_pg.m psycopg2 = py.importlib.import_module('psycopg2'); conn = psycopg2.connect(host="localhost", port=int64(5432), ... user="Al", password="SuperSecret", ... database="deliveries"); cursor = conn.cursor(); query = "select origin,sum(weight*cost_by_weight) from orders O, rates R" + ... " where O.item = R.item group by origin order by origin;"; cursor.execute(query); for row = cursor.fetchall() fprintf('%s %7.2f\n', string(row{1}{1}), row{1}{2}); end conn.close()

and in MATLAB 2020b+ with

File: select_pg_2020b.m

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16  % MATLAB 2020b and newer % select_pg.m psycopg2 = py.importlib.import_module('psycopg2'); conn = psycopg2.connect(pyargs("host","localhost","port",int64(5432), ... "user","Al","password","SuperSecret", ... "database","deliveries")); cursor = conn.cursor(); query = "select origin,sum(weight*cost_by_weight) from orders O, rates R" + ... " where O.item = R.item group by origin order by origin;"; cursor.execute(query); for row = cursor.fetchall() fprintf('%s %7.2f\n', string(row{1}{1}), row{1}{2}); end conn.close()

## Update

As in the SQLite update example, this SQL update scales the weight of packages by 2.2 while leaving the wieghts of cards, letters, and tubes alone:

update orders set weight = weight*2.2 where item = 'package';

The programs below repeat the select statement from the previous section to show total cost by origin. The SQL update is implemente with line 17 of the Python program and lines 18 in the two MATLAB versions. After updating the weight field the programs re-query for the new cummulative costs:

File: select_update_pg.py

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24  #!/usr/bin/env python # select_update_pg.py import psycopg2 conn = psycopg2.connect(host="localhost", port=5432, user="Al", password="SuperSecret", database="deliveries") cursor = conn.cursor() query = "select origin,sum(weight*cost_by_weight) from orders O, rates R" \ " where O.item = R.item group by origin order by origin;" print('Original cost:') cursor.execute(query) for row in cursor.fetchall(): print(f'{row[0]} {row[1]:7.2f}') # update: scale the weight of packages cursor.execute("update orders set weight = weight*2.2 where item = 'package'") print('After the weight correction:') cursor.execute(query) for row in cursor.fetchall(): print(f'{row[0]} {row[1]:7.2f}') conn.close()

MATLAB 2022a+:

File: select_update_pg.m

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26  % MATLAB 2022a and newer % select_update_pg.m psycopg2 = py.importlib.import_module('psycopg2'); conn = psycopg2.connect(pyargs("host","localhost","port",int64(5432), ... "user","Al","password","SuperSecret", ... "database","deliveries")); cursor = conn.cursor(); query = "select origin,sum(weight*cost_by_weight) from orders O, rates R" + ... " where O.item = R.item group by origin order by origin;"; fprintf('Original cost:\n') cursor.execute(query); for row = cursor.fetchall() fprintf('%s %7.2f\n', string(row{1}{1}), row{1}{2}); end % update: scale the weight of packages cursor.execute("update orders set weight = weight*2.2 where item = 'package'"); fprintf('After the weight correction:\n') cursor.execute(query); for row = cursor.fetchall() fprintf('%s %7.2f\n', string(row{1}{1}), row{1}{2}); end conn.close()

MATLAB 2020b+:

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26  % MATLAB 2020b and newer % select_update_pg_2020b.m psycopg2 = py.importlib.import_module('psycopg2'); conn = psycopg2.connect(pyargs("host","localhost","port",int64(5432), ... "user","Al","password","SuperSecret", ... "database","deliveries")); cursor = conn.cursor(); query = "select origin,sum(weight*cost_by_weight) from orders O, rates R" + ... " where O.item = R.item group by origin order by origin;"; fprintf('Original cost:\n') cursor.execute(query); for row = cursor.fetchall() fprintf('%s %7.2f\n', string(row{1}{1}), row{1}{2}); end % update: scale the weight of packages cursor.execute("update orders set weight = weight*2.2 where item = 'package'"); fprintf('After the weight correction:\n') cursor.execute(query); for row = cursor.fetchall() fprintf('%s %7.2f\n', string(row{1}{1}), row{1}{2}); end conn.close()

Join me again on July 23, 2022 to see how MATLAB can work with MongoDB databases using the pymongo Python module.


text:
# Re: [802.3ae] Clause 48: Check_end Question

I guess it's also worth pointing out that the normative description of
the check_end function C48.2.5.1.4 quoted by Doug below doesn't agree
with the informative description of the ||T|| ordered set on p311 of
D4.0 in 48.2.4.3, to wit:

\begin{quote}
Unrecognized running disparity errors which propagate to any Idle
code-groups in ||T|| or to the column following ||T|| are indicated as
/E/ in the preceding column IN THE SAME LANE in which the errors were
recognized. All ||I|| ordered_sets are selected to ensure that
propagated code violations are recognized and not propagated further.
\end{quote}

(My capitals).

Which in combination with Doug's observation, has left me more confused
than ever.

Perhaps another recirculation comment is required?

Gareth

--
/ /\/\ Gareth Edwards              mailto:gareth.edwards@xxxxxxxxxx
\ \  / Design Engineer
/ /  \ System Logic & Networking   Phone:   +44 131 666 2600 x234
\_\/\/ Xilinx Scotland             Fax:     +44 131 666 0222

"Douglas T. (Doug) Massey" wrote:
>
> Gentlemen,
>
> I've just joined the reflector after an extensive search of your archives
> in an effort to answer my question.  The last discussion of the check_end
> function was back in May 2001, so hopefully things have settled down
> enough so that there's a concrete answer.  I realize it's poor netiquette
> for a newbie to just start firing off questions, but *really*, I spent
> the whole weekend searching the archive.  While watching football.  :-)
>
> My question:
>
> The check_end defintion in C48.2.5.1.4 says that an /E/ is returned
> in all lanes less than n in ||T|| (where n is the lane number of the /T/
> in ||T||) for which an RD error or any code-group other than /A/ or /K/
> is recognized in the column after ||T||.  Did this really mean to apply
> to the *entire* column following ||T||, or just the corresponding lane in
> the column following ||T||, for each lane less than n?
>
> If the receiver sees this input:
>
> ... D D A  R ...
> ... D D A  R ...
> ... D T A  R ...
> ... D K A* R ...
>
> where "A*" is an A with a disparity error, should the receiver return
> this as a response:
>
> ... D E I  I ...
> ... D E I  I ...
> ... D T I  I ...
> ... D I E  I ...
>
> It seems the A* disparity error is clearly *not* part of the preceding
> data packet, or the error would have been caught by the disparity-biased
> /K/ that preceded it.  Not only is the single error reported twice (as
> /E/ is replacing the two data code-groups in lanes 0 and 1 of ||T||),
> but it's reporting an error that occurred *after* the data packet.  :-\
>
> The check_end definition goes on to say that /E/ is returned for all
> lanes greater than n in the column preceding ||T||, for which an RD error
> or a code-group other than /K/ is recognized in the corresponding lane
> of ||T||.  The "corresponding lane" part here makes me wonder why that
> phrase wasn't used in the first half of the defintion.  I presume it's
> used in the second half of the definition so that a single RD error in
> the in this example:
>
> ... D T  A R ...
> ... D K  A R ...
> ... D K  A R ...
> ... D K* A R ...
>
> won't cause this kind of response:
>
> ... D T  I I ...
> ... E I  I I ...
> ... E I  I I ...
> ... E E  I I ...
>
> By adding "corresponding lane", only the lane 3 error is pushed-back
> inside the data packet and the data packet ends up with only one error
> (which is the right number, after all).  This makes good sense -- why
> doesn't it apply to the first half of the check_end defintion?
>
> Any insights into this situation?
>
> Doug
> -- -------------------------------------------------------------------
>  ___,  Doug Massey, ASIC Digital Logic Designer
>  \o    IBM Microelectronics Division, Burlington, Vermont           |>
>   |    Phone: (802)769-7095 t/l: 446-7095 fax: x6752                |
>  / \                                                                |
>    .   My homepage:  http://doug.obscurestuff.com                  (|)

format: plain


text:
# How do you solve by elimination x + y = 2 and 2x + y = -1?

Apr 27, 2018

$x = - 3 , y = 5$

#### Explanation:

Subtracting equations,

$x - 2 x = 2 - - 1$

$- x = 3$

$x = - 3$

$y = 2 - x = 2 - - 3 = 5$

Check:

-3 + 5 = 2 quad sqrt

 2(-3) + 5 = -1 quad sqrt


text:
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# (a) Find and identify the traces of the quadric surface $-x^2 - y^2 + z^2 = 1$ and explain why the graph looks like the graph of the hyperboloid of two sheets in Table 1.(b) If the equation in part (a) is changed to $x^2 - y^2 - z^2 = 1$, what happens to the graph? Sketch the new graph.

## a) The traces parallel to the $y z$ -plane are hyperbolas. $z^{2}-y^{2}=1+k^{2}$The traces parallel to the $x z$ -plane are hyperbolas. $z^{2}-x^{2}=1+k^{2}$b) See Graph

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### Video Transcript

So here we want to find and identify the traces of the quadratic surface or aquatic surface. So it's going to be negative acts squared minus y squared minus z squared one. Um And we want to explain why the graph looks like the graph of a hyperba Lloyd of two sheets. And that's because the traces parallel to the y z plane are going to be hyperbole as and if we change the equation uh so this is actually plus one R plus t squared. And if we change it to minus the squared, then we end up getting that the traces parallel to xz the xz plane will be hyper bolos. Um So that would be the resulting graph that we end up getting. And it's going to be able to form Z squared minus x squared equals one plus k squared or z squared minus y squared equals one plus k squared.

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# If A = {2, 3, 4, 5, 6} then which of the following is correct  (A) $1 \in A$ (B) $2 \in A$  (C) $1 \in A$ (D) $1 \in A$

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## 1 Answer

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A, B and C
Hence (B) is the correct answer.
answered Jun 12, 2014


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Corpus ID: 118466144

# Higgs Working Group Report of the Snowmass 2013 Community Planning Study

@article{Dawson2013HiggsWG,
title={Higgs Working Group Report of the Snowmass 2013 Community Planning Study},
author={S. Dawson and A. Gritsan and H. Logan and J. Qian and C. Tully and R. Kooten and A. Ajaib and A. Anastassov and I. Anderson and D. Asner and O. Bake and V. Barger and T. Barklow and B. Batell and M. Battaglia and S. Berge and A. Blondel and S. Bolognesi and J. Brau and E. Brownson and M. Cahill-Rowley and C. Calancha-Paredes and C. Chen and W. Chou and R. Clare and D. Cline and N. Craig and K. Cranmer and M. Gruttola and A. Elagin and R. Essig and L. Everett and E. Feng and K. Fujii and J. Gainer and Y. Gao and I. Gogoladze and S. Gori and R. Gonçalo and N. Graf and C. Grojean and S. Guindon and H. Haber and T. Han and G. Hanson and R. Harnik and S. Heinemeyer and U. Heintz and J. Hewett and Y. Ilchenko and A. Ishikawa and A. Ismail and V. Jain and P. Janot and S. Kanemura and S. Kawada and R. Kehoe and M. Klute and A. Kotwal and K. Krueger and G. Kukartsev and K. Kumar and J. Kunkle and M. Kurata and I. Lewis and Y. Li and L. Linssen and E. Lipeles and R. Lipton and T. Liss and J. List and T. Liu and Z. Liu and I. Low and T. Ma and P. Mackenzie and B. Mellado and K. Melnikov and A. Miyamoto and G. Moortgat-Pick and G. Mourou and M. Narain and H. Neal and J. Nielsen and N. Okada and H. Okawa and J. Olsen and H. Ono and P. Onyisi and N. Parashar and M. Peskin and F. Petriello and T. Plehn and C. Pollard and C. Potter and K. Prokofiev and M. Rauch and T. Rizzo and T. Robens and V. Rodriguez and P. Roloff and R. Ruiz and V. Sanz and J. Sayre and Q. Shafi and G. Shaughnessy and M. Sher and F. Simon and N. Solyak and J. Strube and J. Stupak and S. Su and T. Suehara and T. Tanabe and T. Tajima and V. Telnov and J. Tian and S. Thomas and M. Thomson and K. Tsumura and C. Un and M. Velasco and C. Wagner and S. Wang and S. Watanuki and G. Weiglein and A. Whitbeck and K. Yagyu and W. Yao and H. Yokoya and S. Zenz and D. Zerwas and Y. Zhang and Y. Zhou},
journal={arXiv: High Energy Physics - Experiment},
year={2013}
}
• S. Dawson, +131 authors Y. Zhou
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• Physics
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• 2012
We consider the Higgs boson signals from pair production at the LHC within the framework of the MSSM in the non-decoupling (low-m_A) region. In light of the recent observation of a SM-like HiggsExpand
Exotic Higgs Decay via AZ/HZ Channel: a Snowmass Whitepaper
• Physics
• 2013
While the conventional searches for the Higgs boson focus on its decays to Standard Model (SM) particles: gamma gamma, ZZ, WW, bb and tau tau, in this study, we explore the decays A --> HZ or H -->Expand
Bounding the Higgs width at the LHC using full analytic results for gg → e−e+μ−μ+
• Physics
• 2013
A bstractWe revisit the hadronic production of the four-lepton final state, e−e+μ−μ+, through the fusion of initial state gluons. This process is mediated by loops of quarks and we provide first fullExpand
Bounding the Higgs width at the LHC: Complementary results from H -> WW
• Physics
• 2014
We investigate the potential of the process gg → H→ WW to provide bounds on the Higgs width. Recent studies using off-shell H→ ZZ events have shown that Run 1 LHC data can constrain the Higgs width,Expand
Post LHC7 SUSY benchmark points for ILC physics
• Physics
• 2012
We re-evaluate prospects for supersymmetry at the proposed International Linear $e^+e^-$ Collider (ILC) in light of the first year of serious data taking at LHC with $\sqrt{s}=7$ TeV and $\sim 5$Expand
The Muon Collider as a H=A factory
• Physics
• 2014
Abstract We show that a muon collider is ideally suited for the study of heavy H / A scalars, cousins of the Higgs boson found in two-Higgs-doublet models and required in supersymmetric models. TheExpand
Heavy Higgs Scalars at Future Hadron Colliders (A Snowmass Whitepaper)
We investigate the prospects for discovery or exclusion of additional Higgs scalars at the 14 TeV and 33 TeV LHC in the context of theories with two Higgs doublets. We focus on the modes with theExpand
HZ Recoil Mass and Cross Section Analysis in ILD
• Physics
• 2012
This note describes the details of a simulation study of the Higgs boson production for processes in which the Higgs is produced together with a well measurable di-lepton system using the proposal ofExpand
Closing the Wedge with 300 fb$^{-1}$ and 3000 fb$^{-1}$ at the LHC: A Snowmass White Paper
The discovery of a Higgs boson at the LHC begins the era of directly measuring the mechanism of electroweak symmetry breaking (EWSB). Searching for extensions of the Standard Model (SM) EWSB sectorExpand


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# zbMATH — the first resource for mathematics

## Saker, Samir H.

Compute Distance To:
 Author ID: saker.samir-h Published as: Saker, S. H.; Saker, Samir H.; Saker, Samir; Saker, Samir. H. External Links: MGP
 Documents Indexed: 252 Publications since 1999, including 3 Books Reviewing Activity: 38 Reviews
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#### Co-Authors

 70 single-authored 49 Agarwal, Ravi P. 47 O’Regan, Donal 21 Kubiaczyk, Ireneusz 15 Mahmoud, Ramy Ramadan 13 Bohner, Martin J. 10 Erbe, Lynn Harry 9 Osman, Mahmoud M. 8 Elabbasy, Elmetwally M. 8 Peterson, Allan C. 7 Hassan, Taher S. 5 Alzabut, Jehad O. 5 Braverman, Elena 5 Graef, John R. 5 Krnić, Mario 5 Rabie, Safi S. 4 Agarwal, Sheba 4 Rezk, Haytham M. 4 Tunç, Cemil 4 Zhang, Binggen 3 Li, Wan-Tong 3 Saied, Ahmed I. 3 Sikorska-Nowak, Aneta 2 Anderson, Douglas Robert 2 Arahet, Mohammed A. 2 Băleanu, Dumitru I. 2 Cheng, Sui Sun 2 Džurina, Jozef 2 Elabbasy, El M. 2 Elshenhab, A. M. 2 Kenawy, M. R. 2 Morchało, Jarosław 2 Sadhasivam, Vadivel 2 Saif, K. 2 Sudha, Balakrishnan 2 Thandapani, Ethiraju 2 Wong, Patricia J. Y. 1 Abdou, D. M. 1 Abohela, I. 1 Abuelwafa, M. M. 1 Akın-Bohner, Elvan 1 Baculíková, Blanka 1 Benchohra, Mouffak 1 Chu, Jifeng 1 El-Metwally, Hamdy A. 1 Grace, Said Rezk 1 Islam, Muhammad Nazmul 1 Kalaimani, Thirunavukarasu 1 Khalil, Hammad 1 Khan, Rahmat Ali 1 Lakshmanan, Shanmugam 1 Li, Tatsien 1 Li, Tongxing 1 Liu, Bingwen 1 Logaarasi, Kandhasamy 1 Manojlović, Jelena V. 1 Pang, Peter Y. H. 1 Raja, Thangaraj 1 Rakkiyappan, Rajan 1 Rihan, Fathalla A. 1 Sayed, A. G. 1 Thangavelu, Krishnan 1 Tunç, Ercan 1 Zaman, Gul 1 Zhang, Chenghui
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#### Serials

 18 Applied Mathematics and Computation 12 Mathematical Inequalities & Applications 11 Dynamic Systems and Applications 8 Mathematica Slovaca 8 Mathematical and Computer Modelling 5 Journal of Mathematical Analysis and Applications 5 Rocky Mountain Journal of Mathematics 5 Annales Polonici Mathematici 5 Kyungpook Mathematical Journal 5 Abstract and Applied Analysis 5 Electronic Journal of Qualitative Theory of Differential Equations 5 Discrete Dynamics in Nature and Society 5 Dynamics of Continuous, Discrete & Impulsive Systems. Series A. Mathematical Analysis 5 Journal of Applied Mathematics and Computing 5 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 4 Journal of Computational and Applied Mathematics 4 Bulletin Mathématique de la Société des Sciences Mathématiques de Roumanie. Nouvelle Série 4 Electronic Journal of Differential Equations (EJDE) 4 Dynamics of Continuous, Discrete & Impulsive Systems. Series B. Applications & Algorithms 4 Advances in Difference Equations 3 Indian Journal of Pure & Applied Mathematics 3 Demonstratio Mathematica 3 Acta Mathematica Hungarica 3 The Canadian Applied Mathematics Quarterly 3 Journal of Difference Equations and Applications 3 Communications in Applied Analysis 3 Journal of Inequalities and Applications 3 Analysis (München) 3 Nonlinear Analysis. Real World Applications 3 Nonlinear Functional Analysis and Applications 3 Mediterranean Journal of Mathematics 3 Journal of Mathematical Inequalities 2 Applicable Analysis 2 Fasciculi Mathematici 2 Hiroshima Mathematical Journal 2 Mathematische Nachrichten 2 Proceedings of the American Mathematical Society 2 Annales Societatis Mathematicae Polonae. Seria I. Commentationes Mathematicae 2 Bulletin of the Korean Mathematical Society 2 Nonlinear Dynamics 2 Acta Mathematica Sinica. English Series 2 Communications in Nonlinear Science and Numerical Simulation 2 Discussiones Mathematicae. Differential Inclusions, Control and Optimization 2 Portugaliae Mathematica. Nova Série 2 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 2 Hacettepe Journal of Mathematics and Statistics 2 Science China. Mathematics 2 Journal of Function Spaces 1 Bulletin of the Australian Mathematical Society 1 Computers & Mathematics with Applications 1 IMA Journal of Applied Mathematics 1 Mathematical Methods in the Applied Sciences 1 Periodica Mathematica Hungarica 1 Annales Universitatis Mariae Curie-Skłodowska. Sectio A. Mathematica 1 Bulletin of the London Mathematical Society 1 Czechoslovak Mathematical Journal 1 Journal of the Korean Mathematical Society 1 Journal of the London Mathematical Society. Second Series 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Pacific Journal of Mathematics 1 Proceedings of the Edinburgh Mathematical Society. Series II 1 Publicationes Mathematicae 1 Results in Mathematics 1 Chinese Annals of Mathematics. Series B 1 Applied Mathematics Letters 1 Mathematica Bohemica 1 Journal of Contemporary Mathematical Analysis. Armenian Academy of Sciences 1 Aequationes Mathematicae 1 Applicationes Mathematicae 1 Journal of Mathematical Sciences (New York) 1 Turkish Journal of Mathematics 1 Georgian Mathematical Journal 1 Memoirs on Differential Equations and Mathematical Physics 1 ETNA. Electronic Transactions on Numerical Analysis 1 Journal of Convex Analysis 1 Serdica Mathematical Journal 1 Complexity 1 Nonlinear Studies 1 Communications on Applied Nonlinear Analysis 1 Mathematical Problems in Engineering 1 Journal of Applied Analysis 1 Vietnam Journal of Mathematics 1 ZAMM. Zeitschrift für Angewandte Mathematik und Mechanik 1 Far East Journal of Applied Mathematics 1 Neliniĭni Kolyvannya 1 Far East Journal of Mathematical Sciences 1 Qualitative Theory of Dynamical Systems 1 International Journal of Differential Equations and Applications 1 Acta Mathematica Scientia. Series B. (English Edition) 1 Nonlinear Dynamics and Systems Theory 1 International Journal of Pure and Applied Mathematics 1 Bulletin of the Brazilian Mathematical Society. New Series 1 The Australian Journal of Mathematical Analysis and Applications 1 Journal of Concrete and Applicable Mathematics 1 Nonlinear Oscillations 1 Advances in Dynamical Systems and Applications 1 International Journal of Difference Equations 1 International Journal of Mathematics and Statistics 1 Journal of Applied Mathematics & Informatics 1 Annals of Applied Mathematics
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#### Fields

 145 Ordinary differential equations (34-XX) 105 Difference and functional equations (39-XX) 74 Real functions (26-XX) 40 Biology and other natural sciences (92-XX) 11 Partial differential equations (35-XX) 9 Harmonic analysis on Euclidean spaces (42-XX) 6 Functional analysis (46-XX) 4 Dynamical systems and ergodic theory (37-XX) 4 Operator theory (47-XX) 4 Systems theory; control (93-XX) 3 General and overarching topics; collections (00-XX) 3 Abstract harmonic analysis (43-XX) 2 Sequences, series, summability (40-XX) 1 Number theory (11-XX) 1 Measure and integration (28-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Numerical analysis (65-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX)

#### Citations contained in zbMATH Open

206 Publications have been cited 2,027 times in 785 Documents Cited by Year
Oscillation of second order nonlinear dynamic equations on time scales. Zbl 1075.34028
Bohner, M.; Saker, S. H.
2004
Oscillation criteria for second-order nonlinear neutral delay dynamic equations. Zbl 1062.34068
Agarwal, Ravi P.; O’Regan, Donal; Saker, S. H.
2004
Oscillation criteria for second-order nonlinear delay dynamic equations. Zbl 1125.34046
Erbe, L.; Peterson, A.; Saker, S. H.
2007
Oscillation criteria for second-order nonlinear dynamic equations on time scales. Zbl 1050.34042
Erbe, Lynn; Peterson, Allan; Saker, S. H.
2003
Oscillation of second order delay dynamic equations. Zbl 1126.39003
Agarwal, R. P.; Bohner, M.; Saker, S. H.
2005
Oscillation criteria of second-order half-linear dynamic equations on time scales. Zbl 1082.34032
Saker, S. H.
2005
Oscillation and global attractivity in a periodic Nicholson’s blowflies model. Zbl 1012.34067
Saker, S. H.; Agarwal, S.
2002
Oscillation of second-order nonlinear neutral delay dynamic equations on time scales. Zbl 1097.39003
Saker, S. H.
2006
Oscillation of nonlinear dynamic equations on time scales. Zbl 1045.39012
Saker, S. H.
2004
Asymptotic behavior of solutions of a third-order nonlinear dynamic equation on time scales. Zbl 1075.39010
Erbe, L.; Peterson, A.; Saker, S. H.
2005
Oscillation criteria for a certain class of second order Emden-Fowler dynamic equations. Zbl 1177.34047
Akin-Bohner, Elvan; Bohner, Martin; Saker, Samir H.
2007
Hille and Nehari type criteria for third-order dynamic equations. Zbl 1128.39009
Erbe, L.; Peterson, A.; Saker, S. H.
2007
Oscillation and global attractivity in hematopoiesis model with delay time. Zbl 1026.34082
Saker, S. H.
2003
New oscillation criteria for second-order neutral functional dynamic equations via the generalized Riccati substitution. Zbl 1221.34245
Saker, S. H.; O’Regan, Donal
2011
Oscillation and stability in nonlinear delay differential equations of population dynamics. Zbl 1069.34107
Kubiaczyk, I.; Saker, S. H.
2002
Oscillation and asymptotic behavior of a third-order nonlinear dynamic equation. Zbl 1145.34329
Erbe, L.; Peterson, A.; Saker, S. H.
2006
Oscillation results for second-order nonlinear neutral delay dynamic equations on time scales. Zbl 1128.34042
Saker, Samir H.; Agarwal, Ravi P.; O’Regan, Donal
2007
Oscillation of second-order damped dynamic equations on time scales. Zbl 1128.34022
Saker, Samir H.; Agarwal, Ravi P.; O’Regan, Donal
2007
Oscillation criteria for half-linear delay dynamic equations on time scales. Zbl 1173.34037
Erbe, Lynn; Hassan, Taher S.; Peterson, Allan; Saker, Samir H.
2009
Oscillation and global attractivity in a nonlinear delay periodic model of respiratory dynamics. Zbl 1041.34073
Agarwal, S.; Saker, S. H.
2002
Oscillation criteria for perturbed nonlinear dynamic equations. Zbl 1112.34019
Bohner, M.; Saker, S. H.
2004
New oscillation criteria for second-order nonlinear neutral delay difference equations. Zbl 1028.39003
Saker, S. H.
2003
Philos-type oscillation criteria for second order half-linear dynamic equations on time scales. Zbl 1139.34029
Agarwal, Ravi P.; O’Regan, Donal; Saker, S. H.
2007
Oscillation theorems for second-order nonlinear neutral delay dynamic equations on time scales. Zbl 1153.34040
Saker, Samir H.; O’Regan, Donal; Agarwal, Ravi P.
2008
On the impulsive delay hematopoiesis model with periodic coefficients. Zbl 1179.34092
Saker, S. H.; Alzabut, J. O.
2009
Oscillation and global attractivity in hematopoiesis model with periodic coefficients. Zbl 1048.34114
Saker, S. H.
2003
Oscillation criteria for third-order nonlinear differential equations. Zbl 1174.34052
Baculíkova, B.; Elabbasy, E. M.; Saker, S. H.; Džurina, J.
2008
Positive periodic solutions of discrete three-level food-chain model of Holling type II. Zbl 1099.92079
Sun, Y. G.; Saker, S. H.
2006
Permanence, oscillation and attractivity of the discrete hematopoiesis model with variable coefficients. Zbl 1125.39002
Braverman, E.; Saker, S. H.
2007
Kamenev-type oscillation criteria for second-order linear delay dynamic equations. Zbl 1104.34026
Erbe, L.; Peterson, A.; Saker, S. H.
2006
Existence of periodic solutions, global attractivity and oscillation of impulsive delay population model. Zbl 1124.34054
Saker, S. H.; Alzabut, J. O.
2007
Oscillation of third-order functional dynamic equations on time scales. Zbl 1260.34166
Saker, Samir H.
2011
Oscillation criteria of third-order nonlinear delay differential equations. Zbl 1141.34040
Saker, Samir H.
2006
Dynamic inequalities on time scales. Zbl 1318.26002
Agarwal, Ravi; O’Regan, Donal; Saker, Samir
2014
Oscillation and global attractivity in a nonlinear delay periodic model of population dynamics. Zbl 1041.34061
Saker, Samir H.; Agarwal, Sheba
2002
Oscillation and global attractivity of impulsive periodic delay respiratory dynamics model. Zbl 1096.34053
Saker, S. H.
2005
Some nonlinear dynamic inequalities on time scales. Zbl 1222.26032
Saker, S. H.
2011
Weighted Hardy-type inequalities on time scales with applications. Zbl 1342.26064
Saker, S. H.; Mahmoud, R. R.; Peterson, A.
2016
Boundedness of solutions of second-order forced nonlinear dynamic equations. Zbl 1139.34030
Saker, S. H.
2006
Oscillation for second-order nonlinear neutral delay difference equations. Zbl 1078.39014
Sun, Y. G.; Saker, S. H.
2005
Oscillation criteria for a second-order quasilinear neutral functional dynamic equation on time scales. Zbl 1334.34196
Saker, S. H.
2011
Oscillation and global attractivity of a periodic survival red blood cells model. Zbl 1078.34062
Saker, Samir H.; Agarwal, Sheba
2005
New oscillation criteria for first order nonlinear neutral delay differential equations. Zbl 1031.34065
Kubiaczyk, I.; Saker, S. H.; Morchalo, J.
2003
Oscillation of second-order forced nonlinear dynamic equations on time scales. Zbl 1097.34027
Saker, S. H.
2005
Generalized Hardy, Copson, Leindler and Bennett inequalities on time scales. Zbl 1309.26018
Saker, S. H.; O’Regan, D.; Agarwal, R.
2014
Qualitative analysis of discrete nonlinear delay survival red blood cells model. Zbl 1136.92009
Saker, S. H.
2008
Stability and Hopf bifurcations of nonlinear delay malaria epidemic model. Zbl 1181.37121
Saker, S. H.
2010
Oscillation of continuous and discrete diffusive delay Nicholson’s blowflies models. Zbl 1075.92051
Saker, S. H.
2005
Some dynamic Wirtinger-type inequalities and their applications. Zbl 1236.26030
Agarwal, Ravi P.; Bohner, Martin; O’Regan, Donal; Saker, Samir H.
2011
Some nonlinear dynamic inequalities on time scales and applications. Zbl 1207.26034
Saker, S. H.
2010
Oscillation of second-order sublinear neutral delay difference equations. Zbl 1052.39010
Li, Wan-Tong; Saker, S. H.
2003
Hille-Kneser-type criteria for second-order dynamic equations on time scales. Zbl 1229.34136
Erbe, Lynn; Peterson, Allan C.; Saker, Samir H.
2006
Oscillation and global attractivity in a discrete survival red blood cells model. Zbl 1057.39002
Kubiaczyk, I.; Saker, S. H.
2003
Oscillation criteria for nonlinear perturbed dynamic equations of second-order on time scales. Zbl 1089.39001
Agarwal, Ravi P.; O’Regan, Donal; Saker, S. H.
2006
Oscillation of second-order functional dynamic equations of Emden-Fowler-type on time scales. Zbl 1278.34106
Saker, S. H.
2010
Oscillation theory of third-order nonlinear functional differential equations. Zbl 1272.34092
Graef, John R.; Saker, Samir H.
2013
On the oscillation of certain class of third-order nonlinear delay differential equations. Zbl 1224.34217
Saker, S. H.; Džurina, J.
2010
Oscillation of second order neutral delay differential equations of Emden-Fowler type. Zbl 1051.34052
Saker, S. H.
2003
On the Cushing-Henson conjecture, delay difference equations and attenuant cycles. Zbl 1158.39004
Braverman, E.; Saker, S. H.
2008
Oscillation criteria for a forced second-order nonlinear dynamic equation. Zbl 1168.34025
Erbe, L.; Peterson, A.; Saker, S. H.
2008
Oscillation of superlinear and sublinear neutral delay dynamic equations. Zbl 1192.34077
Saker, S. H.
2008
Some Opial-type inequalities on time scales. Zbl 1221.26034
Saker, S. H.
2011
Periodic solutions, global attractivity and oscillation of an impulsive delay host-macroparasite model. Zbl 1165.34350
Saker, S. H.; Alzabut, J. O.
2007
Existence of positive periodic solutions of nonlinear discrete model exhibiting the Allee effect. Zbl 1087.39015
Sun, Y. G.; Saker, S. H.
2005
Interval oscillation criteria for forced Emden-Fowler functional dynamic equations with oscillatory potential. Zbl 1273.34095
Anderson, Douglas R.; Saker, Samir H.
2013
Oscillation of third-order nonlinear neutral functional dynamic equations on time scales. Zbl 1278.34107
Saker, S. H.; Graef, John R.
2012
Applications of Opial inequalities on time scales on dynamic equations with damping terms. Zbl 1327.37009
Saker, S. H.
2013
Oscillation of third-order difference equations. Zbl 1069.39015
Saker, S. H.
2004
New oscillation criteria for second-order neutral dynamic equations on time scales via Riccati substitution. Zbl 1252.34104
Saker, S. H.; O’Regan, Donal
2012
Dynamic inequalities of Hardy and Copson type on time scales. Zbl 1300.26022
Saker, Samir H.; O’Regan, Donal; Agarwal, Ravi P.
2014
Oscillation of first order neutral delay differential equations. Zbl 1014.34057
Saker, S. H.; Elabbasy, El. M.
2001
Oscillation of solutions to neutral delay differential equations. Zbl 1019.34067
Kubiaczyk, I.; Saker, S. H.
2002
Oscillation of second-order perturbed nonlinear difference equations. Zbl 1035.39007
Saker, S. H.
2003
Oscillation theorems for second order nonlinear functional differential equations with damping. Zbl 1057.34083
Saker, Samir H.; Pang, P. Y. H.; Agarwal, Ravi P.
2003
Oscillation in a discrete partial delay Nicholson’s blowflies model. Zbl 1021.92042
Saker, S. H.; Zhang, B. G.
2002
Higher order dynamic inequalities on time scales. Zbl 1293.26020
Saker, S. H.; Agarwal, R. P.; O’Regan, Donal
2014
Approximate solution of linear and nonlinear fractional differential equations under $$m$$-point local and nonlocal boundary conditions. Zbl 1419.34087
Khalil, Hammad; Khan, Rahmat Ali; Baleanu, Dumitru; Saker, Samir H.
2016
Hardy type inequalities on time scales. Zbl 1359.26002
Agarwal, Ravi P.; O’Regan, Donal; Saker, Samir H.
2016
On oscillation of a certain class of third-order nonlinear functional dynamic equations on time scales. Zbl 1265.34339
Saker, S. H.
2011
Interval oscillation criteria for forced second-order nonlinear delay dynamic equations with oscillatory potential. Zbl 1202.34162
Erbe, Lynn; Hassan, Taher S.; Peterson, Allan; Saker, Samir H.
2010
Dynamics of a class of non-autonomous systems of two non-interacting preys with common predator. Zbl 1069.34071
Elabbasy, E. M.; Saker, S. H.
2005
Oscillation criteria for second order superlinear neutral delay differential equations. Zbl 1082.34057
Saker, S. H.; Manojlović, J. V.
2004
Opial’s type inequalities on time scales and some applications. Zbl 1264.26032
Saker, S. H.
2012
Oscillation criteria for quasi-linear functional dynamic equations on time scales. Zbl 1324.34192
Saker, Samir H.; Grace, Said R.
2012
Forced oscillation of higher-order nonlinear differential equations. Zbl 1099.34034
Sun, Y. G.; Saker, S. H.
2006
Oscillation of delay parabolic differential equations with several coefficients. Zbl 1011.35125
Kubiaczyk, I.; Saker, S. H.
2002
Higher summability and discrete weighted Muckenhoupt and Gehring type inequalities. Zbl 1454.42017
Saker, S. H.; Kubiaczyk, I.
2019
New inequalities of Opial’s type on time scales and some of their applications. Zbl 1244.26050
Saker, Samir H.
2012
Some Opial dynamic inequalities involving higher order derivatives on time scales. Zbl 1248.26037
Saker, Samir H.
2012
Hille and Nehari types oscillation criteria for second-order neutral delay dynamic equations. Zbl 1179.34109
Saker, S. H.
2009
Oscillation criteria for a certain class of second-order neutral delay dynamic equations. Zbl 1180.34067
Saker, S. H.
2009
Oscillation of third-order neutral dynamic equations on time scales. Zbl 1268.34193
Zhang, Chenghui; Saker, Samir H.; Li, Tongxing
2013
Oscillation of second-order nonlinear differential equations with a damping term. Zbl 1075.34029
Elabbasy, Elmetwally M.; Hassan, Taher S.; Saker, Samir. H.
2005
Lyapunov type inequalities for a second order differential equation with a damping term. Zbl 1252.34030
Saker, S. H.
2012
Lyapunov inequalities for half-linear dynamic equations on time scales and disconjugacy. Zbl 1211.26027
Saker, S. H.
2011
Oscillation of damped second-order nonlinear delay differential equations of Emden-Fowler type. Zbl 1132.34046
Bohner, M.; Saker, S. H.
2006
Asymptotic properties of third order functional dynamic equations on time scales. Zbl 1218.34086
Kubiaczyk, I.; Saker, S. H.
2011
Applications of Wirtinger inequalities on the distribution of zeros of the Riemann zeta-function. Zbl 1234.11115
Saker, Samir H.
2010
A new class of dynamic inequalities of Hardy’s type on time scales. Zbl 1300.26021
Saker, S. H.; Graef, John R.
2014
Oscillation of solutions to delay differential equations with positiv and negative coefficients. Zbl 0944.34056
Elabbasy, El M.; Hegazi, A. S.; Saker, S. H.
2000
The weighted discrete Gehring classes, Muckenhoupt classes and their basic properties. Zbl 1458.42018
Saker, Samir H.; Krnić, Mario
2021
Properties of a generalized class of weights satisfying reverse Hölder’s inequality. Zbl 1462.42033
Saker, S. H.; Rabie, S. S.; Agarwal, R. P.
2021
Discrete Hardy’s type inequalities and structure of discrete class of weights satisfy reverse Hölder’s inequality. Zbl 1468.26021
Saker, S. H.; Chu, Jifeng
2021
Higher summability and discrete weighted Muckenhoupt and Gehring type inequalities. Zbl 1454.42017
Saker, S. H.; Kubiaczyk, I.
2019
A higher integrability theorem from a reverse weighted inequality. Zbl 1441.26010
Saker, Samir; O’Regan, Donal; Agarwal, Ravi
2019
More accurate dynamic Hardy-type inequalities obtained via superquadraticity. Zbl 1468.26020
Saker, Samir H.; Rezk, Haytham M.; Krnić, Mario
2019
Levinson type inequalities and their extensions via convexity on time scales. (Levinson type inequalitis and their extensions via convexity on time scales.) Zbl 1409.26016
Saker, S. H.; Osman, M. M.; O’Regan, D.; Agarwal, R. P.
2019
Reverse dynamic inequalities and higher integrability theorems. Zbl 1404.26024
Saker, S. H.; Kubiaczyk, I.
2019
New characterizations of weights in Hardy and Opial type inequalities via solvability of dynamic equations. Zbl 1453.26031
Saker, S. H.; Sayed, A. G.; Sikorska-Nowak, A.; Abohela, I.
2019
Some new dynamic inequalities involving monotonic functions on time scales. Zbl 1416.26057
Saker, S. H.; Awwad, E.; Saied, A.
2019
Distribution of zeros of second order superlinear and sublinear neutral delay differential equations. Zbl 1418.34078
Saker, S. H.; Sudha, B.; Arahet, M. A.; Thandapani, E.
2019
Oscillation of impulsive neutral partial differential equations with distributed deviating arguments. Zbl 1399.35022
Kalaimani, T.; Raja, T.; Sadhasivam, V.; Saker, S. H.
2018
New Carlson-Bellman and Hardy-Littlewood dynamic inequalities. Zbl 1403.26016
Saker, S. H.; Tunç, C.; Mahmoud, R. R.
2018
Editorial: Applications of delay differential equations in biological systems. Zbl 1405.00027
Rihan, F. A.; Tunc, C.; Saker, S. H.; Lakshmanan, S.; Rakkiyappan, R.
2018
Inequalities of Hardy type and generalizations on time scales. Zbl 1384.26046
Saker, Samir H.; Osman, Mahmoud M.; O’Regan, Donal; Agarwal, Ravi P.
2018
A unified approach to Copson and Beesack type inequalities on time scales. Zbl 1403.26023
Saker, S. H.; Mahmoud, R. R.; Peterson, A.
2018
Some dynamic inequalities involving Hilbert and Hardy-Hilbert operators with kernels. Zbl 1401.26034
O’Regan, Donal; Rezk, Haytham M.; Saker, Samir H.
2018
New dynamic inequalities for decreasing functions and theorems of higher integrability. Zbl 1424.26059
Saker, S. H.; O’Regan, D.; Osman, M. M.; Agarwal, R. P.
2018
Some new generalized forms of Hardy’s type inequality on time scales. Zbl 1367.26048
Saker, S. H.; Mahmoud, R. R.; Osman, M. M.; Agarwal, R. P.
2017
New Hilbert dynamic inequalities on time scales. Zbl 1386.26035
Saker, S. H.; Ahmed, A. M.; Rezk, H. M.; O’Regan, D.; Agarwal, R. P.
2017
New generalizations of Németh-Mohapatra type inequalities on time scales. Zbl 1399.26040
Agarwal, R. P.; Mahmoud, R. R.; Saker, S. H.; Tunç, C.
2017
A variety of inverse Hilbert type inequalities on time scales. Zbl 1372.34038
Saker, S. H.; Rezk, H. M.; O’Regan, D.; Agarwal, R. P.
2017
Weighted Hardy-type inequalities on time scales with applications. Zbl 1342.26064
Saker, S. H.; Mahmoud, R. R.; Peterson, A.
2016
Approximate solution of linear and nonlinear fractional differential equations under $$m$$-point local and nonlocal boundary conditions. Zbl 1419.34087
Khalil, Hammad; Khan, Rahmat Ali; Baleanu, Dumitru; Saker, Samir H.
2016
Hardy type inequalities on time scales. Zbl 1359.26002
Agarwal, Ravi P.; O’Regan, Donal; Saker, Samir H.
2016
Hardy and Littlewood inequalities on time scales. Zbl 1342.26065
Saker, S. H.; O’Regan, Donal
2016
Distribution of zeros and disconjugacy of fourth order differential equations. Zbl 1352.34024
Saker, S. H.; Kubiaczyk, I.
2016
Some Bennett-Copson type inequalities on time scales. Zbl 1339.26067
Saker, S. H.; Mahmoud, R. R.; Peterson, A.
2016
Sneak-out principle on time scales. Zbl 1334.26005
Bohner, Martin J.; Saker, Samir H.
2016
Dynamic Littlewood-type inequalities. Zbl 1307.26019
Agarwal, Ravi; Bohner, Martin; Saker, Samir
2015
Discrete, continuous, delta, nabla, and diamond-alpha Opial inequalities. Zbl 1386.26021
Bohner, Martin J.; Mahmoud, Ramy R.; Saker, Samir H.
2015
Converses of Copson’s inequalities on time scales. Zbl 1307.26024
Saker, S. H.; O’Regan, D.; Agarwal, R. P.
2015
Some new dynamic inequalities on discrete time scales. Zbl 1326.26048
Saker, S. H.; O’Regan, Donal; Agarwal, Ravi P.
2015
Some new Opial dynamic inequalities with weighted functions on time scales. Zbl 1320.26029
Saker, S. H.; Osman, M. M.; O’Regan, D.; Agarwal, R. P.
2015
Some new Lyapunov-type inequalities for third order differential equations. Zbl 1326.34042
Graef, John R.; Mahmoud, R.; Saker, Samir H.; Tunç, Ercan
2015
A new Picone’s dynamic inequality on time scales with applications. Zbl 1323.26029
Saker, S. H.; Mahmoud, R. R.; Peterson, A.
2015
Distributions of zeros of solutions for third-order differential equations with variable coefficients. Zbl 1394.34060
Saker, Samir H.; Arahet, Mohammed A.
2015
Extensions of dynamic inequalities of Hardy’s type on time scales. Zbl 1363.26028
Saker, S. H.; O’Regan, Donal
2015
Improvements of dynamic Opial-type inequalities and applications. Zbl 1325.26047
Bohner, Martin J.; Mahmoud, Ramy R.; Saker, Samir H.
2015
Littlewood and Bennett inequalities on time scales. Zbl 1321.26063
Saker, S. H.; O’Regan, D.; Agarwal, R. P.
2015
Qualitative theory of functional differential and integral equations. Zbl 1343.00033
Tunç, Cemil; Benchohra, Mouffak; Liu, Bingwen; Islam, Muhammad N.; Saker, Samir H.
2015
Dynamic inequalities on time scales. Zbl 1318.26002
Agarwal, Ravi; O’Regan, Donal; Saker, Samir
2014
Generalized Hardy, Copson, Leindler and Bennett inequalities on time scales. Zbl 1309.26018
Saker, S. H.; O’Regan, D.; Agarwal, R.
2014
Dynamic inequalities of Hardy and Copson type on time scales. Zbl 1300.26022
Saker, Samir H.; O’Regan, Donal; Agarwal, Ravi P.
2014
Higher order dynamic inequalities on time scales. Zbl 1293.26020
Saker, S. H.; Agarwal, R. P.; O’Regan, Donal
2014
A new class of dynamic inequalities of Hardy’s type on time scales. Zbl 1300.26021
Saker, S. H.; Graef, John R.
2014
Some dynamic inequalities of Hardy type on time scales. Zbl 1295.26023
Saker, S. H.; O’Regan, Donal; Agarwal, R. P.
2014
A note on oscillation criteria for second-order neutral dynamic equations on isolated time scales. Zbl 1470.34239
Li, Tongxing; Saker, S. H.
2014
Oscillation of fourth-order delay differential equations. Zbl 1314.34140
Zhang, C.; Li, T.; Saker, S. H.
2014
Some new disconjugacy criteria for second order differential equations with a middle term. Zbl 1389.34109
Saker, Samir H.
2014
Oscillation and stability of delay models in biology. Zbl 1312.37001
Agarwal, Ravi P.; O’Regan, Donal; Saker, Samir H.
2014
Oscillation theory of third-order nonlinear functional differential equations. Zbl 1272.34092
Graef, John R.; Saker, Samir H.
2013
Interval oscillation criteria for forced Emden-Fowler functional dynamic equations with oscillatory potential. Zbl 1273.34095
Anderson, Douglas R.; Saker, Samir H.
2013
Applications of Opial inequalities on time scales on dynamic equations with damping terms. Zbl 1327.37009
Saker, S. H.
2013
Oscillation of third-order neutral dynamic equations on time scales. Zbl 1268.34193
Zhang, Chenghui; Saker, Samir H.; Li, Tongxing
2013
Properties of solutions of fourth-order differential equations with boundary conditions. Zbl 1286.34039
Saker, Samir H.; Agarwal, Ravi P.; O’Regan, Donal
2013
Oscillation criteria for nonlinear neutral functional dynamic equations on time scales. Zbl 1324.34190
Kubiaczyk, I.; Saker, S. H.; Sikorska-Nowak, Aneta
2013
Oscillation of third-order nonlinear neutral functional dynamic equations on time scales. Zbl 1278.34107
Saker, S. H.; Graef, John R.
2012
New oscillation criteria for second-order neutral dynamic equations on time scales via Riccati substitution. Zbl 1252.34104
Saker, S. H.; O’Regan, Donal
2012
Opial’s type inequalities on time scales and some applications. Zbl 1264.26032
Saker, S. H.
2012
Oscillation criteria for quasi-linear functional dynamic equations on time scales. Zbl 1324.34192
Saker, Samir H.; Grace, Said R.
2012
New inequalities of Opial’s type on time scales and some of their applications. Zbl 1244.26050
Saker, Samir H.
2012
Some Opial dynamic inequalities involving higher order derivatives on time scales. Zbl 1248.26037
Saker, Samir H.
2012
Lyapunov type inequalities for a second order differential equation with a damping term. Zbl 1252.34030
Saker, S. H.
2012
Oscillation of a certain class of third order nonlinear difference equations. Zbl 1253.39015
Saker, S. H.
2012
Some new inequalities of Opial’s type on time scales. Zbl 1242.26034
Saker, Samir H.
2012
Lyapunov’s type inequalities for fourth-order differential equations. Zbl 1245.34037
Saker, Samir H.
2012
Gaps between zeros of second-order half-linear differential equations. Zbl 1291.34064
Saker, S. H.; Agarwal, R. P.; O’Regan, Donal
2012
New oscillation criteria for second-order neutral functional dynamic equations via the generalized Riccati substitution. Zbl 1221.34245
Saker, S. H.; O’Regan, Donal
2011
Oscillation of third-order functional dynamic equations on time scales. Zbl 1260.34166
Saker, Samir H.
2011
Some nonlinear dynamic inequalities on time scales. Zbl 1222.26032
Saker, S. H.
2011
Oscillation criteria for a second-order quasilinear neutral functional dynamic equation on time scales. Zbl 1334.34196
Saker, S. H.
2011
Some dynamic Wirtinger-type inequalities and their applications. Zbl 1236.26030
Agarwal, Ravi P.; Bohner, Martin; O’Regan, Donal; Saker, Samir H.
2011
Some Opial-type inequalities on time scales. Zbl 1221.26034
Saker, S. H.
2011
On oscillation of a certain class of third-order nonlinear functional dynamic equations on time scales. Zbl 1265.34339
Saker, S. H.
2011
Lyapunov inequalities for half-linear dynamic equations on time scales and disconjugacy. Zbl 1211.26027
Saker, S. H.
2011
Asymptotic properties of third order functional dynamic equations on time scales. Zbl 1218.34086
Kubiaczyk, I.; Saker, S. H.
2011
Applications of Opial and Wirtinger inequalities on zeros of third order differential equations. Zbl 1241.34040
Saker, S. H.
2011
On a difference equation with exponentially decreasing nonlinearity. Zbl 1229.92017
Braverman, E.; Saker, S. H.
2011
Nonlinear dynamic inequalities of Gronwall-Bellman type on time scales. Zbl 1340.26053
Saker, Samir
2011
New oscillation criteria for third order nonlinear neutral difference equations. Zbl 1265.39009
Saker, S. H.
2011
Dynamics and control of a system of two non-interacting preys with common predator. Zbl 1229.92082
Zaman, Gul; Saker, Samir H.
2011
Stability and Hopf bifurcations of nonlinear delay malaria epidemic model. Zbl 1181.37121
Saker, S. H.
2010
Some nonlinear dynamic inequalities on time scales and applications. Zbl 1207.26034
Saker, S. H.
2010
Oscillation of second-order functional dynamic equations of Emden-Fowler-type on time scales. Zbl 1278.34106
Saker, S. H.
2010
On the oscillation of certain class of third-order nonlinear delay differential equations. Zbl 1224.34217
Saker, S. H.; Džurina, J.
2010
Interval oscillation criteria for forced second-order nonlinear delay dynamic equations with oscillatory potential. Zbl 1202.34162
Erbe, Lynn; Hassan, Taher S.; Peterson, Allan; Saker, Samir H.
2010
Applications of Wirtinger inequalities on the distribution of zeros of the Riemann zeta-function. Zbl 1234.11115
Saker, Samir H.
2010
On the oscillatory behavior for a certain class of third order nonlinear delay difference equations. Zbl 1208.39019
Saker, S. H.; Alzabut, J. O.; Mukheimer, A.
2010
Periodic solutions and global attractivity of a discrete delay host macroparasite model. Zbl 1190.92037
Braverman, E.; Saker, S. H.
2010
Compatibility of local and global stability conditions for some discrete population models. Zbl 1183.92067
Saker, S. H.
2010
Oscillatory behavior of a certain class of second-order nonlinear perturbed dynamic equations on time scales. Zbl 1195.34140
Saker, Samir H.
2010
Global stability and oscillation of a discrete annual plants model. Zbl 1207.39023
Saker, S. H.
2010
New oscillation criteria for generalized second-order nonlinear neutral functional differential equations. Zbl 1218.34080
Graef, John R.; Saker, S. H.
2010
Oscillatory behavior of third order nonlinear difference equations with delayed argument. Zbl 1215.39015
Saker, S. H.; Alzabut, J. O.
2010
Oscillation criteria for half-linear delay dynamic equations on time scales. Zbl 1173.34037
Erbe, Lynn; Hassan, Taher S.; Peterson, Allan; Saker, Samir H.
2009
On the impulsive delay hematopoiesis model with periodic coefficients. Zbl 1179.34092
Saker, S. H.; Alzabut, J. O.
2009
Hille and Nehari types oscillation criteria for second-order neutral delay dynamic equations. Zbl 1179.34109
Saker, S. H.
2009
Oscillation criteria for a certain class of second-order neutral delay dynamic equations. Zbl 1180.34067
Saker, S. H.
2009
Oscillation theorems for second-order nonlinear neutral delay dynamic equations on time scales. Zbl 1153.34040
Saker, Samir H.; O’Regan, Donal; Agarwal, Ravi P.
2008
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#### Cited by 778 Authors

 94 Saker, Samir H. 52 Agarwal, Ravi P. 43 Li, Tongxing 28 O’Regan, Donal 27 Bohner, Martin J. 25 Zhang, Chenghui 23 Han, Zhenlai 22 Grace, Said Rezk 22 Hassan, Taher S. 16 Erbe, Lynn Harry 16 Wang, Qiru 15 Alzabut, Jehad O. 13 Sun, Shurong 12 Džurina, Jozef 12 Li, Wan-Tong 12 Meng, Fanwei 12 Thandapani, Ethiraju 11 Kang, Shin Min 11 Liu, Zeqing 11 Teng, Zhi-dong 10 Li, Yongkun 10 Peterson, Allan C. 10 Sun, Taixiang 10 Xu, Zhiting 10 Zafer, Ağacık 9 Graef, John R. 9 Jadlovská, Irena 9 Zhang, Quanxin 8 Braverman, Elena 8 Feng, Qinghua 8 Liu, Haidong 8 Nieto Roig, Juan Jose 7 Anderson, Douglas Robert 7 Baculíková, Blanka 7 Ding, Huisheng 7 Huo, Hai-Feng 7 Kubiaczyk, Ireneusz 7 Mahmoud, Ramy Ramadan 7 Qiu, Yangcong 7 Wei, Junjie 7 Xi, Hongjian 7 Xu, Changjin 6 Abbas, Syed 6 Ahmad, Rokiah Rozita 6 Berezansky, Leonid M. 6 Chen, Daxue 6 Din, Ummul Khair Salma 6 Liu, Bingwen 6 Noorani, Mohd Salmi Mohd 6 Selvarangam, Srinivasan 6 Sun, Yuangong 6 Tunç, Ercan 6 Wang, Xiao 5 Ahmed, Fatima N. 5 Chatzarakis, George E. 5 Došlá, Zuzana 5 Elabbasy, Elmetwally M. 5 Eldeeb, Ahmed Abdel-Moneim 5 Karpuz, Başak 5 Li, Weinian 5 Osman, Mahmoud M. 5 Sadhasivam, Vadivel 5 Stamov, Gani Trendafilov 5 Sun, Yibing 5 Tang, Shuhong 5 Tiryaki, Aydin 5 Tunç, Cemil 5 Ume, Jeong Sheok 5 Wang, Chao 5 Yan, Jurang 5 Yang, Jiashan 5 Zhang, Shaoyan 5 Zhang, Zhenguo 5 Zhou, Zhan 4 Agwa, Hassan Ahmed Hassan 4 Aktaş, Mustafa Fahri 4 Candan, Tuncay 4 Elsennary, H. A. 4 Faria, Teresa 4 Gao, Jianfang 4 Gao, Li 4 Ge, Weigao 4 Hassan, Heba A. 4 Idels, Lev V. 4 Jia, Baoguo 4 Khodier, Ahmed Mohamed Mohamed 4 Krnić, Mario 4 Kwun, Young Chel 4 Li, Qiaoluan 4 Li, Zhixiang 4 Liang, Haiyan 4 Liu, Shouhua 4 Liu, Zijian 4 Marini, Mauro 4 Negi, Shekhar Singh 4 Pinelas, Sandra 4 Shen, Jianhua 4 Shi, Bao 4 Sugie, Jitsuro 4 Sun, Ji Tao ...and 678 more Authors
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#### Cited in 149 Serials

 85 Advances in Difference Equations 69 Applied Mathematics and Computation 63 Abstract and Applied Analysis 31 Discrete Dynamics in Nature and Society 29 Journal of Mathematical Analysis and Applications 28 Journal of Applied Mathematics and Computing 26 Computers & Mathematics with Applications 25 Applied Mathematics Letters 22 Journal of Computational and Applied Mathematics 22 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 19 Mathematical and Computer Modelling 18 Journal of Difference Equations and Applications 13 Journal of Inequalities and Applications 13 Nonlinear Analysis. Real World Applications 11 Applied Mathematical Modelling 10 Mediterranean Journal of Mathematics 9 Rocky Mountain Journal of Mathematics 9 Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM 8 Mathematical Methods in the Applied Sciences 8 Mathematica Slovaca 7 International Journal of Differential Equations 6 Chaos, Solitons and Fractals 6 Proceedings of the American Mathematical Society 6 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 6 Journal of Function Spaces 5 Acta Applicandae Mathematicae 5 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 5 Nonlinear Dynamics 5 Hacettepe Journal of Mathematics and Statistics 5 International Journal of Biomathematics 5 Journal of Nonlinear Science and Applications 5 Science China. Mathematics 5 Journal of Mathematics 4 Monatshefte für Mathematik 4 Acta Mathematicae Applicatae Sinica. English Series 4 Communications in Nonlinear Science and Numerical Simulation 4 Journal of Applied Mathematics 4 Journal of Biological Dynamics 4 Journal of Fixed Point Theory and Applications 3 Fasciculi Mathematici 3 Hiroshima Mathematical Journal 3 Mathematische Nachrichten 3 Applications of Mathematics 3 The Journal of Analysis 3 Applied Mathematics. Series B (English Edition) 3 Turkish Journal of Mathematics 3 Opuscula Mathematica 3 Functional Differential Equations 3 Vietnam Journal of Mathematics 3 Mathematical Inequalities & Applications 3 Analysis (München) 3 Acta Mathematica Sinica. English Series 3 Central European Journal of Mathematics 3 Boundary Value Problems 3 Journal of Mathematical Inequalities 3 Journal of Applied Analysis and Computation 2 Applicable Analysis 2 International Journal of Control 2 Journal of the Franklin Institute 2 Ukrainian Mathematical Journal 2 Annales Polonici Mathematici 2 Annales Universitatis Mariae Curie-Skłodowska. Sectio A. Mathematica 2 Fuzzy Sets and Systems 2 Journal of Differential Equations 2 Mathematics and Computers in Simulation 2 Acta Mathematica Hungarica 2 Applied Numerical Mathematics 2 Journal of Dynamics and Differential Equations 2 Journal of Mathematical Sciences (New York) 2 Georgian Mathematical Journal 2 Complexity 2 Arab Journal of Mathematical Sciences 2 Mathematical Problems in Engineering 2 The ANZIAM Journal 2 Discrete and Continuous Dynamical Systems. Series B 2 Bulletin of the Brazilian Mathematical Society. New Series 2 Differential Equations and Applications 2 Advances in Mathematical Physics 2 Nonautonomous Dynamical Systems 2 Open Mathematics 2 Cogent Mathematics & Statistics 1 Bulletin of the Australian Mathematical Society 1 International Journal of Theoretical Physics 1 Journal of Mathematical Biology 1 Journal of Mathematical Physics 1 Mathematical Notes 1 Periodica Mathematica Hungarica 1 Acta Mathematica Vietnamica 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Czechoslovak Mathematical Journal 1 Demonstratio Mathematica 1 International Journal of Mathematics and Mathematical Sciences 1 The Journal of the Indian Mathematical Society. New Series 1 Mathematika 1 Quaestiones Mathematicae 1 Applied Mathematics and Mechanics. (English Edition) 1 Physica D 1 International Journal of Mathematics 1 Japan Journal of Industrial and Applied Mathematics 1 Journal of Contemporary Mathematical Analysis. Armenian Academy of Sciences ...and 49 more Serials
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text:
# Prove the following identity, where the angles involved are acute angles for which the expressions are defined.(x) ((1+tan^2A)/(1+cot^2A))=((1-tanA)/

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closed
Prove the following identity, where the angles involved are acute angles for which the expressions are defined.
(x) ((1+tan^2A)/(1+cot^2A))=((1-tanA)/(1-cotA))^2=tan^2A

by (71.5k points)
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Right hand side
=((1+tan^2A)/(1+cot^2A))
=((1+tan^2A)/((tan^2A+1)/tan^2A))
=tan^2A
Left hand side
=((1-tan^2A)/(1-cot^2A))
=((1-tan^2A)/((tan^2A-1)/tan^2A))
=tan^2A`


text:
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EDIT 7/1/2019: The proof for each finite subset of a Hausdorff space is closed is corrected.

Before I begin, as stated in my articles section, I said I am going to start writing about all the neat maths I’ve learnt throughout my final year project in physics, in which I wrote an introduction to general relativity, (available on the articles page). I’d like to point to a great post written by friend, Ivan, on general relativity. You can find the post here along with all of his other great content.

For those first learning differential geometry, you may be given the definition of a manifold, without any reasoning why the definition is the way it is. We begin with the definition of a topological manifold, if you are unfamiliar with the definition of a topological space, look !!!!here.

A topological manifold is a topological space such that

• X is Hausdorff
• X is second countable
• X is locally euclidean

A Hausdorff space is a topological space such that for any two distinct points in , we can find two open sets and where and and .

Furthermore, a topological space is called \textit{second countable} if there exists a countable basis for the topology. So this means there exists a countable collection of open subsets of , , such that each open subset of can be written as a collection of elements of some subfamily of .

Additionally, a topology is known as locally euclidean if every point in has a neighbourhood that is homeomorphic to some open subset of .

We can see automatically why the locally Euclidean condition useful, once we can say that a space is locally like Euclidean space, many of the properties that Euclidean space enjoys are transferred to our topological manifold in a local sense, not necessarily globally. However, the other two conditions, the Hausdorff requirement and the second countability requirement are not so obvious. To see why need the Hausdorff requirement, lets look at what is called the trivial topology, where a topological space has the topology .

We often like to know what a sequence converges to, and so we will first look at how sequences behave in this topology. The first observation we make is that for any sequence in , it will converge to every point in . Take a sequence in and some point . Now in order for , we need for every open neighbourhood of , there must be points of the sequence also contained in that neighbourhood. Since the only open neighbourhood of is , it follows that . But we chose to be any point in and so the sequence converges to every point in .

The next thing that the map is always continuous for any topological space . To check continuity, we look at the pre-images of the open sets of . Clearly, and so is open. Now, and so is also open, and hence is continuous.

This rather pathological example of a topology illustrates the unwanted behaviours that a space can produce itself. Note, that the behaviours had nothing to do with the sequences or the functions we chose, but was a direct consequence of the discrete topology we had chosen. To avoid all this, we restrict ourselves to Hausdorff spaces, and we will now show two important properties of Hausdorff spaces that solve these problems.

For a topological space that is Hausdorff, each convergent sequence in has a unique limit.

Proof.
Take a sequence in X, and say it converges to two different points and . Since , there exists an such that for every open neighbourhood of , for all . By the Hausdorff property, since there exists an open set that contains and is disjoint to . Hence for all , and so does not converge to . A contradiction and hence and the limit is unique.

In order to solve the continuity problem our spaces need sufficient amounts of open sets in order for the definition of continuity to be useful. Now a good way to ensure this is by taking finite subsets to be closed, and so their complements will be open. Since we can construct a vast number of finite subsets, we will also have a vast number of open sets. We now show that each finite subset of a Hausdorff space is closed.

Proof.
We use the fact if a set contains it’s limit points then it is closed.
Take to be finite, and a sequence such that for some . Say that , and take some , where from the definition of convergence. There is some set disjoint from by the Hausdorff property. However, since for all , there is an open set that contains but does not contain any points of the sequence. A contradiction. Hence, and contains it’s limit points.

EDIT:
This proof is wrong for a few reasons:

• We didn’t use the fact that the subset is finite anywhere in the proof, other then in the first line where we say it is finite – but this is not used later and so the argument still works for any subset. So our argument states that any subset of a Hausdorff space is closed
• The second error is that we have misused the Hausdorff property. The property states that given two distinct points, we can find two disjoint sets containing each point. What we have done in the proof is taken a point and a set containing it , then said we can find a set containing that is disjoint to . This is not the Hausdorff property, and so ultimately the argument breaks down here.

So, a revised proof follows the idea that since the set is finite, , we can write

and since each is a closed set, their finite union is closed. Well, the fact that one point is a closed set is not so obvious, so let’s prove it, and this where the Hausdorff property comes in.

Proof.
Take and by the Hausdorff property, we can find two disjoint open sets and such that and . Now, we note that

Since each is open their union is open and so is open, and hence is closed.

END EDIT

Now we can see why we need the Hausdorff property in the definition. The second countable condition is to ensure the existence of partitions of unity, I will talk about this in detail in some later post, however, for now, you can think of a partition of unity as way to “glue” different functions on a manifold together. These are required for integrating on the manifold and come up frequently in smooth manifold theory.


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# TrigonometryTrig. product

#### jacks

##### Well-known member
The value of $\sin (1^0).\sin (3^0).\sin (5^0)...........\sin (87^0).\sin (89^0)$

where all angles are in degree

#### Sudharaka

##### Well-known member
MHB Math Helper
The value of $\sin (1^0).\sin (3^0).\sin (5^0)...........\sin (87^0).\sin (89^0)$

where all angles are in degree
Hi jacks,

I haven't found a way solve this algebraically. But if you are interested about the answer it is, $$4.0194366942304562\times 10^{-14}$$

#### jacks

##### Well-known member
Hi jacks,

I haven't found a way solve this algebraically. But if you are interested about the answer it is, $$4.0194366942304562\times 10^{-14}$$
Thanks Sudhakara

I am trying to find it with the help of complex no.(like nth -roots of unity)

#### Opalg

##### MHB Oldtimer
Staff member
The value of $\sin (1^0).\sin (3^0).\sin (5^0)...........\sin (87^0).\sin (89^0)$

where all angles are in degree
Follow the method used in this thread, noting that $x=\pm1^\circ,\pm3^\circ,\pm5^\circ,\ldots,\pm89 ^\circ$ are the solutions of the equation $\cos(90x) = 0.$


text:
# What is the temperature, in K, of 2.20 moles of gas occupying 3.5 L at 3.30 atm?

Nov 20, 2016

64 K

#### Explanation:

To figure this out you need to start with the ideal gas equation:

$P \cdot V = n \cdot R \cdot T$

You have P (3.30 atm), V (3.5 l), n (2.20 moles) and you can look up the gas constant, R (0.082057 (latm)/(molK)).

We simply rearrange the ideal gas equation to get T by itself:

$T = \frac{P \cdot V}{n \cdot R}$

Then simply plug in the values you were given, making sure that the units are in liters, atmospheres, and moles (which they are, in this case):

T = (3.30" atm"*3.5" l")/(2.20" moles"*0.082057" (l*atm)/(mol*K)") = 63.9799" K"

Since volume was only given to 2 significant figures, we can only report 2 significant figures for our answer:

64 K.


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# Numerics for the two-phase Stefan problem

## Intruduction

The following videos show the evolution of enthalpy $$h$$ in the two-phase Stefan problem with no-flux boundary in 2D: $\begin{cases} h_t(x,t) - \Delta \chi(h(x,t)) = f(x,t), & \text{in } \Omega \times (0, T)\\ \frac{\partial \chi(u)}{\nu} = 0, & \text{on } \partial \Omega \times (0,T)\\ h(x,0) = h_0(x), \end{cases}$ where $$h$$ is the enthalpy, $$f$$ is the volumetric heat source and $$\chi(h)$$ is the temperature. The function $$\chi$$ is defined as $\chi(s) = \min(s, \max(0, s -1)) = \begin{cases} s & s < 0,\\ 0 & 0 \leq s \leq 1 & s-1 & s > 1, \end{cases}$ see figure 1.

The solutions contain the following regions:

• solid – red
• liquid – yellow
• mushy region – blue

Images were produced using Mathematica 7 and encoded using mencoder. To view these videos, you need to be able to play videos from youtube.


text:
Article

# Search for B -> phi pi decays

• ##### V. Zhulanov
06/2012;
Source: arXiv

ABSTRACT We report on a search for the charmless decays $B^{+} \to\phi\pi^{+}$ and
$B^{0} \to\phi \pi^{0}$ that are strongly suppressed in the Standard Model. The
analysis is based on a data sample of $657 \times 10^6$ $B \bar{B}$ pairs
collected at the $\Upsilon(4S)$ resonance with the Belle detector at the KEKB
asymmetric-energy $e^+ e^-$ collider. We find no significant signal and set
upper limits of $3.3 \times 10^{-7}$ for $B^{+} \to \phi \pi^{+}$ and $1.5 \times 10^{-7}$ for $B^0 \to \phi \pi^0$ at the 90% confidence level.

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• Source
01/2001;


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# OpenMath Content Dictionary: bessel_gen

Canonical URL:
http://www.openmath.org/CDs/bessel_gen.ocd
CD File:
bessel_gen.ocd
CD as XML Encoded OpenMath:
bessel_gen.omcd
Defines:
AngerJ, LommelS1, LommelS2, StruveH, StruveL, WeberE
Date:
23/8/2001
Version:
(Revision )
Review Date:
Status:
private

1/1/5000

This content dictionary contains symbols to describe the functions generated by the bessel functions.

## StruveH

The symbol StruveH takes two arguments. It represents the Struve function, defined as follows. The Struve function StruveH(v,x) solves the inhomogeneous Bessel equation:

$$x^2y^{\prime\prime}+xy^\prime+(x^2-v^2)y= 4\frac{((1/2)~x)^{v+1}}{\pi^{1/2}\Gamma(v+1/2)}$$

Signatures:
sts

 [Next: StruveL] [Last: LommelS2] [Top]

## StruveL

The symbol StruveL takes two arguments. It represents the modified Struve function, defined as follows. The modified Struve function StruveL(v,x) solves the inhomogeneous Bessel equation:

$$x^2y^{\prime\prime}+xy^\prime-(x^2+v^2)y= 4\frac{((1/2)~x)^{v+1}}{\pi^{1/2}\Gamma(v+1/2)}$$

Signatures:
sts

 [Next: AngerJ] [Previous: StruveH] [Top]

## AngerJ

The symbol AngerJ takes two arguments. It represents the Anger function, defined as follows. The Anger function AngerJ(v,x) solves the inhomogeneous Bessel equation:

$$x^2y^{\prime\prime}+xy^\prime+(x^2-v^2)y=\frac{(x-v){\rm sin}(v\pi)}{\pi}$$

Signatures:
sts

 [Next: WeberE] [Previous: StruveL] [Top]

## WeberE

The symbol WeberE takes two arguments. It represents the Weber function, defined as follows. The Weber function WeberE(v,x) solves the inhomogeneous Bessel equation:

$$x^2y^{\prime\prime}+xy^\prime+(x^2-v^2)y=\frac{(v-x){\rm cos}(v\pi)-(v+x)}{\pi}$$

Signatures:
sts

 [Next: LommelS1] [Previous: AngerJ] [Top]

## LommelS1

The LommelS1 symbol represents the Lommel function of the first kind. The Lommel functions are solutions to the differential function:

$$z^2y^{\prime\prime}+zy^\prime+(z^2-\nu^2)y=z^{\mu+1}$$

The Lommel function of the first kind is specifically:

$$U_1(u,v)=\sum_{s=0}^\infty {(-1)}^s {\left ( \frac{u}{v} \right )}^{1+2s}J_{1+2s}(\pi x y)$$

Signatures:
sts

 [Next: LommelS2] [Previous: WeberE] [Top]

## LommelS2

The LommelS1 symbol represents the Lommel function of the second kind.

The Lommel functions are solutions to the differential function:

$$z^2y^{\prime\prime}+zy^\prime+(z^2-\nu^2)y=z^{\mu+1}$$

The Lommel function of the second kind is specifically:

$$U_2(u,v)=\sum_{s=0}^\infty {(-1)}^s {\left ( \frac{u}{v} \right )}^{2+2s}J_{2+2s}(\pi x y)$$

Signatures:
sts

 [First: StruveH] [Previous: LommelS1] [Top]


text:
# Industrial Engineering

 Question 1
The demand and forecast of an item for five months are given in the table.

$\begin{array}{|c|c|c|}\hline \textbf{Month} & \textbf{Demand} & \textbf{Forecast} \\ \hline \text{April} & \text{225} & \text{200} \\ \hline \text{May} & \text{220} & \text{240}\\ \hline \text{June} & \text{285} & \text{300} \\ \hline \text{July} & \text{290} & \text{270} \\ \hline \text{August} & \text{250} & \text{230} \\ \hline \end{array}$

The Mean Absolute Percent Error (MAPE) in the forecast is _______% (round off to two decimal places)
 A 4.45 B 12.25 C 18.42 D 8.08
GATE ME 2021 SET-2      Production Planning and Control
Question 1 Explanation:
$\begin{array}{|c|c|c|c|c|} \hline \text { March } & \mathrm{Di} & \mathrm{Fi} & \mathrm{ei} & \left|\frac{\mathrm{ei}}{\mathrm{Di}} \times 100\right| \\ \hline \text { April } & 225 & 200 & 25 & 11.11 \% \\ \hline \text { May } & 220 & 240 & -20 & 9.09 \% \\ \hline \text { June } & 285 & 300 & -15 & 5.26 \% \\ \hline \text { July } & 290 & 270 & 20 & 6.896 \% \\ \hline \text { August } & 250 & 230 & 20 & 8.0 \% \\ \hline & & & & \sum \frac{e i}{D i} \times 100 \mid=40.356 \\ \hline \end{array}$
$\text{MAPE}=\frac{\sum\left|\frac{e i}{D i} \times 100\right|}{n}=8.0712 \%$
 Question 2
Daily production capacity of a bearing manufacturing company is 30000 bearings. The daily demand of the bearing is 15000. The holding cost per year of keeping a bearing in the inventory is Rs. 20. The setup cost for the production of a batch is Rs. 1800. Assuming 300 working days in a year, the economic batch quantity in number of bearings is ______ (in integer).
 A 36254 B 20145 C 40250 D 42145
GATE ME 2021 SET-2      Production Planning and Control
Question 2 Explanation:
\begin{aligned} Q^{\star} &=\sqrt{\frac{2 D \times C_{0}}{C_{h}} \times \frac{P}{P-d}} \\ &=\sqrt{\frac{2 \times 15000 \times 300 \times 1800}{20} \times\left(\frac{30000}{30000-15000}\right)} \\ &=40249.2 \simeq 40250 \text { units } \end{aligned}
 Question 3
A factory produces $m(i=1,2,...m)$ products, each of which requires processing on $n(j=1,2,...n)$ workstations. Let $a_{ij}$ be the amount of processing time that one unit of the $i^{th}$ product requires on the $j^{th}$ workstation. Let the revenue from selling one unit of the $i^{th}$ product be $r_i$ and $h_i$ be the holding cost per unit per time period for the $i^{th}$ product. The planning horizon consists of $T \;(t=1,2,...T)$ time periods. The minimum demand that must be satisfied in time period $t$ is $d_{it}$, and the capacity of the $j^{th}$ workstation in time period $t$ is $c_{jt}$. Consider the aggregate planning formulation below, with decision variables $S_{it}$ (amount of product $i$ sold in time period $t$ ), $X_{it}$ (amount of product $i$ manufactured in time period $t$ ) and $I_{it}$ (amount of product $i$ held in inventory at the end of time period $t$.

$max\sum_{t=1}^{T}\sum_{i=1}^{m}(r_iS_{it}-h_iI_{it})$
subject to
$S_{it}\geq d_{it}\;\;\forall i,t$
< capacity constraint >
< inventory balance constraint >
$X_{it},S_{it}, I_{it} \geq 0;\; I_{i0}=0$

The capacity constraints and inventory balance constraints for this formulation are
 A $\sum_{j}^{m}a_{ij}X_{it}\leq c_{jt}\;\forall \; i,t\text{ and }I_{it}=I_{i,t-1}+X_{it}-d_{it}\; \forall \;i,t$ B $\sum_{i}^{m}a_{ij}X_{it}\leq c_{jt}\;\forall \; i,t\text{ and }I_{it}=I_{i,t-1}+X_{it}-d_{it}\; \forall \;i,t$ C $\sum_{i}^{m}a_{ij}X_{it}\leq d_{it}\;\forall \; i,t\text{ and }I_{it}=I_{i,t-1}+X_{it}-S_{it}\; \forall \;i,t$ D $\sum_{i}^{m}a_{ij}X_{it}\leq d_{it}\;\forall \; i ,t\text{ and }I_{it}=I_{i,t-1}+S_{it}-X_{it}\; \forall \;i,t$
GATE ME 2021 SET-2      Inventory Control
Question 3 Explanation:
\begin{aligned} m & \rightarrow i \ldots m \leftarrow \text { product } \\ n & \rightarrow i \ldots n \leftarrow \text { workstation } \\ a_{\bar{j}} & \rightarrow \text { time } \end{aligned}
$r_{i} \rightarrow$ selling price
$h_{i} \rightarrow$ holding cost
$T \rightarrow t=1,2, \ldots T$
$d_{i t} \rightarrow$demand of product in time t
$c_{j t} \rightarrow$capacity of workstation in time t
$S_{i t} \rightarrow$Number of product sold in time t
$x_{i t} \rightarrow$Number of product produced in time t
$I_{i t} \rightarrow$Number of product i hold in inventory at end of period t
Capacity constraint
$a_{i j} x_{i t} \leq c_{j t}$
Inventory constraint
$l_{i t}=I_{i, t-1}+x_{i t}-S_{i t}$
 Question 4
A PERT network has 9 activities on its critical path. The standard deviation of each activity on the critical path is 3. The standard deviation of the critical path is
 A 3 B 9 C 27 D 81
GATE ME 2021 SET-2      PERT and CPM
Question 4 Explanation:
In CPM,
$\begin{array}{l} \sigma=\sqrt{\text { sum of variance along critical path }} \\ \sigma=\sqrt{\sigma^{2}+\sigma^{2}+\ldots .+\sigma^{2}} \\ \sigma=\sqrt{9 \sigma^{2}}=\sqrt{9 \times 9}=9 \end{array}$
 Question 5
Activities A, B, C and D form the critical path for a project with a PERT network. The means and variances of the activity duration for each activity are given below. All activity durations follow the Gaussian (normal) distribution, and are independent of each other.

$\begin{array}{|l|c|c|c|c|}\hline \text{Activity} & \text{A} & \text{B} & \text{C} & \text{D} \\ \hline \text{Mean (days)} & \text{6} & \text{11} & \text{8} & \text{15} \\ \hline \text{Variance (days^{2})} & \text{4} & \text{9} & \text{4} & \text{9}\\ \hline \end{array}$

The probability that the project will be completed within 40 days is _____ (round off to two decimal places).
(Note: Probability is a number between 0 and 1).
 A 0.25 B 0.5 C 0.65 D 0.85
GATE ME 2021 SET-1      PERT and CPM
Question 5 Explanation:

PERT-CPM
\begin{aligned} T_{S} &=40 \text { days, } T_{E}=6+11+8+15 \\ T_{E} &=40 \text { days, } \\ 2 &=\frac{T_{S}-T_{E}}{\sigma}=0 \rightarrow 50 \% \end{aligned}

Probability of completing project in expected time is always 0.5.
 Question 6
A set of jobs A, B, C, D, E, F, G, H arrive at time t = 0 for processing on turning and grinding machines. Each job needs to be processed in sequence - first on the turning machine and second on the grinding machine, and the grinding must occur immediately after turning. The processing times of the jobs are given below.

$\begin{array}{|l|l|l|l|l|l|l|l|l|}\hline \text{Job} & \text{A} & \text{B} & \text{C} & \text{D} & \text{E} & \text{F} & \text{G} & \text{H} \\ \hline \text{Turning (minutes)} & \text{2} & \text{4} &\text{8}&\text{9} &\text{7} &\text{6} &\text{5} &\text{10} \\ \hline \text{Grinding (minutes)} & \text{6} & \text{1} &\text{3} &\text{7} &\text{9}&\text{5} &\text{2} &\text{4} \\ \hline \end{array}$
If the makespan is to be minimized, then the optimal sequence in which these jobs must be processed on the turning and grinding machines is
 A A-E-D-F-H-C-G-B B A-D-E-F-H-C-G-B C G-E-D-F-H-C-A-B D B-G-C-H-F-D-E-A
GATE ME 2021 SET-1      Queuing Theory and Transportation
Question 6 Explanation:
Sequencing,
$\begin{array}{|c|c|c|} \hline A & (2) & 6 \\ \hline B & 4 & (1) \\ \hline C & 8 & (3) \\ \hline D & 9 & (7) \\ \hline E & (7) & 9 \\ \hline F & 6 & (5) \\ \hline G & 5 & (2) \\ \hline H & 10 & (4) \\ \hline \end{array}$
AEDFHCGB
 Question 7
For a single item inventory system, the demand is continuous, which is 10000 per year. The replacement is instantaneous and backorders (S units) per cycle are allowed as shown in the figure.

As soon as the quantity (Q units) ordered from the supplier is received, the backordered quantity is issued to the customers. The ordering cost is Rs. 300 per order. The carrying cost is Rs. 4 per unit per year. The cost of backordering is Rs. 25 per unit per year. Based on the total cost minimization criteria, the maximum inventory reached in the system is ________ (round off to nearest integer).
 A 181.94 B 1319.09 C 1137.14 D 1802.16
GATE ME 2020 SET-2      Inventory Control
Question 7 Explanation:
Given data: D=10000 items/year, $C_{o}$=Rs. 300/order,
$C_{h}$=Rs. 4/unit/year, $C_{b}$=Rs. 25/unit/year,
For minimum tool cost
\begin{aligned} \text { Quantity ordered, } Q=& \sqrt{\frac{2 D C_{o}}{C_{h}} \times\left(\frac{C_{b}+C_{h}}{C_{o}}\right)}\\ &=\sqrt{\frac{2 \times 10000 \times 300}{4} \times\left(\frac{25+4}{25}\right)} \\ Q &=1319.09 \text { unit } \end{aligned}
Now, for minimum cost, optimum units backordered
\begin{aligned} (Q-S) \times C_{h}&=(S) \times C_{b}\\ S\left(C_{b}+C_{h}\right) &=Q \times C_{h} \\ S &=\frac{1319.09 \times 4}{(25+4)}=181.94 \text { units } \end{aligned}
Maximum inventory in the system, $Q_{\max }=Q-S$
\begin{aligned} &=1319.09-181.94 \\ &=1137.15 \text { unit } \\ &\approx 1137 \text { units } \end{aligned}
Alternate:
Maximum inventory in system $=\sqrt{\frac{2 D C_{o}}{C_{h}} \times\left(\frac{C_{b}}{C_{b}+C_{h}}\right)}$
$Q_{\max }=\sqrt{\frac{2 \times 10000 \times 300}{4} \times\left(\frac{25}{29}\right)}=1137.147 \text { units }$
 Question 8
The forecast for the monthly demand of a product is given in the table below.

The forecast is made by using the exponential smoothing method. The exponential smoothing coefficient used in forecasting the demand is
 A 0.1 B 0.4 C 0.5 D 1
GATE ME 2020 SET-2      Production Planning and Control
Question 8 Explanation:
\begin{aligned} F_{t}&=F_{t-1}+\alpha\left(D_{t-1}-F_{t-1}\right)\\ \text{For 2nd month }F_{t}&=31.8, \text{ for }1^{\text {st }} \text{month}\\ F_{t-1} &=32 \text { and } D_{t-1}=30 \\ 31.8 &=32+\alpha(30-32) \\ 2 \alpha &=32-31.8 \\ \alpha &=0.1 \end{aligned}
 Question 9
Consider the following network of activities, with each activity named A-L, illustrated in the nodes of the network

The number of hours required for each activity is shown alongside the nodes. The slack on the activity L, is ________ hours.
 A 1 B 2 C 3 D 4
GATE ME 2020 SET-2      PERT and CPM
Question 9 Explanation:
Time along path A-B-C-F-I-J-K = 42 hours
Time along path A-B-C-E-H-L = 31 hours
Time along path A-B-C-D-G-H-L = 40 hours
Slack for L = 42 - 40 = 2 hours
 Question 10
In Materials Requirement Planning, if the inventory holding cost is very high and the setup cost is zero, which one of the following lot sizing approaches should be used?
 A Economic Order Quantity B Lot-for-Lot C Base Stock Level D Fixed Period Quantity, for 2 periods
GATE ME 2020 SET-2      Production Planning and Control
Question 10 Explanation:
In Lot-for-lot, holding cost is high and ordering cost is less.

There are 10 questions to complete.


text:
Acta Entomologica Sinica ›› 2020, Vol. 63 ›› Issue (8): 961-972.

• RESEARCH PAPERS •

### Role of the cytochrome P450 gene AsCYP6Z2 in the maintenance of deltamethrin resistance in Anopheles sinensis (Diptera: Culicidae)

HAN Bao-Zhu, CHE Lin-Rong, CHEN Xiao-Jie, YAN Zhen-Tian, QIAO Liang*, CHEN Bin*

1.  (Institute of Entomology and Molecular Biology, Chongqing Normal University, Chongqing 401331, China)
• Online:2020-08-20 Published:2020-09-09

Abstract: 【Aim】 To investigate whether the cytochrome P450 gene AsCYP6Z2 is related to the pyrethroid resistance in Anopheles sinensis. 【Methods】 The coding region of the AsCYP6Z2 gene of  An. sinensis was cloned. The expression profiles of this gene in different developmental stages of female mosquitoes of the deltamethrinsusceptible strain (WX-LS) and resistant strain (YN-LR) of An. sinensis and its expression profiles in different segments of female pupae of WX-LS were detected by real-time quantitative PCR (qPCR). The posterior segment of female pupal abdomen was incubated with 25 mg/mL deltamethrin solution and acetone (control), respectively, and the consequent expression response of CYP6Z2 between the deltamethrin treatment group and the acetone control group was compared by qPCR. After injection with dsAsCYP6Z2 (the RNAi group) and dsEGFP (the control group) into the 10 h old pupa, the difference in the expression level of AsCYP6Z2 between the RNAi group and the control group was compared by qPCR, the knockout rate of female adults after exposure to 0.05% deltamethrin film in 1 h and the mortality of female adults after exposure to 0.05% deltamethrin film for 1 h and then recovered for 24 h in the RNAi group and the control group were determined by bioassay method. Furthermore, the amino acid residues interacting with deltamethrin were predicted by using molecular docking. 【Results】 The coding region of AsCYP6Z2 gene (GenBank accession no.: MT840336) was cloned, and its ORF is 1 251 bp in length, encoding 416 amino acids without signal peptide and transmembrane domain. Developmental expression profiles revealed that AsCYP6Z2 gene was highly expressed in the period from 30 h old pupa to 3 h old adult, and its expression level in the resistant strain was significantly higher than that in the susceptible strain. Tissue expression profiles revealed that AsCYP6Z2 was highly expressed in the posterior segments of abdomen, followed by in the anterior segments of abdomen, throax and head. At 12 h and 24 h after incubation of the posterior segments of female pupal abdomen with 25 mg/mL deltamethrin solution, the expression level of AsCYP6Z2 increased by 4-fold and 13-fold as compared with the control (incubated with acetone), respectively. After RNAi of AsCYP6Z2, the expression level of AsCYP6Z2 gene in the RNAi group decreased by about 80% compared with the control group (dsEGFP injection group). When the female adults were exposed to 0.05% deltamethrin film in 1 h, the individuals in the RNAi group showed significant knockdown phenomenon about 20 min in advance, and the knockdown rate was significantly higher than that in the control group. In addition, the mortality of individuals in the RNAi group after exposure to 0.05% deltamethrin film for 1 h and then recovered for 24 h increased by 17% compared to the control group, indicating that silencing the AsCYP6Z2 gene results in a significant increase in mosquito sensitivity to deltamethrin. The molecular docking between deltamethrin and the predicted AsCYP6Z2 protein showed that deltamethrin can enter the binding pocket of AsCYP6Z2 protein, forming a Pi-sulfide interaction with Cys-155 and generating more stable hydrogen bonds. The side chain can also form a stable hydrophobic interaction network with Ala-165, Val-72, Leu-76, Leu-82, Ala-24 and other amino acid residues of AsCYP6Z2. 【Conclusion】 The results indicate that the AsCYP6Z2 gene is involved in maintaining the deltamethrin resistance phenotype of An. sinensis, laying a foundation for further exploring the molecular mechanism of AsCYP6Z2 gene in the metabolism of pyrethroid insecticides.