Catholic Russia Converted Ideas

It follows some Mathematics... Concerns: Post Secondary Maths, levels: 1st to 3rd year after secondary Maths (higher education or post secondary equivalent).

Maths Post-secondary: a bit of Convolution Product of Cauchy

Prerequisites

At least complete Maths secondary school (at least 12th grade), but is better to have already level 14 completed.... To feel more comfortable with the subject, ideally still 1 or 2 years maths after high/secondary school should be considered. Some Knowledge of manipulation Double Summations, Series, Power Series could help. Other Web sites, e.g., Wikiversité, with subjects such as Series, Power Series, Double Summations, in French (levels 14 and 15), may help to understand better the subject. Automatic translation possible with Chrome and Edge. Please refer to similar translation instructions for www.christianideas.eu here, on top of page for better idea...

Details of Demo Generalized Cauchy Product of Wikipedia

As exercise, some details of Demo Generalized Cauchy Product of Wikipedia, added by me, are now available.

Changes seemed to be approved by Wikipedia (English). But,if, eventually, those changes are removed, a backup copy of those demo details still remains here available.

Practicing Product of Series and Polynomials

Please enjoy some theory practice / solved exercises over Convolution Product Cauchy: Product of Polynomials and Series...

Sorry, for the moment only draft versions, too much time would be lost with equation editor details... Comments corrections are welcome, you can send emails via page www.christianideas.eu/index.php/contact...

Some Practice: Understanding Multi Summations in Multinomial Formula (a bit improved: 31/10/2020)

Please enjoy some theory and practice over the Theorem of the Multinomial, explaininig multi Summations in detail, using Convolution Product Cauchy, now with small improvements...

Paradox: Cardinality of ℝ has order 2^|ℕ| = ℵ₁, but also 2|ℕ|² = ℵ₀! (added: 23.9.2021).

This demo exists already, I'm going only to expose it in my own way. This is common in maths, demonstrations...

How can we represent a real number?

A real number is a positive, negative number (or zero), thus a number x of style: x = -289.5872 .

Because real numbers can grow up to infinite in absolute value, but also the decimal amount (right to the comma) can have an infinite number of digits, we could represent the real number x in this way:

x = sign * d_i1d_i2d_i3...d_in.d_f1d_f2d_f3...d_fm

If the real number x equals -289.5872 this notation means:

the sign of x is '-1', because x is a negative number.

The Integer part of x, left to decimal point equals 289, dus:

d_i1d_i2d_i3=289

with n=3, meaning the integer value of x is composed of 3 digits.

Right to decimal point '.', we have the decimal part of x, represented here by '5872'.

Thus, here, d_f1d_f2d_f3...d_fm equals 5872

where m = 4 (fractional part has 4 digits), where this 5872 should be seen as 0.5872 x 10^m

and thus d_f1=5, d_f2=8, d_f3=7, d_f4=2 .

The real number x can also be seen as:

x = sign*x_i.x_f=sign * d_i1d_i2d_i3...d_in.d_f1d_f2d_f3...d_fm,

where sign is the applied sign of the real x

and

x_i and x_f are natural positive (or null) numbers, thus,

sign ∈ {-1,1},

x_i ∈ ℕ and x_f ∈ ℕ .

This means that x_i=⌊|x|⌋ can be any natural number.

The same for x_f, the fractional part of real x, right to the comma.

And how many different possibilities we have for ⌊|x|⌋?

Because x_i can be any natural number, the total possibilities is the cardinality of ℕ self, thus,

|ℕ| = ℵ₀ .

In a similar way, the cardinality of x_f is also the cardinality of ℕ self, thus, also |ℕ| = ℵ₀.

Seen in this way, the cardinality of real number x is very easy to estimate. Even the ambiguity 0∈ ℕ is only a less important detail for this purpose.

Thus, the cardinality of a real number x , |x|= |sign ∈ {-1,1} |*| x_i|*|x_f|

Please note that, because x_i = d_i1d_i2d_i3...d_in is a positive integer number (or null) of n digits, and each digit can be any number ∈ {0,1,2,3,4,5,6,7,8,9}, | x_i|= 10ⁿ.

This means that there are 10ⁿ different ways to represent ⌊|x|⌋ (in practice |ℕ|= ℵ₀.

Thus, |x| = 2 * |10ⁿ|*|10^m|=2*|ℕ|* |ℕ|.

Assuming 0 is counted twice, because 0 ∈ x_i and 0 ∈ x_f => we have to remove 1 to the value of |x| calculated above.

Thus, |x| = 2 * |10^n+m|-1 = 2*|ℵ₀|² -1 .

Because n ∈ ℕ and m ∈ ℕ => n+m ∈ ℕ also. They may have all cardinality of |ℕ| also^*. Speccially irrational numbers like ϖ or √2 have decimal part with infinite digits... others are much smaller like e. g. 0.5=1/2 ...

Thus, |x| = 2*|10^|ℕ|| -1.

Because 10 = 2^log₂10, we have also:

Thus, |x| = 2*2^{log₂10*|ℕ|} -1.

Thus, |x| = 2^{1+ log₂10*|ℕ|} -1.

Thus, we can estimate the order of |x| = 2^ℵ₀, which defines the cardinality of ℝ.

* - Watch out: contradiction possible, because |ℕ| = 2^log₂|ℕ| and |x| = 2*|ℕ|*|ℕ|-1 = 2* 2^2log₂|ℕ|-1 = 2^{1+ 2log₂|ℕ|} -1. Or log₂|ℕ| should be different from ℵ₀, because ℵ₁= 2^ℵ₀ => ℵ₀= log₂ ℵ₁.

This results from concept of infinite, which may introduce such ambiguities and may lead afterwards to paradoxes, e.g. ∞ x ∞ = ∞² = ∞. why not consider |ℕ|² >|ℕ|? It should be if |ℤ|>|ℕ|... Not to accept this while consider ℵ₁ > ℵ₀ may lead to incoherences, even paradoxes...

The easiest is to keep accepting theory of infinite sets as it is... but in this case, one should watch out however the coherency of results, when dealing with the infinite. E.g. I don't accept that |ℤ|=|ℕ|.

It's evident |ℤ|=2*|ℕ| + c, where c is a correction factor (e.g. -1, according to definition of the moment for |ℕ|)...
We can also see it in this way: |ℤ| is of same order of |ℕ| which is ℵ₀. This reasoning helps to understand official cardinality theory => ∞/2 = ∞... but it's not the only logic...

There are different logics when we use the concept infinite... Because of this, the logic to be used should be seen case per case... present theory is already valid in most of the cases, only watch out incoherences...

It could also be possible that I introduced errors when claiming also the possibility that | ℝ|= ℵ₀ ... Officially it is ℵ₁, and we can also demonstrate it here... eventually further analysis needed? or it doesn't worth it... ???

Demonstrations eventually better explained over | ℝ| exists, e. g., at Wikipedia, cardinality of continuum. But it worth to analyze and practice it, speccially for those with university scientific profile...

Maths Post-secondary:Complex Analysis (updated: 31.10.2020)

Prerequisites

Hyper-geometric series and functions requires already a post secondary knowledge of maths. It's recommended to have knowledge of 1st 2 years general maths of a scientific high school course or equivalent (behalf eventually math's specialization's).

Practice over Hypergeometric Function to get cos(z)

As reference, you may begin with wikipedia article "Generalized Hypergeometric Function".

Please enjoy Solved Exercise: proof ₀F₁ ( ; 1/2; -z²/4) = cos(z), using rising factorial formula for hypergeometric series and functions. If God helps, I'll try to set this in wikipedia, Generalized Hypergeometric Function: The series ₀F₁. Let us see if it is approved. A backup of wikipedia edition is already available here A backup of wikipedia edition is already available here.

Sorry, for the moment only draft versions, too much time would be lost with rigorous equation editor details... even so, several hours already lost to try to show exercises + demonstrations with a +- adequate presentation. Comments corrections are welcome. You can send emails via page www.christianideas.eu/index.php/contact...

Possibility of services help to studies, e. g. to students maths up to 3rd secondary, but only here near to NW Brussels(no question to rewrite new books of maths...), more details, refer to page contact, address...

Possibility also of courses discernment christian ideas, e. g., to institutions, enterprises, willing to pay for such services e.g schools to help instructors and or students for better discernment pro God, now that official teaching is becoming anesthetized in some domains => compare with 'about' section, for a 1st idea...

(updated: 30/10/2021) Section Computer Science

Left: Our Lady, Nordic Look. Right: Those who honor Jesus, with full trust, through this picture , shall be saved

(28/10/2021)Some Solutions for Threads Exercises

In this section, I'm going to expose some resolutions for the exercises proposed by the excellent book from Badr Benmammar over Threads and Concurrent Programming (Java). It is assumed implicitly that you have bought the book, in order to correctly benefit from these resolutions. You should try to solve it first and/or review the book in case of difficulties and only look the resolutions afterwards ...

The Resolutions here are based on the French version of the book. I hope he converts quick quick to true faith... not so easy in Muslim lands... here www.christianideas.eu section 'about' tries to help...

anyhow, the pedagogic quality of the book is good... excellent to begin (less superficially) with Threads if you have already some knowledge of Java programming language, Introduction to Computer Science and some knowledge of Object Oriented Programming...

If you find any error remark etc you can contact me, via page contact... Thanks.

(... with the ruse of evil in these modern times, it's better to master some post secondary subjects, if possible to have univ degree like LEIC IST Lisbon, in order to try to counter evil sophisms against true faith...)

Resolution Exercise 3 page 132: Counters

Resolution Exercise 3a page 132: Compteurs.java (pdf) Result Sample

Resolution Exercise 3b page 132: Compteurs2.java (pdf) Compteur2.java (pdf) compteurs2Result Sample

Resolution Exercise 5 page 134: Table of 7.

Resolution of Exercise 5 page 134: TableOf7Task.java (pdf) TableOf7Main.java (pdf)

You should try to solve it on your own. Anyhow it's interesting to run it, in an adequate platform, e.g., eclipse for Java, and see the results (already +- available from book)...

Resolution Exercise 7b page 137: Factorials

Resolution of Exercise 7b page 137: Factorial4.java (pdf) results of Factorial4 (pdf)

Java Threads example: car Park (based Leic94 IST)

This exercise is based on a problem proposed in Distributed Systems, 1993, LEIC (Computer Science Engineering), LEIC94, IST Lisbon.

It goes over a car park with 2 main rooms, park1 and park2, separated by a narrow hall with only 1 sense.

It is proposed to simulate cars arriving to the car park, remaining for some time in park1, using the hall to go to park2, remaining some time in park2, before exiting the park.

Here we assume park1 has place for 3 cars. 2 cars may be in the intermediate hall. 3 Cars may be parked at same time in park2.

The Car Park program proposed here is done in Java, using threads .

A basic sample output is also proposed, simulating an arrival to the car park of 15 cars. No sophisticated graphical interface, sorry. Maybe next version... ???

Another Barber Saloon Threads Resolution (updated 4/11/2021)

Still a resolution for the Sleeping Barber. I had it difficult, and had to check different bibliography, books, examples in the internet.

Finally, I did my own resolution, available here, but with help of this example on-line, univ helsinki, SleepingBarber.java (a cross check for debugging).

Resolution is based on existing examples, but it is not the same; I tried to use my own logic, it follows here below. Another resolution, thus. Some incoherences of synchronization were noticed. That's why a bit below follows an improved version. Another check for bugs + analysis of results maybe still required, but several of incoherences of 1st versions were already corrected.

the java file BarberSaloon.java (pdf).

Results: file resultsBarberSaloon.txt (pdf)
(3 outputs for the Sleeping Barber: Saloon a. 'many clients' ; b. 'normal' ; c. 'calm' ).

Improved version, BarberSaloon3:

the java file BarberSaloon3.java (pdf).

Results: file resultsBarberSaloon3.txt (pdf)
(~10 outputs for the Sleeping Barber3 java threads application : versions 'many clients' , 'saloon normal' , 'calm' ...).

(19/11/2021) Another Java Solution for the Dining Philosophers Problem

Some Considerations over the Solution Presented here

You may find in the internet and literature available (Threads, Operating Systems...) different solutions for the Dining Philosophers problem. I implemented a solution, in Java, with basic text results, and you can find here the files in pdf format.

This solution takes into account that if N Philosophers are sit around a round table, only maximum ⌊ N/2 ⌋ may eat at same time and no 2 neighbors philosophers may eat at the same time (because there's not enough available 'legitimate' chopsticks for both).

In case of 7 Philosophers, thus, maximum 3 philosophers may be eating at a time and if Philosopher0 is eating, neighbors Philosopher6 and Philosopher2 have to wait a bit.

An anti starvation correction factor is added.

The chopsticks are ignored in this solution. Why? They may be used, yes, but they're not absolutely needed to implement the solution. We need one solution without deadlock and without starvation, in order to get the philosophers eating and thinking in a round table. Imposing that both neighboors are not eating, and anti circular wait criteria (maximum ⌊ N/2 ⌋ philosophers eating at same time...) + anti starvation correction, should be enough to get a correct solution.

Watch out: the solution presented here is not necessarily the most efficient... but it happens in a somewhat "spontaneously", "random" way... A mutex is used in order to access / change the shared variable NrPhilosophersEating, while a resource semaphore is added to impose a maximum of ⌊ N/2 ⌋ Philosophers eating at same time...

the java file Philosopher.java (pdf).

Results: file resultsPhilosophers.txt (pdf)
( some outputs for the Dining Philosophers problem with 5, 6 and 9 Philosophers ...).

Other resolutions are available on the internet, e. g., GeeksforGeeks: Dining Philosopher Problem Using Semaphores or The Dining Philosophers Problem, at Indiana University...

Previous resolution was a bit improved/optimized in version 2, but now it became also a bit more complex... that's why previous files remain... no spin locks used but sleep + wait synchronous (semaphores) + threads in Java; anti starvation measures improved: a minimal time criteria was added... extra synchronization practice added... => main thread is waked up when last thread (Philosoph) finishes... This exercise may help for exercise from page 144 book Benmammar threads (in french)... for solutions using the chopsticks, please refer to other solutions in available literature: books, internet... the solutions using chopsticks are not necessarily more efficient, because mutex here is used only to update shared global var...

The improved files follow here below, in .pdf format, in catholic Russia converted ideas style...

the java file Philosopher2.java (pdf)

Results: file resultsPhilosophers2.txt (pdf)
(outputs for the Dining Philosophers problem with 5, 6, 7 and 9 Philosophers ...).

(24/11/2021) Producer Consumer: Resolution Exercise 14 (french) book Benmammar Threads (page 147).

14.1. cond1: nbObj==taille

(number of objects == length)

cond2: nbObj==0

(number of objects == 0)

14.2 "last=(last+1) % length " allows circular increment of index buffer (for Producer Thread).

14.3 type of object buffer: Object [], eventually Object[length]... we could go even further here up to Integer[length]...

Object [] is more generic...

File main.java.pdf + small sample outputProducerConsumer.txt.pdf to follow here later...
the rest of the code is available in pages 146 + 147 of book Benmammar, behalf cond1 and cond2 mentionend here above...
Enjoy!
(exercise compatible Computer Science Engineering, 2nd year, Operating Systems, e.g. LEIC IST Lisbon (now Bologna version). Done by 5 year LEIC diplomed 1994 (Leic94).

(26/11/2021) Thread Synchronization: a Resolution Exercise 15 (french) book Benmammar Threads (page 148).

Here goes a 1st resolution of problem of a "one way Street", with a sample (text) output, in .pdf format.

Files available (implemented in java):

onewayStreet.java (.pdf)

FabricCars.java (.pdf)

FabricCarsFromSense1.java (.pdf)

FabricCarsFromSense2.java (.pdf)

Car.java (.pdf)

CarFromSense1.java (.pdf)

CarFromSense2.java (.pdf)

onewayStreetResults.txt (.pdf)

Enjoy!

(21/9/2021) Some Interesting Links to Help to Studies

If you subscribe by Chegg.com, you can access on-line to many solved exercises from books e.g. Apostol Maths or Operating Systems Silberschatz.

Christian Ideas Background sample.

Candle: Our Lady of the Roses Honored Exposed and Death doesn't enter inside.

Jesus Divine Mercy: Those who honor Jesus, with full trust, through this picture , shall be saved.

Jesus Divine Mercy: Those who honor Jesus, with full trust, through this picture (above), shall be saved

I try to pray for protection to all pro God of planet until 00:00h, to try to disinfest, but it's better to complement it with 24h protective prayer, e.g. attentive rosary or (easier/shorter) 7 sorrows (here further below).

http://www.christianideas.eu/#about tries to help...

Over Web site of Ideas from Catholic Russia Converted,

made in Belgium, E.U.,

www.christianideas.eu:

DISCERNMENT Criteria, e.g. true faith catho conservative non naive: risk of sect new age in Rome=> the Apocalypse... => better to be in state of grace go to confession to catholic priest asap, after Benedict XVI
Risk of Great Famine => news from heaven +- serious to e.g. Enoch, G Lomax, L de Maria, J Leary...

Ideas (pro God) to (try) to resist Great Famine:
- St Onofre with a Crumb of Bread,
- Blessed grapes L Maria + S Damiano...
MODERN LIES unmasked
(Lies of Darwinism, Fake Dates...)

History + demographics since 2000BC unmask fake dates. Hominids were hybrids which existed before great Flood, confirms Jesus at from old web site from V De Tarlé apparitionsmariales.org …

Proactive Darwinism: ~mouse evolves=> bat => vampire, thus ancestor man/whale etc goes to=> Batman => Dracula... within same ~million years…
Y haplogroups DNA migrations tend to proof Atlantis sank => Ice ages before Moses crossed the Red Sea? Science & Bible theory
DANGER OF APOC after Benedict XVI => St Malachy prophecy:

CHIP 666 IN BODY, WW3, risk vaccines Pest Grippe with 666 smart particles /changing DNA RNA , throw virus (by plane) to kill vaccinated, “good” apocalyptic new age sect, THE GLOBAL EMPIRE SOCIALIST COMMUNIST OF ANTICHRIST... => lots of apocalyptic prophecy at www.tldm.org (for scenario Russia not converted)
ICON OF AUTOMATIC Eternal SALVATION
(also here above)

THOSE WHO TRUST 100% IN JESUS through THIS PICTURE SHALL BE SAVED (a Jesus of St Faustina with rays blue red)
PROTECTIONS against EVIL, but some suffering needed, sorry!
(a summary a bit further below)
IMMORTALITY SUGGESTION:

TO PRAY GOD for ETERNAL SALVATION for THOSE WHO NEEED IT MOST, CALMS 'only' DANGERS for LIFE.
(you have nothing to loose, if you feel dying, even if formula is limited …
after: begin discreet fast + attentive daily prayer(as rosary) until it calms/improves => ~30 days for diabetes,
ok not so easy, but it's better than cancer operations, (1-3 days should calm grippe…))
GLBT + Modern Sex BEHAVIOURS: Unhealthy, even KILL...
It attracts pests… Vaccine Papilloma protected only 70%...
it’s possible to attack underconscious, e.g., via discrete sorcery… => Nero case study...
***2 BILLIONs+ MURDERS*** SINCE ~1960:
the ABORTION horrors... It attracts pests…
IDEAS AGAINST AGING & GRIPPE/PEST /Evil

Dangers of Vaccins: e.g. 666 etc.
BETTER ALTERNATIVES + Pro God: Fast & prayer (good against evil => Medjugorje) until it calms... (discreet fast & prayer or in solidarity group, prayer style (attentive daily) rosary or 7 sorrows... some food may help: avoid white sugars (fruits honey better if sweet food needed), but 1/8 glass whiskey or vodka (=> let it disinfect (few minutes) at the throat…), 1/6 glass vinegar, 2 cloves raw good garlic mixed e.g. in salad to help counter pest... + immortality suggestion in dramatic cases to calm a bit and in place of dying win forces to pray a rosary /7sorrows... + details links above below

VACCINATED RISK TO DIE WITHIN ~7 YEARS WITHOUT FORMULAS PRO GOD (see above; formulas from news from heaven maybe work against vaccines… Exorcism water? miraculous medal, faithful see light cross in sky after great warning, Oils?... ?? )
IDEAS FOR A BETTER LOOK (Ladies & Veil)

How FAKE PUBS BRUNETTE & Erotica ARE KILLING CATHOLIC MARRIAGE FOR LIFE: Sarah x Agar…

(because of unhappy husband: too few beautiful ladies to choose… SOS Aesthetics...

correlations 30 years to detect trends:

... lady educating children in micro appart feels so happy as Husband with lady with not cared aesthetics... eats white sugared stuff=> brunette Scheherazade look puts husbands away...) Aesthethic care is to have heart for husband. Comparative Tables at section 'Our Lady of Fatima deserves better look'
MODERN WOMAN IDEOLOGY UNMASKED:
Demographic fall in West (+ Russia)…
stats (1950 or) 1970-2019: Germany x India…
LINKS TO some HEAVEN NEWS
Censured on Twitter: @_ChristianIdeas
At https://www.facebook.com/christian.ideas some images
Possible:
T shirts Posters “Songs” Christian Ideas and/or Russia Converted Catholic (‘made in Belgium’)...
School
(e.g. Maths, Computer Science: exercises, complements to Wikipedia…)
Christian Ideas at Linkedin
(https://be.linkedin.com/in/christian-ideas-104ba893)

If You Want to Defend Good,

PROTECTIONS against EVIL + Take Cross Recommended

(IMMORTALITY SUGGESTION at 1st Sign of Danger,

CONTRACT WITH GOD (ICON AUTOMATIC SALVATION THROUGH DIVINE MERCY), (home page or below), + Daily (better, Attentive):

Rosary, and / or

7 Sorrows, and / or

Crusade Prayer 33,

Crusade Prayer 140 (to speak without fears),

to be in state or go to confession catholic priest asap ...

+ details at christianideas.eu

I try to pray for protection all pro God of planet until 00:00h, to try to disinfest, but it's better to complement it, with 24h protective prayer, e.g., attentive rosary or (easier/shorter) 7 Sorrows prayer.

Satan demanded to God 75-100 years to destroy Vatican + money + power => www.tldm.org. Satan had that time, that money, that power. 150 years later, despite dangers + evil, Vatican still resists. Let us see evolution... ??? apocalyptic? reversal pro God (again)???

Note: www.christianideas.eu began in ~2009 and keeps growing. IT REMAINS INCOMPLETE + NOT PERFECT.

Because IT IS NOT FINISHED, NO FINAL VERSION (.pdf) EXISTS. IT KEEPS GROWING/IMPROVING and there's still many changes to do (and few time, resources...). A complete review of the web site should be done, but it's already better than nothing...

If God helps, I'll try to improve and/or correct eventual detected errors, contents + design, little by little. A backup .zip exists (link colomn above). It contains most of the site, behalf the heavy assets.

Please feel free to print it, copy it, behalf, eventually, songs ... (contents license above left with some extra explanations, but the general goal is absolute freedom for use of text + images, in a good intentioned True Faith pro God use...)

Good intentioned Pub pro God True Faith welcome!!!
(protections from God recommended then! Evil doesn't like it...)

Below: Our Lady of the Roses Honored Exposed and Death doesn't Enter inside.

(source: Jesus at old web site apparitionsmariales )

Right Click + save as to download images...

Content's License

School: Maths...

Annex: School

Section Maths...