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Mathematics Made Difficult has 39 ratings and 10 reviews. Saharvetes said: This is one of the most hilarious books about mathematics ever written, and li. Mathematics Made Difficult – Carl E. Linderholm – Free ebook download as PDF File .pdf), Text File .txt) or read book online for free. An atttempt to explain. Keywords. Counting System Fair Exchange Disjoint Neighborhood Monoid Homomorphism Isomorphic System. These keywords were added by machine and.

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Mathematicx to Book Page. Mathematics Made Difficult by Carl E. Hardcoverpages. To see what your friends thought of this book, please sign up. To ask other readers questions about Mathematics Made Difficultplease sign up. Not a question, a comment? This book was written by my Dad. I am so happy his jokes are still being enjoyed. Sadly I am too mathematically illiterate difficylt understand them but he was very funny about language too.

“Mathematics Made Difficult” by Carl E. Linderholm | jblblog

See 1 question about Mathematics Made Difficult…. Lists with This Book. This book is not yet featured on Listopia. Mar 17, Saharvetes rated it it was amazing Recommends it for: Mathematicians, undergraduate-level and higher.

This is one of the most hilarious books about mathematics ever written, and likely to remain a classic for a long time. Unfortunately it is out of print, but it is not entirely impossible to find a copy. The jokes in the book are at varying levels of mathematical sophistication, involving everything from simple puns to advanced graduate-level mathematics, and a fair bit of in-jokes about the foibles of mathematical culture. The first chapter, of about 70 pages, is on Arithmetic and includes a lo This is one of the most hilarious books about mathematics ever written, and likely to remain a classic for a long time.

The first chapter, of about 70 pages, is on Arithmetic and includes a lot of Category Theory, naturally ; the book eventually covers Algebra, Topology and Geometry. Among other highlights, its category-theoretic construction of the integers and its description of all the mess involved in the terms “improper fraction” and “mixed fraction” stand out for their utter mathematical rigour and chaos. Also notable is its lament on the sad love-life of brackets, where ‘ ‘ and ‘ ‘ though paired and meant for each other can never meet for there is always something between them.

And so on and on. Some sample quotes from the book: It is not correct in logic to prove something by saying it over again; that only works in politics, and even there it is usually considered desirable to repeat the proposition hundreds of times before considering it as definitely established. Jan 19, Simon Mcleish rated it it was amazing Shelves: Originally published on my blog here in April When I was a mathematics graduate student, this book was passed around the department, delighting those of us working in pure mathematics.

Basically, it takes apart the sort of mathematical ideas generally taken for granted, and shows that they are much more complicated than it first seems if you want to make them rigorous. There is some cheating when ideas from category theory are introduced and make the explanations even more abstract than th Originally published on my blog here in April There is some cheating when ideas from category theory are introduced and make the explanations even more abstract than they need to be.

There is, of course, a subject for a serious book in this; I can think of two without any effort Rudy Rucker’s Infinity and the Mind and the far older Bertrand Russell’s Introduction to Mathematical Philosophy. Mathematics Made Difficult is not in any sense a book which aims to educate and inform its readers. Much of the mathematics is presented in a way which would probably not make a great deal of sense to anyone not already familiar with it a course in the foundations of number theory is really the minimum needed to understand most of it, and one in category theory for the detail.

What is enjoyable about Mathematics Made Difficult is that it is very funny, full of parodies of school textbook problems and bad puns.


Mathematics is not easy to turn into humour, and this book is one of the very small number of consistently successful examples. May 20, Benjamin rated it it was amazing. I read this towards the beginning of my college math degree and most of the complexities beyond basic abstract algebra concepts were lost on me.

However, it’s plain to see that Linderholm’s main point when writing this book was to poke fun at the way that mathematics is written about and make jokes about how informal we are being when we talk about mathematics i.

Even though I’m sure I didn’t pick up on some of the book, I read this towards the beginning of my college math degree and most of the complexities beyond basic abstract algebra concepts were lost on me.

Even though I’m sure I didn’t pick up on some of the book, I enjoyed reading the whole thing. The sections of the book are prefaced with a ridiculous story pertaining to the current topic, followed by a hypothetical dialogue between the author and a mystery person doubting his claims. These sections are generally understandable to everyone; it’s only when the author begins to derive the point he is trying to make with advanced and I do mean advanced mathematics that the reader may get lost — and that’s not necessarily a bad thing, because the point is to be overly complex about things we take for granted.

I’ll be picking this one up again when I finish my undergrad to see how things have changed. However, I actually learned a good bit from the book and got a lot of laughs out of it as well, and I’d recommend it to anyone who’s read any mathematical literature. Jul 31, J. Well, this is certainly one of a kind. It’s a mathematical comedy! A spoof of mathematical-ness, but deeply rooted in mathematics itself an ‘insider’ spoof, as it were.

Tons of category theory, and tons of puns! One of the weirdest and best things I’ve ever read. I wish there were more like it. May 28, Vincent Luczkow rated it it was ok Shelves: I loved the premise, but thought almost all of the humor fell flat. It would have been much better if it had just focused on overcomplicating simple proofs. Jan 22, Roi Orzach rated it it was amazing. After reading plenty of books where every example was riddled with phrases such as, “the proof is trivial and is left as an example to the reader,” “the following is an obvious consequence of,” and other proofs from the category of proof by intimidation, this book was an extreme juxtaposition of the above.

Being what some might call a math-nut I found this book extremely comedic. This book After reading plenty of books where every example was riddled with phrases such as, “the proof is trivial and is left as an example to the reader,” “the following is an obvious consequence of,” and other proofs from the category of proof by intimidation, this book was an extreme juxtaposition of the above.

This book is a classic and should be read as it makes the reader rethink even the most seemingly simple of proofs. Although, what I enjoyed most about the book is how it showed there is no set proof method in mathematics.

I would recommend it to anyone who enjoys math, but wants a more relaxed version of a textbook. Near the end of the book, the mathematics got complicated as it approached the graduate level curriculum. My one negative comment on the book is the high price amazon sells the book for. However, the way the author satires common non-rigorous proof methods, more than makes up for the price.

For anyone with a math major, or interest in math I would not only recommend this book, but I would insist upon it. Dec 07, Ril rated it it was amazing. The best math book I’ve ever read, showing us just how many ways can a mathematician fail and how common bad explanations are around us.

May 22, Andreas Furth rated it it was amazing. This finally achieved the maghematics old goal of making mathematics even a tiny bit difficult.

Jun 17, George rated it it was amazing. Hilarious for those acquainted with the subject matter. Can be enjoyed even by undergraduate students who have taken a course in number theory. Marhematics 29, Thatsgreateric rated it it was amazing. Nobody accepts a challenge anymore. If you watch Teen Mom religiously, a glance over this textbook might just save your nth marriage. Adam rated it it was amazing Feb 14, Andrei rated it it was amazing Sep 10, Jeff Rogers rated it really difficullt it Oct 01, M rated it really linedrholm it Feb 17, Nirav rated it liked it Feb 27, Meromorph rated it it was amazing Oct 23, Marco rated it lindedholm was amazing Dec 26, Sunjay rated it it was ok Feb 11, Sean McAfee rated it liked it Mar 13, Twb rated it it was amazing Jan 21, Samuel TX Khoo rated it it was amazing Apr 09, Louis rated it it was amazing Apr 18, Olexandr Demura rated it really liked it May 25, Fred Hebert rated it it was amazing Sep 14, Linderholj rated it really liked it Feb 15, Jon Shea rated it it was amazing Nov 25, Simon Rubinstein-Salzedo rated it liked it Oct 19, Jeremy rated it it was ok Apr 20,


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Vanuit het buitenland belt u Of kijk op: Please read the explanation on this page and the next carefully before you fill in the form. You can only use this form if one of the following situations applies to you: You do not have or do not need a Regular Provisional Residence Permit MVV ; or You have an MVV for a specific purpose of stay, but you want to apply for a residence permit for a another purpose of stay; or You want to change your residence permit for a specific purpose of stay into a residence permit for a another purpose of stay; or Your personal situation has changed and you must submit a new application; or The situation of your sponsor has changed and you must submit a new application.

In all other cases, it is not possible to use this form to submit an application. On page 3 of this form you can read which form you must use to submit your application.

The institute must submit the application on your behalf. How to fill in this form Fill in one form axnvraagformulier each person for whom an application is being submitted. The form consists of 19 pages and 21 appendices. Tick under 6 page 7 the box stating the purpose of stay for which you are submitting an application for a residence permit. Which appendices you have to fill in depends on your situation.

This has been indicated in the questions and on the appendices. Do not submit this form until you have filled in this form completely and collected all the required evidence and documents, so do not submit it in parts. If your application is not complete it cannot be assessed properly. Non-payment or overdue payment and the submission of an incomplete application may slow down the handling of the application.

You can only tick one purpose of stay on each application form. Where the form refers to you or the applicant, the child is meant. Fill in one form for each child. Please answer all questions on behalf of the child. If the aanvrazgformulier is younger than 12 years of age, you do not have to fill in point 3, the Antecedents Declaration.

It is possible that the minor child has Dutch nationality by operation of law, and does not need a residence permit at all.

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This may be the case in the following situations: At the time the child was born, the child s father was living in the Netherlands and his father s father or mother was living in the Netherlands when he was born himself; or At the time the child was born, wwia child s mother was living in the Netherlands and her mother s father or mother was living in the Netherlands when she was born herself. Have you been staying with your spouse or partner or registered partner for a period of three years or longer?

Have you had, for a period of three years or longer, a residence permit to stay with a person who is permitted to stay in the Netherlands permanently or with a Dutch national? In that case, you may qualify for a residence permit for the purpose of continued residence.

The advantage of a residence permit for continued residence is that the extension of the period of validity of this residence permit Sanvraagformulier of the foreign national the applicant I have filled in this form truthfully. I know that, for the purpose of implementing the Aliens Actthe personal data filled in will be processed and passed on to the aanvraagformuiler that require these details for this purpose. I will immediately inform the IND of any changes in the situation that relates to the residence permit.

The residence permit for continued residence is therefore also called an independent residence permit. How to submit this application Before you submit the application, call 0.

The IND employee will tell you which information you must bring with you to the appointment. Each person submitting an application must be present when the application is being submitted.

You must bring the originals of all the required evidence and documents with you.

The IND verifies these documents and makes copies of them, after which the IND will return all original documents to you. The copies will be added to your application. Please visit for the nearest IND desk. What will happen with your application? Once you have submitted your application at one of the IND aavnraagformulier and you have paid the application costs feesyour application will be assessed by the IND.

According to the law, the IND must make a decision on your application within 6 months. You will receive a written notice when the handling of your application has been completed.

When your application is granted, you will receive a letter with information about where you can pick up your residence document. Period of validity of the residence permit You can use this form to submit an application for a Temporary VVR. The Temporary VVR is valid for one year, unless it becomes evident within that year that you no longer meet the conditions that apply to the purpose of stay you have stated in this application.

You must also use this form if you currently have a VVR for study purposes wi you want to make use of the so-called orientation year for highly skilled migrants.

You can only apply for a VVR aanvraagformu,ier one purpose of stay. Application costs charges Applying for a residence permit costs money. These costs must be paid the moment you submit the application. The costs depend on the purpose of stay for which you submit an application. This form does not include any information about the costs or a possible exemption from paying charges.

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aanvraabformulier If you want to be informed of the costs in advance, please visit or call 0. If the assessment of your application establishes that you do not qualify for the requested aangraagformulier permit the money will not be refunded. Other forms Do you already have a valid MVV and do you want aanvraagformulier apply for a residence permit for the same purpose? Do you have Bulgarian or Romanian nationality? In those cases, you may, if you wish aanvraagfoormulier do so, apply for a certificate of lawful residence on the basis of EU Law instead of applying for a VVR.

In that case, do not use this form, but use the form Application for Verification against EU Law certificate of lawful residence. Are you a national of the Union or a family member of a national of the Union and have you stayed in the Netherlands for a continuous period of 5 years or more?

You can also use this form if you are a national of the Union who, after having worked as an employee or on a self-employed basis, has retired or has taken early retirement, who has become permanently unfit for work, or who has worked as a frontier worker.

Do you want to extend your current residence permit? In that case, use the form Application for an Extension of the Residence Permit. Under specific conditions it is possible for formerly privileged foreign nationals, foreign nationals who remigrated with application of Article 8 of the Dutch Remigration Act, and adult individuals who qualify for re-entry, as referred to in Article 3.

In that case, use the form Aanvraag of wijziging verblijfsvergunning regulier voor onbepaalde tijd. If you want to be considered for a residence permit for reasons that are based on asylum-related grounds, you cannot use this form.

You must apply for asylum at the Application Centre in Ter Apel. For more information about this, call 0. If you want to stay in the Netherlands for study purposes, the following applies: If you want to attend a higher education course and you do not have a provisional residence permit, then do not use this form, but contact the educational institution. The educational institution must submit the application on your behalf.

New passport photo, signature, and Appendix Photo Card This form must be accompanied by a Photo Card, which is necessary for making your residence permit. Please place your colour passport photo and your signature on this Photo Card. The passport photo will be placed on a chip on the residence permit. Your signature will also be included on the residence permit.

Requirements of the colour passport photo Your colour passport photo, which you must place on the enclosed Photo Card, must meet the following requirements: Your passport photo may not have been used for a residence permit before and it must bear a clear resemblance. In addition, your passport photo must meet the Dutch passport requirements. You can find these requirements at If your passport photo does not meet these requirements, it will not be possible to make a residence permit and issue it to you.

So it is important that you send along a proper passport photo. Always have a new passport photo made by a professional photographer who is familiar with the applicable requirements for passport photos in the Netherlands.

Bring the Photo Card along when you are submitting your application. Border-crossing document When you are going to submit your application, you must also bring along your border-crossing document e.

A sticker will be affixed to this document and a copy will be made of it. This copy will be added to your application. Foreign documents Any official foreign documents about persons that are required for the application must have been legalised or provided with an Apostille stamp by the competent authorities of the issuing country.

This may relate to documents such as birth certificates, certificates of unmarried status not older than 6 monthsmarriage certificates, and court decisions regarding adoption and guardianship. This may take a great deal of time.

We therefore advice you to have the relevant documents legalised or provided with an Apostille stamp in the country of origin several months before submitting the application. Is this not the case? If this is not the case, you must have your documents translated by a translator who has been sworn in as a translator by the Dutch court. Submit the translation s and the document s together with the application to the IND. If you do not have the document s translated in the Netherlands by a translator who has been sworn in as a translator by the Dutch court, but abroad, not only the document, but also the translation must have been legalised or provided with an Apostille stamp by the competent authorities of the issuing country.

Work permit If you want to work as an employee, you will often need a work permit. For further information about the work permit, please contact UWV WERKbedrijf which is the work placement division of the Netherlands Employees Insurance Agency Tuberculosis If you want to be considered for a residence permit, you must first take a tuberculosis test and, if necessary, undergo treatment.

You must prove this with an original recent Tuberculosis Test Reference Form filled in and signed by the Dutch Municipal Health Service GGD if you are applying for a residence permit for the first time. You are also not obliged to undergo a TB test if you have one of the following documents: The IND does this to establish whether you qualify for an asylum residence permit.

The Minister for Immigration and Asylum is responsible for this. If you have any questions about this data processing, you can ask these questions in a letter to the IND, PostbusGE Rijswijk, the Netherlands.

You can also send a request to the same address asking the IND for an overview of the data processed about you.

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The source of our words is our thoughts and what’s in our heart. The words we speak are an outer manifestation of what is inside the heart. For out of the abundance of the heart the mouth speaks Matthew If we speak words of hate, then there is hate inside of our heart. If we speak words of doubt, then there is doubt and unbelief inside us. If we speak words dr.ajko love and kindness, then love reigns in our heart. Jesus said that what proceeds from our mouths is what defiles us.

Jesus said that the words we speak proceed from the deepest recesses of our heart.

For out of the heart proceed evil thoughts, murders, adulteries, fornications, thefts, false witness, blasphemies. These are the things which defile a man: Thoughts, plus the condition of our hearts, always precedes our actions or words.

Whatever is going on in the inner man eventually is displayed through words and deeds. Thoughts also trigger emotions, whether good or bad emotions. If a person continually dwells on negative thoughts, then they will continue to battle negative emotions. If a person dwells on positive thoughts, then they will feel more at peace and have a rr.aiko song of praise. The Apostle Paul, in Phil 4: He says to meditate on thoughts that are: An individual becomes in life what they continually think and say.

Your Faith Has Made You Whole: The Power of Thoughts / Dr. Aiko Hormann

A person can rise no higher than how they think of themselves or perceive something to be. As our mind and heart expands, then we are able to expand. If a person thinks and believes that they will always live in poverty and never hormaann above a certain financial level, then chances are that they won’t. Until their thinking changes on the matter, then they will remain stuck where they are.

The Lord is always encouraging us to come up higher, and to believe Him to do what seems to be impossible for us. The Word of God renews our minds.

“Science is finally catching up with the bible”

Often times we can’t seem to breakthrough and receive all of God’s blessings that He’s promised. Aiko Hormann says in her research. The soul consists of the mind, will and emotions. The heart of man is influenced by both the spirit and the soul. At salvation, our spirits were saved. But our souls are in the process of being reformed and conformed into the likeness of Christ. The flesh part of us wants to sin and do its own thing. Our flesh carnal nature wars with our spirit. There is the daily battle of the flesh and spirit.

Making the decision to yield to the Holy Spirit involves dying to the flesh, dying to selfishness. When someone hurts us, our initial reaction is to operate in the flesh and strike back in anger. Paul said in Romans 8: So then they that are in the flesh cannot please God. But ye are not in the flesh, but in the Spirit, if so be that the Spirit of God dwell in you.

Now if any man have not the Spirit of Christ, he is none of his. And if Christ be in you, the body is dead because of sin; but the Spirit is life because of righteousness. For years I struggled with negative and foreboding thoughts because of the many years of verbal abuse. I battled daily with thoughts of unworthiness and low self-value.

I struggled with thoughts of hopelessness. It was difficult forgetting the past and not continually dwelling on past and present problems. Because of evil words spoken over my life, I battled with strongholds in the mind, believing certain lies of the devil.

Although verbal abuse was almost daily for many years and many cruel angry words were said to hormannn, there were a few lies in particular that plagued me the most — day and night. The tape would play over and over again in my mind. I seemed to remain trapped in a prison of these lies, and would weep often because I felt the situation was impossible. The Lord would confirm to me over and over again things He planned to do in my life.

He would speak through His Word, through rhema words in my spirit, and through several prophecies the same basic message spoken by many different people who don’t all know each other, spoken over the years at different times. Over the years I received at least fifteen prophecies, maybe more.

I wrote down most of them, but forgot to record some of them. So I don’t really know for sure how many prophetic words were spoken, but it was many.

Anyways, for several years I couldn’t seem to get past some verbal abuse statements said to me in my youth which was opposite of what God kept on saying to me. I seemed to give more weight to the lies spoken, then to all the words God kept on confirming to me over and over again.

I had to make a decision and choose whose report I was going to believe. I choose to believe what God says. I sure am thankful that Gormann is patient and gracious, and works with us. I was always putting myself down and condemning myself, like being a cruel taskmaster to my own self.

If someone said or did a certain thing that ticked me off, uormann trigger mechanism would go off and unhealed traumatic memories would flood my mind and I would experience the emotions related to the event of a particular memory.

The primary area that the enemy targets is our mind. If he can lead us into deception, then he has a certain amount of control over us. And as was said earlier, we are in life what we think and say.

When the devil gets horkann to believe a lie, then the lie becomes a stronghold in the mind.

It entraps us into a dr.aoko of our own limited or wrong thinking. A stronghold causes us to believe a lie rather than God’s truth. A stronghold is imaginations that exalt themselves above the knowledge of God or in other words, the person with the stronghold in the mind exalts the lie above the truth of God’s Word.

What’s New

The lie carries more weight than what God says. I first learned about Dr. Aiko Hormann is a Christian research scientist filled with the Holy Spirit who specializes in the functions of the brain. In addition to her medical expertise from her research, she has many years of experience in the area of deliverance and ministering healing to the soul mind, will and emotions. Hormann explains in detail the correlation between the spirit, soul, and body with the use of visual charts and illustrations.

She talks about the war between the flesh and spirit, the condition of the heart, the renewal of the mind, strongholds in the mind, obsessive thought patterns, and how to get free. She also talks about healing for the emotions and healing for past memories. She talks about the power of thoughts literal power, yet unseen power.

Hormann discovered through research and actual studies that thoughts carry more power activity than sound waves emitted from a local radio or television station. Thoughts are very powerful, but words are even MORE powerful.

Aiko Hormann talks about the airwave activity of thoughts, depending on positive thoughts or negative thoughts. Worshipping the Lord and dwelling on God’s Word invite angelic good angelic visitation, whereas thoughts of hate and unbelief are an invitation to demonic activity seeking to find a door or entrance to wreak havoc in your life. If a born again Christian has areas of their soul that are unhealed, especially in the mind, then the devil takes advantage and attacks with oppression, harassment, deception believing lies.

Hormann says that sin, old memories, past hurts, negative emotions, etc clog the flow of the Holy Spirit in our lives, and blessings are delayed. When our mind and heart gets unclogged, then the river of the Holy Ghost is no longer dammed up. She also talks about the parts of the brain that store memories. When something traumatic or hurtful happens, the memory is stored in a certain part of the brain like a computer file.

And not only the memory is stored in a file, but the emotions that go along with the memory are also stored. Hormann gave the names of these parts of the brain there is more than one area of the brain that stores memories. When a trigger mechanism goes off like someone doing something to push your buttonsthen that old computer file in the brain comes up and you experience the emotions you originally experienced when the event originally took place. Hormann explains that actually God has placed within our body three brains that control the body, mind and emotions and explains it in detail in her teaching on the 3 brains: Aiko Hormann says that when she prays for people concerning the healing of memories and emotions, then she also includes in her prayer the physical aspect.

She identifies the exact name of the part of the brain that stores memories, and prays that the file in the brain that stores the old memory would be healed and that the trauma and emotions attached to the memory would be disconnected from the file. It doesn’t mean a person necessarily forgets what happened, but that the emotional and psychological responses that are triggered from memories are no longer there.

Aiko Hormann said that she once ministered to a woman who had four ongoing issues that she had been battling with for years. Second, she battled with fear. Third, she struggled with severe anxiety. Fourth, whenever her husband would show her affection, even non-sexual, she would jump out of her skin. The first thing Dr. And by a word of knowledge 1 Corinthians Aiko Hormann that the woman had been sexually violated as a child.

The woman recalled that indeed she had been molested by an uncle.


H Ansari-Toroghy, F FarshadifarOn comultiplication modules. Korean Ann Math, 25 (2) (), pp. 5. H Ansari-Toroghy, F FarshadifarComultiplication. Key Words and Phrases: Multiplication modules, Comultiplication modules. 1. Introduction. Throughout this paper, R will denote a commutative ring with identity . PDF | Let R be a commutative ring with identity. A unital R-module M is a comultiplication module provided for each submodule N of M there exists an ideal A of.

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Let G be a group with identity e. Let R be a G -graded commutative ring and M a graded R -module. In this paper we will obtain some results concerning the graded comultiplication modules over a commutative graded ring. Graded comultiplication module ; Graded multiplication module ; Graded submodule. Graded multiplication modules gr -multiplication modules over commutative graded modulfs have been studied by many authors extensively see comultkplication 1 — 7 ].

As a dual concept of gr -multiplication modules, graded comultiplication modules gr -comultiplication modules were introduced and studied by Ansari-Toroghy and Farshadifar [8]. Here we will study the class of graded comultiplication modules and obtain some further results which are dual to classical results on graded multiplication modules see Section 2. First, we recall some basic properties of graded rings and modules which will be used in the sequel.

We refer to [9] and [10] for these basic properties and more information on graded rings and modules. Let G be a group with identity e and R be a commutative ring with identity 1 R. Let I be an ideal of R. An ideal of a G -graded ring need not be G -graded. Let R be a G -graded ring and M an R -module. In this case, N g is called the g – component of N.

Let R be a G -graded ring and M a graded R -module. A graded submodule N of a graded R -module M is said to be graded minimal gr – minimal if it is minimal in the lattice of graded submodules of M. A graded R -module M is said to be gr – uniform resp. A graded R -module M is said to be gr – simple if 0 and M are its only graded submodules. A graded R -module M is said to be gr – Artinian if satisfies the descending chain condition for graded submodules.

A non-zero graded submodule N of a graded R -module M is said to be a graded second gr – second if for each homogeneous element a of Rthe endomorphism of M given by multiplication by a is either surjective or zero see [8].

The following lemma is known see [12] and [6]but we write it here for the sake of references. Let R be a G – graded ring and M a graded R – module. Then the following hold: If M is a gr – comultiplication gr – prime R – modulethen M is a gr – simple module.

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Let K be a non-zero graded submodule of M. By[ 8Lemma 3. Therefore M is a gr -simple module. Let R be a G-graded ring and M a graded R – module. This completes the proof because the reverse inclusion is clear.

On semiprime comultiplication modules over pullback ringsAll

Recall that a G -graded ring R is said to be a gr -comultiplication ring if it is a gr -comultiplication R -module see [8]. Let R be a gr comultiplixation comultiplication ring and M a graded R – module.

If M is a gr – faithful R – module, then for each proper graded ideal J of R0: Let J be a proper graded ideal of R. A similar argument yields a similar contradiction and thus completes the proof.

By [ 8Theorem 3. Let R be G – graded ring and M a gr – comultiplication R – module. If every gr – prime ideal of R is contained in a unique gr – maximal ideal of Rthen every gr – second submodule of M contains a unique gr – minimal submodule of M.

Let N be a gr -second submodule of M. Since N is a gr -second submodule of Mby [ 8Proposition 3. Thus by [ 8Lemma 3. Let R be a G – graded ringM a gr – comultiplication R – module and 0: Let N be a gr -finitely generated gr -multiplication submodule of M.

Note first that K: Since M is a gr -comultiplication module, 0: R N and hence 0: Let R be a G – graded ring and M a gr – comultiplication R – module. By [ 1Theorem 3.

Then M is gr – hollow module. It follows that M is gr -hollow module. Let R be a G – graded ring and M a gr – faithful gr – comultiplication module with the property 0: Suppose first that N is a gr -small submodule of M. Since N is a gr -small submodule of M0: Thus I is a gr -large ideal of R. Suppose first that N is a gr -large submodule of M.

Since N is a gr -large submodule of M0: So I is a gr -small ideal of R. It follows that 0: Then M is gr – uniform if and only if R is gr – hollow. Since M is gr -uniform, 0: Hence I is a gr -small ideal of R. Therefore R is gr -hollow.

Therefore M is gr -uniform. Then M is a gr – comultiplication module if and only if M is gr – strongly self-cogenerated. Suppose first that M is gr -comultiplication R -module and N a graded submodule of M. Conversely, let N be a graded submodule of M. Therefore M is a gr -comultiplication module.

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Some properties of graded comultiplication modules : Open Mathematics

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Abstract Let G be a group with identity e. Proof Let K be a non-zero graded submodule of M. Proof Let J be a proper graded ideal of R. Proof Let N be a gr -second submodule of M. Proof Let N be a gr -finitely generated gr -multiplication submodule of M. Proof Note first that K: Proof Suppose first that N is a gr -small submodule of M. Proof Suppose first that N is a gr -large submodule of M.

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PJME – Motorcycle Engineers, 2 stroke engine specialist aprilia cagiva We only use SPS Re-boring machines that can bore from 35m/m up to m/m. Reboring the engine will increase your displacement and the power of the engine. Not all engines can be rebored read our rebore article for. Cylinder Block Reboring. Engines are subject to wear and stress from day-to-day driving, overheating and overloading. Contaminates that enter the engine.

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Customizing a car guide Read more Sport Catalysts Power gains from a sports catalyst Read more Wide body kits and flared arches Read more Wheel Painting Painted alloy wheels — painting your wheels. Need for speed pro street Read more Join our forum today and benefit from overposts on tuning styling and friendly car banter. You will also have full access to the modifed car gallery, project car updates and exclusive member only areas.

All car owners of all ages and from all countries are welcome. Please share this page with your friends on: You can increase the power of an engine by increasing its capacity. This is a fairly involved process and requires a good deal of research and preparation.

Unless you want to have to retrace your steps and go a different route midway in to the job. However there are a few things we should take into account. The cylinders are the main part of any engine and is where compression and combustion takes place.

A 1 litre engine has a cylinder capacity equal in volume to 1 litre 0. The mixture is then compressed ready for ignition and combustion within the cylinder. The ratio of compression is another key element in an engine and if it is too high you can create engine knock also known as detonation so this is another thing to factor in when increasing the cylinder capacity of an engine. A cylinder comprises usually a cast iron block but in some engines constructed of aluminium there is a steel liner fitted such as those pioneered by Alfa Romeo.

In this article we are talking primarily of cast iron blocks as these have more scope for cylinder capacity increasing. Essentially the more you start with the bigger the power gain will be. If you have an aluminium block you may be able to fit a slightly thinner liner and your only other option would be a stroker kit which is something torquecars will cover in a future article in more detail.

Drilling out the cast iron block to a wider dimension will increase the cylinder capacity. Obviously with a larger diameter cylinder you will need to match this to a larger diameter piston. While this sounds like a simple job you must drill out maintaining concentricity ensuring they are machined parallel to the crank centre line and to the same deck height. Remember to always cut a cross hatch pattern into the cylinder wall to assist with bedding in the piston rings and maintaining a good compression ratio.

Do not attempt to do a rebore yourself with a mill as you will not get a good enough finish – it will create chatter marks whereas a proper jig borer will be accurate to within a thousandth and then finished with a precise honing.

Blocks are often similarand even engines have the same block but the internal cylinder dimension is different. In the case of these engines a rebore to a larger size and the fitting of pistons from the larger sized engine will effectively increase the engine cylinder capacity. In some rare cases the only difference between the larger sized engine is the shape, size and profile of the pistons.

After the cylinder rebore get the chamber volume measurements and machine the heads to balance these as well removing any material necessary to get the Compression Ratio right.

Don’t be surprised if you can’t get pistons to match your chosen rebore dimension if you have not done the research first. A proper machine shop will tell you what cylinder dimensions work best with which piston and they will also take stress tests to determine the maximum amount or reboring that the block can handle.

The other way of increasing the engine size is by using a stroker kit. The crank in a stroker kit allows a much longer stroke in the engine thereby increasing the cylinder capacity. Common kits increase the 2. Combining a stroker kit with a rebore will maximise the power increase available if done properly.

The cc’c of enyine motor are governed by bore x stroke x of cylinders. If your engine suffers from a scored cylinder and is suffering from low compression you may look at reboring the engine and while you are at it you may just as well bore it out to a greater capacity and fit new pistons to match the larger bore. When stripping down an rngine always replace the cylinder head bolts and rod bolts. There is no need to replace the main bearing cap bolts with new ones.

It is also worth replacing the core plugs which pop out when the engine freezes. When engines are left without coolant and engine oil for more rehoring a few days corrosion can be a real problem.

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Even when buying an engine from a scrap yard or doing an engine swap TorqueCars would recommend stripping it down first, replacing worn parts, and rebuilding it to save problems later on. At least replace the core plugs, the head gasket and cylinder head bolts and while these are off you get an opportunity to inspect the engine for damage and can decide in advance whether a rebore, re machined crank and new pistons would be cost effective – for the extra cost involved you will save yourself a great deal of hassle later on when the engine breaks down.

With a stripped down engine you have a fantastic opportunity for tuning and can save a small fortune if you get all of the engine modifications done at the same time so look into engine balancingfitting larger valves, gas flowed machined headcrank lightening and even a lighter flywheel and clutch as most of these will involve a great deal of man hours stripping and rebuilding the engine again. Do not use any oil additives in this run in period or for the first miles as these will stop the bedding in process.

Why not join us in the forum to discuss all aspects of car tuning with our reborimg experts and enthusiasts? This entry was filed under Engine ModsTuning. You can leave a response below or join our forum to discuss this article and car modification in detail with our members.

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If you liked this page please share it with your friends, drop a link to it in your favourite forum or use the bookmarking options to save it to your social media profile. Feedback Please use our forums if you wish to ask a tuning questionand please note we do not sell parts or services, we are just an online magazine. Mail not published required.

Your Constructive comments on this article. Am in the process of rebuilding my engine, thank you for your constructive advice. Running in only takes less than 50 miles IF dome properly and the only thing that needs RI is the rings as they are the only things in a motor that have metal to metal contact.

Suggest that you read motormans running in secrets. I drive a toyota run X i80i RSi 2zzge engine kw i recently redid the engine so i increased the diameter of the cylinder and got bigger matching pistons the car is even faster than it used to be this really does help increase horsepower. Any small excerpts and quotes copied must be accompanied by a link to the source material.

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We accept no responsibility for damage caused due to following a recommendation made on this site or in the forum. It is your responsibility to check and verify any car tuning tip, car styling tip or other articles content with a qualified mechanic before undertaking work or following instructions.

Something suitable for one model of car may be completely unsuitable for another – so we can only give generic theory. Please drive sensibly we do not endorse speeding or racing on the public highway or driving recklessly or in a manner than could endanger life or property.

Modified cars and car tuning reborung a specialist area and professional guidance should always be sought in your performance car project. Save racing for the track and keep the roads safe. We do not store or collect personally identifiable information. Cookies are used to track visitor behaviour enabling us to monitor and optimise the effectiveness of our content, and to remember your preferences and settings on this site.

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Help us improve, leave a suggestion enginw tip Click here to cancel reply. Tuning Best Performance spark plugs, rrboring coils and HT leads Remote turbo charger kit guide Superchargers – A guide to supercharger kits benefits vs disadvantages Guide to Essential Engine Cooling Mods Increase engine displacement with a rebore.

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TRATAMIENTO DE LAS FRACTURAS TORACOLUMBARES MÚLTIPLES .. de las fracturas dorsolumbares agudas no osteoporóticas mediante cifoplastia. ANATOMIA DE COLUMNAVERTEBRAL Compuesta por 24 vertebras articuladas y 9 vertebras fusionadas. . Clasificar las fracturas dorsolumbares mediante un sistema relevante en la práctica. Evaluar y mejorar las habilidades personales en.

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To demonstrate that the extrapedicular unilateral percutaneous treatment in multiple thoracolumbar fractures is effective, minimally invasive and can treat several vertebrae at the same time in the fracturass surgery.

From January to January patients with multiple vertebral fractures in the thoracolumbar junction of various etiologies were treated, of which were women and 60 men. The extrapedicular unilateral treatment shows good clinical results that are maintained over time, is performed on an dorsolumbarfs basis with minimal complications, and enables rapid incorporation of patients to their daily activities.

Our study shows that unilateral extrapedicular percutaneous kyphoplasty is an effective treatment for multiple thoracolumbar vertebral dorsolubmares. This method makes the procedure less invasive, allowing multiple levels are treated fracturss the same surgical intervention, resulting in relief of pain and stability of the spine, minimal complications and immediate return of the patient to daily activities. Minimally invasive surgical procedures; Spinal fractures; Thoracic vertebrae; Lumbar dorsolumbbares.

Spinal fractures are a big health fraacturas, with approximatelynew cases each year in the United States,of which fractruas intense pain andof which require hospitalization. Worldwide, a new spinal fracture occurs every 22 seconds. The thoracolumbar junction is characterized as being biomechanically vulnerable, i. Many of these patients become dependent and can be relegated to a wheelchair or a bed in the not too distant future.

The planning of dorsolumbars treatment of this location should have these objectives: The role of surgery in the treatment of spinal fractures is controversial. While techniques based on postural reduction and rest have remained virtually unchanged, surgical treatment has experienced constant renovation. This has been the result of three basic elements.

The objective of our study is to demonstrate that, differently from many authors who perform bilateral transpedicular kyphoplasty, the unilateral extrapedicular approach is a less invasive method that permits treating multiple levels in the same surgical procedure with few complications and that provides continued pain relief and improved quality of life to patients over time.

The study sample was made up of patients diagnosed with multiple spine fractures of the thoracolumbar junction of various etiologies, treated at the International Institute of Larkin Hospital in Miami, Florida, during the period dogsolumbares January to January Two hundred and forty-six of them were women between 45 and 93 years of age.

Informed consent was obtained from all patients and the protocol to be followed was explained to them. The diagnosis was based on a thorough physical exam supported by simple AP and lateral view x-rays, computed axial tomography with three-dimensional image reconstruction, especially dorsoljmbares the STIR sequence that clearly shows edema that appears as hyper intense in an acute fracture with compression.

A decision for surgical treatment was always preceded by failed conservative management where the primary clinical symptom was difficult-to-control pain of long evolution and progressive intensity, exacerbated when in a standing position and hindering the patient’s ability to walk, forcing bed rest.

An evaluation of pain was conducted in all cases using the Visual Analog Scale VAS and of functional quality using the Oswestry scale 11 prior to surgery, immediately following surgery, after one month, six months, and then yearly with support by telephone or in-home visits. To perform the kyphoplasty, we used the Kyphon system from Medtronic Figure 1Kyphon System Figure 2 with fluoroscopy. The patient was placed in a prone position on the operating table to achieve the extension of the thoracic and lumbar spines, and the planning of the approach was conducted by fluoroscopy.

Figure 3 In most patients, local anesthesia and sedation were sufficient, although in some cases, due to their health condition, we preferred to use general anesthesia. Once the entry points were defined, the skin was numbed with lidocaine and a 2mm incision was made for the introduction of the cannulated needle, Figure 4 though which we introduced a drill with which we created a space in the vertebral body.

At this time, a sample was taken to perform a biopsy.

The drill was removed and balloons that have radiopaque markers were introduced in order to achieve precise placement. The balloon was inflated using a contrast injection system with a volume of 4 to 5 ml and a maximum pressure of psi.

The balloon remained inflated for between 4 and 5 minutes, after which time it was deflated and removed. Then, using a device also introduced through the cannula, the PMMA was injected under low pressure. In our experience, we used Kyphx r HV-R bone cement. After waiting for five minutes, the cannula was removed and the small wound closed with Dermabond.

As regards data processing and analysis, we input the data into a percentage system where they were converted to statistical tables. In our study sample, there was predominance of female patients It should be noted that 11 of the patients treated were older than 90 years of age. Figures 5 and 6. In terms of the causes treated, most cases were from osteoporosis In terms of the location of the fractures, the thoracolumbar junction was the most affected at It is significant that 17 patients 5.

Figures 8 and 9. Most of the procedures were performed as outpatient Figures 10 and Regarding functional capacity, we achieved a reduction from We used the Oswestry scale Figure 12 to measure this indicator. In terms of the behavior of pain, there was no relief in only 5 cases, which represents 1. Figure 13 We also measured the VAS, which decreased from Surgery for vertebral fractures of the thoracolumbar spine has undergone a significant evolution mostly due to the enormous developments in radiology techniques, the intense research conducted about the biomechanics and kinetics of the spine, as well as to the new spine restoration materials, where balloon kyphoplasty plays a very important role.

Regardless of the location of the fracture, we propose using the unilateral extrapedicular technique, in which the point of entry is immediately superior and lateral to the pedicle, medial to the head of the rib and sometimes through the head of the rib in the dorsal location.

If the entry point is very lateral, the lung cavity may be perforated, and if it is very low, the segmental artery may be affected. The explanation for the predominance of women above 60 years of age could be due to the fact that the most frequent causes of idiopathic osteoporosis are advanced age and menopause.

It is also known that the tumor that most often metastasizes to the vertebrae is primary breast cancer, 17 that largely justifies our results. In agreement with reports by other authors, the most affected region in our study was the thoracolumbar spine. At first, it was thought that the ideal patient to undergo this type of procedure was that who suffered pain secondary to a fracture that persisted for more than 4 to 6 weeks.

Although a rule cannot be established, better recovery at this level of the spine is achieved the earlier the treatment is performed. According to reports from other researchers, the procedure can be performed as outpatient, 21 which was fully confirmed by our study.

With the help of telephone calls and home visits, we provided follow-up for more than two years with most of our patients. Kyphoplasty is an optimal technique for the treatment of pathological fractures.

The rapid improvement of pain maintained over time, as well as the functional recovery of the patients, make it a perfectly valid technique. Our study showed that according to what has been mentioned above, we could provide pain relief and a return to normal work, in addition to good spine stability, results that have all been maintained over time.

In a multicenter report of patients with fractures treated through kyphoplasty, the percentage of serious complications reached 0.

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Our study shows that percutaneous unilateral extrapedicular kyphoplasty is an effective treatment for multiple thoracolumbar fractures from pathological causes. It proved to be a safe method for patient dogsolumbares relief and improved functional capacity maintained over time, with few complications.

This much less invasive procedure reduces surgery time per level and permits multilevel treatment in the same surgical intervention. Minimally invasive treatment of osteoporotic vertebral body compression fractures. Current medical, rehabilitation, and surgical management of vertebral compression fractures.

J Womens Health Larchmt. Siegal T, Siegal T. Surgical decompression of anterior and posterior malignant epidural tumors compressing the spinal cord: An ex vivo biomechanical evaluation of an inflatable bone tamp used in the treatment of compression fracture. Spine Phila Pa Dorsokumbares study of complaints and their relation to vertebral destruction in patients with osteoporosis. Benign versus pathologic compression fractures of vertebral bodies: Radiology and anatomy of lumbar and lumbosacral fractures.

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Rea G, Miller C, editors. Roland M, Fairbank J. The roland-morris disability questionnaire and the oswestry disability questionnaire. Minimally invasive treatments of osteoporotic vertebral compression fractures. Kyphosis correction and ddorsolumbares restoration effects of percutaneous vertebroplasty.

Incidence of vertebral fracture in europe: J Bone Miner Res.

Occurrence of new vertebral body fracture after percutaneous vertebroplasty in patients with osteoporosis. Surgical management of primary and metastatic tumors of the spine. Fractures, dislocations, and fracture-dislocations of the spine.

J Bone Joint Surg Am. Heini PF, Orler R. Kyphoplasty for treatment of osteoporotic vertebral fractures. Initial outcome and efficacy of “kyphoplasty” in the treatment of painful osteoporotic vertebral compression fractures. Kyphoplasty treatment of vertebral fractures: Mortality after all major types of osteoporotic fracture in men and women: Retropective analysis of the outcomes of balloom kyphoplasty to treat vertebral body compression fracture VCF refractory to medical management.

All the authors declare that there are no potential conflicts of interest regarding this article. This is an open-access article distributed under the terms of the Creative Commons Attribution License.

Services on Demand Journal. December 11, ; Accepted: How to cite this article.


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1946 LEY 0065 PDF

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A full attendance is desired. Notice is hereby Kiven that every person, firm, and com pany liable to make returns under the above Acts, arc required to duly make and furnish to me in the prescribed torm or lorms a return of his or its income for the year ended 30th June.

The returns are to be furnished ot later than the dates set out herc undcr: Due date for lodsment of returns: Due date of lodg ment of returns: Em ployees who are members of the De encc Force and whose income during ip year ended 30th June. Em ployees who are members of the Defence Force and whose Income during the ‘year ended 30th June, Due date for lodf.

Id All companies — use Form C. Due date for lodgment of re turns: Gcorse and 005 Streets, Bris bane. Return forms may be obtained at the Taxation ,ey. George and Elizabeth Streets. Brisbane, or at the Taxation Depart ment. Postage on all Returns must In all cases be nald by the sender. Dated this First day ot July, We expect lo fill all- orders within next few days. All -J Employees of above firm are re quested to report for work this Mon day i Morning.

Index of /giga1/documentos//

Notice X is hereby glvm that every person, firm, and company liable to make re turns under the above Acts, are required to duly make and furnish to me in the 19446 form or forms a return of — Particulars of land owned at mldnleht on 30th June, The returns arc to be lurnished not later than the noth September, Returns are to be ad dressed to the Commissioner of Taxes. Cieorge and Elizabeth Streets. Taxation Building, George and Elizabeth Streets, Brisbane, ‘ostaec on all returns must in all cases be paid by the sender.

Dated this First’ day of July, Com missioner of Taxss. Quarterly Meet ing postponed’ to Tuesday, 23rd’ July, owing to restrictions. Bridge Party, which was to be held on 17th July, has lieen postponed.

L Service offers for Sale by Tender with all defects, the following Vehicles: One Model Ford 12cwt. Tender ornis available al inspect’on location. Tenders close at Noon, ely July, at A.

Highest or any lender not neces sarily accepted. The lowest or any lender not necessarily accepted. District Engineer, Rock hampton. Rooting, water proofing and insulation specialists and contractors. A Quick service, sand, gravel, cement, A nshes.

Tunley, Wickham St. Louvres, best potent and price, anti-glare glass, and all colours, quotations at Timber and Joinery Yards, 44 Annerley Rd. For immediate delivery or sand.

Gravel, cement, and carriage of all other building requirements ring J or J, and J. A T Woolloongabba Hardware. Lsy SHES, 6 yds. Connolly’s steel residen tial window frames, four standard sizes.

Index of /giga1/documentos/19000479/19000479-0065

For brick or wood. Inspection of samples invited. Stuart, Wilson House, Charlotte street, Brisbane. Wanted supply of logs for Rocklea Sawmill. For gravel, sand, metal,? J- bricklayers and plasterers’ sand, re inforcing bars, and cement, drain pipes, M Petrie Bight, weatherboard building. White house, Phone J FOR sale, quantity guttering. For par ticulars Telephone M Sole agents, Queensland Pastoral Supplies. Queensland Pas toral Supplies, Bowen St.

Will not leak or crack. Immune against white ants and borers, as cood ns bricl and much cheaper — supplies available now. Phone 23, Roche W dale. Robinson Bros, Phone J Tip- truck, owner decrease the? Austra ian Machinery Co. Buy car, utility, no objection, out A of order, after 6 P. Can sell on term;;, cash to seller. The most stubborn dirt and grime yields to Snow Palm. Keep a cake ir. BEST cash ‘price offered for all makes cars, utilities. Valley, 2 doors from baths.

08 Jul – Advertising – Trove

Hancox, Ken nedy Terrace, Bardon. Utility, for essential or non-essential hiring— by the day. Phone B or BB. Maxwell, Post Office, Gladstone. Bale, Dodge Tourer, good -jnditlon. Ring M after S p. IVOR sale, Pontiac sedan. In good P order, p. Full particulars, ring Bcechmont Post Office. FORD truck, model. Jlecr, lla Milton Rd. We now have all lathes nnd other machines driven by motor Rower. We are therefore in a ‘position to undertake all mechanical and en gineering icpairs.

Pryor, Logan Road. CELL Graham 8, sedan, p. lej

M, after 6 p. Burton, Theale Terrace, Ashgrove, pey. Prompt etish’ for all makes of used cars and tru: New Internationals have ar? Permits required for sizes under 2 tons. Army Disposals all sizes key priorities, 1 to 6. Brooks, Hamilton Avenue, Surfers’ Paradise. Sunday, will pkx few extras. Lowest prices, g’teed farm milting punt cpt. Allan’s, Ann St. We are gear spe cialists to all trades. Mars Machine Tool Mfg.

Rear ends, suitable timber trailers,? A- fitted with Motors, gene rators, domestic electrical appliances, etc.