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### Retractions in Intersection Types

Mario Coppo, Mariangiola Dezani-Ciancaglini, Alejandro Díaz-Caro, Ines Margaria, Maddalena Zacchi
2017 Electronic Proceedings in Theoretical Computer Science
Moreover, the characterisation of retraction in the standard intersection types is discussed.  ...  The main result is a necessary and sufficient condition two strict intersection types must satisfy in order to assure the existence of two terms showing the first type to be a retract of the second one  ...  Type σ is a simple retract of type τ (notation σ s τ) if σ τ and R is a simple right inverse.  ...

### Proof Systems for Retracts in Simply Typed Lambda Calculus [chapter]

Colin Stirling
2013 Lecture Notes in Computer Science
in simply typed lambda calculus ρ is a retract of τ , if there are terms C : ρ → τ and D : τ → ρ such that D(C (x ρ )) = βη x DECISION PROBLEM: given ρ, τ , is ρ a retract of τ ?  ...  Bruce and Longo [STOC 85] solve problem for = β by providing a simple proof system.  ...  Retracts must share "target" type a.  ...

### Evaluation of midle ear space using a temporal bone CT 側頭骨CTによる中耳腔形態の評価

Hirokazu Kawano, Tetuya Touno, Tamotsu Morimitsu
1991 Otology Japan
The dimensions of the epitympanum in simple otitis media type and tensa adhesive type were significantly larger than those of the other types.  ...  The temporal bones were classified into six types; simple otitis media type, attic retraction type with or without cholesteatoma, tensa adhesive type with or without cholesteatoma, and normal type.  ...  The dimensions of the epitympanum in simple otitis media type and The supratubal recess in normal type was significantly larger than that of other types.  ...

### Page 210 of Illinois Journal of Mathematics Vol. 5, Issue 2 [page]

1961 Illinois Journal of Mathematics
no simple closed curve (Lemmas 2 and 6), p mele n A*) is a de- formation retract of p'(A*).  ...  same type.  ...

### Page 914 of Annals of Mathematics Vol. 40, Issue 4 [page]

1939 Annals of Mathematics
In this paper conditions will be developed under which a locally connected continuum M can be retracted onto an arc or a simple closed curve by trans- formations of the type indicated in the title.  ...  Introduction It is well known that any topological n-cell, and hence certainly any simple are, is a retract of any containing topological space; and any topological poly- hedron, in particular any simple  ...

### Page 467 of Annals of Mathematics Vol. 42, Issue 2 [page]

1941 Annals of Mathematics
is i-simple for i = 2, 3, - Proor.  ...  If n= 1 then Sj is a deformation retract of S’ — s* if and only if iS, St) = 1, or — S{°) is cyclic infinite, and if S’ — Sj” is i-simple fori = 2, 3, Proor.  ...

### Alar Rim Composite Graft: A Safe and Simple Way to Correct Alar Retraction

Jeong Jin Chun, Seok Min Yoon, Syeo Young Wee, Chang Yong Choi, Hyuk Soo Oh, Hyun Gyo Jeong
2018 Archives of Aesthetic Plastic Surgery
In this study, we propose a simple procedure that effectively and safely corrects alar retraction using an auricular chondrocutaneous composite graft.  ...  The vestibule is exposed due to alar retraction and the lateral type of alar retraction is observed.  ...

### The encodability hierarchy for PCF types [article]

John Longley
2018 arXiv   pre-print
Working with the simple types over a base type of natural numbers (including product types), we consider the question of when a type σ is encodable as a definable retract of τ: that is, when there are  ...  Furthermore, we show that the induced linear order on isomorphism classes of types is actually a well-ordering of type ϵ_0, and indeed that there is a close syntactic correspondence between simple types  ...  exploits the fact that every simple type is encodable in a pure type (see [7, Chapter 4] ).  ...

### Diverse cellular and molecular modes of axon degeneration

Lukas J. Neukomm, Marc R. Freeman
2014 Trends in Cell Biology
In this review we discuss the diversity of cellular mechanisms by which axons degenerate.  ...  The elimination of large portions of axons is a widespread event in the developing and diseased nervous system.  ...  Work in the M.R.F. laboratory is supported from the NIH, The ALS Therapy Alliance, and M.R.F. is an Investigator of the Howard Hughes Medical Institute.  ...

### Retractions of Types with Many Atoms [article]

Laurent Regnier, Pawel Urzyczyn
2002 arXiv   pre-print
We define a sound and complete proof system for affine beta-eta-retractions in simple types built over many atoms, and we state simple necessary conditions for arbitrary beta-eta-retractions in simple  ...  and polymorphic types.  ...  Acknowledgement Thanks are due to Aleksy Schubert for spotting a bug in an earlier version of this paper.  ...

### A simple but novel idea of indirect internal retraction technique of M.M. Sankar with ordinary ET tube for Anterior Cervical Discectomy and Fusion Surgery

P.Pallavan. M.ch., Research Performed at Government Stanley Medical College, Chennai, Tamilnadu, India
2019 Journal of Medical Science And clinical Research
However, until now no evidence supports the fact that whether the type of endotracheal tube (ordinary and flexometallic) and side of its fixation aid in surgical indirect internal retraction. we present  ...  It involves retraction of trachea-oesophageal complex medially and great vessels of neck laterally of for adequate exposure of anterior spinal column in cervical spine surgery.  ...  [1] The relation between retractor application and using type of ETT has rarely been mentioned in the literature.  ...

### Page 34 of The American Journal of the Medical Sciences Vol. 179, Issue 1 [page]

1930 The American Journal of the Medical Sciences
Retraction of the nipple of the malignant type has been observed now and then in every type of benign lesion of the breast, less frequently in encapsulated adenoma, a little more frequently in chronic  ...  I brought this out in 1921.4 It is well understood that retraction of the nipple of the congenital type, or of long duration, dating back to an old mastitis, is not a sign of cancer.  ...

### Page 4245 of Mathematical Reviews Vol. , Issue 93h [page]

1993 Mathematical Reviews
In Part II we consider in particular retractive nil-extensions of unions of groups.” 93h:20070 20M20 Gomes, Gracinda M.S.  ...  The important point is to find what type of subsemigroups of left simple semigroup is suitable. It is the reflexive unitary subsemigroup.  ...

### Page 6830 of Mathematical Reviews Vol. , Issue 2000j [page]

2000 Mathematical Reviews
If A isa given algebra of some type, then an algebra B of the same type is a retract injective hull of A if B is retract injective, A is a subalgebra of B, and whenever B’ is a retract injective algebra  ...  It is shown that minimal varieties generated by simple algebras of type 2,3 or 4 are residually small iff they are congruence modular.  ...

### Page 1064 of Journal of Applied Physics Vol. 26, Issue 9 [page]

1955 Journal of Applied Physics
This result is in disagreement with the apparent superposability found for retraction curves of filaments of this same type by Cleereman, Karam, and Williams.*?  ...  to be the case for simple viscoelastic systems."  ...
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