A very weak square principle

1997 ◽  
Vol 62 (1) ◽  
pp. 175-196 ◽  
Author(s):  
Matthew Foreman ◽  
Menachem Magidor
Keyword(s):  
Ad Hoc ◽  
Free Abelian Group ◽  
Weak Version ◽  
Fourth Section ◽  
The Third ◽  
The Subject ◽  
Image Position ◽  
Combinatorial Device ◽  
Torsion Free ◽  
Weak Square

In this paper we explicate a very weak version of the principle □ discovered by Jensen who proved it holds in the constructible universe L. This principle is strong enough to include many of the known applications of □, but weak enough that it is consistent with the existence of very large cardinals. In this section we show that this principle is equivalent to a common combinatorial device, which we call a Jensen matrix. In the second section we show that our principle is consistent with a supercompact cardinal. In the third section of this paper we show that this principle is exactly equivalent to the statement that every torsion free Abelian group has a filtration into σ-balanced subgroups. In the fourth section of this paper we show that this principle fails if you assume the Chang's Conjecture:In the fifth section of the paper we review the proofs that the various weak squares we consider are strictly decreasing in strength. Section 6 was added in an ad hoc manner after the rest of the paper was written, because the subject matter of Theorem 6.1 fit well with the rest of the paper. It deals with a principle dubbed “Not So Very Weak Square”, which appears close to Very Weak Square but turns out not to be equivalent.

scholarly journals III. On certain formulæ for differentiation

1859 ◽  
Vol 9 ◽  
pp. 93-94
Keyword(s):  
General Expression ◽  
Fourth Section ◽  
Definite Integrals ◽  
The Third ◽  
The Subject

In seeking for a formula in the theory of multiple definite inte­grals, I was several years ago led to investigate the successive differ­ential coefficients.of (√ x + λ ¯ ‒ √ x + μ ¯ ) 2 i , and the results which.I then obtained are given in my paper, “On certain formulæ for dif­ferentiations, with applications to the evaluation of definite integrals*.” I subsequently sought for the successive differential coefficients of the more general expression {( x + λ) ( x + μ) } ½ k (√ x + λ ¯ — √ x + μ ¯ ) 2 i , but the investigation was not finished. My attention was recalled to the subject by two remarkable identities obtained in Prof. Donkin’s memoir, “On the equation of Laplace’s Functions, &c.,”by a comparison of his results with those of Prof. Boole, which identities I perceived to belong to the class of formulæ above referred to : the first of the two identities is in fact readily deduced from a formula in my paper; the demonstration of the second is much more difficult, and I have only succeeded in making it depend on the establishment of the equality of the coefficients of two expressions of the same form. I have since resumed the unfinished investigation above referred to. The several results which I have obtained are given in the present memoir. I remark that, putting for shortness P=2 x + λ + μ, Q = √( x + λ) ( x + μ) ¯ , R=(√ x + λ ¯ ‒ x + μ) 2 ¯ , the subject to which the results all belong is the differentiation of the expression P α Q β R γ ; the before-mentioned expression {( x + λ) ( x + μ) ½ k (√ x + λ) ‒ (√ x + μ) ¯2 i is of this form, and the question in relation to it is to obtain the development of ∂ r x P α Q β R γ , where a = 0. The question arising from the second of Prof. Donkin’s identities is to obtain the development of (P ‒1 Q 4 ∂ x ) γ P α Q β R γ , where a —γ ‒ β. As the demonstration of these identities is one of the objects of the present memoir, I have given in the first section their reduction to the form in which they are considered. The second section treats of the development of the expression ∂ r x P α Q β R γ where a = 0; the third section of that of the expression {P -1 Q 4 ∂ x } r P α Q β R γ where a =γ—β; the fourth section contains the applica­tion of the formulæ to the demonstration of the two identities and some other applications of the formulææ.

A Review of Micro Heat Exchanger Flow Physics, Fabrication Methods and Applications

2001 ◽  
Author(s):  
W. Jerry Bowman ◽  
Daniel Maynes
Keyword(s):  
Heat Transfer ◽  
Heat Exchanger ◽  
Design Optimization ◽  
Heat Exchangers ◽  
Review Of The Literature ◽  
Fourth Section ◽  
The Third ◽  
Heat Exchanger Design ◽  
Micro Heat Exchanger ◽  
The Subject

Abstract A review of the literature in the area of micro heat exchangers is presented to provide a concise overview of the recent advances in this field of study. The review is divided into six sections. The first section reviews research focused on understanding friction and heat transfer in microchannels. The second section deals with heat exchanger design, optimization and comparison studies. The third section deals with fabrication methods used for constructing micro heat exchangers. The fourth section reviews applications of micro heat exchangers. The last two sections of the paper deal with miscellaneous topics and other reviews on the subject. The total review focuses on advances made after the early 1990’s.

scholarly journals On the Koszul map of Lie algebras

2016 ◽  
Vol 28 (1) ◽  
Author(s):  
Yves Cornulier
Keyword(s):  
Abelian Group ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Free Abelian Group ◽  
Bilinear Maps ◽  
Nilpotent Lie Algebra ◽  
Torsion Free Abelian Group ◽  
The Third ◽  
Torsion Free

AbstractWe motivate and study the reduced Koszul map, relating the invariant bilinear maps on a Lie algebra and the third homology. We show that it is concentrated in degree 0 for any grading in a torsion-free abelian group, and in particular it vanishes whenever the Lie algebra admits a positive grading. We also provide an example of a 12-dimensional nilpotent Lie algebra whose reduced Koszul map does not vanish. In an appendix, we reinterpret the results of Neeb and Wagemann about the second homology of current Lie algebras, which are closely related to the reduced Koszul map.

Proctorial Representation in the House of Lords during the Reign of Edward VI

1969 ◽  
Vol 8 (2) ◽  
pp. 1-27 ◽  
Author(s):  
Vernon F. Snow
Keyword(s):  
Sixteenth Century ◽  
Roman Law ◽  
Henry Viii ◽  
Fourth Section ◽  
The Third ◽  
Satisfactory Treatment ◽  
House Of Lords ◽  
History Of ◽  
The Subject ◽  
The Relationship

This is the third in a series of studies dealing with the history of the proxy system in the House of Lords. The first, after tracing the origin of proxies to the Roman law of agency, dealt with the emergence and spread of representation by proctors in the ecclesiastical and political assemblies of medieval England. The second study demonstrated how the proxy system was perfected in the upper house during the reign of Henry VIII and how the Crown benefited from that system. The ensuing article concerns proctorial representation during the crucial years of the Edwardian Reformation. Because of the brief period under consideration — only six years — it seemed best to cast the study in an analytical rather than a chronological framework. The first section deals with the general characteristics of proctorial representation in mid-Tudor times; the second and third sections cover the spiritual and temporal lords, respectively; and the fourth section treats the relationship between the proxy system and conciliar government.IKnowledge of the proxy system in the mid-sixteenth-century House of Lords remains somewhat fragmentary and limited in scope. A satisfactory treatment of the subject does not exist. Constitutional and legal historians have paid little attention to proxies and less to the procedure governing their use in the upper house. As one might expect, Bishop Stubbs dealt with proxies in medieval Parliaments and correctly associated them with parliamentary privileges, but at the same time he concluded that “its history has not yet been minutely traced.

Contemporary Relevance of Nehru

2012 ◽  
Vol 19 (1) ◽  
pp. 149-168
Author(s):  
Baljit Singh
Keyword(s):  
World View ◽  
Cultural Nationalism ◽  
The Body ◽  
The Other ◽  
Washington Consensus ◽  
Fourth Section ◽  
The Third ◽  
Third Phase ◽  
The Subject ◽  
The One

The subject contemporary relevance of Nehru is unfolded into five sections. First section introduces the subject by contextualising Nehru’s ideas in the contemporary scenario. Nehruvian ideological system and its utility in the age of globalisation constitute the body of this article. His nationalism, socialism and world view are located and discussed in the second, third and fourth sections, respectively. Nehru’s idea of composite culture, contested by cultural nationalism from the one end and ethno-nationalism from the other end of spectrum comprises the second section. The third section discusses the conception, consolidation, retreat and revival of Nehruvian model of economic development in the light of Washington Consensus and Post-Washington Consensus. His idea of socialism and the mixed economy are debated in liberal, neoliberal and post-neoliberal scenario. His world view faced rough weather during the second and third phase of India’s foreign policy. The former was set in motion after his death, whereas the latter started taking shape in the Post-Soviet world, which has acquired the hegemonic overtones. Contemporary significance of Nehru’s world view in the hegemonic world is probed in the fourth section. The last section sums up the discussion in the form of concluding observations.

scholarly journals Editorial: Australian TESOL contexts; a state in flux

2017 ◽  
Vol 26 (1) ◽  
Author(s):  
Rod Neilsen ◽  
Michiko Weinmann ◽  
Ruth Arber
Keyword(s):  
English Language ◽  
Ad Hoc ◽  
Linguistic Diversity ◽  
Kindergarten Children ◽  
Australian Government ◽  
The Third ◽  
Factors Influencing ◽  
The Subject ◽  
Just Society ◽  
K 12

The factors influencing the multiple contexts of English language provision in Australia are complex, and this issue of TESOL in Context holds a lens to some of them: the first of the three articles presents a historical overview of provision for English as an Additional Language or Dialect (EAL/D, formerly English as a Second Language or ESL) in Australia, the subject of the second is screening for EAL kindergarten children, and the third discusses issues of internationalisation in a K-12 school. Reading these we are reminded that as TESOL professionals we work in an environment of continual change, forced to respond in a frequently ad hoc manner to a number of pressures, including federal and state politics. As far back as 2002 Joe Lo Bianco expressed concern (in this journal) that EAL/D learner needs were still not being met at that time, and the three articles in this issue throw light on why this is still too often the case, despite recent legislative emphasis on a ‘fairer Australia’ (Australian Government, 2011) in which a stronger acknowledgement, understanding and support for linguistic diversity should provide the foundation for a socially just society. 

Halal Branding

2017 ◽  
pp. 20-37
Author(s):  
Ali Shahnazari
Keyword(s):  
Final Section ◽  
Global Level ◽  
Fourth Section ◽  
The Third ◽  
Holy Quran ◽  
The Holy Quran ◽  
Food Market ◽  
Halal Food ◽  
The Subject

Muslim and Islamic marketing is very important on the global level. This chapter investigates Muslim's food market. In the first section, the foundations of Halal food are explained, and the roots of the concept of Halal and the challenges facing it are described. The second section includes Islamic branding and the foundations of Islamic branding. The Islamic foundation of Halal is a subject that comes together with the description of Halal food in the Holy Quran and is the subject of the third section. In the fourth section, Halal branding is explored, and in the fifth section, the legal and practical issues of Halal branding are analyzed. The final section includes models of Halal food and brand in which six models are put forward. The most recent of these models includes all the essential concepts of the previous models.

Review of Kikhney, L. (2017). Under the sign of acmeism: Collected articles. Moscow: Azbukovnik. 608 pages.

2019 ◽  
pp. 384-389
Author(s):  
V. A. Gavrikov
Keyword(s):  
General Theory ◽  
World View ◽  
Specific Character ◽  
Silver Age ◽  
Fourth Section ◽  
The Third ◽  
Space And Time ◽  
The Subject ◽  
Written Word ◽  
Time Continuum

The main goal of the collection is to define the specific character of Acmeism as a separate trend inside Russian Modernism. This specification is derived through a series of basic categories like space and time continuum, the philosophy of the written word, and poetic semantics, etc. The collection is divided into several sections. The first, a summary of the general theory about the subject, discusses the significance of Acmeism in the Silver Age semantic paradigm. The second section is devoted to O. Mandelstam’s poetry, and in particular his logos concept. The third centres on A. Akhmatova’s poetics, with particular attention to her world view. It also includes several papers on A Poem Without a Hero [Poema bez geroya]. The fourth section covers various aspects of works by acmeists N. Gumilyov, V. Narbut, and M. Zenkevich. 

Halal Branding

2014 ◽  
pp. 160-176
Author(s):  
Ali Shahnazari
Keyword(s):  
Final Section ◽  
Global Level ◽  
Fourth Section ◽  
The Third ◽  
Holy Quran ◽  
The Holy Quran ◽  
Food Market ◽  
Halal Food ◽  
The Subject

Muslim and Islamic marketing is very important on the global level. This chapter investigates Muslim's food market. In the first section, the foundations of Halal food are explained, and the roots of the concept of Halal and the challenges facing it are described. The second section includes Islamic branding and the foundations of Islamic branding. The Islamic foundation of Halal is a subject that comes together with the description of Halal food in the Holy Quran and is the subject of the third section. In the fourth section, Halal branding is explored, and in the fifth section, the legal and practical issues of Halal branding are analyzed. The final section includes models of Halal food and brand in which six models are put forward. The most recent of these models includes all the essential concepts of the previous models.

Sums of Complexes in Torsion Free Abelian Groups

1969 ◽  
Vol 12 (4) ◽  
pp. 479-480 ◽  
Author(s):  
H. Heilbronn ◽  
P. Scherk
Keyword(s):  
Abelian Group ◽  
Free Abelian Group ◽  
Abelian Groups ◽  
Preceding Paper ◽  
Torsion Free Abelian Group ◽  
Linearly Independent ◽  
Free Abelian Groups ◽  
Image Position ◽  
Torsion Free

Let A, B, denote two non-void finite complexes (= subsets) of the torsion free abelian group G,Let d(A),… denote the maximum number of linearly independent elements of A,… and let n = n(A, B) denote the number of elements of A + B whose representation in the form a + b is unique. In the preceding paper, Tarwater and Entringer [1] proved that n ≥ d(A).

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