The correct form of the single-eigenvalue distribution for the non-zero mean-matrix ensembles

1980 ◽  
Vol 13 (5) ◽  
pp. L129-L131 ◽  
Author(s):  
N Ullah
Keyword(s):  
Eigenvalue Distribution ◽  
Correct Form ◽  
Matrix Ensembles

scholarly journals Spectral distributions of periodic random matrix ensembles

2019 ◽  
Vol 10 (01) ◽  
pp. 2150011
Author(s):  
Roger Van Peski
Keyword(s):  
Random Matrix ◽  
Spectral Distribution ◽  
Eigenvalue Distribution ◽  
Limiting Spectral Distribution ◽  
Gaussian Unitary Ensemble ◽  
Random Matrix Ensembles ◽  
Spectral Distributions ◽  
Matrix Ensembles ◽  
General Correspondence ◽  
Unitary Ensemble

Koloğlu, Kopp and Miller compute the limiting spectral distribution of a certain class of real random matrix ensembles, known as [Formula: see text]-block circulant ensembles, and discover that it is exactly equal to the eigenvalue distribution of an [Formula: see text] Gaussian unitary ensemble. We give a simpler proof that under very general conditions which subsume the cases studied by Koloğlu–Kopp–Miller, real-symmetric ensembles with periodic diagonals always have limiting spectral distribution equal to the eigenvalue distribution of a finite Hermitian ensemble with Gaussian entries which is a ‘complex version’ of a [Formula: see text] submatrix of the ensemble. We also prove an essentially algebraic relation between certain periodic finite Hermitian ensembles with Gaussian entries, and the previous result may be seen as an asymptotic version of this for real-symmetric ensembles. The proofs show that this general correspondence between periodic random matrix ensembles and finite complex Hermitian ensembles is elementary and combinatorial in nature.

scholarly journals Universal Behavior of the Corners of Orbital Beta Processes

2019 ◽  
Author(s):  
Cesar Cuenca
Keyword(s):  
Random Matrix ◽  
Bessel Functions ◽  
Eigenvalue Distribution ◽  
Base Field ◽  
Hermitian Matrices ◽  
Empirical Measures ◽  
Universal Behavior ◽  
Fixed Set ◽  
Matrix Ensembles ◽  
Principal Submatrices

Abstract There is a unique unitarily-invariant ensemble of $N\times N$ Hermitian matrices with a fixed set of real eigenvalues $a_1> \dots > a_N$. The joint eigenvalue distribution of the $(N-1)$ top-left principal submatrices of a random matrix from this ensemble is called the orbital unitary process. There are analogous matrix ensembles of symmetric and quaternionic Hermitian matrices that lead to the orbital orthogonal and symplectic processes, respectively. By extrapolation, on the dimension of the base field, of the explicit density formulas, we define the orbital beta processes. We prove the universal behavior of the virtual eigenvalues of the smallest $m$ principal submatrices, when $m$ is independent of $N$ and the eigenvalues $a_1> \dots > a_N$ grow linearly in $N$ and in such a way that the rescaled empirical measures converge weakly. The limiting object is the Gaussian beta corners process. As a byproduct of our approach, we prove a theorem on the asymptotics of multivariate Bessel functions.

Learning Zulu

2016 ◽  
Author(s):  
Mark Sanders
Keyword(s):  
Language Learning ◽  
Cultural History ◽  
South African ◽  
Press Coverage ◽  
African History ◽  
African Culture ◽  
The Past ◽  
Correct Form ◽  
Linguistic Purism

When this book's author began studying Zulu, he was often questioned why he was learning it. This book places the author's endeavors within a wider context to uncover how, in the past 150 years of South African history, Zulu became a battleground for issues of property, possession, and deprivation. The book combines elements of analysis and memoir to explore a complex cultural history. Perceiving that colonial learners of Zulu saw themselves as repairing harm done to Africans by Europeans, the book reveals deeper motives at work in the development of Zulu-language learning—from the emergence of the pidgin Fanagalo among missionaries and traders in the nineteenth century to widespread efforts, in the twentieth and twenty-first centuries, to teach a correct form of Zulu. The book looks at the white appropriation of Zulu language, music, and dance in South African culture, and at the association of Zulu with a martial masculinity. In exploring how Zulu has come to represent what is most properly and powerfully African, the book examines differences in English- and Zulu-language press coverage of an important trial, as well as the role of linguistic purism in xenophobic violence in South Africa. Through one person's efforts to learn the Zulu language, the book explores how a language's history and politics influence all individuals in a multilingual society.

Further Problems in the Interpretation and Homology of the Insect Ovipositor

1964 ◽  
Vol 96 (1-2) ◽  
pp. 405-417 ◽  
Author(s):  
G. G. E. Scudder
Keyword(s):  
Experimental Study ◽  
Normal Development ◽  
Organ Formation ◽  
Larval Stages ◽  
Insect Phylogeny ◽  
Correct Form ◽  
Developmental Capacity ◽  
Mode Of Development ◽  
Dual Origin

AbstractAn attempt is made to re-evaluate the data on the origin of the ovipositor in insects and to explain its mode of development in living forms. Comparative developmental data from other groups of animals is cited to substantiate the claim that part of the insect ectodermal genitalia is appendicular rather than sternal in origin. It is suggested that the primary abdominal segmental appendages have provided a source of competent tissue which through subtle changes in selection, has evolved along many pathways, to form the gonocoxae, the pleuropodia, the pseudoplacenta and perhaps the prolegs in many different taxa.It is shown, by aid of sections through the insect embryo and larval stages, that the primary embryonic segmental appendages on the abdomen, do not differentiate; there is no loss of tissue and it cannot be proven that such appendages have been lost in insect phylogeny. The fact that they are represented still in the modern embryo, indicates that they have been retained. To explain the observable developmental details, it is suggested that abdominal limb histogenesis is arrested or suppressed in normal development, but this limb tissue retains its competence to differentiate. Thus development may be initiated again at a later time in postembryonic life. In this manner, the original limb tissue is available for organ formation in the maturing insect.The study has suggested that the appendages on the eighth and ninth segments of the abdomen initiate but do not complete their development in the polypod embryo. Possibly the potential limb tissue is arrested in development because it has not undergone some vital change as regards its capacity to respond (competence) to an inductor, perhaps the inductor is not available or perhaps it is not available in the correct form.There is evidence to suggest that the developmental capacity of the limb anlagen are reduced with time, so that full limb formation is not possible in postembryonic life: this can explain the development of abdominal coxae in the Thysanura and hence gonocoxae in higher insects. It is noted that should Gustafson's suggestion that the eversible sacs and gonapophyses are homologous with primary segmental genitalic ampullae prove acceptable, then the female ectodermal genitalia in insects would appear to have a dual origin.It is emphasized that the speculation expressed are being subjected to experimental study in an attempt to verify the suggested ontogeny and phylogeny.

scholarly journals The Balance between Energy, Environmental Security, and Technical Performance: The Regulatory Challenge of Nanofluids

Nanomaterials ◽  
2021 ◽  
Vol 11 (8) ◽  
pp. 1871
Author(s):  
Maria José Lourenço ◽  
João Alexandre ◽  
Charlotte Huisman ◽  
Xavier Paredes ◽  
Carlos Nieto de Castro
Keyword(s):  
Base Fluid ◽  
Safety Issue ◽  
Common Goal ◽  
Energy Applications ◽  
Technical Performance ◽  
Correct Form ◽  
Heat Collector ◽  
General Data ◽  
Near Future ◽  
Regulatory Challenge

Nowadays, numerous studies on nanomaterials (NMs) and Nanofluids (NFs) are account a plethora of applications. With the scientific society’s common goal of fulfilling the target of sustainable development proposed by the UN by 2030, it is necessary to combine efforts based on the scientific and technological knowledge already acquired, to apply these new systems with safety. There are thousands of publications that examine the use of NFs, their benefits and drawbacks, properties, behaviors, etc., but very little is known about the safety of some of these systems at a laboratory and industrial scale. What is the correct form of manipulating, storing, or even destroying them? What is their life cycle, and are they likely to be reused? Depending on the nanoparticles, the characteristics of the base fluid (water, propylene glycol, or even an ionic liquid) and the addition or not of additives/surfactants, the safety issue becomes complex. In this study, general data regarding the safety of NF (synthetic and natural) are discussed, for a necessary reflection leading to the elaboration of a methodology looking at the near future, intended to be sustainable at the level of existing resources, health, and environmental protection, paving the way for safer industrial and medical applications. A discussion on the efficient use of nanofluids with melanin (natural NM) and TiO2 in a pilot heat collector for domestic solar energy applications illustrates this methodology, showing that technical advantages can be restricted by their environment and safety/security implications.

scholarly journals Jacobi Ensemble, Hurwitz Numbers and Wilson Polynomials

2021 ◽  
Vol 111 (3) ◽  
Author(s):  
Massimo Gisonni ◽  
Tamara Grava ◽  
Giulio Ruzza
Keyword(s):  
Generating Functions ◽  
Combinatorial Interpretation ◽  
Hurwitz Numbers ◽  
Jacobi Ensemble ◽  
Matrix Ensembles ◽  
Wilson Polynomials ◽  
Unitary Ensemble ◽  
Topological Expansion

AbstractWe express the topological expansion of the Jacobi Unitary Ensemble in terms of triple monotone Hurwitz numbers. This completes the combinatorial interpretation of the topological expansion of the classical unitary invariant matrix ensembles. We also provide effective formulæ for generating functions of multipoint correlators of the Jacobi Unitary Ensemble in terms of Wilson polynomials, generalizing the known relations between one point correlators and Wilson polynomials.

scholarly journals Domination number and Laplacian eigenvalue distribution

2016 ◽  
Vol 53 ◽  
pp. 66-71 ◽  
Author(s):  
Stephen T. Hedetniemi ◽  
David P. Jacobs ◽  
Vilmar Trevisan
Keyword(s):  
Domination Number ◽  
Eigenvalue Distribution ◽  
Laplacian Eigenvalue

scholarly journals Another Law for the 3-Metabelian Groups

1966 ◽  
Vol 6 (4) ◽  
pp. 512-512
Author(s):  
I. D. Macdonald
Keyword(s):  
Mathematical Society ◽  
Metabelian Groups ◽  
Commutator Identity ◽  
Australian Mathematical Society ◽  
Correct Form ◽  
Image Position

Journal of the Australian Mathematical Society 4 (1964), 452–453The second paragraph should be deleted. The alleged commutator identity (3) is false and is certainly not due to Philip Hall. The correct form isas Dr. N. D. Gupta of Canberra has pointed out to me. According to Professor B. H. Neumann, this identity appeared in his (Professor Neumann's) thesis.Nevertheless the theorem is valid and the proof given is correct.

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