scholarly journals The norming set of a symmetric 3-linear form on the plane with the $l_1$-norm

10.53733/177 ◽  
2021 ◽  
Vol 51 ◽  
pp. 95-108
Author(s):  
Sung Guen Kim
Keyword(s):  
Linear Form ◽  
Linear Forms

An element $(x_1, \ldots, x_n)\in E^n$ is called a {\em norming point} of $T\in {\mathcal L}(^n E)$ if $\|x_1\|=\cdots=\|x_n\|=1$ and$|T(x_1, \ldots, x_n)|=\|T\|,$ where ${\mathcal L}(^n E)$ denotes the space of all continuous $n$-linear forms on $E.$For $T\in {\mathcal L}(^n E),$ we define $${Norm}(T)=\Big\{(x_1, \ldots, x_n)\in E^n: (x_1, \ldots, x_n)~\mbox{is a norming point of}~T\Big\}.$$${Norm}(T)$ is called the {\em norming set} of $T$. We classify ${Norm}(T)$ for every $T\in {\mathcal L}_s(^3 l_{1}^2)$.  

scholarly journals On a characterization theorem on a-adic solenoids

2019 ◽  
Vol 489 (3) ◽  
pp. 227-231
Author(s):  
G. M. Feldman
Keyword(s):  
Gaussian Distribution ◽  
Real Line ◽  
Linear Form ◽  
Conditional Distribution ◽  
Random Variables ◽  
Characterization Theorem ◽  
The Other ◽  
Independent Random Variables ◽  
Linear Forms ◽  
The Real

According to the Heyde theorem the Gaussian distribution on the real line is characterized by the symmetry of the conditional distribution of one linear form of independent random variables given the other. We prove an analogue of this theorem for linear forms of two independent random variables taking values in an -adic solenoid containing no elements of order 2. Coefficients of the linear forms are topological automorphisms of the -adic solenoid.

scholarly journals Characterization of a centromere-linked recombination hot spot in Saccharomyces cerevisiae.

1987 ◽  
Vol 7 (11) ◽  
pp. 3871-3879 ◽  
Author(s):  
M Neitz ◽  
J Carbon
Keyword(s):  
Saccharomyces Cerevisiae ◽  
Restriction Fragment ◽  
Linear Form ◽  
Dna Hybridization ◽  
Hot Spot ◽  
Genetic Exchange ◽  
Linear Forms ◽  
Dna Fragment ◽  
Stimulation Of

A 1.5-kilobase-pair SalI-HindIII (SH) restriction fragment from the region of Saccharomyces cerevisiae chromosome XIV immediately adjacent to the centromere appears to contain sequences that act as a hot spot for mitotic recombination. The presence of SH DNA on an autonomously replicating plasmid stimulates homologous genetic exchange between yeast genomic sequences and those present on the plasmid. In all recombinants characterized, exchange occurs in plasmid yeast sequences adjacent to rather than within the SH DNA. Hybridization analyses reveal that SH-containing plasmids are present in linear as well as circular form in S. cerevisiae and that linear forms are generated by cleavage at specific sites. Presumably, it is the linear form of the plasmid that is responsible for the stimulation of genetic exchange. Based on these observations, it is proposed that this DNA fragment contains a centromere-linked recombination hot spot and that SH-stimulated recombination occurs via a mechanism similar to double-strand-gap repair (J. W. Szostak, T. Orr-Weaver, J. Rothstein, and F. Stahl, Cell 33:25-35 1983).

scholarly journals A counterexample using 4-linear forms

2004 ◽  
Vol 70 (3) ◽  
pp. 469-473 ◽  
Author(s):  
David Pérez-García
Keyword(s):  
Banach Spaces ◽  
Linear Form ◽  
Linear Forms ◽  
Infinite Dimensional

We prove that, for n ≥ 4 and arbitrary infinite dimensional Banach spaces X1,…Xn, there exists an extendible n-linear form T: X1 x…x Xn →  that is not integral.

scholarly journals The SalGI restriction endonuclease. Mechanism of DNA cleavage

1982 ◽  
Vol 203 (1) ◽  
pp. 85-92 ◽  
Author(s):  
A Maxwell ◽  
S E Halford
Keyword(s):  
Restriction Endonuclease ◽  
Linear Form ◽  
Dna Cleavage ◽  
Tertiary Structure ◽  
Recognition Site ◽  
Optimal Conditions ◽  
Supercoiled Dna ◽  
Linear Forms ◽  
Open Circle ◽  
Concerted Reaction

The cleavage of supercoiled DNA of plasmid pMB9 by restriction endonuclease SalGI has been studied. Under the optimal conditions for this reaction, the only product is the linear form of the DNA, in which both strands of the duplex have been cleaved at the SalGI recognition site. DNA molecules cleaved in one strand at this site were found to be poor substrates for the SalGI enzyme. Thus, both strands of the DNA appear to be cleaved in a concerted reaction. However, under other conditions, the enzyme cleaves either one or both strands of the DNA; the supercoiled substrate is then converted to either open-circle or linear forms, the two being produced simultaneously rather than consecutively. We propose a mechanism for the SalGI restriction endonuclease which accounts for the reactions of this enzyme under both optimal and other conditions. These reactions were unaffected by the tertiary structure of the DNA.

scholarly journals A NOTE ON BADLY APPROXIMABLE LINEAR FORMS

2011 ◽  
Vol 83 (2) ◽  
pp. 262-266 ◽  
Author(s):  
MUMTAZ HUSSAIN
Keyword(s):  
Hausdorff Dimension ◽  
Linear Form ◽  
Linear Forms ◽  
Badly Approximable

AbstractIn this paper we investigate the analogue of the classical badly approximable setup in which the distance to the nearest integer ‖⋅‖ is replaced by the sup norm |⋅|. In the case of one linear form we prove that the hybrid badly approximable set is of full Hausdorff dimension.

scholarly journals Mesures coniques et intégrale de Daniell

1981 ◽  
Vol 31 (1) ◽  
pp. 46-58 ◽  
Author(s):  
Richard Becker
Keyword(s):  
Linear Form ◽  
Riesz Space ◽  
Integration Theory ◽  
Continuous Linear ◽  
Linear Forms ◽  
Proper Cone ◽  
Weak Space

AbstractLet X be a weakly complete proper cone contained in a weak space E and h(E) the Riesz space generated by the continuous linear forms on E. A positive conical measure μ on X is a positive linear form on h(E)|x. G. Choquet has proved μ is a Daniell integral on E when E is weakly complete, but μ is not generally a Daniell integral on X. However we give an integration theory for functions on X and compare this theory with the classical Daniell theory. The case where μ is maximal in the sense of G. Choquet is remarkable.

Linear Forms in Monic Integer Polynomials

2013 ◽  
Vol 56 (3) ◽  
pp. 510-519
Author(s):  
Artūras Dubickas
Keyword(s):  
Linear Form ◽  
Monic Polynomial ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Linear Forms ◽  
Integer Polynomials ◽  
Necessary And Sufficient

Abstract. We prove a necessary and sufficient condition on the list of nonzero integers u1…, uk, k≥2, under which a monic polynomial f∊2ℤ[x] is expressible by a linear form u1 f1 + … + ukfk in monic polynomials f1…fk ∊ ℤ[x]. This condition is independent of f. We also show that if this condition holds, then the monic polynomials f1, … fk can be chosen to be irreducible in ℤ[x].

Characterization of a centromere-linked recombination hot spot in Saccharomyces cerevisiae

1987 ◽  
Vol 7 (11) ◽  
pp. 3871-3879
Author(s):  
M Neitz ◽  
J Carbon
Keyword(s):  
Saccharomyces Cerevisiae ◽  
Restriction Fragment ◽  
Linear Form ◽  
Dna Hybridization ◽  
Hot Spot ◽  
Genetic Exchange ◽  
Linear Forms ◽  
Dna Fragment ◽  
Stimulation Of

A 1.5-kilobase-pair SalI-HindIII (SH) restriction fragment from the region of Saccharomyces cerevisiae chromosome XIV immediately adjacent to the centromere appears to contain sequences that act as a hot spot for mitotic recombination. The presence of SH DNA on an autonomously replicating plasmid stimulates homologous genetic exchange between yeast genomic sequences and those present on the plasmid. In all recombinants characterized, exchange occurs in plasmid yeast sequences adjacent to rather than within the SH DNA. Hybridization analyses reveal that SH-containing plasmids are present in linear as well as circular form in S. cerevisiae and that linear forms are generated by cleavage at specific sites. Presumably, it is the linear form of the plasmid that is responsible for the stimulation of genetic exchange. Based on these observations, it is proposed that this DNA fragment contains a centromere-linked recombination hot spot and that SH-stimulated recombination occurs via a mechanism similar to double-strand-gap repair (J. W. Szostak, T. Orr-Weaver, J. Rothstein, and F. Stahl, Cell 33:25-35 1983).

scholarly journals Introduction to Fermionic Structures in C4 Space-Time

2018 ◽  
Author(s):  
Dimitris Mastoridis ◽  
K. Kalogirou
Keyword(s):  
Geometric Structure ◽  
Linear Form ◽  
Quadratic Forms ◽  
Space Time ◽  
Square Root ◽  
Linear Forms ◽  
New Approach ◽  
Dirac Formalism

We explore several ways, in order to include fermionic structures naturally in a physical theory in C4. We begin with the standard Dirac formalism and we proceed by using Cartan's property of triality as a second option. Afterwards, we suggest a new approach (in a preliminary basis), by introducing an 1-linear form, as the "square root of the geometry" derived by the usual 2-linear forms (quadratic forms). Keeping this way, we introduce n-linear forms, in order to formulate a new geometric structure, which could be suitable for the formulation of a pure geometric unied theory.

scholarly journals Best Diophantine approximations to a set of linear forms

1983 ◽  
Vol 34 (1) ◽  
pp. 114-122 ◽  
Author(s):  
J. C. Lagarias
Keyword(s):  
Diophantine Approximation ◽  
Linear Form ◽  
Best Approximation ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Linear Forms ◽  
Simultaneous Diophantine Approximation ◽  
Diophantine Approximations ◽  
Necessary And Sufficient ◽  
Infinite Set

AbstractWe define the notion of a best Diophantine approximation vector to a set of linear forms. This generalizes definitions of a best approximation vector to a single linear form and of a best simultaneous Diophantine approximation vector. We derive necessary and sufficient conditions for the existence of an infinite set of best Diophantine approximation vectors. Finally, we prove that such approximation vectors are spaced far apart in an appropriate sense.

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