scholarly journals Free-Boolean independence with amalgamation

2019 ◽  
Vol 22 (04) ◽  
pp. 1950028
Author(s):  
Weihua Liu ◽  
Ping Zhong
Keyword(s):  
Central Limit ◽  
Property A ◽  
Positivity Property ◽  
Boolean Independence

In this paper, we develop the notion of free-Boolean independence in an amalgamated setting. We construct free-Boolean cumulants and show that the vanishing of mixed free-Boolean cumulants is equivalent to our free-Boolean independence with amalgamation. We also provide a characterization of free-Boolean independence by conditions in terms of mixed moments. In addition, we study free-Boolean independence over a [Formula: see text]-algebra and prove a positivity property. A central limit law for our free-Boolean independence with amalgamation is also studied.

scholarly journals Isothermic surfaces in sphere geometries as Moutard nets

2007 ◽  
Vol 463 (2088) ◽  
pp. 3171-3193 ◽  
Author(s):  
Alexander I Bobenko ◽  
Yuri B Suris
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Gauss Map ◽  
Point Property ◽  
Property A ◽  
Lie Geometry ◽  
Möbius Geometry ◽  
Isothermic Surfaces ◽  
Three Dimensional Space

We give an elaborated treatment of discrete isothermic surfaces and their analogues in different geometries (projective, Möbius, Laguerre and Lie). We find the core of the theory to be a novel characterization of discrete isothermic nets as Moutard nets. The latter are characterized by the existence of representatives in the space of homogeneous coordinates satisfying the discrete Moutard equation. Moutard nets admit also a projective geometric characterization as nets with planar faces with a five-point property: a vertex and its four diagonal neighbours span a three-dimensional space. Restricting the projective theory to quadrics, we obtain Moutard nets in sphere geometries. In particular, Moutard nets in Möbius geometry are shown to coincide with discrete isothermic nets. The five-point property, in this particular case, states that a vertex and its four diagonal neighbours lie on a common sphere, which is a novel characterization of discrete isothermic surfaces. Discrete Laguerre isothermic surfaces are defined through the corresponding five-plane property, which requires that a plane and its four diagonal neighbours share a common touching sphere. Equivalently, Laguerre isothermic surfaces are characterized by having an isothermic Gauss map. S-isothermic surfaces as an instance of Moutard nets in Lie geometry are also discussed.

Logical constants

2018 ◽  
Author(s):  
Timothy McCarthy
Keyword(s):  
Fundamental Problem ◽  
Logical Consequence ◽  
Logical Form ◽  
Logical Truth ◽  
Semantic Property ◽  
Truth Conditions ◽  
Property A ◽  
Logical Constants ◽  
Language L

A fundamental problem in the philosophy of logic is to characterize the concepts of ‘logical consequence’ and ‘logical truth’ in such a way as to explain what is semantically, metaphysically or epistemologically distinctive about them. One traditionally says that a sentence p is a logical consequence of a set S of sentences in a language L if and only if (1) the truth of the sentences of S in L guarantees the truth of p and (2) this guarantee is due to the ‘logical form’ of the sentences of S and the sentence p. A sentence is said to be logically true if its truth is guaranteed by its logical form (for example, ‘2 is even or 2 is not even’). There are three problems presented by this picture: to explicate the notion of logical form or structure; to explain how the logical forms of sentences give rise to the fact that the truth of certain sentences guarantees the truth of others; and to explain what such a guarantee consists in. The logical form of a sentence may be exhibited by replacing nonlogical expressions with a schematic letter. Two sentences have the same logical form when they can be mapped onto the same schema using this procedure (‘2 is even or 2 is not even’ and ‘3 is prime or 3 is not prime’ have the same logical form: ‘p or not-p’). If a sentence is logically true then each sentence sharing its logical form is true. Any characterization of logical consequence, then, presupposes a conception of logical form, which in turn assumes a prior demarcation of the logical constants. Such a demarcation yields an answer to the first problem above; the goal is to generate the demarcation in such a way as to enable a solution of the remaining two. Approaches to the characterization of logical constants and logical consequence are affected by developments in mathematical logic. One way of viewing logical constanthood is as a semantic property; a property that an expression possesses by virtue of the sort of contribution it makes to determining the truth conditions of sentences containing it. Another way is proof-theoretical: appealing to aspects of cognitive or operational role as the defining characteristics of logical expressions. Broadly, proof-theoretic accounts go naturally with the conception of logic as a theory of formal deductive inference; model-theoretic accounts complement a conception of logic as an instrument for the characterization of structure.

scholarly journals Remarks on the range of a vector measure

1994 ◽  
Vol 36 (2) ◽  
pp. 157-161 ◽  
Author(s):  
Jesús M. F. Castilo ◽  
Fernando Sánchez
Keyword(s):  
Vector Measure ◽  
Null Sequence ◽  
Property A ◽  
Weakly Compact ◽  
Countably Additive Vector Measure ◽  
Additive Vector ◽  
Standing Problem ◽  
Additive Vector Measure

A long-standing problem is the characterization of subsets of the range of a vector measure. It is known that the range of a countably additive vector measure is relatively weakly compact and, in addition, possesses several interesting properties (see [2]). In [6] it is proved that if m: Σ → Χ is a countably additive vector measure, then the range of m has not only the Banach–Saks property, but even the alternate Banach-Saks property. A tantalizing conjecture, which we shall disprove in this article, is that the range of m has to have, for some p > 1, the p-Banach–Saks property. Another conjecture, which has been around for some time (see [2]) and is also disproved in this paper, is that weakly null sequences in the range of a vector measure admit weakly-2-summable sub-sequences. In fact, we shall show a weakly null sequence in the range of a countably additive vector measure having, for every p < ∞, no weakly-p-summable sub-sequences.

scholarly journals Factorizations in preduals associated to ρ-contractions

2015 ◽  
Vol 53 (1) ◽  
pp. 3-17
Author(s):  
Bernard Chevreau ◽  
Aurelian Crăciunescu
Keyword(s):  
Functional Calculus ◽  
Property A ◽  
Absolutely Continuous ◽  
The Way

Abstract We establish directly factorization results for classes of ρ-contractions, corresponding to those obtained for certain classes of contractions. As an example of result which is not an immediate consequence of the fact that any ρ-contraction is similar to an ordinary contraction we give an "optimal" characterization of absolutely continuous ρ-contractions whose associated functional calculus has Property (Aא₀). Along the way we show that a ρ-contraction is absolutely continuous if and only if it admits an absolutely continuous unitary ρ-dilation generalizing a well- known result for usual contractions.

A CENTRAL LIMIT THEOREM FOR BOSE ${\mathcal Z}$-INDEPENDENT QUANTUM RANDOM VARIABLES

1999 ◽  
Vol 02 (02) ◽  
pp. 289-299 ◽  
Author(s):  
MICHAEL SKEIDE
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Limit Distribution ◽  
Fock Space ◽  
Random Variables ◽  
Independent Operator ◽  
Boolean Independence

We present a central limit theorem for Bose [Formula: see text]-independent operator-valued random variables. Furthermore, we show that the central limit distribution may be represented by an algebra of creators and annihilators on a symmetric Fock module. As an example we recover the distribution of creators and annihilators on the truncated Fock space, i.e. the central limit distribution of Boolean independence.

scholarly journals Local spectral properties of commutators

1995 ◽  
Vol 38 (2) ◽  
pp. 313-329 ◽  
Author(s):  
Kjeld B. Laursen ◽  
Vivien G. Miller ◽  
Michael M. Neumann
Keyword(s):  
Spectral Properties ◽  
Extension Property ◽  
Linear Operators ◽  
Local Spectrum ◽  
Property A ◽  
Single Valued Extension Property ◽  
Decomposable Operators ◽  
Spectral Subspaces ◽  
Continuous Linear Operators

For a pair of continuous linear operators T and S on complex Banach spaces X and Y, respectively, this paper studies the local spectral properties of the commutator C(S, T) given by C(S, T)(A): = SA−AT for all A∈L(X, Y). Under suitable conditions on T and S, the main results provide the single valued extension property, a description of the local spectrum, and a characterization of the spectral subspaces of C(S, T), which encompasses the closedness of these subspaces. The strongest results are obtained for quotients and restrictions of decomposable operators. The theory is based on the recent characterization of such operators by Albrecht and Eschmeier and extends the classical results for decomposable operators due to Colojoară, Foiaş, and Vasilescu to considerably larger classes of operators. Counterexamples from the theory of semishifts are included to illustrate that the assumptions are appropriate. Finally, it is shown that the commutator of two super-decomposable operators is decomposable.

ISOLATION AND CHARACTERIZATION OF POLYHYDROXYALKANOATES (PHAS) PRODUCING BACTERIA FROM BRACKISH STREAM

2016 ◽  
Vol 78 (7) ◽  
Author(s):  
Nor Azimah Mohd Zain ◽  
Laila Muftah Ali Zargoun ◽  
Nur Fatihah Elias ◽  
Mohd Firdaus Abdul-Wahab ◽  
Mohd Suardi Suhaimi
Keyword(s):  
Nile Blue ◽  
Blue Staining ◽  
Pseudomonas Sp ◽  
Property A ◽  
Identification Procedure ◽  
Sudan Black B ◽  
Isolation And Characterization ◽  
Ft Ir ◽  
Lipid Granules

Polyhydroxyalkanoates (PHAs) are biopolymers which have similar characteristics with petrochemical plastics but a step better due to its biodegradable property. A total of 23 strains were isolated from two different brackish sources. In order to detect the PHAs granules, the PHAs producing bacteria were first screened with Sudan Black B staining. Twenty strains were observed with lipid granules and were subjected to further confirmation with Nile blue staining.  From the Nile blue staining, only 10 strains have the ability in producing PHAs and 2 were identified as strong PHAs producers. This study focuses on the 2 strains named S1 and L1. Further identification procedure was carried out and found that strain S1 and L1 belongs to Pseudomonas sp. L1 strain was found to be promising for PHAs production since it accumulated PHAs for about 88.3%. The PHAs produced by this strain was analyzed using Fourier Transform Infrared Spectroscopy (FT-IR) and Nuclear Magnetic Resonance (NMR) analysis and was identified as poly-3-hydroxybutyrate (P-3HB).

scholarly journals Birkhoff sum fluctuations in substitution dynamical systems

2017 ◽  
Vol 39 (7) ◽  
pp. 1971-2005 ◽  
Author(s):  
ELLIOT PAQUETTE ◽  
YOUNGHWAN SON
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Dynamical Systems ◽  
Central Limit ◽  
Cantor Sets ◽  
Substitution Matrix ◽  
Substitution Dynamical Systems ◽  
New Criterion

We consider the deviation of Birkhoff sums along fixed orbits of substitution dynamical systems. We show distributional convergence for the Birkhoff sums of eigenfunctions of the substitution matrix. For non-coboundary eigenfunctions with eigenvalue of modulus $1$, we obtain a central limit theorem. For other eigenfunctions, we show convergence to distributions supported on Cantor sets. We also give a new criterion for such an eigenfunction to be a coboundary, as well as a new characterization of substitution dynamical systems with bounded discrepancy.

scholarly journals Influence of culture conditions on the production of extracellular polymeric substances (EPS) by Arthrospira platensis

2020 ◽  
Author(s):  
Mariana Barbalho Silva ◽  
Edwin G. Azero ◽  
Cláudia M. L. L. Teixeira ◽  
Cristina T. Andrade
Keyword(s):  
Food Industry ◽  
Extracellular Polymeric Substances ◽  
Biomass Concentration ◽  
Arthrospira Platensis ◽  
Culture Conditions ◽  
Photon Flux ◽  
Photon Flux Density ◽  
Dilute Solution ◽  
Property A

Abstract Arthrospira platensis is a cyanobacterium that exhibits a large biotechnological interest at food industry because its high protein content, pigments, lipids and carbohydrates. The extracellular polymeric substances (EPS) are co-products of secondary metabolism that present thickening or gelling property. A 3-level factorial design was used to study the combined effect of different nitrate concentrations and photon flux density (PFD) to evaluate the biomass and EPS production by Arthrospira platensis. Characterization of the EPS produced the rheological behavior were also evaluated. The best result for biomass production was obtained at condition 6 (2 g.L-1 NaNO3 and 600 µE.m-2s-1) leading a biomass concentration of 1.292 mg.L-1. Condition 1 (0.25 g.L-1NaNO3 and 200 µE.m-2s-1) produce the major EPS content (111 mg.g-1) followed by condition 9 (2 g.L-1NaNO3 and 1000 µE.m-2s-1). Rheological studies performed for the product at 5 and 10g.L-1 concentrations revealed a dilute solution behavior.

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