scholarly journals Chebyshev-Steffensen Inequality Involving the Inner Product

Mathematics ◽  
2022 ◽  
Vol 10 (1) ◽  
pp. 122
Author(s):  
Milica Klaričić Bakula ◽  
Josip Pečarić
Keyword(s):  
Upper Bounds ◽  
Inner Product ◽  
The Real ◽  
Steffensen Inequality

In this paper, we prove the Chebyshev-Steffensen inequality involving the inner product on the real m-space. Some upper bounds for the weighted Chebyshev-Steffensen functional, as well as the Jensen-Steffensen functional involving the inner product under various conditions, are also given.

scholarly journals Biorthogonality in the real sequence spaces ℓp

1997 ◽  
Vol 40 (2) ◽  
pp. 325-330
Author(s):  
Anthony J. Felton ◽  
H. P. Rogosinski
Keyword(s):  
Linear Subspace ◽  
Sequence Spaces ◽  
Inner Product ◽  
Real Sequence ◽  
Closed Linear Subspace ◽  
The Real ◽  
Infinite Dimensional

In this paper we generalise some of the results obtained in [1] for the n-dimensional real spaces ℓp(n) to the infinite dimensional real spaces ℓp. Let p >1 with p ≠ 2, and let x be a non-zero real sequence in ℓp. Let ε(x) denote the closed linear subspace spanned by the set of all those sequences in ℓp which are biorthogonal to x with respect to the unique semi-inner-product on ℓp consistent with the norm on ℓp. In this paper we show that codim ε(x)=1 unless either x has exactly two non-zero coordinates which are equal in modulus, or x has exactly three non-zero coordinates α, β, γ with |α| ≥ |β| ≥ |γ| and |α|p > |β|p + |γ|p. In these exceptional cases codim ε(x) = 2. We show that is a linear subspace if, and only if, x has either at most two non-zero coordinates or x has exactly three non-zero coordinates which satisfy the inequalities stated above.

An extension of the Ahlfors distortion theorem

1954 ◽  
Vol 50 (2) ◽  
pp. 261-265
Author(s):  
F. Huckemann
Keyword(s):  
Conformal Mapping ◽  
Real Axis ◽  
Upper Bounds ◽  
Distortion Theorem ◽  
Lower And Upper Bounds ◽  
The Real ◽  
Strip Domain ◽  
Parallel Strip ◽  
Image Position ◽  
Two Sides

1. The conformal mapping of a strip domain in the z-plane on to a parallel strip— parallel, say, to the real axis of the ζ ( = ξ + iμ)-plane—brings about a certain distortion. More precisely: consider a cross-cut on the line ℜz = c joining the two sides of the frontier of the strip domain (in these introductory remarks we suppose for simplicity that there is only one such cross-cut on that line), and denote by ξ1(c) and ξ2(c) the lower and upper bounds of ξ on the image in the ζ-plane. The theorem of Ahlfors (1), now classical, states thatprovided thatwhere a is the width of the parallel strip and θ(c) the length of the cross-cut.

OPERATOR ACCRETIVE KUAT PADA RUANG HILBERT

2018 ◽  
Vol 1 (1) ◽  
pp. 60
Author(s):  
Razis Aji Saputro ◽  
Susilo Hariyanto ◽  
Y.D. Sumanto
Keyword(s):  
Hilbert Space ◽  
Linear Operator ◽  
Vector Space ◽  
Cauchy Sequence ◽  
Accretive Operator ◽  
Inner Product ◽  
Accretive Operators ◽  
The Real ◽  
Adjoint Operators

Pre-Hilbert space is a vector space equipped with an inner-product. Furthermore, if each Cauchy sequence in a pre-Hilbert space is convergent then it can be said complete and it called as Hilbert space. The accretive operator is a linear operator in a Hilbert space. Accretive operator is occurred if the real part of the corresponding inner product will be equal to zero or positive. Accretive operators are also associated with non-negative self-adjoint operators. Thus, an accretive operator is said to be strict if there is a positive number such that the real part of the inner product will be greater than or equal to that number times to the squared norm value of any vector in the corresponding Hilbert Space. In this paper, we prove that a strict accretive operator is an accretive operator.

The determinant of the sum of two matrices

1995 ◽  
Vol 52 (3) ◽  
pp. 425-429 ◽  
Author(s):  
Chi-Kwong Li ◽  
Roy Mathias
Keyword(s):  
Singular Values ◽  
Upper Bounds ◽  
Complex Field ◽  
Lower And Upper Bounds ◽  
The Real

Let A and B be n × n matrices over the real or complex field. Lower and upper bounds for |det(A + B)| are given in terms of the singular values of A and B. Extension of our techniques to estimate |f(A + B)| for other scalar-valued functions f on matrices is also considered.

scholarly journals Why do human languages have homophones?

2020 ◽  
Author(s):  
Sean Trott ◽  
Ben Bergen
Keyword(s):  
Communication Systems ◽  
Design Feature ◽  
Upper Bounds ◽  
Natural Consequence ◽  
Human Communication ◽  
The Real ◽  
Minimal Pairs ◽  
Outer Sheath ◽  
Multiple Meanings ◽  
Lexical Neighborhoods

Human languages are replete with ambiguity. This is most evident in homophony––where two or more words sound the same, but carry distinct meanings. For example, the wordform “bark” can denote either the sound produced by a dog or the protective outer sheath of a tree trunk. Why would a system evolved for efficient, effective communication display rampant ambiguity? Some accounts argue that ambiguity is actually a design feature of human communication systems, allowing languages to recycle their most optimal wordforms (those which are short, frequent, and phonotactically well-formed) for multiple meanings. We test this claim by constructing five series of artificial lexica matched for the phonotactics and distribution of word lengths found in five real languages (English, German, Dutch, French, and Japanese), and comparing both the quantity and concentration of homophony across the real and artificial lexica. Surprisingly, we find that the artificial lexica exhibit higher upper-bounds on homophony than their real counterparts, and that homophony is even more likely to be found among short, phonotactically plausible wordforms in the artificial than in the real lexica. These results suggest that homophony in real languages is not directly selected for, but rather, that it emerges as a natural consequence of other features of a language. In fact, homophony may even be selected against in real languages, producing lexica that better conform to other requirements of humans who need to use them. Finally, we explore the hypothesis that this is achieved by “smoothing” out dense concentrations of homophones across lexical neighborhoods, resulting in comparatively more minimal pairs in real lexica.

scholarly journals A Note on Simulation Pricing of π-Options

Risks ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 90
Author(s):  
Zbigniew Palmowski ◽  
Tomasz Serafin
Keyword(s):  
Monte Carlo ◽  
Numerical Analysis ◽  
Upper Bounds ◽  
Monte Carlo Algorithm ◽  
Market Environment ◽  
The Real ◽  
Relative Maximum ◽  
Real Market ◽  
Maximum Drawdown

In this work, we adapt a Monte Carlo algorithm introduced by Broadie and Glasserman in 1997 to price a π-option. This method is based on the simulated price tree that comes from discretization and replication of possible trajectories of the underlying asset’s price. As a result, this algorithm produces the lower and the upper bounds that converge to the true price with the increasing depth of the tree. Under specific parametrization, this π-option is related to relative maximum drawdown and can be used in the real market environment to protect a portfolio against volatile and unexpected price drops. We also provide some numerical analysis.

scholarly journals Privacy-Preserving Task-Matching and Multiple-Submissions Detection in Crowdsourcing

Sensors ◽  
2021 ◽  
Vol 21 (9) ◽  
pp. 3036
Author(s):  
Jie Xu ◽  
Zhaowen Lin ◽  
Jun Wu
Keyword(s):  
Real World ◽  
Low Cost ◽  
Privacy Preserving ◽  
Aggregate Data ◽  
Inner Product ◽  
Detection Scheme ◽  
The Real ◽  
Fine Grained ◽  
Proof Of Knowledge ◽  
Privacy Risks

Crowdsourcing enables requesters to publish tasks to a platform and workers are rewarded for performing tasks of interest. It provides an efficient and low-cost way to aggregate data and solve problems that are difficult for computers but simple for humans. However, the privacy risks and challenges are still widespread. In the real world, the task content may be sensitive and only workers who meet specific requirements or possess certain skills are allowed to acquire and perform it. When these distributed workers submit their task answers, their identity or attribute privacy may also be exposed. If workers are allowed to submit anonymously, they may have the chance to repeat their answers so as to get more rewards. To address these issues, we develop a privacy-preserving task-matching and multiple-submissions detection scheme based on inner-product cryptography and proof of knowledge (PoK) protocol in crowdsourcing. In such a construction, multi-authority inner-product encryption is introduced to protect task confidentiality and achieve fine-grained task-matching based on the attributes of workers. The PoK protocol helps to restrict multiple submissions. For one task, a suitable worker could only submit once without revealing his/her identity. Moreover, different tasks for one worker are unlinkable. Furthermore, the implementation analysis shows that the scheme is effective and feasible.

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