scholarly journals Constraining Logits by Bounded Function for Adversarial Robustness

2021 ◽  
Author(s):  
Sekitoshi Kanai ◽  
Masanori Yamada ◽  
Shin'ya Yamaguchi ◽  
Hiroshi Takahashi ◽  
Yasutoshi Ida
Keyword(s):  
Bounded Function

Solvability of the abstract evolution equations in L s -spaces with critical temporal weights

2021 ◽  
Vol 19 (1) ◽  
pp. 111-120
Author(s):  
Qinghua Zhang ◽  
Zhizhong Tan
Keyword(s):  
Cauchy Problem ◽  
Asymptotic Behavior ◽  
Evolution Equation ◽  
Nonlinear Operator ◽  
Evolution Equations ◽  
Bounded Function ◽  
Inhomogeneous Term ◽  
Linear Evolution ◽  
Abstract Evolution Equations ◽  
Linear Evolution Equation

Abstract This paper deals with the abstract evolution equations in L s {L}^{s} -spaces with critical temporal weights. First, embedding and interpolation properties of the critical L s {L}^{s} -spaces with different exponents s s are investigated, then solvability of the linear evolution equation, attached to which the inhomogeneous term f f and its average Φ f \Phi f both lie in an L 1 / s s {L}_{1\hspace{-0.08em}\text{/}\hspace{-0.08em}s}^{s} -space, is established. Based on these results, Cauchy problem of the semi-linear evolution equation is treated, where the nonlinear operator F ( t , u ) F\left(t,u) has a growth number ρ ≥ s + 1 \rho \ge s+1 , and its asymptotic behavior acts like α ( t ) / t \alpha \left(t)\hspace{-0.1em}\text{/}\hspace{-0.1em}t as t → 0 t\to 0 for some bounded function α ( t ) \alpha \left(t) like ( − log t ) − p {\left(-\log t)}^{-p} with 2 ≤ p < ∞ 2\le p\lt \infty .

scholarly journals On one approach to the approximation of solutions to the direct kinematics problem of parallel manipulators

2020 ◽  
Vol 10 (1) ◽  
pp. 65-70
Author(s):  
Andrei Gorchakov ◽  
Vyacheslav Mozolenko
Keyword(s):  
Neural Network ◽  
Bounded Function ◽  
Parallel Manipulators ◽  
Feedforward Neural Network ◽  
Numerical Implementation ◽  
Continuous Bounded Function ◽  
Space Filling ◽  
Space Filling Curves ◽  
Direct Kinematics

AbstractAny real continuous bounded function of many variables is representable as a superposition of functions of one variable and addition. Depending on the type of superposition, the requirements for the functions of one variable differ. The article investigated one of the options for the numerical implementation of such a superposition proposed by Sprecher. The superposition was presented as a three-layer Feedforward neural network, while the functions of the first’s layer were considered as a generator of space-filling curves (Peano curves). The resulting neural network was applied to the problems of direct kinematics of parallel manipulators.

scholarly journals Existence of a bounded function of the maximal spectral type

1982 ◽  
Vol 2 (3-4) ◽  
pp. 259-261 ◽  
Author(s):  
V. M. Alexeyev
Keyword(s):  
Hilbert Space ◽  
Spectral Type ◽  
Measure Space ◽  
Bounded Function

Let us denote by the Hilbert space of all functions on the measure space Ω, square-integrable with respect to the measure μ.

scholarly journals Public Increasing Trust of Biometric Technology

2020 ◽  
Vol 9 (4) ◽  
pp. 1073-1079
Keyword(s):  
Information Systems ◽  
Bounded Function ◽  
Current Theory ◽  
Mutual Interaction ◽  
Common Belief ◽  
Work Process ◽  
Biometric Technology ◽  
Automated Technology

Publically agree to technology of biometric is compound based at extreme believe. The bounded function at believe to biometrics usually record in various types of biometrics with correlative samples associated with familiarity and confidential. To develop a complete understand trust of people recognition about biometrics, we employed current theory to develop a regular calculation of trust in biometrics from user’s theory. We increased confidence of first concern in terms of mutual interaction, technology, information systems and adoption of automated technology. Identified common belief components in these circumstances. Modified objects with reference to biometric technology. Managed an Examine study to determine the reliability of this new scale for sub-factors and trust. Our statistics give rise to seventh recently elements companion with user believe to technology of biometric. We will know work process with recommend conclusion also.

On a Theorem of Hayman Concerning Quasi-Bounded Functions

1959 ◽  
Vol 11 ◽  
pp. 593-600
Author(s):  
P. B. Kennedy
Keyword(s):  
Meromorphic Functions ◽  
Bounded Function ◽  
Fatou Theorem ◽  
Regular Functions ◽  
Bounded Functions ◽  
Image Position ◽  
Special Case

If f(z) is regular in |z| < 1, the expressionis called the characteristic of f(z). This is the notation of Nevanlinna (4) for the special case of regular functions; in this note it will not be necessary to discuss meromorphic functions. If m(r,f) is bounded for 0 < r < 1, then f(z) is called quasi-bounded in |z| < 1. In particular, every bounded function is quasibounded. The class Q of quasi-bounded functions is important because, for instance, a “Fatou theorem” holds for such functions (4, p. 134).

Approximation Par des Fonctions Lipschitziennes et Critere de Convergence Etroite D'une Suite de Probabilites

1984 ◽  
Vol 27 (4) ◽  
pp. 514-516 ◽  
Author(s):  
I. Rihaoui
Keyword(s):  
Weak Convergence ◽  
Metric Space ◽  
Bounded Function ◽  
Uniform Limit ◽  
Bounded Functions ◽  
New Criterion ◽  
Uniformly Continuous

AbstractIn this paper, we prove that a real valued bounded function, defined on a metric space and uniformly continuous is the uniform limit of a sequence of Lipschitzian bounded functions.As a consequence, a new criterion for the weak convergence of probabilities is given.

Variable exponents and grand Lebesgue spaces: Some optimal results

2015 ◽  
Vol 17 (06) ◽  
pp. 1550023 ◽  
Author(s):  
Alberto Fiorenza ◽  
Jean Michel Rakotoson ◽  
Carlo Sbordone
Keyword(s):  
Variable Exponent ◽  
Bounded Function ◽  
Rearrangement Invariant Space ◽  
Invariant Space ◽  
Lebesgue Spaces ◽  
Bounded Set ◽  
Decreasing Rearrangement ◽  
Grand Lebesgue Spaces ◽  
Measurable Bounded Function ◽  
Grand Lebesgue Space

Consider p : Ω → [1, +∞[, a measurable bounded function on a bounded set Ø with decreasing rearrangement p* : [0, |Ω|] → [1, +∞[. We construct a rearrangement invariant space with variable exponent p* denoted by [Formula: see text]. According to the growth of p*, we compare this space to the Lebesgue spaces or grand Lebesgue spaces. In particular, if p*(⋅) satisfies the log-Hölder continuity at zero, then it is contained in the grand Lebesgue space Lp*(0))(Ω). This inclusion fails to be true if we impose a slower growth as [Formula: see text] at zero. Some other results are discussed.

scholarly journals Homoclinic Solutions for a Class of Second Order Nonautonomous Singular Hamiltonian Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Ziheng Zhang ◽  
Fang-Fang Liao ◽  
Patricia J. Y. Wong
Keyword(s):  
Hamiltonian Systems ◽  
Bounded Function ◽  
Homoclinic Solution ◽  
Second Order ◽  
Homoclinic Solutions ◽  
Global Maximum ◽  
Continuous Bounded Function ◽  
Almost Periodic ◽  
Strong Force ◽  
Singular Hamiltonian Systems

We are concerned with the existence of homoclinic solutions for the following second order nonautonomous singular Hamiltonian systemsu¨+atWuu=0, (HS) where-∞<t<+∞,u=u1,u2, …,uN∈ℝNN≥3,a:ℝ→ℝis a continuous bounded function, and the potentialW:ℝN∖{ξ}→ℝhas a singularity at0≠ξ∈ℝN, andWuuis the gradient ofWatu. The novelty of this paper is that, for the case thatN≥3and (HS) is nonautonomous (neither periodic nor almost periodic), we show that (HS) possesses at least one nontrivial homoclinic solution. Our main hypotheses are the strong force condition of Gordon and the uniqueness of a global maximum ofW. Different from the cases that (HS) is autonomousat≡1or (HS) is periodic or almost periodic, as far as we know, this is the first result concerning the case that (HS) is nonautonomous andN≥3. Besides the usual conditions onW, we need the assumption thata′t<0for allt∈ℝto guarantee the existence of homoclinic solution. Recent results in the literature are generalized and significantly improved.

Sets of determination and kernels of certain associated operators

2010 ◽  
Vol 53 (2) ◽  
pp. 503-510
Author(s):  
Arne Stray
Keyword(s):  
Unit Circle ◽  
Unit Disc ◽  
Closed Subset ◽  
Bounded Function ◽  
Harmonic Extension ◽  
Linear Map ◽  
Associated Operators

AbstractLet m be a measure supported on a relatively closed subset X of the unit disc. If f is a bounded function on the unit circle, let fm denote the restriction to X of the harmonic extension of f to the unit disc. We characterize those m such that the pre-adjoint of the linear map f → fm has a non-trivial kernel.

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