Walsh Series and Transforms
Theory and Applications
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Article
Biodiversity, Isolation and Sequencing of Lactococcus lactis Bacteriophages from Dairy Industry Plants in Russia
Starter culture lysis by Lactococcus lactis bacteriophages is one of the leading causes of the fermentation failure in dairy industry. In the present work we performed a PCR grou** of lactophages identified in ...
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Article
Coronal Electron Density Fluctuations Inferred from Akatsuki Spacecraft Radio Observations
Trans-coronal radio observations were taken during the 2011 observing campaign of the Akatsuki spacecraft through superior conjunction. The observed X-band (8.4 GHz) signals exhibit frequency fluctuations (FF)...
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Article
Boas–Kac roots of positive definite functions of several variables
We obtain necessary and sufficient conditions for a continuous real-valued positive definite function of m variables (m > 1) with support in a bounded convex centrally symmetric body in the space ℝ ...
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Article
Lattice Lotka-Volterra model with long range mixing
A spatio-temporal process in the Lattice Lotka Volterra (LLV) model, when realized on low dimensional support, is studied. It is shown that the introduction of a long-range mixing causes a drastic change in th...
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Article
Fundamental nonlinear-optical interactions in photonic fibers: Time-spectral visualization
The nonlinear dynamics of optical signals propagating in fibers or waveguides can be quite complex. Many nonlinear regimes manifest themselves in spectral transformations observed at the output of the fiber. S...
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Chapter and Conference Paper
Phase-sensitive resonance in scattering of continuous waves on femtosecond solitons in photonic crystal fibers
Using cross-correlation frequency-resolved optical gating we observe the phase-sensitive resonance in the interaction of a soliton with a continuous wave in a birefringent photonic crystal fiber, which leads t...
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Article
Spectral-temporal dynamics of ultrashort Raman solitons and their role in third-harmonic generation in photonic crystal fibers
We use cross-correlation frequency-resolved optical gating to obtain spectral-temporal portraits of ultrashort Raman solitons in photonic crystal fibers at telecommunication wavelengths. Power-dependent Raman ...
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Article
Transformation and control of ultra-short pulses in dispersion-engineered photonic crystal fibres
Photonic crystal fibres (PCFs) offer greatly enhanced design freedom compared to standard optical fibres. For example, they allow precise control of the chromatic dispersion (CD) profile—the frequency dependen...
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Article
Diabetes-induced changes in calcium homeostasis and the effects of calcium channel blockers in rat and mice nociceptive neurons
Distal neuropathy is the most common complication of diabetes mellitus, making it important to reveal the cellular mechanisms leading to its development, one of which might be the alteration in intracellular ...
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Article
Minimization of dispersion in an ultrafast chirped pulse amplifier using adaptive learning
Minimizing residual frequency dispersion that accompanies pulse stretching, amplification, and recompression is an important consideration in ultrashort chirped-pulse amplifiers. Here we show how an adaptive l...
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Chapter and Conference Paper
Adaptive Control of Pulse Phase In A Chirped Pulse Amplifier
By monitoring the magnitude of the spectral blueshift in a plasma breakdown experiment, we demonstrate that a femtosecond chirped pulse amplifier can use experimental feedback to adaptively find the phase that...
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Article
Modelling protein three-dimensional structure using tritium planigraphy
We propose the use of data on the topography of the label-accessible surface of a protein molecule obtained by the method of tritium planigraphy as a criterion for choosing the optimal intermediate arrangement...
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Book
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Chapter
Walsh Series with Monotone Decreasing Coefficients
Let {c n }, n = 0, 1, …, be a monotone decreasing sequence of real numbers, i. e., Δc n ≡ c n - cn+1 ≥ 0 for n = 0, 1, …...
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Chapter
Divergent Walsh-Fourier Series. Almost Everywhere Convergence of Walsh-Fourier Series of L2 Functions
In Chapter 2 we saw that even for a continuous function it is necessary to impose additional conditions to insure that its Walsh- Fourier series converges at every point. Without such conditions, as we remarke...
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Chapter
Summability of Walsh Series by the Method of Arithmetic Means
As we saw in §2.3, there exist continuous functions whose Walsh- Fourier series diverge at a given point. We shall show in Chapter 9 that there exist integrable functions whose Walsh-Fourier series diverge eve...
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Chapter
Generalized Multiplicative Transforms
Let 1 ≤ p < ∞. A complex valued function f(x) is said to belong to L p (0, ∞) if ∫0∞|f(x)| p dx > ∞. The norm of f(x) in the space L p ...
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Chapter
Lacunary Subsystems of the Walsh System
The Rademacher system, {r k (x)} = {w2 k , k = 0,1,…, which was used to define the Walsh system (see §1.1), is a typical example of what is called a lac...
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Chapter
Other Applications of Multiplicative Functions and Transformations
Filtering is one of the fundamental techniques of digital signal processing. By a digital filter we shall mean a transformation which takes a sequence of numbers {x(n)}, called the input, in another sequence {y(n
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Chapter
Operators in the Theory of Walsh-Fourier Series
In this chapter, and the next, we shall obtain several results about Walsh-Fourier series by using properties of operators which take one space of measurable functions to another. We begin with definitions and...
