Search results for "Exponent"
showing 10 items of 896 documents
On central polynomials and codimension growth
2022
Let A be an associative algebra over a field of characteristic zero. A central polynomial is a polynomial of the free associative algebra that takes central values of A. In this survey, we present some recent results about the exponential growth of the central codimension sequence and the proper central codimension sequence in the setting of algebras with involution and algebras graded by a finite group.
First and second critical exponents for an inhomogeneous Schrödinger equation with combined nonlinearities
2022
AbstractWe study the large-time behavior of solutions for the inhomogeneous nonlinear Schrödinger equation $$\begin{aligned} iu_t+\Delta u=\lambda |u|^p+\mu |\nabla u|^q+w(x),\quad t>0,\, x\in {\mathbb {R}}^N, \end{aligned}$$ i u t + Δ u = λ | u | p + μ | ∇ u | q + w ( x ) , t > 0 , x ∈ R N , where $$N\ge 1$$ N ≥ 1 , $$p,q>1$$ p , q > 1 , $$\lambda ,\mu \in {\mathbb {C}}$$ λ , μ ∈ C , $$\lambda \ne 0$$ λ ≠ 0 , and $$u(0,\cdot ), w\in L^1_{\mathrm{loc}}({\mathbb {R}}^N,{\mathbb {C}})$$ u ( 0 , · ) , w ∈ L loc 1 ( R N , C ) . We consider both the cases where $$\mu =0$$ μ = 0 and $$\mu \ne 0$$ μ ≠ 0 , respectively. We establish existence/nonexistence of global weak solutions. In ea…
Sequentially Forecasting Economic Indices Using Mixture Linear Combinations of EP Distributions
2021
This article displays an application of the statistical method moti- vated by Bruno de Finetti's operational subjective theory of probability. We use exchangeable forecasting distributions based on mixtures of linear com- binations of exponential power (EP) distributions to forecast the sequence of daily rates of return from the Dow-Jones index of stock prices over a 20 year period. The operational subjective statistical method for comparing distributions is quite different from that commonly used in data analysis, because it rejects the basic tenets underlying the practice of hypothesis test- ing. In its place, proper scoring rules for forecast distributions are used to assess the values o…
Do we understand the solid-like elastic properties of confined liquids?
2021
Recently, in polymeric liquids, unexpected solid-like shear elasticity has been discovered, which gave rise to a controversial discussion about its origin (1⇓–3). The observed solid-like shear modulus G depends strongly on the distance L between the plates of the rheometer according to a power law G ∝ L − p with a nonuniversal exponent ranging between p = 2 and p = 3 . Zaccone and Trachenko (4) have published an article in which they claim to explain these findings by a nonaffine contribution to the liquid shear modulus. The latter is represented as Δ G ∝ − ∑ λ = L , T 1 V … [↵][1]1To whom correspondence may be addressed. Email: giancarlo.ruocco{at}roma1.infn.it. [1]: #xref-corresp-1-1
Ice deformed in compression and simple shear: control of temperature and initial fabric
2012
AbstractLayered and polycrystalline ice was experimentally deformed in general shear involving axial compression (strain magnitude 0.5-17%) and simple shear (strain magnitude γ = 0.1-1.4). As the temperature is increased from -20°C to -2°C, there is at least a twofold enhancement in octahedral shear strain rate, which coincides with the onset of extensive dynamic recrystallization and a change in grain-size distribution at -15°C. Between -150C and -10°C the c-axis preferred orientation rapidly evolves with the initiation of two-maxima fabrics in shear zones. From -10°C to -2°C there is progressive evolution of a final c-axis pattern that is asymmetric with respect to the direction of shorte…
Rapid parameter estimation of discrete decaying signals using autoencoder networks
2021
Machine learning: science and technology 2(4), 045024 (2021). doi:10.1088/2632-2153/ac1eea
Numerical approach for signal delay in general distributed networks
2003
The authors consider a general network with telegraph equations modelling distributed elements and having, additionally, nonlinear capacitors. A global asymptotic exponential stability of the solution is given. A simple computable upper bound of the delay time is given. Numerical examples illustrate the usefulness of the results. >
Cathodoluminescence decay kinetics in Ge+, Si+, O+ implanted SiO2 layers
2003
Abstract Cathodoluminescence spectral shapes and respective band decay times show no similarity between luminescence centers in different crystal and amorphous modifications of SiO2 and GeO2. On the other hand, the additionally produced red luminescence centers (650 nm) by oxygen implantation into SiO2 layers are of the same nature as in stoichiometric SiO2 and are attributed to the non-bridging oxygen hole center (NBOHC). On the other hand, the elevated blue luminescence (460 nm) in Si implanted SiO2 belongs to the silicon related oxygen deficient center (SiODC) as in stoichiometric layers also. Ge implantation into SiO2 and thermal post-annealing leads to a huge violet luminescence (400 n…
Experimental Study of the Stage-Discharge Relationship for an Upstream Inclined Grid with Longitudinal Bars
2013
AbstractIn this paper, the outflow process of an upstream inclined grid with longitudinal bars is studied by using the dimensional analysis and the incomplete self-similarity theory. Next, the theoretical analysis shows that a power equation can be used for establishing the stage-discharge equation. The coefficient and an exponent of the power equation depend on the slope angle and the void ratio. Finally, this new stage discharge is tested by using measurements obtained by laboratory runs conducted in this investigation.
Closure to “Experimental Study of the Stage-Discharge Relationship for an Upstream Inclined Grid with Longitudinal Bars” by C. Di Stefano and V. Ferro
2014
The discusser would like to thank the authors of the original paper for investigating the outflow process of an upstream inclined grid with longitudinal bars using the dimensional analysis and the incomplete self-similarity theory. The discusser, however, would like to add a few points. Using the theoretical analysis the authors of the original paper showed that a power equation can be used for establishing the stage-discharge equation of an upstream inclined grid with longitudinal bars. The authors of the original paper also showed that the coefficient and exponent of the power equation depend on the slope angle and the void ratio. They proposed a stage-discharge equation