87,731 research outputs found
The Hardy–Littlewood lemma and the estimate for the d-barNeumann problem in a general norm
No full textWe prove a generalized Hardy-Littlewood lemma on a non-smooth domain in the "f-norm" and give an application to a corresponding estimate for the partial derivative-Neumann problem by means of suitable weights. (c) 2013 Elsevier Inc. All rights reserved
The H∞-Functional Calculi for the Quaternionic Fine Structures of Dirac Type
No full textIn recent works, various integral representations have been proposed for specific sets of functions. These representations are derived from the Fueter-Sce extension theorem, considering all possible factorizations of the Laplace operator in relation to both the Cauchy-Fueter operator (often referred to as the Dirac operator) and its conjugate. The collection of these function spaces, along with their corresponding functional calculi, are called the quaternionic fine structures within the context of the S-spectrum. In this paper, we utilize these integral representations of functions to introduce novel functional calculi tailored for quaternionic operators of sectorial type. Specifically, by leveraging the aforementioned factorization of the Laplace operator, we identify four distinct classes of functions: slice hyperholomorphic functions (leading to the S-functional calculus), axially harmonic functions (leading to the Q-functional calculus), axially polyanalytic functions of order 2 (leading to the P-2-functional calculus), and axially monogenic functions (leading to the F-functional calculus). By applying the respective product rule, we establish the four different H-infinity versions of these functional calculi
An Introduction to Hyperholomorphic Spectral Theories and Fractional Powers of Vector Operators
No full textThe aim of this paper is to give an overview of the spectral theories associated with the notions of holomorphicity in dimension greater than one. A first natural extension is the theory of several complex variables whose Cauchy formula is used to define the holomorphic functional calculus for n-tuples of operators (A1, ... , An). A second way is to consider hyperholomorphic functions of quaternionic or paravector variables. In this case, by the Fueter-Sce-Qian mapping theorem, we have two different notions of hyperholomorphic functions that are called slice hyperholomorphic functions and monogenic functions. Slice hyperholomorphic functions generate the spectral theory based on the S-spectrum while monogenic functions induce the spectral theory based on the monogenic spectrum. There is also an interesting relation between the two hyperholomorphic spectral theories via the F-functional calculus. The two hyperholomorphic spectral theories have different and complementary applications. We finally discuss how to define the fractional Fourier’s law for nonhomogeneous materials using the spectral theory on the S-spectrum
Existence and Interior Regularity Theorems for ∂ ̄ on Q-Convex Domains
No full textWe establish for a q-convex domain Ω ⊂ Cn existence results in Lp,k-12(Ω,loc) and Cp,k-1∞(Ω) for the equation ∂ ̄ u= f, where f is a (p, k)-form on Ω of degree k≥ q such that ∂ ̄ f= 0
Enzymatic responses of cucumber roots to different levels of Fe supply
No full textDevelopment of the coordinated response to decreasing Fe availability was studied in cucumber plants grown in nutrient solution (NS) over a range of FeIII-EDTA concentrations (from 0.1 to 80 μM). Physiological and biochemical parameters were evaluated in intact roots, root extracts and plasma membrane (pm) vesicles. Acidification of the NS was evident in plants grown at ≤ 1 μM FeIII-EDTA and inversely related to the external Fe concentration. FeIII-EDTA reduction by intact roots was also gradually depressed by increasing Fe supply. The rate of net nitrate uptake by the roots was directly related to the amount of FeIII-EDTA added to the NS. Activity of pmH+-ATPase was significantly higher in plants grown without added Fe as compared to those grown at 80 μM Fe. A lower increase, dependent on Fe concentration, was observed at 0.1, 1, 5 or 10 μM FeIII-EDTA. Activity of pmFeIII-EDTA reductase was also increased by Fe deprivation and strongly correlated with pmH+-ATPase activity. PEP-carboxylase activity gradually increased with decreasing Fe concentration in the NS. Changes in activity and amount of the enzyme showed a close correlation with parameters measured in intact roots (nitrate uptake, FeIII-EDTA reduction). Results show that the development of the Fe-deficiency response in cucumber roots can be finely tuned by the level of Fe supply. Adjustments to different levels of available Fe involve a correlated modulation of pm-associated enzymes. PEP-carboxylase activity appeared to be a suitable metabolic marker of the Fe nutritional status of the plant
Sottogruppi del lupus eritematoso
No full textTesi di Specialità in Dermatologia e Venereologia, Università di Milano (rel. Prof. F. Gianotti
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