Search results for "complex"
showing 10 items of 5889 documents
The space H(Ω,(zj)) of holomorphic functions
2008
Abstract Let Ω be a domain in C n . Let H ( Ω ) be the linear space over C of the holomorphic functions in Ω, endowed with the compact-open topology. Let ( z j ) be a sequence in Ω without adherent points in Ω. In this paper, we define the space H ( Ω , ( z j ) ) and some of its linear topological properties are studied. We also show that, for some domains of holomorphy Ω and some sequences ( z j ) , the non-zero elements of H ( Ω , ( z j ) ) cannot be extended holomorphically outside Ω. As a consequence, we obtain some characterizations of the domains of holomorphy in C n .
Asymptotics for Capelli polynomials with involution
2021
Let F be the free associative algebra with involution ∗ over a field F of characteristic zero. We study the asymptotic behavior of the sequence of ∗- codimensions of the T-∗-ideal Γ∗ M+1,L+1 of F generated by the ∗-Capelli polynomials Cap∗ M+1[Y, X] and Cap∗ L+1[Z, X] alternanting on M + 1 symmetric variables and L + 1 skew variables, respectively. It is well known that, if F is an algebraic closed field of characteristic zero, every finite dimensional ∗-simple algebra is isomorphic to one of the following algebras: · (Mk(F ), t) the algebra of k × k matrices with the transpose involution; · (M2m(F ), s) the algebra of 2m × 2m matrices with the symplectic involution; · (Mh(F ) ⊕ Mh(F )op, e…
On the order of indeterminate moment problems
2013
For an indeterminate moment problem we denote the orthonormal polynomials by P_n. We study the relation between the growth of the function P(z)=(\sum_{n=0}^\infty|P_n(z)|^2)^{1/2} and summability properties of the sequence (P_n(z)). Under certain assumptions on the recurrence coefficients from the three term recurrence relation zP_n(z)=b_nP_{n+1}(z)+a_nP_n(z)+b_{n-1}P_{n-1}(z), we show that the function P is of order \alpha with 0<\alpha<1, if and only if the sequence (P_n(z)) is absolutely summable to any power greater than 2\alpha. Furthermore, the order \alpha is equal to the exponent of convergence of the sequence (b_n). Similar results are obtained for logarithmic order and for more ge…
Optimal implementation of neural activation functions in programmable logic using fuzzy logic
2006
Abstract This work presents a methodology for implementing neural activation function in programmable logic using tools from fuzzy logic. This methodology will allow implementing these intrinsic non-linear functions using comparators and simple linear modellers, easily implemented in programmable logic. This work is particularized to the case of a hyperbolic tangent, the most common function in neural models, showing the excellent results yielded with the proposed approximation.
Sequestering ability of polyaminopolycarboxylic ligands towards dioxouranium(VI) cation
2006
Abstract In the present paper, some results of an investigation (at t = 25 °C by potentiometry, ISE-H+ glass electrode) on the sequestering ability of five different polyaminopolycarboxylic ligands [Nitrilotriacetate (NTA), ethylenediamine-N,N,N′,N′-tetraacetate (EDTA), ethylene glycol-bis(2-aminoethylether)-N,N,N′,N′-tetraacetate (EGTA), diethylenetriamine-N,N,N′,N″,N″-pentaacetate (DTPA), triethylenetetraamine-N,N,N′,N″,N′′′,N′′′-hexaacetate (TTHA)] towards dioxouranium(VI) cation in sodium chloride aqueous solutions, at I = 0.7 mol L−1 are reported. Calculations performed on potentiometric data gave evidence of the formation of the following species (log β in parenthesis): UO2(NTA)H0 (12…
Sequestration of (CH3)Hg+ by amino‐polycarboxylic chelating agents
2012
Abstract The speciation of mono-methylmercury(II) cation (MeHg+) in the presence of Nitrilotriacetate (NTA), Ethylenediamine-N,N,N′,N′-tetraacetate (EDTA), diethylenetriamine-N,N,N′,N″,N″-pentaacetate (DTPA) and (S,S)- Ethylenediamine-N,N′-disuccinic acid (S,S-EDDS) was investigated at I = 0.1 mol L− 1 (NaCl) with the aim to assess a trend of sequestering capacity of the amino‐polycarboxylic (APCs) ligand class towards this cation in aqueous solution. The results obtained gave evidence for the formation of a mononuclear [MeHg(APC)] complex species, differently protonated MeHg(HiL) species (i = 1 to 3, depending on the APC considered), a mixed hydroxo species [MeHg(APC)(OH)] and a binuclear …
Weak aurophilic interactions in a series of Au(III) double salts.
2015
In this work, several new examples of rare AuIII⋯AuIII aurophilic contacts are reported. A series of gold(III) double salts and complexes, viz. [AuX2(L)][AuX4] (L = 2,2′-bipyridyl, X = Cl 1, Br 2; L = 2,2′-bipyrimidine, X = Cl 3, Br 4; L = 2,2′-dipyridylamine, X = Cl 5, Br 6), [AuX3(biq)] (biq = 2,2′-biquinoline, X = Cl 7, Br 8), [LH][AuX4] (L = 2,2′-bipyridyl, X = Cl 9; L = 2,2′-bipyrimidine, X = Cl 12; L = 2,2′-dipyridylamine, X = Cl 14, Br 15; L = 2,2′-biquinoline, X = Cl 17, Br 18), [AuBr2(bpy)]2[AuBr4][AuBr2] 10, [AuCl2(bpm)][AuCl2] 11, (bpmH)2[AuBr4][AuBr2] 13, and (dpaH)[AuBr2] 16 (1, 2, and 7 were reported earlier) was synthesized by coordination of a particular ligand to the AuIII …
Explicit Granger causality in kernel Hilbert spaces
2020
Granger causality (GC) is undoubtedly the most widely used method to infer cause-effect relations from observational time series. Several nonlinear alternatives to GC have been proposed based on kernel methods. We generalize kernel Granger causality by considering the variables cross-relations explicitly in Hilbert spaces. The framework is shown to generalize the linear and kernel GC methods, and comes with tighter bounds of performance based on Rademacher complexity. We successfully evaluate its performance in standard dynamical systems, as well as to identify the arrow of time in coupled R\"ossler systems, and is exploited to disclose the El Ni\~no-Southern Oscillation (ENSO) phenomenon f…
The expansion $\star$ mod $\bar{o}(\hbar^4)$ and computer-assisted proof schemes in the Kontsevich deformation quantization
2019
The Kontsevich deformation quantization combines Poisson dynamics, noncommutative geometry, number theory, and calculus of oriented graphs. To manage the algebra and differential calculus of series of weighted graphs, we present software modules: these allow generating the Kontsevich graphs, expanding the noncommutative & x22c6;-product by using a priori undetermined coefficients, and deriving linear relations between the weights of graphs. Throughout this text we illustrate the assembly of the Kontsevich & x22c6;-product up to order 4 in the deformation parameter Already at this stage, the & x22c6;-product involves hundreds of graphs; expressing all their coefficients via 149 w…
Novel bioactive bromopyrrole alkaloids from the Mediterranean sponge Axinella verrucosa
2005
The Mediterranean sponge Axinella verrucosa has been investigated for its alkaloid composition and has been found to produce a complex mixture of bromopyrrole alkaloids. Along with the previously isolated compounds 5-18, four novel alkaloids of this class, compounds 1-4, have been isolated, and their structures established through spectroscopic methods. Compounds 1-4 were found to display neuroprotective activity against the agonists serotonin and glutamate in vitro.