Spectrum ofA Research Articles

Spinless particle motion near black hole horizon

The motion of a light spinless particle in the vicinity of a heavy central mass is analyzed. We have derived the wave function and energy spectrum ofa particle. It is shown the ground state of a particle in the centrally symmetric gravitational field. The excited state of a particle is considered. The given problem relates to a semi-classical formulation of gravity, where matter is quantized, but gravity is not. One of the aims of this study to show the quantum behavior of a particle near to a black hole.

Orthogonality Property of the Discreteq-Hermite Matrix Polynomials

In this paper, we prove that the solution of the autonomousq-difference systemDqYx=AYqxwith the initial conditionY0=Y0whereAis a constant square complex matrix,Dqis the Jacksonq-derivative and0<q<1, is asymptotically stable if and only ifℜλ<0for allλ∈σAwhereσAis the set of all eigenvalues ofA(the spectrum ofA). This results are exploited to provide the orthogonality property of the discreteq-Hermite matrix polynomials.

Two Different Quinohemoprotein Amine Dehydrogenases Initiate Anaerobic Degradation of Aromatic Amines in Aromatoleum aromaticum EbN1.

Aromatic amines like 2-phenylethylamine (2-PEA) and benzylamine (BAm) have been identified as novel growth substrates of the betaproteobacterium Aromatoleum aromaticum EbN1, which degrades a wide variety of aromatic compounds in the absence of oxygen under denitrifying growth conditions. The catabolic pathway of these amines was identified, starting with their oxidative deamination to the corresponding aldehydes, which are then further degraded via the enzymes of the phenylalanine or benzyl alcohol metabolic pathways. Two different periplasmic quinohemoprotein amine dehydrogenases involved in 2-PEA or BAm metabolism were identified and characterized. Both enzymes consist of three subunits, contain two heme c cofactors in their α-subunits, and exhibit extensive processing of their γ-subunits, generating four intramolecular thioether bonds and a cysteine tryptophylquinone (CTQ) cofactor. One of the enzymes was present in cells grown with 2-PEA or other substrates, showed an α2β2γ2 composition, and had a rather broad substrate spectrum, which included 2-PEA, BAm, tyramine, and 1-butylamine. In contrast, the other enzyme was specifically induced in BAm-grown cells, showing an αβγ composition and activity only with BAm and 2-PEA. Since the former enzyme showed the highest catalytic efficiency with 2-PEA and the latter with BAm, they were designated 2-PEADH and benzylamine dehydrogenase (BAmDH). The catalytic properties and inhibition patterns of 2-PEADH and BAmDH showed considerable differences and were compared to previously characterized quinohemoproteins of the same enzyme family.IMPORTANCE The known substrate spectrum of A. aromaticum EbN1 is expanded toward aromatic amines, which are metabolized as sole substrates coupled to denitrification. The characterization of the two quinohemoprotein isoenzymes involved in degrading either 2-PEA or BAm expands the knowledge of this enzyme family and establishes for the first time that the necessary maturation of their quinoid CTQ cofactors does not require the presence of molecular oxygen. Moreover, the study revealed a highly interesting regulatory phenomenon, suggesting that growth with BAm leads to a complete replacement of 2-PEADH by BAmDH, which has considerably different catalytic and inhibition properties.

On ClusterC⁎-Algebras

We introduce aC⁎-algebraA(x,Q)attached to the clusterxand a quiverQ. IfQTis the quiver coming from triangulationTof the Riemann surfaceSwith a finite number of cusps, we prove that the primitive spectrum ofA(x,QT)timesRis homeomorphic to a generic subset of the Teichmüller space of surfaceS. We conclude with an analog of the Tomita-Takesaki theory and the Connes invariantT(M)for the algebraA(x,QT).

Geometric spectral theory for compact operators

For annn-tupleA=(A1,⋯,An)\mathbb {A}=(A_1,\cdots ,A_n)of compact operators we define the joint point spectrum ofA\mathbb {A}to be the set\[σp(A)={(z1,⋯,zn)∈Cn:ker⁡(I+z1A1+⋯+znAn)≠(0)}.\sigma _p(\mathbb {A})=\{(z_1,\cdots ,z_n)\in \mathbb {C}^n:\ker (I+z_1A_1+\cdots +z_nA_n)\not =(0)\}.\]We prove in several situations that the operators inA\mathbb {A}pairwise commute if and only ifσp(A)\sigma _p(\mathbb {A})consists of countably many, locally finite, hyperplanes inCn\mathbb C^n. In particular, we show that ifA\mathbb {A}is annn-tuple ofN×NN\times Nnormal matrices, then these matrices pairwise commute if and only if the polynomial\[pA(z1,⋯,zn)=det(I+z1A1+⋯+znAn)p_{\mathbb {A}}(z_1,\cdots ,z_n)=\det (I+z_1A_1+\cdots +z_nA_n)\]is completely reducible, namely,\[pA(z1,⋯,zn)=∏k=1N(1+ak1z1+⋯+aknzn)p_{\mathbb {A}}(z_1,\cdots ,z_n)=\prod _{k=1}^N(1+a_{k1}z_1+\cdots +a_{kn}z_n)\]can be factored into the product of linear polynomials.

Dual Algebras and A-Measures

Weak-star closures of Gleason parts in the spectrum of a function algebra are studied. These closures relate to the bidual algebra and turn out both closed and open subsets of a compact hyperstonean space. Moreover, weak-star closures of the corresponding bands of measures are reducing. Among the applications we have a complete solution of an abstract version of the problem, whether the set of nonnegative A-measures (called also Henkin measures) is closed with respect to the absolute continuity. When applied to the classical case of analytic functions on a domain of holomorphyΩ⊂Cn, our approach avoids the use of integral formulae for analytic functions, strict pseudoconvexity, or some other regularity ofΩ. We also investigate the relation between the algebra of bounded holomorphic functions onΩand its abstract counterpart—thew* closure of a function algebraAin the dual of the band of measures generated by one of Gleason parts of the spectrum ofA.

Multipliers of commutative Banach algebras, power boundedness and Fourier-Stieltjes algebras

Let A be a semisimple and regular commutative Banach algebra with bounded approximate identity. We study multipliers of A, in particular power bounded ones, and the associated ideals of A and A-invariant projections of the dual space of A. Samples of the results are general versions of the classical theorems of Choquet�Deny and of Foguel about measures on locally compact abelian groups. The results are linked to sets of synthesis in the Gelfand spectrum of A, and the main applications are concerned with Fourier and Fourier�Stieltjes algebras of locally compact groups.

Dynamic critical exponents for Swendsen–Wang and Wolff algorithms obtained by anonequilibrium relaxation method

Using a nonequilibrium relaxation method, we calculate the dynamic critical exponentz of the two-dimensional Ising model for the Swendsen–Wang and Wolffalgorithms. We examine dynamic relaxation processes following a quenchfrom a disordered or an ordered initial state to the critical temperatureTc, and measure the exponential relaxation time of the system energy. For theSwendsen–Wang algorithm with an ordered or a disordered initial state,and for the Wolff algorithm with an ordered initial state, the exponentialrelaxation time fits well to a logarithmic size dependence up to a lattice sizeL = 8192. For the Wolff algorithm with a disordered initial state, we obtain an effective dynamic exponentzexp = 1.19(2) upto L = 2048. For comparison, we also compute the effective dynamic exponents through the integratedcorrelation times. In addition, an exact result of the Swendsen–Wang dynamic spectrum ofa one-dimensional Ising chain is derived.

A newAphidius species (Hymenoptera: Braconidae: Aphidiinae) from high-montane areas of southeastern Europe

Aphidius montenegrinus sp.n. from Serbia and Montenegro is described and illustrated. It parasitizedAcyrthosiphon daphnidis Ilharco, onDaphne alpina L. The parasitoid was described and illustrated using scanning electron microscope photographs and line drawing. The new species is a member of theAcyrthosiphon aphid parasitoid guild and was collected from Zabojsko Jezero Lake in Montenegro. The parasitoid and the hyperparasitoid spectrum ofA. daphnidis are presented for the first time.

On commuting operator exponentials

Let A A , B B be bounded operators on a Banach space with 2 π i 2\pi i -congruence-free spectra such that e A e B = e B e A e^Ae^B=e^Be^A . E. M. E. Wermuth has shown that A B = B A AB=BA . Ch. Schmoeger later established this result, using inner derivations and, in a second paper, has shown that: for a , b a,b in a complex unital Banach algebra, if the spectrum of a + b a+b is 2 π i 2\pi i -congruence-free and e a e b = e a + b = e b e a e^ae^b=e^{a+b}=e^be^a , then a b = b a ab=ba (and thus, answering an open problem raised by E. M. E. Wermuth). In this paper we use the holomorphic functional calculus to give alternative simple proofs of both of these results. Moreover, we use the Borel functional calculus to give new proofs of recent results of Ch. Schmoeger concerning normal operator exponentials on a complex Hilbert space, under a weaker hypothesis on the spectra.

Coherence Time Resolvable Diffraction and New Tunnelling Electronics

With the help of the perturbation method and the Feynman path integraltechnique, we analytically demonstrate that, when the electronic spectrum ofa mesoscopic box is measured through two connecting leads, there existsa class of new diffraction phenomena in the coherence timedomain, based on the new coherent tunnelling model. It is shown that the newdiffraction effect determines the minimal resolvable coherence time tothe Heisenberg limit. In particular, Fraunhofer optical phenomena,such as missing order and grating effects, can be reproduced in themeso-systems. The predicted periodic oscillations as a function ofvoltage are in excellent agreement with experimental observations.

On a strong form of a conjecture of Boyle and Handelman

Let ρr,m(x, λ ): = (x − λ) rm=0 � r+i−1 i � x m−i λ i . In this paper it is shown that if λ1 ,...,λ n are complex numbers such that λ1 = λ2 = ... = λr > 0a nd 0≤ � n=1 λ k ≤ nλ k ,fo r 1 ≤ k ≤ m := n − r ,t hen n � i=1 (λ − λi) ≤ ρr,m(λ, λ1), for all λ ≥ 6.75λ1. (∗) Moreover, if r ≥ m ,t hen (∗) holds for all λ ≥ λ1, while if r< m, but r is close to m ,a ndn is large, one can lower the constant of6 .75 in the inequality (∗). The inequality (∗) is inspired by, and related to, a conjecture ofBoyle and Handelman on the nonzero spectrum ofa nonnegative matrix.

The homogeneous spectrum of a graded commutative ring

Suppose Γ \Gamma is a torsion-free cancellative commutative monoid for which the group of quotients is finitely generated. We prove that the spectrum of a Γ \Gamma -graded commutative ring is Noetherian if its homogeneous spectrum is Noetherian, thus answering a question of David Rush. Suppose A A is a commutative ring having Noetherian spectrum. We determine conditions in order that the monoid ring A [ Γ ] A[\Gamma ] have Noetherian spectrum. If rank ⁡ Γ ≤ 2 \operatorname {rank} \Gamma \le 2 , we show that A [ Γ ] A[\Gamma ] has Noetherian spectrum, while for each n ≥ 3 n \ge 3 we establish existence of an example where the homogeneous spectrum of A [ Γ ] A[\Gamma ] is not Noetherian.

H∞functional calculus in real interpolation spaces, II

LetA be a linear closed one-to-one operator in a complex Banach spaceX, having dense domain and dense range. IfA is of type! (i.e. the spectrum ofA is contained in a sector of angle 2!, symmetric about the real positive axis, and k (I A) 1 k is bounded outside every larger sector), then A has a bounded H 1 functional calculus in the real interpolation spaces between X and the intersection of the domain and the range of the operator itself.

Vacuum-UV absorption spectrum of a laser-produced chromiumplasma: 3p-subshell photoabsorption by Cr2+ ions

The dual laser plasma photoabsorption technique has been used tomeasure the time-resolved vacuum-UV photoabsorption spectrum ofa chromium plasma. Resonant photoabsorption cross sections, constructedwith the aid of Hartree-Fock calculations, and weighted in accordancewith the plasma temperature, have been used to produce the syntheticCr2+ spectra. The relevant plasma temperature and ionization balanceare obtained from simple analytical models for various times during theexpansion phase of the plasma plume. The experimental spectra taken atdelays of 32, 62 and 90 ns compare well with Cr2+spectra computedfor corresponding predicted temperatures. It is found that in order toproduce synthetic spectra that match experiment well, it is necessary totake into account absorption from many states belonging to the Cr2+ground state configuration 3p63d4, while states from the nearestmetastable configuration 3p63p34s make a negligible contribution.

Calcul Fonctionnel Holomorphe Global Unicité et Invariance Par Les Homomorphismes D’algebres de Banach

LetA be a commutative Banach algebra with unit. Denote byX A, the global spectrum ofA. There is a holomorphic functional calculusθ A:O(X A)→A such thatθ A(â)=a. In this paper, we show the uniqueness of the global holomorphic functional calculus and we establish its compatibility with Banach algebra morphisms. We also extend this holomorphic functional calculus to the case ofImc algebras.

On a conjecture of Hubner

In this paper we show that for a bounded linear operatorA on a complex Hilbert spaceH, the points on the boundary of the numerical range ofA with infinite curvature and unique tangent are in the essential spectrum ofA, thus positively answering a conjecture raised by Hubner in [3].

The convergence of Krylov subspace methods for large unsymmetric linear systems

The convergence problem of many Krylov subspace methods,e.g., FOM, GCR, GMRES and QMR, for solving large unsymmetric (non-Hermitian) linear systems is considered in a unified way when the coefficient matrixA is defective and its spectrum lies in the open right (left) half plane. Related theoretical error bounds are established and some intrinsic relationships between the convergence speed and the spectrum ofA are exposed. It is shown that these methods are likely to converge slowly once one of the three cases occurs:A is defective, the distribution of its spectrum is not favorable, or the Jordan basis ofA is ill conditioned. In the proof, some properties on the higher order derivatives of Chebyshev polynomials in an ellipse in the complex plane are derived, one of which corrects a result that has been used extensively in the literature.

Polyhedral reachable set with positive controls

Given a reachable discrete-time linear system (A,b), the reachable set is a cone when a positive constraint is imposed on the input. The problem to be studied is the geometrical structure of the reachable set ℛ= cone(b, Ab, A2b,...) in terms of the spectrum ofA. In particular, conditions which ensure ℛ, or its closureR, is a polyhedral proper cone are derived. The impact of the given results on finite-time reachability and positive realizability is also discussed.

Spectrally determined growth is generic

Let A A be the infinitesimal generator of a C 0 C_0 -semigroup of operators in a Hilbert space. We consider the class of operators A + B A+B , where B B is bounded. It is proved that the spectrum of A + B A+B determines the growth of the associated semigroup for “most" operators B B (in the sense of Baire category).