On the asymptotic behavior of graphs determined by their generalized spectra

In Wang and Xu (2006) [15] and [16] the authors introduced a family of graphs H_n and gave some methods for finding graphs among this family that are determined by their generalized spectra. This paper is a continuation of our previous work. We further show that almost all graphs in H_n are determined by their generalized spectra. This gives some evidences for the conjecture that almost all graphs are determined by their generalized spectra.     

Spectral characterization of graphs whose second largest eigenvalue is less than 1

Graphs with second largest eigenvalue λ₂?1 are extensively studied, however, whether they are determined by their adjacency spectra or not is less considered. In this paper we completely characterize all the connected bipartite graphs with λ₂<1 that are determined by their adjacency spectra. In addition, we prove that all the connected non-bipartite graphs with girth no less than 4 and λ₂<1 are determined by their adjacency spectra.     

Laplacian spectral characterization of 3-rose graphs

A 3-rose graph is a graph consisting of three cycles intersecting in a common vertex, J. Wang et al. showed all 3-rose graphs with at least one triangle are determined by their Laplacian spectra. In this paper, we complete the above Laplacian spectral characterization and prove that all 3-rose graphs are determined by their Laplacian spectra.     

C1-algebras generated by Hankel operators and Toeplitz operators

Results relating the spectra and essential spectra of Hankel operators to their symbols are obtained by various considerations of the C¹-algebras that they generate. Such considerations exploit the elementary relationships between Hankel operators and Toeplitz operators and established techniques in the theory of Toeplitz operators and their generated C¹-algebras.     

The nuclear magnetic resonance spectra of four spin systems

The spectra of a number ofp-disubstituted benzenes were analyzed earlier by Richards and Schaeffer by assuming that the twometa H-H coupling constants are equal and thepara H-H coupling constant is zero. In the present work a method for analysing this type of spectra, without making any simplifying assumptions, is proposed. The proton resonance spectra ofp-bromochlorobenzene,p-chlorotoluene andp-chloroiodobenzene were obtained and analyzed as examples, and all the parameters were determined in each case. The general form of this type of spectra for different values of chemical shift is discussed.     

<Emphasis Type="Italic">B</Emphasis>-essential and <Emphasis Type="Italic">B</Emphasis>-Weyl spectra of sum of two commuting bounded operators

In this paper, we devote our research to the B-essential spectra of the sum of two bounded linear operators defined on a Banach space by means of the B-essential spectra of each of the two operators where their products are finite rank operators.     

G-symmetric spectra,semistability and the multiplicative norm

In this paper we develop the basic homotopy theory of G-symmetric spectra (that is, symmetric spectra with a G-action) for a finite group G, as a model for equivariant stable homotopy with respect to a G-set universe. This model lies in between Mandell's equivariant symmetric spectra and the G-orthogonal spectra of Mandell and May and is Quillen equivalent to the two. We further discuss equivariant semistability, construct model structures on module, algebra and commutative algebra categories and describe the homotopical properties of the multiplicative norm in this context.     

Ultraviolet spectra of α-carboxystilbenes—I

The ultraviolet spectra of α-carboxy and α-carbomethoxystilbenes obtained in the Claisen/Stobbe reaction of methyl phenyl acetate and aromatic aldehydes is reported. All these compounds possess the characteristiccis stilbene spectral curve. Electronic effects of substituents in the acid show characteristic bathochromic shifts. A fewtrans α-carboxystilbenes have been prepared and their spectra have the characteristictrans stilbene pattern.     

Spectral Characterization of Odd Graphs Ok,k ≤6

Letk be an integer withk≥2. The Odd graphO _k has the(k- l)-subsets of 1,2,..., 2k-1 as vertices, and two vertices are adjacent if and only if their corresponding subsets are disjoint. We prove that the odd graphsO _k (k ≤ 6) are characterized by their spectra among connected regular graphs.     

A model structure for coloured operads in symmetric spectra

We describe a model structure for coloured operads with values in the category of symmetric spectra (with the positive model structure), in which fibrations and weak equivalences are defined at the level of the underlying collections. This allows us to treat R-module spectra (where R is a cofibrant ring spectrum) as algebras over a cofibrant spectrum-valued operad with R as its first term. Using this model structure, we give sufficient conditions for homotopical localizations in the category of symmetric spectra to preserve module structures.     

Essential spectra of quasi-parabolic composition operators on Hardy spaces of analytic functions

In this work we study the essential spectra of composition operators on Hardy spaces of analytic functions which might be termed as “quasi-parabolic.” This is the class of composition operators on H² with symbols whose conjugate with the Cayley transform on the upper half-plane are of the form φ(z)=z+ψ(z), where ψ∈H^∞(H) and ℑ(ψ(z))>?>0. We especially examine the case where ψ is discontinuous at infinity. A new method is devised to show that this type of composition operator fall in a C*-algebra of Toeplitz operators and Fourier multipliers. This method enables us to provide new examples of essentially normal composition operators and to calculate their essential spectra.     

On recognition by spectrum of the simple groups B 3(q), C 3(q), and D 4(q)

The spectrum of a finite group is the set of its element orders. Two groups are isospectral whenever they have the same spectra. We consider the classes of finite groups isospectral to the simple symplectic and orthogonal groups B ₃(q), C ₃(q), and D ₄(q). We prove that in the case of even characteristic and q > 2 these groups can be reconstructed from their spectra up to isomorphisms. In the case of odd characteristic we obtain a restriction on the composition structure of groups of this class.     

Dynamics of chaotic maps for modelling the multifractal spectrum of human brain Diffusion Tensor Images

The multifractal spectra of 3d Diffusion Tensor Images (DTI) obtained by magnetic resonance imaging of the human brain are studied. They are shown to deviate substantially from artificial brain images with the same white matter intensity. All spectra, obtained from 12 healthy subjects, show common characteristics indicating non-trivial moments of the intensity. To model the spectra the dynamics of the chaotic Ikeda map are used. The DTI multifractal spectra for positive q are best approximated by 3d coupled Ikeda maps in the fully developed chaotic regime. The coupling constants are as small as α = 0.01. These results reflect not only the white tissue non-trivial architectural complexity in the human brain, but also demonstrate the presence and importance of coupling between neuron axons. The architectural complexity is also mirrored by the deviations in the negative q-spectra, where the rare events dominate. To obtain a good agreement in the DTI negative q-spectrum of the brain with the Ikeda dynamics, it is enough to slightly modify the most rare events of the coupled Ikeda distributions. The representation of Diffusion Tensor Images with coupled Ikeda maps is not unique: similar conclusions are drawn when other chaotic maps (Tent, Logistic or Henon maps) are employed in the modelling of the neuron axons network.     

Body Wave Propagation and Site Effects

The interaction between seismic radiation and near-surface geology plays a role of primary importance in the risk hazard mitigation especially due to the so called site effects. Such kind of phenomena depends on the geological conditions that may cause spatial variability of ground motion, such as producing an amplification of the seismic signal at defined frequencies. For this reason the analysis of site effects plays a key role in the seismic risk mitigation and the numerical simulation represents a powerful tool in this field. This work contemplates the simulation of seismic signals and analysis of their power spectra, varying the intensity of the impulse and its location in the domain, as well as the number of layers and/or their physical properties in order to guess a possible relation between the maximum of peak amplification and the geometrical and physical characteristics of the medium where seismic waves propagate. The seismic wave propagation is described by means of an Initial Boundary Value Problem on a three-dimensional domain with an arbitrary topography, whose numerical integration, obtained by implementing the Finite Element Method, provides the analyzed seismic signals. We present several cases and analyze the corresponding power spectra in order to recognize the maximum frequency involved in the soil shaking amplification.     

The florachromes: Their chemical nature and spectroscopic behaviour

This memoir presents detailed studies of the two florachromes discovered by the author and shown by him to be responsible for the colours exhibited by a great many flowers, the two florachromes being present in the petals either separately or together as the case may be. Their characteristic absorption spectra have been photographed and reproduced and also represented as spectrophotometric records of their aqueous solutions and of the acetone extracts of the floral pigments. In appropriate circumstances, the florachromes in solution are found to be quite stable and continue to exhibit their characteristic spectroscopic behaviours permanently. The interesting discovery is recorded that Florachrome B is present as the colouring matter of the fleshy leaves of the shrubSetcreasia purpurea and can be readily obtained therefrom. The relation between the structure of the florachromes and of the well-known organic compound flavone which is itself a colourless solid is discussed and an explanation is given why there are two florachromes with distinct spectroscopic behaviours.     

The ultraviolet and infrared spectra of some lichen depsides and depsidones

The ultraviolet and infrared spectral data for a number of lichen depsides, depsidones and their fission products have been recorded. The U.V. spectra of the orcinol depsides, orcinol depsidones andβ-orcinol depsidones are characteristic while those of theβ-orcinol depsides less useful for diagnostic purposes. The I.R. spectra are more useful and the carbonyl region is significant for this purpose.     

Two interacting hard disks within a circular cavity: towards a quasi-equilibrium quantal equation of states

Two interacting hard disks confined in a circular cavity are investigated. Each disk shows a free motion except when bouncing elastically with its partner and with the boundary wall. According to the analysis of Lyapunov exponents, this system is classically nonintegrable and almost chaotic because of the (short-range) interaction between the disks. The system can be quantized by incorporating the excluded volume effect for the wave function. Eigenvalues and eigenfunctions are obtained by tuning the relative size between the disks and the billiard. The pressure P is defined as the derivative of each eigenvalue with respect to the cavity volume V. Since the energy spectra of eigenvalues versus the disk size show a multitude of level repulsions, P–V characteristics shows the anomalous pressure fluctuations accompanied by many van der Waals-like peaks in each of excited eigenstates taken as a quasi-equilibrium. For each eigenstate, we calculate the expectation values of the square distance between two disks, and point out their relationship with the pressure fluctuations. Role of Bose and Fermi statistics is also investigated.     

Digraphs with real and gaussian spectra

The conventional binary operations of cartesian product, conjunction, and composition of two digraphs D₁ and D₂ are observed to give the sum, the product, and a more complicated combination of the spectra of D₁ and D₂ as the resulting spectrum. These formulas for analyzing the spectrum of a digraph are utilized to construct for any positive integer n, a collection of n nonisomorphic strong regular nonsymmetric digraphs with real spectra. Further, an infinite collection of strong nonsymmetric digraphs with nonzero gaussian integer value is found. Finally, for any n, it is shown that there are n cospectral strong nonsymmetric digraphs with integral spectra.     

On scalar extensions and spectral decompositions of complex symmetric operators

In this paper we prove that a complex symmetric operator with property (δ) is subscalar. As a corollary, we get that such operators with rich spectra have nontrivial invariant subspaces. We also provide various relations for spectral decomposition properties between complex symmetric operators and their adjoints.     

Local spectral properties of reflectionless Jacobi, CMV, and Schrödinger operators

We prove that Jacobi, CMV, and Schrödinger operators, which are reflectionless on a homogeneous set E (in the sense of Carleson), under the assumption of a Blaschke-type condition on their discrete spectra accumulating at E, have purely absolutely continuous spectrum on E.