Narrow Results

Let ${𝒳}$ and ${𝒴}$ be Banach spaces. When ${𝒜}$ and ${ℬ}$ are linear relations in ${𝒳}$ and ${𝒴}$, respectively, we denote by ${{ℳ}}_{{𝒞}}$ the linear relation matrix acting on ${𝒳}\times {𝒴}$ of the form ${{ℳ}}_{{𝒞}}=\left(\right.\begin{array}{cc}\hfill {𝒜}\hfill & \hfill {𝒞}\hfill \\ \hfill 0\hfill & \hfill {ℬ}\hfill \end{array}\left)\right.$, where $0$ is the zero operator and ${𝒞}$ is a bounded operator from ${𝒴}$ to ${𝒳}$. In this paper, we prove that if ${\sigma }_{\ast }(.)$ denotes the Weyl spectrum, the Browder spectrum or the Drazin spectrum of a linear relation, then for every ${𝒞}\in {ℒ}({𝒴},{𝒳}),$ we have the equality ${\sigma }_{\ast }({𝒜})\cup {\sigma }_{\ast }({ℬ})={\sigma }_{\ast }({{ℳ}}_{{𝒞}})\cup {𝒲}$ where ${𝒲}$ a subset of ${\sigma }_{\ast }({𝒜})\cap {\sigma }_{\ast }({ℬ})$. Moreover, we explore how Weyl’s theorem and Browder’s theorem hold for linear relation matrices.

Computational studies exploring the extent to which differences in proximal axial ligands modulate structure, spectra, and function of peroxidases have been performed. To this end, three heme models of compound I were characterized differing only in the axial ligand. The axial ligands considered were L=ImH, Im^-, that are alternative protonation models for a typical peroxidase with an imidazole ligand such as horseradish peroxidase (HRP-I), and L=SCH- that is a model for an unsual peroxidase, chloroperoxidase (CPO-I). Density functional calculations (DFTs) were performed to determine the optimized geometries and electronic structure of each of these three species. Their electronic spectra were also calculated at the DFT optimized geometries, using the INDO/S/CI method. The results of these studies led to the following conclusions: (1) the presence of the nearby Asp in a typical peroxidase does indeed decrease the energy required to deprotonate the imidazole making the two forms essentially degenerate, (2) neither the state of protonation of the imidazole ligand nor the change in axial ligand from an imidazole in typical peroxidases such as HRP to a mercaptide in CPO significantly alters the characteristics of the lowest energy spin state or the electronic structure of compound I in a way that can obviously affect function, (3) both the Im^- and ImH forms of the peroxidase compound I (HRP-I) lead to the same dramatic reduction in intensity relative to the ferric resting form observed experimentally. However, only in the ImH form of HRP-I does the calculated relative shift of one component of the Soret bands relative to CPO-I agree with that observed in the transient spectra of HRP-I compared to CPO-I. These results taken together strongly indicate that factors other than the nature of the proximal axial ligand are the main determinants of function.

The graph isomorphism problem is to check if two given graphs are isomorphic. Graph isomorphism is a well studied problem and numerous algorithms are available for its solution. In this paper we present algorithms for graph isomorphism that employ the spectra of graphs. An open problem that has fascinated many a scientist is if there exists a polynomial time algorithm for graph isomorphism. Though we do not solve this problem in this paper, the algorithms we present take polynomial time. These algorithms have been tested on a good collection of instances. However, we have not been able to prove that our algorithms will work on all possible instances. In this paper, we also give a new construction for cospectral graphs.

In this paper is described an expert system (ES) developed in order to enable the analysis of emission spectra, which are obtained by measurements of activities of radioactive elements, i.e., isotopes, actually cesium. In the structure of those spectra exists two parts: first on lower energies, which originates from the Compton effect, and second on higher energies, which contains the photopeak. The aforementioned ES is made to perform analysis of spectra in whole range of energies. Analysis of those spectra is very interesting because of the problem of environmental contamination by radio nuclides.

Using exclusively an action variable, we quantize a static, spherically symmetric black hole. The spacings of the quantized entropy spectrum and area spectrum are found to be equal to the values given by Bekenstein. Interestingly, we find the spectra are independent of the hairs of the black holes and the mode of motion of a particle outside the spacetime, which depends only on the intrinsic properties of the gravity. Our result shows that the spectra are universal provided the spacetime owns a horizon.

We summarize the main results reported by EAS-TOP in the study of cosmic rays in the energy range 10¹² – 10¹⁶ eV (from the direct measurements up to above the "knee"), i.e. the region which is generally considered to represent the high energy galactic radiation.

Experimental data on inclusive cross-sections of particles produced in high energy proton–(anti)proton collisions at ISR, RHIC and Tevatron are analyzed in the framework of z-scaling. New features of the scaling function ψ(z) are established. These are flavor independence of ψ(z) including particles with heavy flavor content and saturation at low z. The flavor independence means that the shape of the scaling function ψ(z) is the same for different hadron species. The saturation corresponds to flattening of ψ(z) for z < 0.1. Relations of model parameters used in data z-presentation with some thermodynamical quantities (entropy, specific heat, temperature) are discussed. It is shown that behavior of the particle spectra at low z is controlled by a parameter c interpreted as a specific heat of the created medium associated with production of the inclusive particle. The saturation regime of ψ(z) observed at low z is assumed to be preferable in searching for phase transitions of hadron matter and for study of nonperturbative QCD in high energy proton–(anti)proton collisions at U70, RHIC, Tevatron and LHC.

Perturbative and nonperturbative terms of the cross-sections of ultraperipheral production of lepton pairs in ion collisions are taken into account. It is shown that production of low-mass $e^{+}{e}^{-}$ pairs is strongly enhanced (compared to perturbative estimates) due to the nonperturbative Sommerfeld–Gamow–Sakharov (SGS) factor. Coulomb attraction of the nonrelativistic components of those pairs leads to the finite value of their mass distribution at lowest masses. Their annihilation can result in an increased intensity of 511 keV photons. It can be recorded at the NICA collider and is especially crucial in astrophysical implications regarding the 511 keV line emitted from the Galactic center. The analogous effect can be observed in lepton pairs production at LHC. Energy spectra of lepton pairs created in ultraperipheral nuclear collisions and their transverse momenta are calculated.

The random forest method is used for the first time to provide results for some heavy meson spectra, such as $b\bar{b}$ mesons. The performance of our model in predicting the mass spectra of $b\bar{b}$ mesons from 1S to 6S states is investigated. The predictions are in a good accordance with the latest experimental data and other theoretical approaches.

A composite mechanoluminescent layer has been produced on the surface of polymethylmethacrylate by liquid-phase embedding of ${\mathrm{\text{SrAl}}}_2{\mathrm{\text{O}}}_4:({\mathrm{\text{Eu}}}^{2+},{\mathrm{\text{Dy}}}^{3+})$ phosphor microparticles into the polymethylmethacrylate surface layer. The photoluminescence and mechanoluminescence of the obtained layer have been investigated. The mechanoluminescence was excited by the short acoustic pulses and by the dynamic pressure of the stylus sliding over the mechanoluminescent layer surface. A possible mechanism of mechanoluminescence excitation is under discussion. The produced composite layer is shown to exhibit high efficiency of “mechano-optical” transformation.

In this paper, the influence of different dimensionless distance on heat transfer characteristics in a rectangular enclosure is studied using lattice Boltzmann method (LBM). It is shown that the relation between the Rayleigh number (Ra) and the Nusselt number (Nu) using LBM is in promising agreement with that of the previous experimental data by Corvaro and Paroncini [Appl. Therm. Eng.28 (2007) 25]. It is found that the characteristic of heat transport is closely related to the dimensionless distance of heat source. Special attention is paid to investigate the relation between Ra and Nu. Some relations between Ra and Nu for different dimensionless distance are approximately established in natural convection. It is further found that the heat transport is enhanced with the increase of dimensionless distance.

We present a semi-analytical theory to describe the nonlinear scattering of Raman photon pairs from a cylindrical microparticle comprising of quantum particles in double Raman configuration. The normally ordered Stokes and anti-Stokes spectra are computed to gain insights into the quantum optical properties of the system and the variation of the spectra with microparticle’s size, orientation as well as observation angles are also analyzed and compared with the results obtained in our previous work involving mesoscopic spherical particle. Our results show several features in the spectra that are unique to the case of cylindrical microparticle and not found in the spherical particle case, such as the shifting of the side peaks originally formed due to ac Stark shifts towards the center at certain range of particle radius values, occurrence of side peaks with magnitudes comparable to that of the central peak, formation of additional peaks at certain observation angles and strong dependence of the spectra on the microparticle’s cylinder axis orientation. Most of these effects are either caused by the inhomogeneity of the incident pump and control laser fields within the volume of the cylindrical microparticle or simply due to the lack of three-dimensional symmetry of cylindrical geometry.

Some experiments show fractional models can represent the mechanical properties of some materials appropriately, but the way to determine the parameters of the fractional models need further discussion. In this paper, fractional order spectra are presented for complex viscoelastic materials, which mechanical analogy are made by fractional elements connected in series or parallel. Fractional order spectra link the material's constitutive relation and the fractional derivatives closely and reflect the characteristic of networks of mechanical analogy. They provide an effective method to determine the parameters of some fractional models. The experimental method to measure fractional order spectra of complex viscoelastic materials is shown.

A two-component analysis of spectra to p_t = 12 GeV/c for identified pions and protons from 200 GeV Au–Au collisions is presented. The method is similar to an analysis of the n_ch dependence of p_t spectra from p–p collisions at 200 GeV, but applied to Au–Au centrality dependence. The soft-component reference is a Lévy distribution on transverse mass m_t. The hard-component reference is a Gaussian on transverse rapidity y_t with exponential (p_t power-law) tail. Deviations of data from the reference are described by hard-component ratio r_AA, which generalizes nuclear modification factor R_AA. The analysis suggests that centrality evolution of pion and proton spectra is dominated by changes in parton fragmentation. The structure of r_AA suggests that parton energy loss produces a negative boost Δy_t of a large fraction (but not all) of the minimum-bias fragment distribution, and that lower-energy partons suffer relatively less energy loss, possibly due to color screening. The analysis also suggests that the anomalous p/π ratio may be due to differences in the parton energy-loss process experienced by the two hadron species. This analysis provides no evidence for radial flow.

We study the impact of the in-medium mass splitting between bosons and anti-bosons on their spectra and elliptic flow. The in-medium mass splitting may cause a separation in the transverse momentum spectra, as well as a division in the elliptic flow between bosons and anti-bosons. The magnitude of this effect becomes greater as the in-medium mass splitting increases. With the increasing rapidity, the splitting effect of the spectra increases and the splitting effect of the elliptic flow decreases. These phenomena may provide a way to differentiate whether the influences on boson and anti-boson in the medium are consistent.

At DFT/B3LYP/LANL2DZ theoretical level, a series of MgX clusters with Mg₃X₃ hexagon, Mg₄X₄-t tetrahedron and Mg₄X₄-o octagon conformations are investigated. Their wavelengths of absorption spectra are calculated with time-dependent Density Functional Theory (TDDFT) using water as solvent. Firstly, the lowest vibrational frequencies, bond lengths, Dipole Moment and Raman spectra of them present regular change. Dipole Moment result shows that different clusters have different charges. From Raman spectra, we have discovered that they correlate with the conformation and variety of clusters. Conformations of MgO clusters have different optimizing characters with MgS, MgSe and MgTe molecules. Secondly, through Molecular Orbital and Nature Bond Orbital (NBO) analysis, we have found that all these clusters are materials with wider gaps. MgTe structures have stronger bonding. Besides, MgO have different transition from the other clusters. The order of wavelengths of absorption spectra is MgTe > MgSe > MgS. In a word, except MgO molecules, these clusters have similar or regular characters. These results are significant for experimental study of MgX nanocrystals.

We consider a two-magnon systems in an ν-dimensional isotropic non-Heisenberg ferromagnet with spin value S = 3/2 and nearest-neighbor interactions. Spectrum and bound states (BS) of the system for all values of full quasi-momentum Λ, and for arbitrary value of lattice dimensionality ν, and for all values of Hamiltonian parameters are investigated. We show that (i) for arbitrary ν ≥ 2 and for full quasi-momentum in the form Λ = (Λ₁; Λ₂; … ;Λ_ν) = (Λ₀;Λ₀; …; Λ₀) the change of energy spectrum of the system is similar to that observed in the case of ν = 1. In this case the operator with J + J₁ - 23J₂ ≠ 0 has only one additional BS. (ii) The energy z of this additional BS is degenerate ν - 1 times. (iii) If Λ ≠ (Λ₀;Λ₀;…;Λ₀), we show the existence no more 2ν + 1 bound states in the system in ν-dimensional lattice.

Surfzone wave characteristics, measured using a wave and tide gauge (WTG) during a flood tide, were studied at three different beaches having different nearshore slopes. The spectral wave characteristics viz., wave-height and mean wave period were estimated considering different sample sizes. Inter-comparisons of wave climate between each of three beaches for a similar tide level are presented. The wave-height and mean wave period values obtained from the wave analysis for each of the record using waves by wave method show that surfzone wave-height increased with time during a flood tide and the mean wave period decreased with time up to mid tide and then increased during the rest of the measurement period at Keri and Miramar beaches. At Candolim, the reversing trend of mean wave period increase is observed to occur much before reaching the mid tide level. The surfzone waves during a flood tide indicated that the wave-heights increased with time while the mean wave period showed a decreasing trend in general. The variation of breaker index showed a decreasing trend from low tide to high tide ranging between 0.45 and 0.23. The surf similarity parameter estimated corroborates with the visual observations.

A summary of dynamic measurements are presented that illustrate relations between linear seismic demand and true nonlinear response of unreinforced masonry buildings with flexible diaphragms and rocking piers subjected to a series of simulated earthquake motions.

Breast cancer is one of the leading causes of cancer-related deaths in a global scenario. In the present study, biochemical changes exerted upon Pentoxifylline (PTX) treatment had been appraised in human breast cancer cells using Raman spectroscopy. There are no clinically approved methods to monitor such therapeutic responses available. The spectral profiling is suggestive of changes in DNA, protein and lipid contents showing a linear relationship with drug dosage. Further, multivariate analysis using principal-component based linear-discriminant-analysis (PC-LDA) was employed for classifying the control and the PTX treated groups. These findings support the feasibility of Raman spectroscopy as an alternate/adjunct label-free, objective method for monitoring drug-induced modifications against breast cancer cells.