Improved upper and lower bounds for the spectral radius of digraphs

Let G be a digraph with n vertices and m arcs without loops and multiarcs. The spectral radius ρ(G) of G is the largest eigenvalue of its adjacency matrix. In this paper, sharp upper and lower bounds on ρ(G) are given. We show that some known bounds can be obtained from our bounds.     

Hyperbolic Octonion Formulation of Gravitational Field Equations

In this paper, the Maxwell-Proca type field equations of linear gravity are formulated in terms of hyperbolic octonions (split octonions). A hyperbolic octonionic gravitational wave equation with massive gravitons and gravitomagnetic monopoles is proposed. The real gravitoelectromagnetic field equations are recovered and written in compact form from an octonionic potential. In the absence of charges, this reduces to the Klein-Gordon equation of motion for the massive graviton. The analogy between massive gravitational theory and electromagnetism is shown in terms of the present formulation.     

Generalized Hyperbolic Octonion Formulation for the Fields of Massive Dyons and Gravito-Dyons

The close analogy between electromagnetic theory and linear gravity is discussed by the hyperbolic (split) octonion formalism. Using the similarities between the relevant field equations of massive dyons in electromagnetic theory and gravito-dyons in linear gravity, a new mathematical model is proposed to formulate these fields in a compact and simple form. The generalized wave equation including both massive dyon and monopole terms is derived. Similarly, the most generalized form of hyperbolic octonionic Klein–Gordon equation is obtained for the hypothetical particle carrying simultaneously both electromagnetic and gravitational charges (masses).     

EPR of Cu2+-doped Cs2CO3 and CsHCO3: evidence of the Jahn–Teller effect

Cu²⁺-doped Cs₂CO₃ and CsHCO₃ single crystals were investigated by electron paramagnetic resonance between 113–273 and 173–313 K, respectively. For both single crystals, two sites were observed for the Cu²⁺ at ambient temperature for arbitrary orientations of the single crystals in the magnetic field. However, when the temperature is varied, the spectra indicate the equivalence of the two sites at 225 and 240 K for the single crystals, respectively, to the above order. Below and above these temperatures two sites for Cu²⁺ appear, and below 133 and 173 K the signals do not vary and two sites were always observed. This is attributed to the transition of the dynamic Jahn–Teller effect to a static situation at lower temperatures. Cu²⁺ seems to replace Cs⁺ and the charge compensation is fulfilled by another Cs⁺. Spin-Hamiltonian parameters for both single crystals at ambient temperature are reported and discussed.     

Electron paramagnetic resonance and FT-IR spectroscopic studies of DL-2-aminoadipic acid and ammonium acetate powders

Exposure of powder forms of DL-2-aminoadipic acid and ammonium acetate to gamma radiation results in the formation of free radicals detected by the electron paramagnetic resonance spectroscopy at room temperature. In these compounds, the observed paramagnetic species were attributed to the HOOCCH₂CH₂CH₂CHCOOH and CH₂COONH₄ radicals, respectively. The g values and the hyperfine coupling constants of the unpaired electron with the environmental protons were determined for these two radicals. In work, the observed paramagnetic species were found to be stable at room temperature for more than two months. Also, these compounds were characterised by FT-IR and UV–VIS. Their thermal stabilities were determined by TGA and DTA measurements. Thermal analyses were shown to be unstable of the HOOCCH₂CH₂CH₂CH(NH₂)COOH and CH₃COONH₄ against thermo-oxidative decomposition.     

Cross Sections for Neutron–Deuteron Elastic Scattering in the Energy Range 135–250 MeV

We report new measurements of the neutron–deuteron elastic scattering cross section at energies from 135 to 250 MeV and center-of-mass angles from 80^? to 130^?. Cross sections for neutron-proton elastic scattering were also measured with the same experimental setup for normalization purposes. Our nd cross section results are compared with predictions based on Faddeev calculations including three-nucleon forces, and with cross sections measured with charged particle and neutron beams at comparable energies.     

Evaluation of mathematical models for flexible job-shop scheduling problems

With the rapid development in computer technologies, mathematical programming-based technique to solve scheduling problems is significantly receiving attention from researchers. Although, it is not efficient solution method due to the NP-hard structure of these problems, mathematical programming formulation is the first step to develop an effective heuristic. Numerous comparative studies for variety scheduling problems have appeared over the years. But in our search in literature there is not an entirely review for mathematical formulations of flexible job shop scheduling problems (FJSP). In this paper, four the most widely used formulations of the FJSP are compiled from literature and a time-indexed model for FJSP is proposed. These formulations are evaluated under three categories that are distinguished by the type of binary variable that they rely on for using of sequencing operations on machines. All five formulations compared and results are presented.     

Decomposing torsion modules

E. Matlis proved that if R is an integral domain with quotient field Q and K is the R-module Q/R, then all torsion R-modules decompose into a direct sum of local submodules if and only if K decomposes into a direct sum of local submodules. Thus K is a test module to determine whether torsion modules decompose. We generalize this result to commutative rings. If R is a commutative ring and a torsion theory of R is given by a Gabriel topology , then form the ring of quotients R_ and let K be the cokernel of the canonical ring homomorphism from R to R_. In some special cases, every -torsion R-module decomposes into a direct sum of local submodules if and only if K decomposes. However, there is an example where this is not the case. The principal result is: given R,  and K, there is a related filter _K of ideals of R, which is a subset of , such that all _K-pretorsion R-modules decompose into a direct sum of local submodules if and only if K decomposes. The relationship between  and _K is investigated.     

Chain conditions in modules with krull dimension

Any ring with Krull dimension satisfies the ascending chain condition on semiprime ideals. This result does not hold more generally for modules. In particular if Ris the first Weyl algebra over a field of characteristic 0 then there are Artinian R-modules which do not satisfy the ascending chain condition on prime submodules. However, if Ris a ring which satisfies a polynomial identity then any R-module with Krull dimension satisfies the ascending chain condition on prime submodules, and, if Ris left Noethe-rian, also the ascending chain condition on semiprime submodules.     

Anti-diabetic Properties of Calcium Channel Blockers: Inhibition Effects on Aldose Reductase Enzyme Activity

Applied Biochemistry and Biotechnology - Aldose reductase (AR) belongs to NADPH-dependent oxidoreductases and converts glucose to sorbitol in the polyol pathway. AR inhibition is essential to...