Discrete geometric function theory !

The foundations are laid here for a discrete analytic function theory which can be applied to geometric difference (or q-difference) functions. Using the concept of a q-analytic function. a discrete contour integral is defined and analogues are found for Cauchy integral theorems. Appropriate discrete analytic continuation and multiplication operators are outlined and their properties examined. The development of the theory of q-analytic functions is seen to be closely allied to that monodiffric functions, but significant advantages and distinctive differences are noted     

Calculus demonstrations using MATLAB

The note discusses ways in which technology can be used in the calculus learning process. In particular, five MATLAB programs are detailed for use by instructors or students that demonstrate important concepts in introductory calculus: Newton's method, differentiation and integration. Two of the programs are animated. The programs and the graphical user interface have been specifically designed to help the student understand the processes behind these important introductory concepts. Each program has a series of demonstrations that show unusual, difficult or important cases.     

Nuclear excitation by electron capture followed by fast x-ray emission

The resonance strength of the two-step process of nuclear excitation by electron capture followed by γ decay of the nucleus can be significantly increased in highly charged ions if the resonant capture proceeds via an excited electronic state with subsequent fast x-ray emission. For fully ionized ²³⁸₉₂U and ²³²₉₀Th, the x-ray decay stabilizes the system against internal conversion of the captured electron, with an increase of both nuclear lifetimes and resonance strengths of up to two orders of magnitude compared with the case when occupied atomic orbitals prevent the x-ray de-excitation. Applications of this effect to the measurement of the not yet experimentally observed nuclear excitation by electron capture and to dense astrophysical plasmas are discussed.     

Performance evaluation of IDW,Kriging and multiquadric interpolation methods in producing noise mapping: A case study at the city of Isparta,Turkey

In order to produce an accurate noise map of a city or a region, it is necessary to make noise measurements at certain locations and these measurements must be modeled with the most suitable mathematical algorithm. A homogeneous and representative distribution of the noise measurement points is the first key factor in the production of sound noise maps. The second key element is the calculation of the noise values of gridding points based on noise measurement points according to the selected mathematical calculation method and the generation of maps according to these gridding points. In this study, a noise map of the Isparta city center and its periphery was produced using inverse distance weighted (IDW), Kriging and multiquadric interpolation methods with different parameters and four grid resolution. Then, the influence of parameter selection for each method was investigated in themself by taking into account grid resolution, namely 10 ∗ 10 m, 50 ∗ 50 m, 100 ∗ 100 m and 200 ∗ 200 m, and the performance of three method with 50 ∗ 50 m grid resolution were compared with each other. In addition, the noise mapping of the city of Isparta were produced by Kriging method with respect to maximum, average and minimum noise data and they were evaluated by considering the national environmental noise thresholds.     

Isomerization dynamics and control of the eta2/N equilibrium for pyridine complexes

A series of pyridine complexes are prepared of the general form TpW(NO)(PMe3)(pyr) where pyr is either pyridine or a substituted pyridine. Depending on substitution pattern, the pyridine can be either N- or eta2-coordinated, and the role of the pyridine substituents and metal oxidation state in determining this equilibrium is explored. For eta2-pyridine complexes, the substituent pattern and solubility characteristics also determine the ratio of coordination diastereomers. Rates of both intra- and interfacial linkage isomerizations are explored along with the pyridine rotational barrier. This study is supported by DFT calculations and X-ray data and includes characterization of both eta2-pyridine and eta2-pyridinium complexes.     

Human Group IIA Phospholipase A2—Three Decades on from Its Discovery

Phospholipase A₂ (PLA₂) enzymes were first recognized as an enzyme activity class in 1961. The secreted (sPLA₂) enzymes were the first of the five major classes of human PLA₂s to be identified and now number nine catalytically-active structurally homologous proteins. The best-studied of these, group IIA sPLA₂, has a clear role in the physiological response to infection and minor injury and acts as an amplifier of pathological inflammation. The enzyme has been a target for anti-inflammatory drug development in multiple disorders where chronic inflammation is a driver of pathology since its cloning in 1989. Despite intensive effort, no clinically approved medicines targeting the enzyme activity have yet been developed. This review catalogues the major discoveries in the human group IIA sPLA₂ field, focusing on features of enzyme function that may explain this lack of success and discusses future research that may assist in realizing the potential benefit of targeting this enzyme. Functionally-selective inhibitors together with isoform-selective inhibitors are necessary to limit the apparent toxicity of previous drugs. There is also a need to define the relevance of the catalytic function of hGIIA to human inflammatory pathology relative to its recently-discovered catalysis-independent function.     

On exponential sums studied by Indlekofer and Kátai

We continue the study of sums of the form

A high-spin iron(IV)-oxo complex supported by a trigonal nonheme pyrrolide platform

We report the generation and characterization of a new high-spin iron(IV)-oxo complex supported by a trigonal nonheme pyrrolide platform. Oxygen-atom transfer to [(tpa(Mes))Fe(II)](-) (tpa(Ar) = tris(5-arylpyrrol-2-ylmethyl)amine) in acetonitrile solution affords the Fe(III)-alkoxide product [(tpa(Mes2MesO))Fe(III)](-) resulting from intramolecular C-H oxidation with no observable ferryl intermediates. In contrast, treatment of the phenyl derivative [(tpa(Ph))Fe(II)](-) with trimethylamine N-oxide in acetonitrile solution produces the iron(IV)-oxo complex [(tpa(Ph))Fe(IV)(O)](-) that has been characterized by a suite of techniques, including mass spectrometry as well as UV-vis, FTIR, M?ssbauer, XAS, and parallel-mode EPR spectroscopies. Mass spectral, FTIR, and optical absorption studies provide signatures for the iron-oxo chromophore, and M?ssbauer and XAS measurements establish the presence of an Fe(IV) center. Moreover, the Fe(IV)-oxo species gives parallel-mode EPR features indicative of a high-spin, S = 2 system. Preliminary reactivity studies show that the high-spin ferryl tpa(Ph) complex is capable of mediating intermolecular C-H oxidation as well as oxygen-atom transfer chemistry.