ON THE CONVERGENCE OF THE PARABOLIC APPROXIMATION OF A CONSERVATION LAW IN SEVERAL SPACE DIMENSIONS

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Quenching of highly vibrationally excited pyrimidine by collisions with CO2

Relaxation of highly vibrationally excited pyrimidine (C(4)N(2)H(4)) by collisions with carbon dioxide has been investigated using diode laser transient absorption spectroscopy. Vibrationally hot pyrimidine (E(')=40 635 cm(-1)) was prepared by 248-nm excimer laser excitation, followed by rapid radiationless relaxation to the ground electronic state. The nascent rotational population distribution (J=58-80) of the 00(0)0 ground state of CO(2) resulting from collisions with hot pyrimidine was probed at short times following the excimer laser pulse. Doppler spectroscopy was used to measure the CO(2) recoil velocity distribution for J=58-80 of the 00(0)0 state. Rate constants and probabilities for collisions populating these CO(2) rotational states were determined. The measured energy transfer probabilities, indexed by final bath state, were resorted as a function of DeltaE to create the energy transfer distribution function, P(E,E(')), from E(')-E approximately 1300-7000 cm(-1). P(E,E(')) is fitted to a single exponential and a biexponential function to determine the average energy transferred in a single collision between pyrimidine and CO(2) and parameters that can be compared to previously studied systems using this technique, pyrazineCO(2), C(6)F(6)CO(2), and methylpyrazineCO(2). P(E,E(')) parameters for these four systems are also compared to various molecular properties of the donor molecules. Finally, P(E,E(')) is analyzed in the context of two models, one which suggests that the shape of P(E,E(')) is primarily determined by the low-frequency out-of-plane donor vibrational modes and one which suggests that the shape of P(E,E(')) can be determined by how the donor molecule final density of states changes with DeltaE.     

Rotationally resolved IR-diode laser studies of ground-state CO2 excited by collisions with vibrationally excited pyridine

Relaxation of highly vibrationally excited pyridine (C5NH5) by collisions with carbon dioxide has been investigated using diode laser transient absorption spectroscopy. Vibrationally hot pyridine (E' = 40,660 cm(-1)) was prepared by 248 nm excimer laser excitation followed by rapid radiationless relaxation to the ground electronic state. Pyridine then collides with CO2, populating the high rotational CO2 states with large amounts of translational energy. The CO2 nascent rotational population distribution of the high-J (J = 58-80) tail of the 00(0)0 state was probed at short times following the excimer laser pulse to measure rate constants and probabilities for collisions populating these CO2 rotational states. Doppler spectroscopy was used to measure the CO2 recoil velocity distribution for J = 58-80 of the 00(0)0 state. The energy-transfer distribution function, P(E,E'), from E' - E approximately 1300-7000 cm(-1) was obtained by re-sorting the state-indexed energy-transfer probabilities as a function of DeltaE. P(E,E') is fit to an exponential or biexponential function to determine the average energy transferred in a single collision between pyridine and CO2. Also obtained are fit parameters that can be compared to previously studied systems (pyrazine, C6F6, methylpyrazine, and pyrimidine/CO2). Although the rotational and translational temperatures that describe pyridine/CO2 energy transfer are similar to previous systems, the energy-transfer probabilities are much smaller. P(E,E') fit parameters for pyridine/CO2 and the four previously studied systems are compared to various donor molecular properties. Finally, P(E,E') is analyzed in the context of two models, one indicating that P(E,E') shape is primarily determined by the low-frequency out-of-plane donor vibrational modes, and the other that indicates that P(E,E') shape can be determined from how the donor molecule final density of states changes with DeltaE.     

ON LACUNARY STATISTICAL CONVERGENCE OF ORDER α

In this article, we introduce the concept of lacunary statistical convergence of order α of real number sequences and give some inclusion relations between the sets of lacunary statistical convergence of order α and strong Nαθ(p)-summability. Furthermore, some relations between the spaces Nαθ(p) and Sαθare examined.     

Competition between photochemistry and energy transfer in UV-excited diazabenzenes. 4. UV photodissociation of 2,3-, 2,5-, and 2,6-dimethylpyrazine

The quantum yield for HCN formation via 248 nm photodissociation of 2,3-, 2,5-, and 2,6-dimethylpyrazine (DMP, C6N2H8) was measured using diode laser probing of the HCN photoproduct. The total quantum yield is phi = 0.039 +/- 0.07, 0.14 +/- 0.02, and 0.30 +/- 0.06 for 248 nm excitation of 2,3-, 2,5- and 2,6-DMP, respectively. Analysis of the quenching data within the context of a gas kinetic, strong collision model allows an estimate of the rate constant for HCN production via DMP photodissociation, ks = 4.1 x 10(3), 1.0 x 10(3), and 1.3 x 10(4) s(-1) for 2,3-, 2,5- and 2,6-DMP, respectively. Unlike HCN produced from the photodissociation of pyrazine and methylpyrazine, the amount of HCN produced via a prompt, unquenched dissociation channel was essentially zero, suggesting little multiphoton UV absorption. The rate constants for HCN formation together with previously measured rate constants for HCN production from photodissociation of pyrazine and methylpyrazine have been used to investigate possible reaction mechanisms. The position of the methyl group affects the HCN rate constant, suggesting that the mechanism for pyrazine dissociation involves an initial step that is hindered by the addition of the methyl groups. The proposed initial molecular motion of the mechanism, an out-of-plane H atom migration across a N atom, is consistent with (1) the position of the methyl groups, (2) the dissociation lifetime of the various pyrazine molecules studied, and (3) the observed large energy transfer magnitudes from pyrazine near dissociation. These so-called "supercollisions" have been linked to low-frequency, out-of-plane motion, suggesting that the molecular motions leading to efficient energy transfer are the same motions involved in dissociation. In addition, the pyrazine (C4N2H4) 248 nm photoproduct (C3H3N) was identified as acrylonitrile using IR spectroscopy, an observation that aids in understanding the dissociation mechanism.     

Collisional relaxation of the three vibrationally excited difluorobenzene isomers by collisions with CO2: effect of donor vibrational mode

Relaxation of highly vibrationally excited 1,2-, 1,3-, and 1,4-difluorobenzne (DFB) by collisions with carbon dioxide has been investigated using diode laser transient absorption spectroscopy. Vibrationally hot DFB (E' approximately 41,000 cm(-1)) was prepared by 248 nm excimer laser excitation followed by rapid radiationless relaxation to the ground electronic state. Collisions between hot DFB isomers and CO2 result in large amounts of rotational and translational energy transfer from the hot donors to the bath. The CO2 nascent rotational population distribution of the high-J (J = 58-80) tail of the 00(0)0 state was probed at short times following the excimer laser pulse to measure rate constants and probabilities for collisions populating these states. The amount of translational energy gained by CO2 during collisions was determined using Doppler spectroscopy to measure the width of the absorption line for each transition. The energy transfer probability distribution function, P(E,E'), for the large DeltaE tail was obtained by resorting the state-indexed energy transfer probabilities as a function of DeltaE. P(E,E') was fit to a biexponential function to determine the average energy transferred in a single DFB/CO2 collision and fit parameters describing the shape of P(E,E'). P(E,E') fit parameters for DFB/CO2 and the previously studied C6F6/CO2 system are compared to various donor molecular properties. A model based on Fermi's Golden Rule indicates that the shape of P(E,E') is primarily determined by the low-frequency out-of-plane donor vibrational modes. A fractional mode population analysis is performed, which suggests that for energy transfer from DFB and C6F6 to CO2 the two key donor vibrational modes from which energy leaks out of the donor into the bath are nu11 and nu16. These "gateway" modes are some of the same modes determined to be the most efficient energy transfer modes by quantum scattering studies of benzene/He collisions.     

SOME GEOMETRIC PROPERTIES OF A NEW DIFFERENCE SEQUENCE SPACE INVOLVING LACUNARY SEQUENCES

In this paper, we define a new generalized difference sequence space involving lacunary sequence. Then, we examine k-NUC property and property （β） for this space and also show that it is not rotund where p = （pr） is a bounded sequence of positive real numbers with pr ≥ 1 for all r ∈ N.     

How does cold constrain life cycles of terrestrial plants and animals?

Short summer seasons with low thermal energy input characterise polar ecosystems. Climatic variables and physical isolation of terrestrial habitats act as selective filters which must be passed to allow colonisation, establishment and survival in these extreme environments. Life history studies of the terrestrial biota of such ecosystems give little evidence of adaptive responses to low temperatures having evolved in situ, even though behavioural, ecophysiological and biochemical features allowing tolerance of the likely extremes are well-developed. Observed life history strategies are often consistent with the general predictions of adversity (A) or stress (S) selection. However, biota successful in these extreme environments may be better-grouped by the lack of particular life history features, rather than common possession.     

On lacunary statistical convergence of order α

In this article, we introduce the concept of lacunary statistical convergence of order α of real number sequences and give some inclusion relations between the sets of lacunary statistical convergence of order α and strong N_θ^α(p)-summability. Furthermore, some relations between the spaces N_θ^αS_θ^α are examined.