Meteorological conditions on days of radon measurements in air over the eastern Arabian Sea off Bombay

Meteorological conditions prevailing over and west of Bombay on the four days on which Bhatet al. (1974) made measurements of radon concentration at different altitudes from the surface to 3·7 km and distances of 0–50 and 350–400 km west of Bombay, do not appear to support their conclusions about airmasses.     

Mathematical Modelling of Atmospheric Flow over a Shelter-belt

The paper presents a mathematical and numerical study of the flow with pollution dispersion in the atmospheric boundary layer (ABL) over a simplified topography with a shelter-belt placed before the pollutant (coal dust) source. The flow is supposed to be viscous, incompressible, turbulent and stationary. A two different numerical models are briefly mentioned. The shelter-belt is supposed to be a solid and impermeable obstacle significantly changing the flow-field and hence it gives the possibility of influencing the level of the pollutant concentrations in the downstream region. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Radon concentration of air over the Eastern Arabian Sea

The radon concentrations of air samples collected during the South West monsoon period at altitudes up to 4 km over the Arabian Sea at two locations,i.e., 0–50 km and 300–400 km west of Bombay, are reported. Radon was extracted from air, using a simple single stage apparatus. The concentration of radon in the monsoon air mass was found to range around 80–100 dpm/m³ STP, indicative of its recent continental origin. The results suggest that the coastal monsoon air mass, up to 400 km west of Bombay coast, is generally homogeneous and vertically well mixed. During the post-monsoon condition, a strong gradient in the radon concentration in the vertical is observed. The concentration of radon decreases from 157 dpm/m³ at sea level to 35 dpm/m³ at about 3·7 km altitude, suggesting a vertical turbulent diffusion coefficient of ～6×10⁴ cm²/sec. In contrast, the near absence of vertical gradient of radon in the monsoon air mass indicates that the vertical turbulence is much stronger during the monsoon period.     

Atmospheric gamma-rays of 1–200 GeV over Hyderabad

Using a stack of hypersensitized nuclear emulsions, exposed under 10.2 g.cm^?2 of residual atmosphere over Hyderabad, India, gamma-rays of energy > 1 GeV have been studied. It is found that the observed differential energy spectrum can be best represented by two power law spectra, one for energies less than 30 GeV and the other for higher energies but with the same spectral index of 2.6; however the intensities at energies greater than 30 GeV are about three times higher than what would be expected from the extrapolation of the spectrum at lower enerjies. The implication of this observation has been examined. The neutral pion production spectrum over Hyderabad has been derived from the gamma-ray spectrum. Using this information the energy spectrum of atmospheric electrons has been deduced and a comparison made with the observed spectrum below the geomagnetic threshold energy over Hyderabad; therefrom an upper limit of 0.5 particles/(m².sr.sec.) has been deduced for the flux of re-entrant albedo electrons above 2 GeV.     

关于域上上三角矩阵的诱导映射

令F是一个域,T_n(F)是F上所有n×n上三角矩阵的集合.本文分别给出了矩阵保相似性及保交换性的定义,并使用矩阵技术和初等方法,得到了T_n(F)的保相似性及保交换性的诱导映射的一般形式,并且给出了例子,来解释一些结果之间的关系.     

Explicit upper bounds for exponential sums over primes

We give explicit upper bounds for linear trigonometric sums over primes.

     

Low energy gamma-ray measurements over Hyderabad,India

The results of the first low energy gamma-ray (0.2 to 1 MeV) measurements at equatorial latitudes conducted by two-balloon flights over Hyderabad, India (7.6° N GM), are presented. The energy resolution of the detectors was sufficient to detect the γ-ray peak at 0.5 MeV due to the electron-positron annihilation. The flux of the 0.5 MeV photons was found to be 0.090 ± 0.012 photons/cm² sec at an atmospheric depth of 10 gm cm² and 0.048 ± 0.011 photons/cm² sec at the top of the atmosphere. Comparison of our results with those obtained at higher latitudes, show the existence of a considerable latitude variation of the 0.5 MeV flux, about a factor of 4 between 55° and 7° latitudes at an altitude of 10 gm/cm².     

保体上上三角幂等矩阵的诱导映射

假设T_m(D)是体D上所有上三角m×m矩阵的集合.首先分别给出诱导映射和保幂等性的定义.然后为了刻画T_m(D)的保幂等的诱导映射,提出类序列的概念,同时描述类序列的性质.最后,使用矩阵技术和初等方法,借助于分类讨论得到了T_m(D)的保幂等的诱导映射的一般形式并且给出了某些例子,用以解释某些结果之间的关系.     

On Drinfeld's universal formal group over thep-adic upper half plane

Conclusion All of our results are stated for 2-dimensional modules with action by the quaternion division algebra overQ _p . Drinfeld's results are true in much greater generality. We remark that our results generalize easily to the case of 2-dimensional modules with action by quaternion algebras over extensions ofQ _p by applying the theory of formal -modules. We suspect that Drinfeld's higher dimensional modules over are determined by formulae similar to that in Theorem 46, but with and generalized to moduli for higher dimensionalQ _p -subspaces of ; however, we have not investigated this in any detail.Although this work amplifies Drinfeld's original paper by supplying many details in certain cases, it is seriously limited in that it considers lifts of SFD modules to unramified rings only. The most interesting points in thep-adic upper half plane are the points defined over ramified rings, which reduce modp to the singular points on the special fiber. What happens there? We do not have a simple answer.Drinfeld's moduli for formal groups on thep-adic upper half plane is the basis for his proof that Shimura curves havep-adic uniformizations. In a later work, we hope to exploit improved versions of the techniques in this work to better understand the arithmetic of Shimura curves. In particular, in the course of work onp-adicL-functions, we have been led to construct certain p-adic periods associated to the cohomology of sheaves on Shimura curves which depend essentially on the existence of ap-adic uniformization. We hope to use Drinfeld's moduli to obtain a more natural construction of these periods in terms of the Gauss-Manin connection, and thereby to gain a better understanding of how they might come to appear in special values ofp-adicL-functions.This research was partially supported by an NSF Postdoctoral Fellowship     

The ring of upper triangular invariants as a module over the Dickson invariants

This research is supported in part by the Natural Sciences and Engineering Research Council of Canada     

Explicit upper bound of the solution-free region for a Diophantine equation over number fields

Lithuanian Mathematical Journal - It is known that there exist only finitely many trivial solutions of a certain Diophantine equation over number fields except for the case the rational number...     

An optimization problem in the electricity market

New types of optimization problems are faced by the generating companies that operate on deregulated electricity markets. The characteristics of these problems depend on the various market structures. In the framework of the recently settled Italian electricity market, one of these new problems is the transition from hourly energy programs, defined by the market, to more detailed power generation dispatches, defined for intervals of 15 min. Such a more detailed plan is needed on the one hand by the national system operator (Terna, Rete Elettrica Nazionale) for the assessment of power system stability and security, and on the other hand by the power plant operators for its implementation. The transition procedure should respect the hourly energy constraints and take the main operating constraints of the generating units into account. The paper presents possible solutions of the problem through linear optimization models and reports computational results on real-world instances.      

Strategic bidding in continuous electricity auctions: an application to the Spanish electricity market

In this paper we introduce an asymmetric model of continuous electricity auctions with limited production capacity and bounded supply functions. The strategic bidding is studied with this model by means of an electricity market game. We prove that for every electricity market game with continuous cost functions a mixed-strategy Nash equilibrium always exists. In particular, we focus on the behavior of producers in the Spanish electricity market. We consider a very simple form for the Spanish electricity market: an oligopoly consisting just of independent hydro-electric power production units in a single wet period. We show that a pure-strategy Nash equilibrium for the Spanish electricity market game always exists.     

(Strongly) Gorenstein injective modules over upper triangular matrix Artin algebras

Let \(\Lambda = \left( {\begin{array}{*{20}{c}} A&M \\ 0&B \end{array}} \right)\) be an Artin algebra. In view of the characterization of finitely generated Gorenstein injective Λ-modules under the condition that M is a cocompatible (A,B)-bimodule, we establish a recollement of the stable category \(\overline {Ginj\left( \Lambda \right)} \). We also determine all strongly complete injective resolutions and all strongly Gorenstein injective modules over Λ.     

Derivations of the Lie algebra of infinite strictly upper triangular matrices over a commutative ring

Let 𝒩(∞,R) be the Lie algebra of infinite strictly upper triangular matrices over a commutative ring R. We show that every derivation of 𝒩(∞,R) is a sum of diagonal and inner derivations.     

Improved upper bounds for the number of rational points on algebraic curves over finite fields

Currently, the best known bounds on the number of rational points on an absolutely irreducible, smooth, projective algebraic curve of genus g, defined over a finite field %plane1D;53D;_q, generally come either from Serre's refinement of the Weil bound if the genus is small compared to q, or from the optimization of the explicit formulae if the genus is large. We give methods for improving these bounds in both cases. Examples of improvements on the bounds include lowering them for a wide range of small genus when q = 8, 32, 2¹³, 27, 243, 125, and when q = 2^s, s > 1. For large genera, isolated improvements are obtained for q = 3, 8, 9.