Jacobi elliptic functions and change of variable in a convolution

We solve the functional equation

The Solow model improved through the logistic manpower growth law

In this paper the neo-classical economic Solow-Swan model (1956) has been improved replacing its Malthusian manpower law with the Verhulst (logistic) one. The relevant ordinary differential equation for the ratio capital/work has been then integrated in closed form via the Hypergeometric function₂ F ₁. The logistic growth injection for the manpower is detected to induce a more slow dynamics onto the Solow-Swan system, which keeps its stability. Increasing developments are displayed as the technologic progress rises. Further sceneries are tested and the congruence of the new solution with the classical one is shown switching to zero the selflimitation coefficent in the logistic law. Research supported by MURST grant:Metodi matematici in economia     

Exceptional congruences for the coefficients of certain eta-product newforms

Let F(z)=∑_n=1^∞a(n)qⁿ denote the unique weight 16 normalized cuspidal eigenform on . In the early 1970s, Serre and Swinnerton-Dyer conjectured that

     

Limits of balayage measures

LetA be a subset of a balayage space (X,W) and a measure onX. It is shown that for every sequence _n of measures such that lim_nn and lim_{n n} ^A = the limit measure is of the formf+[(1-f)]^A for some (unique) Borel function 0f1_Cb(A). Furthermore, conditions are given such that any such functionf occurs.     

Toeplitz and Hankel type operators on the upper half-plane

An orthogonal decomposition of admissible wavelets is constructed via the Laguerre polynomials, it turns to give a complete decomposition of the space of square integrable functions on the upper half-plane with the measurey dxdy. The first subspace is just the weighted Bergman (or Dzhrbashyan) space. Three types of Ha-plitz operators are defined, they are the generalization of classical Toeplitz, small and big Hankel operators respectively. Their boundedness, compactness and Schatten-von Neumann properties are studied.Research was supported by the National Natural Science Foundation of China.     

Fluctuation kinetics of diffusion-controlled processes: Strong effects due to correlations and fluctuations

We summarize some recent results related to fluctuation-induced kinetics of diffusion-controlled processes. We show that kinetic behavior can be drastically changed due to fluctuation effects, spatial correlations between particles, and anomalous transport properties. In addition, we show that correlation-induced kinetics in some systems can govern the temporal evolution over the entire time domain.     

Representations of lie groups and multidimensional special functions

This work is devoted to the construction and investigation of two new classes of special functions, related to representations of groups of motions in the spaces of constant curvature as well as the unitary group of large ranks. These are special functions with matrix indices and some types of orthogonal polynomials in several continuous and discrete variables. The functions introduced generalize a number of classical scalar special functions in one variable.     

Production of a bose einstein condensate of metastable helium atoms

We recently observed a Bose-Einstein condensate in a dilute gas of ⁴He in the 2³S₁ metastable state. In this article, we describe the successive experimental steps which led to the Bose-Einstein transition at 4.7 μK: loading of a large number of atoms in a MOT, efficient transfer into a magnetic Ioffé-Pritchard trap, and optimization of the evaporative cooling ramp. Quantitative measurements are also given for the rates of elastic and inelastic collisions, both above and below the transition. Received 15 October 2001     

New cw far infrared molecular lasers from ClO2, HCCF,FCN, CH3NC,CH3F,and propynal

Many new laser lines between 100 μm and 1 mm have been detected by optically pumping several polyatomic molecules with C¹⁶O₂ and C¹⁸O₂ lasers. Tentative assignment of the lasing transitions has been possible in some cases.