By the method of weight coefficients and techniques of real analysis, a Hardy-Hilbert-type inequality with a general homogeneous kernel and a best possible constant factor is given. The equivalent forms, the operator expressions with the norm, the reverses and some particular examples are also considered.

In this paper, by the use of the weight coefficients, the transfer formula and the technique of real analysis, an extended multidimensional Hardy-Hilbert-type inequality with a general homogeneous kernel and a best possible constant factor is given. Moreover, the equivalent forms, the operator expressions and a few examples are considered.

In supersymmetric quantum mechanics, shape invariance is a sufficient condition for solvability. We show that all conventional additive shape-invariant superpotentials that are independent of ℏ can be generated from two partial differential equations. One of these is equivalent to the one-dimensional Euler equation expressing momentum conservation for inviscid fluid flow, and it is closed by th...

We measured in thermal emission the 63-Jlm line due to thermospheric atomic oxygen Oep), using a far-infrared spectrometer on a balloon platform at 37 km altitude over Palestine, Texas (32°N), on June 20, 1983. From measurements of the equivalent width of this line at two elevation angles, we find a weak angular dependence: the equivalent width increases by a factor of 1.5 :t 0.3 as the angle d...

The concept of an equivalent stress intensity factor Keq is used in the study fatigue crack growth mixed-mode situations. A problem seldom discussed research literature are consequences coexistence several alternative definitions mixed mode Keq, leading to rather different results associated with definitions. This note highlights problem, considering hitherto not analyzed simultaneously. Values...