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This method is used to solve a multidimensional version of the viscous Burgers equation, and a heterogeneous advection equation.
We consider a multidimensional version of an inequality due to Leray as a substitute for Hardy's inequality in the case p="n≥2.
For multidimensional version of Theorem 1.2 see [3].
Our generalization will include a multidimensional version of the Hilbert-type inequality in the whole plane.
A multidimensional version of this equivalence theorem concerning Hardy-type inequalities was proved by Oguntuase et al. [12].
Analogous to Remarks 2.3 and 2.5, we obtain multidimensional version of inequality (1.3) for as follows: (2.125).
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Then there are multidimensional versions of membranes (2-branes, 3-branes, etc)., which work as reminders of why the author's mother's head hurt.
Here, too, is occasion to contemplate a universe made up of tiny vibrating strings instead of particles, strings "so small that a direct observation would be tantamount to reading the text on this page from a distance of 100 light-years". Then there are multidimensional versions of membranes (2-branes, 3-branes, etc)., which work as reminders of why the author's mother's head hurt.
The multidimensional version requires a variation of the notion of recurrence, taking into account the various degrees of freedom.
Inter-item correlations of the subscales of the multidimensional version 1.0 as well as that of the short-form scales rarely were below r = 0.6, while the Cronbach alpha was always greater than 0.9 (an exception was made for the sub-dimension "fatigue" where alpha = 0.859).
Values underlined in Table 1 represent hypotheses of convergence, of which several were found between the IONB-QoL (multidimensional version) subscales and those of the EORTC-QLQ C30 questionnaire.
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