The special position of the Riccati differential equation are not all entire, actually admits meromorphic solutions in the complex plane. This article is mainly devoted to presenting some contributions to this problem.We should perhaps point out here that the problem of whether such meromorphic solutions are rational or transcendental in the case when the coefficients are rational, has been treated earlier by H. Wittich [13] and [17].In this article, the term "meromorphic function" means meromorphic in the wholo complex plane, unless otherwise explicitly stated. Almost all of our treatment is concentrated in the special case of (1.1):

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RhoA plays a crucial role in neuronal polarization, where its action restraining axon outgrowth has been thoroughly studied. We now report that RhoA has not only inhibitory but also a stimulatory effect on axon development depending on when and where exerts its action and the downstream effectors involved. In cultured hippocampal neurons, FRET imaging revealed that RhoA activity selectively localizes in growth cones of undifferentiated neurites, while in developing axons it displays a biphasic pattern, being low in nascent axons and high in elongating ones. RhoA-Rho kinase (ROCK) signaling prevents axon initiation but has no effect on elongation, while formin inhibition reduces axon extension without significantly altering initial outgrowth. Besides, RhoAmDia promotes axon elongation by stimulating growth cone microtubule stability and assembly, as opposed to RhoA-ROCK that restrains growth cone microtubule assembly and protrusion. Finally, we show that similar mechanisms might operate during axonal regeneration, with RhoAROCK slowing axon regrowth after axotomy and RhoA-mDia favoring extension of regenerated axons.

The ability of a cell to regulate its mechanical properties is central to its function. Emerging evidence suggests that interactions between the cell nucleus and cytoskeleton influence cell mechanics through poorly understood mechanisms. Here we show that A- and B-type nuclear lamin isoforms distinctively modulate both nuclear and cellular volume and selectively stabilize the linker of nucleoskeleton and cytoskeleton (LINC) complexes that couple the nucleus to cytoskeletal actin and vimentin. We reveal, further, that loss of each of the four-known lamin isoforms in the mouse embryonic fibroblasts differentially affects cortical and cytoplasmic stiffness as well as cellular contractility, and then propose a LINC complex mediated model that explains these impaired mechanical phenotypes. Finally, we demonstrate that loss of each lamin isoform softens the nucleus in a manner that correlates with loss of heterochromatin. Together, these findings uncover distinctive roles for each lamin isoform in maintaining cellular and nuclear mechanics.