in this paper, we study some ring theoretic properties of the amalgamated duplication ring $rbowtie i$ of a commutative noetherian ring $r$ along an ideal $i$ of $r$ which was introduced by d'anna and fontana. indeed, it is determined that when $rbowtie i$ satisfies serre's conditions $(r_n)$ and $(s_n)$, and when is a normal ring, a generalized cohen-macaulay ring and finally a filter ring.

in this paper, we introduce a class of $j$-quasipolar rings. let $r$ be a ring with identity. an element $a$ of a ring $r$ is called {it weakly $j$-quasipolar} if there exists $p^2 = pin comm^2(a)$ such that $a + p$ or $a-p$ are contained in $j(r)$ and the ring $r$ is called {it weakly $j$-quasipolar} if every element of $r$ is weakly $j$-quasipolar. we give many characterizations and investiga...

Using the helicity amplitude technique, we derive differential decay widths and angular distributions for cascade $D\to K_{1}(1270,1400)\ell^+\nu_{\ell}\to (K\pi\pi)\ell^+\nu_{\ell} (\ell=e,\mu)$, in which electron muon mass is explicitly included. a set of phenomenological results K_1$ form factors, calculate partial branching fractions $D^0\to K_1^-\ell^+\nu_{\ell}$ $D^+\to K_1^0\ell^+\nu_{\e...

in this paper, we investigate various kinds of extensions of twin-good rings. moreover, we prove that every element of an abelian neat ring r is twin-good if and only if r has no factor ring isomorphic to z2  or z3. the main result of [24] states some conditions that any right self-injective ring r is twin-good. we extend this result to any regular baer ring r by proving that every element of a...

electrosensory lateral line lobe (ELL) of mormyrid electric fish. The mormyrid ELL is one member of a group of cerebellum-like sensory structures found in fish, amphibians and mammals (Fig. 1). These structures possess a molecular layer, an underlying sensory input layer and an intervening layer of large cells. The large cells have apical dendrites that receive input from parallel fibers, and b...

The ``Brownian bees'' model describes a system of $N$-independent branching Brownian particles. At each event the particle farthest from origin is removed so that number particles remains constant at all times. Berestycki et al. [arXiv:2006.06486] proved $N\ensuremath{\rightarrow}\ensuremath{\infty}$ coarse-grained spatial density this lives in spherically symmetric domain and described by solu...