We prove that the count of Maslov index 2 $J$-holomorphic discs passing through a generic point real Lagrangian submanifold in closed spherically monotone symplectic manifold must be even. As corollary, we exhibit genuine phenomenon terms involutions, namely Chekanov torus $\mathbb{T}_{\text{Chek}}$ $S^2\times S^2$, which is not Hamiltonian isotopic to Clifford $\mathbb{T}_{\text{Clif}}$, can s...

In the present paper we study generalized left derivations on Lie ideals of rings with involution. Some of our results extend other ones proven previously just for the action of generalized left derivations on the whole ring. Furthermore, we prove that every generalized Jordan left derivation on a 2-torsion free ∗-prime ring with involution is a generalized left derivation.

A square involution is a square permutation which is also an involution. In this paper we give the enumeration of square involutions, using purely combinatorial methods, by establishing a bijective correspondence with a class of lattice paths. As a corollary to our result, we enumerate various subclasses of square involutions, including the classes of triangular, decomposable, and fat involutions.

Breast cancer patients diagnosed within five years following pregnancy have increased metastasis and decreased survival. A hallmark of postpartum biology that may contribute to this poor prognosis is mammary gland involution, involving massive epithelial cell death and dramatic stromal remodeling. Previous studies show pro-tumorigenic properties of extracellular matrix (ECM) isolated from roden...

After puberty, the thymus undergoes a dramatic loss in volume, in weight and in the number of thymocytes, a phenomenon termed age-associated thymic involution. Recently, it was reported that age-associated thymic involution did not occur in mice expressing a rearranged transgenic (Tg) TCRalphabeta receptor. This finding implied that an age-associated defect in TCR rearrangement was the major, i...

Let $X$ be a Banach space of $dim X > 2$ and $B(X)$ be the space of bounded linear operators on X. If $L : B(X)to B(X)$ be a Lie higher derivation on $B(X)$, then there exists an additive higher derivation $D$ and a linear map $tau : B(X)to FI$ vanishing at commutators $[A, B]$ for all $A, Bin B(X)$ such that $L = D + tau$.

‎we determine the‎ ‎form of polynomially bounded solutions to the loewner differential ‎equation that is satisfied by univalent subordination chains of the‎ ‎form $f(z,t)=e^{int_0^t a(tau){rm d}tau}z+cdots$‎, ‎where‎ ‎$a:[0,infty]rightarrow l(mathbb{c}^n,mathbb{c}^n)$ is a locally‎ ‎lebesgue integrable mapping and satisfying the condition‎ ‎$$sup_{sgeq0}int_0^inftyleft|expleft{int_s^t‎ ‎[a(tau)...

The segment-polarity class of segmentation genes in Drosophila are primarily involved in the specification of sub-segmental units. In addition, some of the segment-polarity genes have been shown to specify cell fates within the central nervous system. One of these loci, gooseberry, consists of two divergently transcribed genes, gooseberry and gooseberry neuro, which share a paired box as well a...