The object of the present paper is to study semi-symmetric metric connection on a 3-dimensional trans-Sasakian manifold. We found necessary condition under which vector field manifold will be strict contact field. Then, we obtained extended generalized phi-recurrent with respect connection. Next, satises ~L.~ S = 0 studied.

We prove that the complex cobordism class of any hyper-K\{a}hler manifold dimension $2n$ is a unique combination with rational coefficients classes products punctual Hilbert schemes $K3$ surfaces. also similar result using generalized Kummer varieties instead schemes. As key step, we establish closed formula for top Chern character their tangent bundles.

The object of this paper is to study invariant submanifolds M of Kenmotsu manifolds M̃ admitting a quarter symmetric metric connection and to show that M admits quarter symmetric metric connection. Further it is proved that the second fundamental forms σ and σ with respect to LeviCivita connection and quarter symmetric metric connection coincide. Also it is shown that if the second fundamental f...

Background: Hyper IgE syndrome (HIES) is a rare primary immune deficiency, described as Job`s syndrome characterized by increased serum levels of IgE, eczema, recurrent cutaneous and pulmonary infections. In this paper, we presented a case of Hyper IgE syndrome.Case Presentation: A 16-year-old Iranian boy presented with a one year history of skin lesions in knees and elbows was diagnosed of pso...

We consider hyper-Kähler manifolds of complex dimension 4 which are fibrations. It is known that the fibers are abelian varieties and the base is P. We assume that the general fiber is isomorphic to a product of two elliptic curves. We prove that such a hyper-Kähler manifold is deformation equivalent to a Hilbert scheme of two points on a K3 surface. 1. Preliminaries First we define our main ob...

We present an approach, based on learning intrinsic data manifold, for the initialization of internal state values long short-term memory (LSTM) recurrent neural networks, ensuring consistency with initial observed input data. Exploiting generalized synchronization concept, we argue that converged, “mature” states constitute a function this learned manifold. The dimension manifold then dictates...

hyper igm syndrome (him sx) is a rare congenital primary immunodeficiency that affects males more than females (70%, x-iinked recessive), but there are reports of autosomal recessive and autosomal dominant inheritances. in this study, we review medical histories of 2 affected girls and one affected boy. our 3 cases fulfill clinical and laboratory criteria of this syndrome. their clinical signs ...

In this paper, we will study compatible triples on Lie algebroids. Using a suitable decomposition for a Lie algebroid, we construct an integrable generalized distribution on the base manifold. As a result, the symplectic form on the Lie algebroid induces a symplectic form on each integral submanifold of the distribution. The induced Poisson structure on the base manifold can be represented by m...

We classify all warped $dS_5$ backgrounds in $D=11$ supergravity with enhanced supersymmetry. show that preserving $N=16$ supersymmetries consist of either a stack M5 branes transverse space $\mathbb{R}^5$, or generalized M5-brane configuration $\mathbb{R} \times N_4$, where $N_4$ is hyper-Kahler manifold and the $M5$-brane harmonic function determined by potential on $N_4$. Moreover, we find t...