We prove that δ-derivations of a simple finite-dimensional Lie algebra over field characteristic zero, with values in module, are either inner derivations, or, the case adjoint multiplications by scalar, or some exceptional cases related to sl(2). This can be viewed as an extension classical first Whitehead Lemma.

Exploiting advanced light-absorbing conjugated polymers is of great significance to achieve the blue dream low-energy solar steam generation and clean water collection. Herein, an interfacial chemistry strategy developed massively synthetize polybenzobisthiazole (CP) microspheres with a narrow bandgap 0.274 eV high absorbance 94.0%. The CP are combined polyvinyl alcohol (PVA) hydrogel form Janu...

We consider a Lévy flyer of order alpha that starts from a point x(0) on an interval [O,L] with absorbing boundaries. We find a closed-form expression for the average number of flights the flyer takes and the total length of the flights it travels before it is absorbed. These two quantities are equivalent to the mean first passage times for Lévy flights and Lévy walks, respectively. Using fract...

Cellobiohydrolase CbhA from Clostridium thermocellum cellulosome is a multi-modular protein composed starting from the N-terminus of a carbohydrate-binding module (CBM) of family 4, an immunoglobulin(Ig)-like module, a catalytic module of family 9 glycoside hydrolases (GH9), X1(1) and X1(2) modules, a CBM of family 3 and a dockerin module. Deletion of the Ig-like module from the Ig-GH9 construc...

Three equivalence relations are considered on the set of n x n matrices with elements in Fo' an · abelian group with absorbing zero adjoined. They are the relations of diagonal similarity, diagonal equivalence, and restricted diagonal equivalence. These relations are usually considered for matrices with elements in a field, but only multiplication is involved. Thus our formulation in terms of a...

We perform classical three-dimensional Monte Carlo simulations of ultracold neutrons scattering through an absorbing-reflecting mirror system in the Earth's gravitational field. We show that the underlying mixed phase space of regular skipping motion and random motion due to disorder scattering can be exploited to realize a vectorial velocity filter for ultracold neutrons. The absorbing-reflect...

Given any simple Lie superalgebra g, we investigate the structure of an arbitrary simple weight g-module. We introduce two invariants of simple weight modules: the shadow and the small Weyl group. Generalizing results of Fernando and Futorny we show that any simple module is obtained by parabolic induction from a cuspidal module of a Levi subsuper-algebra. Then we classify the cuspidal Levi sub...

The study was aimed at designing and developing a Physics module based on learning style and appropriate technology in secondary educational setting by employing Isman Instructional Design Model and to test the effectiveness of the module. The paper draws attention to the design principles which employs Isman Instructional Design Model. The prototype module was tested among two teachers and 14 ...

It is convenient to have an abstract framework for discussing statistical theory. The general problem is that there exists an unknown parameter θ0, which we wish to find out about. To have something concrete in mind, consider for example a population with the N(θ0 , 1) distribution, where θ0 is an unknown constant. If we do not have any a priori information about θ0 then it stands to reason tha...

Can quantum communication be more efficient than its classical counterpart? Holevo’s theorem rules out the possibility of communicating more than n bits of classical information by the transmission of n quantum bits—unless the two parties are entangled, in which case twice as many classical bits can be communicated but no more. In apparent contradiction, there are distributed computational task...