For a graph of an n-cycle ∆ with Alexander dual ∆, we study the free resolution of a subideal G(n) of the Stanley-Reisner ideal I∆∗ . We prove that if G(n) is generated by 3 generic elements of I∆∗ , then the second syzygy module of G(n) is isomorphic to the second syzygy module of (x1, x2, . . . , xn). A result of Bruns shows that there is always a 3-generated ideal with this property. We show...

The ground field k is algebraically closed and of characteristic zero. Let g be a simple Lie algebra over k. The goal of this note is to prove a closed formula for the Dynkin index of a principal sl2-subalgebra of g, see Theorem 3.2. The key step in the proof uses the “strange formula” of Freudenthal–de Vries. As an application, we (1) compute the Dynkin index any simple g-module regarded as sl...

MHD flow and heat transfer have been analyzed for a front poloidal channel in the outboard module of a Dual Coolant Lithium Lead (DCLL) blanket, with a flow channel insert made of a silicon carbide composite. The US reference DCLL blanket module [C. Wong, S. Malang, M. Sawan, S. Smolentsev, S. Majumdar, B. Merrill, D.K. Sze, N. Morley, S. Sharafat, P. Fogarty, M. Dagher, P. Peterson, H. Zhao, S...

Our investigation of coalgebras over commutative rings R is based on the close relationship between comodules over a coalgebra C and modules over the dual algebra C∗. If C is projective as an R-module the category of right C-comodules can be identified with the category σ[C∗C] of left C∗-modules which are subgenerated by C. In this context semiperfect coalgebras are described by results from mo...

The action of a reductive algebraic group G on G/P−, where P− is a parabolic subgroup, differentiates to a representation of the Lie algebra g of G by vector fields on U+, the unipotent radical of a parabolic opposite to P−. We show that both the regular functions on U+ and the polynomial vector fields on U+ form g-modules that are dual to parabolically induced modules, construct an explicit co...

Most learning systems applied to problem solving have the goal of learning knowledge for solving problems more eeciently. However, very few systems have focused on the acquisition of planning operator descriptions. In this paper, we present a system that learns operator deenitions from the interaction with a completely unknown environment. In order to achieve better learning convergence, severa...

A self-dual algebra is an associative or Lie algebra A together with an A bimodule isomorphism A → A∨op, where A∨ = Homk(A, k), the dual bimodule to A (considered as an A bimodule), and A∨op is the the same underlying k module as A∨ but is an A bimodule whose left operation by an element a ∈ A is the same as the right operation by a on A∨, and similarly with left and right interchanged. This in...

This research aims in designing a method for implementing end-to-end voice encryption over mobile network such as GSM that independent to phone devices, operating system and network devices. The proposing method is an encryption system in domain frequency to keep the encryption signal remain within the range of sound frequencies that can be transmitted through GSM/2G/3G. This method differ comp...

We introduce the notion of hyper-self-duality for Bose-Mesner algebras as a strengthening of formal self-duality. LetM denote a Bose-Mesner algebra on a finite nonempty set X . Fix p ∈ X , and letM∗ and T denote respectively the dual Bose-Mesner algebra and the Terwilliger algebra ofMwith respect to p. By a hyper-duality ofM, we mean an automorphism ψ of T such that ψ(M) =M∗, ψ(M∗) =M; ψ2(A) = ...