Let $S(G^{sigma})$ be the skew-adjacency matrix of the oriented graph $G^{sigma}$, which is obtained from a simple undirected graph $G$ by assigning an orientation $sigma$ to each of its edges. The skew energy of an oriented graph $G^{sigma}$ is defined as the sum of absolute values of all eigenvalues of $S(G^{sigma})$. Two oriented graphs are said to be skew equienergetic iftheir skew energies...

This paper will consider supersymmetric nonlinear sigma models in two space-time dimensions. First, the rich variety of possible supersymmetries in two dimensions will be discussed. Next, a slight detour into some complex geometry will be taken to gather some useful definitions and results. Finally, it will be shown that requiring the sigma model to have extended supersymmetry imposes various g...

An effective sigma model describing behavior of the 3d rigid string with a θ-term at θ = π is proposed. It contains non-perturbative corrections resulting from summation over different genera of the 2d surfaces. The effective theory is the SU (2) WZW model coupled to the Nambu-Goto action. RG analysis shows the existence of a IR fixed point at which the normal to the surface has long range corr...

In this paper, we investigate matrices acting on finite commutative groups and rings. In fact, we study modules on ring of matrices over ZN and also modules over the ring (F2 , ⨁,∧); these new algebraic constructions are a generalization of some of the constructions which were previously presented by the authors of this paper. We present new linearized and nonlinear MDS diffusion layers, based ...

We prove the existence of local constancy phenomena for reductions in a general (odd) prime power setting two-dimensional irreducible crystalline representations Gal(? ¯ p /? ). These depend on two parameters: trace and weight k. They appear example context classical modular forms tame level. find an (explicit) result with respect to using Fontaine’s theory (?,?)-modules, its refinement due Ber...

Unlike rigid actuators, soft actuators can easily adapt to complex environments. Understanding the relationship between deformation of and external factors such as pressure would enable rapid designs based on specific requirements, flexible, compliant endoscopes. An effective model is demonstrated that predicts a actuator virtual work principle geometrically exact Cosserat rod theory. The proce...

Let $mathcal{A}$ be a Banach algebra and $mathcal{M}$ be a Banach $mathcal{A}$-bimodule. We say that a linear mapping $delta:mathcal{A} rightarrow mathcal{M}$ is a generalized $sigma$-derivation whenever there exists a $sigma$-derivation $d:mathcal{A} rightarrow mathcal{M}$ such that $delta(ab) = delta(a)sigma(b) + sigma(a)d(b)$, for all $a,b in mathcal{A}$. Giving some facts concerning general...

The general non-split scalar coset of supergravity theories is discussed.The symmetric space sigma model is studied in two equivalent formulations and for different coset parametrizations.The dualisation and the local first order formulation is performed for the non-split scalar coset G/K when the rigid symmetry group G is a real form of a non-compact semisimple Lie group (not necessarily split...

The experimental charge density distribution of dimethyl-trans-2-oxohexahydro-pyrimidine-4,6-dicarboxylate 1 has been determined using single-crystal X-ray diffraction data measured at 100 K, in terms of the rigid-pseudoatom formalism. Multipole refinement converged at R(F) = 0.034 for 7283 reflections with I > 3 sigma (I) and sin theta/lambda < or = 1.13 A(-1). Covalent and hydrogen bonding in...

We first study a free particle on an (n − 1)-sphere in an extended phase space, where the originally second-class Hamiltonian and constraints are now in strong involution. This allows for a Schrödinger representation and a Hamilton-Jacobi formulation of the model. We thereby obtain the free particle energy spectrum corresponding to that of a rigid rotator. We extend these considerations to a mo...