Classical Assignment Problem (AP) is a well-known topic world-wide. In this problem ij c denotes the cost for assigning the th j job to the th i person. This cost is usually deterministic in nature. But in realistic situations, it may not be practicable to know the precise values of these costs. In such uncertain situations, instead of exact values of costs, if we can evaluate the preferences f...

We consider the complexity of computing the determinant over arbitrary finite-dimensional algebras. We first consider the case that A is fixed. We obtain the following dichotomy: If A/ radA is noncommutative, then computing the determinant over A is hard. “Hard” here means #P-hard over fields of characteristic 0 and ModpP-hard over fields of characteristic p > 0. If A/ radA is commutative and t...

We look at two examples of homotopy Lie algebras (also known as L∞ algebras) in detail from two points of view. We will exhibit the algebraic point of view in which the generalized Jacobi expressions are verified by using degree arguments and combinatorics. A second approach using the nilpotency of Grassmann-odd differential operators ∆ to verify the homotopy Lie data is shown to produce the sa...

In this paper, we investigate the entanglement of multi-partite Grassmannian coherent states (GCSs) described by Grassmann numbers for n > 2 degree of nilpotency. Choosing an appropriate weight function, we show that it is possible to construct some wellknown entangled pure states, consisting of GHZ, W, Bell, cluster type and bi-separable states, which are obtained by integrating over tensor pr...

We obtain minimal shape-preserving projections onto the n-th degree algebraic polynomials via a geometric approach.

In this work we consider a given root of family n-degree polynomials as one-variable function that depends only on the independent term. Then prove satisfies several ordinary differential equations (ODE). More concretely, it simple separated variables ODE, first order generalized Abel ODE degree n−1 and an (n−1)-th linear ODE. Although some our results are not new, approach is self-contained. F...

The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. We study the application of a supersymmetric model with two constrained supermultiplets to inflationary cosmology. The first superfield S is a stabilizer chiral superfield satisfying a nilpotency condition of degree 2, S 2 ¼ 0. The second superfield Φ is the inflaton chiral sup...

Let $G = (V, E)$ be a simple graph. Denote by $D(G)$ the diagonal matrix $diag(d_1,cdots,d_n)$, where $d_i$ is the degree of vertex $i$  and  $A(G)$ the adjacency matrix of $G$. The  signless Laplacianmatrix of $G$ is $Q(G) = D(G) + A(G)$ and the $k-$th signless Laplacian spectral moment of  graph $G$ is defined as $T_k(G)=sum_{i=1}^{n}q_i^{k}$, $kgeqslant 0$, where $q_1$,$q_2$, $cdots$, $q_n$ ...

the noorabad-kermanshah ophiolite is part of eastern mediterranean-zagros-oman tethyan ophiolites, that this area is located in south-southwest of the main zagros thrust fault. this ophiolite consists of peridotites, serpentinites and pegmatite gabbros as mantle sequence whereas crustal sequences are composed of locally layered gabbros, isotropic gabbros, sheeted dike complex, basaltic to andes...