In this paper, we propose a polynomial time algorithm for fractional assignment problems. The fractional assignment problem is interpreted as follows. Let G = (I; J;E) be a bipartite graph where I and J are vertex sets and E I J is an edge set. We call an edge subset X( E) an assignment if every vertex is incident to exactly one edge from X: Given an integer weight c ij and a positive integer w...

We show that an Artin group G with all m ij ≥ 7 is relatively hyperbolic in the sense of Farb with respect to the collection of subgroups a i , a j (where m ij < ∞).

A statistic to measure the level of connectedness achieved among flocks would help producers to assess the risk of comparing EBV of animals from different flocks. The objectives of this research were to evaluate the pattern of change over time in selected connectedness measures and to determine how effectively these measures quantify the level of risk due to potential bias in EBV comparisons ac...

A particle that is constrained to freely move on a hyperspherical surface in an $N\left( \geq 2\right) $ dimensional flat space experiences curvature-induced gauge potential, whose form was given long ago (J. Math. Phys. \textbf{34}(1993)2827). We demonstrate the momentum for hypersphere geometric one including potential and its components obey commutation relations $\left[ p_{i},p_{j}\right] =...

‎Let $\Omega$ be a bounded domain in $R^{n}$ with smooth boundary‎ ‎$\partial\Omega$‎. ‎In this article‎, ‎we will investigate the spectral‎ ‎properties of non-self adjoint elliptic differential operator\\‎ ‎$(Au)(x)=-\sum^{n}_{i,j=1}\left(\omega^{2\alpha}(x)a_{ij}(x)‎ ‎\mu(x)u'_{x_{i}}(x)\right)'_{x_{j}}$‎, ‎acting Hilbert space ‎$H=L^{2}{(\Omega)}$. Dirichlet-type boundary conditions‎. ‎Here‎...

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...

People with disabilities such as multiple sclerosis and Parkinson's disease have difficulty operating conventional movement-sensing joysticks (MSJs) because of varying levels of tremor. We developed an isometric joystick (IJ) that has performed as well as a conventional MSJ when used by persons with upper-limb impairments in real and virtual wheelchair driving tasks. The Weighted-Frequency Four...

We study the variability of predictions made by bagged learners and random forests, and show how to estimate standard errors for these methods. Our work builds on variance estimates for bagging proposed by Efron (1992, 2012) that are based on the jackknife and the infinitesimal jackknife (IJ). In practice, bagged predictors are computed using a finite number B of bootstrap replicates, and worki...