Cyclotomic rings of integers (data)

arXiv (Cornell University), 2020

In complex vector spaces maximal sets of equiangular lines, known as SICs, are related to real quadratic number fields in a dimension dependent way. If the dimension is of the form n 2 +3 the base field has a fundamental unit of negative norm, and there exists a SIC with anti-unitary symmetry. We give eight examples of exact solutions of this kind, for which we have endeavoured to make them as simple as we can-as a belated reply to the referee of an earlier publication, who claimed that our exact solution in dimension 28 was too complicated to be fit to print. An interesting feature of the simplified solutions is that the components of the fiducial vectors largely consist of algebraic units.

arXiv (Cornell University), 2015

We describe a protocol for quantum information splitting (QIS) of a restricted class of three-qubit states among three parties Alice, Bob and Charlie, using a pair of GHZ states as the quantum channel. There are two different forms of this three-qubit state that is used for QIS depending on the distribution of the particles among the three parties. There is also a special type of four-qubit state that can be used for QIS using the above channel. We explicitly construct the quantum channel, Alice's measurement basis and the analytic form of the unitary operations required by the receiver for such a purpose.

Operations and Supply Chain Management: An International Journal

The rapid advancement in IT communication enables the availability of demand data in a seamless manner. One manifestation of this technological advancement within the supply chain (SC) domain has been the emergence of a push-pull boundary (PPB). Push-pull boundary is a virtual demarcation point separating the portion of the SC under decentralized from that operating under centralized information sharing. However, the impact of key issues like adoption of inventory ordering policy characterized by the various echelons of a SC network structure while positioning the push-pull boundary need to be investigated comprehensively (Ahn and Kaminsky, 2005). This paper is concerned with the 'Average Fill Rate' and 'Average Total Inventory Cost' performance behaviour of a SC network structure. These performances typically results from different parameters that involves: (i) inventory ordering policy, (ii) push-pull boundary under the influence of information sharing, (iii) forecasting error, and (iv) lead time and their standard deviations. The study is accomplished via Taguchi experimental design framework and simulation analysis. The results suggest the effect of various factors on SC network system wide performance and identify the appropriate combinations of these factors for optimal performance concerned.

Journal of Applied Mathematics and Physics

An explicit algebraic stress model (EASM) has been formulated for two-dimensional turbulent buoyant flows using a five-term tensor representation in a prior study. The derivation was based on partitioning the buoyant flux tensor into a two-dimensional and a three-dimensional component. The five-term basis was formed with the two-dimensional component of the buoyant flux tensor. As such, the derived EASM is limited to two-dimensional flows only. In this paper, a more general approach using a seven-term representation without partitioning the buoyant flux tensor is used to derive an EASM valid for two-and three-dimensional turbulent buoyant flows. Consequently, the basis tensors are formed with the fully three-dimensional buoyant flux tensor. The derived EASM has the two-dimensional flow as a special case. The matrices and the representation coefficients are further simplified using a four-term representation. When this four-term representation model is applied to calculate two-dimensional homogeneous buoyant flows, the results are essentially identical with those obtained previously using the two-dimensional component of the buoyant flux tensor. Therefore, the present approach leads to a more general EASM formulation that is equally valid for two-and three-dimensional turbulent buoyant flows.

Advances in Accounting, 2011

a b s t r a c t a r t i c l e i n f o Environmental uncertainty induces variability in an organization's reported earnings, and accentuates the information asymmetry between its managers and outside stakeholders. Managers operating in an environment of high uncertainty, therefore, have an incentive to reduce such variability by smoothing income numbers. We investigate the stock market response to earnings smoothness for firms operating in an environment of high uncertainty. We measure income smoothing by the negative correlation of a firm's change in discretionary accruals with its change in pre-managed earnings as per . Using future earnings response coefficient (FERC) methodology to measure the informativeness of smoothed earnings, and two measures of environmental uncertainty, this paper documents that current stock price incorporates more information about future earnings for firms operating in high uncertain environments, thus supporting the informational value view of income smoothing.

Hacettepe Journal of Mathematics and Statistics, 2016

In this article, we have suggested new methods of ratio exponential type imputation and proposed their corresponding point estimators to deal with the problems of non-response in sample surveys for the prior outlay of an auxiliary variable x. The expression of the biases and their mean square errors of the proposed estimators have been derived, upto the first order of large sample approximation under SRSWOR scheme and compared with the mean method of imputation, ratio method of imputation, regression method of imputation and the estimators of Singh and Horn (Metrika [16]), Singh and Deo (Statistical Papers [15]), Toutenburg et al. (Statistical Papers [18]), Singh (Statistics [17]) and Gira (Applied Mathematical Sciences [5]). After comparison, the condition which makes the proposed forty four estimators more efficient than others are found. To verify the theoretical results, simulation studies are performed on five real data sets.

Structural Equation Modeling: A Multidisciplinary Journal, 2017

This article describes the REREFACT R package, which provides a postrotation algorithm that reorders or reflects factors for each replication of a simulation study with exploratory factor analysis (EFA). The purpose of REREFACT is to provide a general algorithm written in freely available software, R, dedicated to addressing the possibility that a nonuniform order or sign pattern of the factors could be observed across replications. The algorithm implemented in REREFACT proceeds in 4 steps. Step 1 determines the total number of equivalent forms, I, of the vector of factors, η. Step 2 indexes, i = 1, 2 … I, each equivalent form of η (i.e., ηi) via a unique permutation matrix, P (i.e., Pi). Step 3 determines which ηi each replication follows. Step 4 uses the appropriate Pi to reorder or re-sign parameter estimates within each replication so that all replications uniformly follow the order and sign pattern defined by the population values. Results from two simulation studies provided evidence for the efficacy of the REREFACT to identify and remediate equivalent forms of η in models with EFA only (i.e., Example 1) and in fuller parameterizations of exploratory structural equation modeling (i.e., Example 2). How to use REREFACT is briefly demonstrated prior to the Discussion section by providing annotations for key commands and condensed output using a subset of simulated data from Example 1.

Journal of Mathematical Chemistry, 2016

In this article, we have suggested new methods of ratio exponential type imputation and proposed their corresponding point estimators to deal with the problems of non-response in sample surveys for the prior outlay of an auxiliary variable x. The expression of the biases and their mean square errors of the proposed estimators have been derived, upto the first order of large sample approximation under SRSWOR scheme and compared with the mean method of imputation, ratio method of imputation, regression method of imputation and the estimators of Singh and Horn (Metrika [16]), Singh and Deo (Statistical Papers [15]), Toutenburg et al. (Statistical Papers [18]), Singh (Statistics [17]) and Gira (Applied Mathematical Sciences [5]). After comparison, the condition which makes the proposed forty four estimators more efficient than others are found. To verify the theoretical results, simulation studies are performed on five real data sets.

Atmospheric Measurement Techniques, 2015

A new retrieval scheme for cloud optical thickness, effective radius, and thermodynamic phase was developed for ground-based measurements of cloud shortwave solar spectral transmittance. Fifteen parameters were derived to quantify spectral variations in shortwave transmittance due to absorption and scattering of liquid water and ice clouds, manifested by shifts in spectral slopes, curvatures, maxima, and minima. To retrieve cloud optical thickness and effective particle radius, a weighted least square fit that matched the modeled parameters was applied. The measurements for this analysis were made with the ground-based Solar Spectral Flux Radiometer in Boulder, Colorado, between May 2012 and January 2013. We compared the cloud optical thickness and effective radius from the new retrieval to two other retrieval methods. By using multiple spectral features, we find a closer fit (with a root mean square difference over the entire spectra of 3.1% for a liquid water cloud and 5.9% for an...

International Journal of Machine Intelligence and Sensory Signal Processing, 2013

A mathematical model of artificial neural networks with hysteresis is formulated using neutral delay differential equations. Hysteresis modifies the systems such that they cannot produce unique output for any given input, rather output is produced based on the past history of the system. Motivated by the applications of complex valued neural networks in artificial neural networks, we studied the global dynamics of complex valued neural network with hysteresis. The result extends and improves the earlier publications due to the fact that it removes some restrictions on the neural delay. In this paper continuous hysteresis neuron model has been used to arrive at the sufficient condition for global exponential stability of a unique equilibrium. The hypothetical insight has been successfully applied and verified using relevant numerical examples.