We prove two supercongruences for the coefficients of power series expansions in t of modular forms where t is a modular function. As a result, we settle two recent conjectures of Chan, Cooper and Sica. Additionally, we provide a table of supercongruences for numbers which appear in similar power series expansions and in the study of integral solutions of Apéry-like differential equations.

Uncertainties in demand and supply, which are two major contributions to system dynamics, are unavoidable attributes in supply chains. Agent technology has been a renowned enabler to achieve flexibility and adaptability, which are regarded as the distinctive characteristics of future supply chains, to overcome system dynamics (Chan and Chan, 2005). In order to testify the usefulness of these ch...

Slope stability assessment is a critical research area in civil engineering. Disastrous consequences of slope collapse necessitate better tools for predicting their occurrences. This research proposes a hybrid Artificial Intelligence (AI) for slope stability assessment based on metaheuristic and machine learning. The contribution of this study to the body of knowledge is multifold. First, advan...

Abstract To propose an effective and reasonable excavation plan for rock joints to control the overall stability of surrounding mass predict prevent engineering disasters, this study is aimed at predicting joint shear strength using combined algorithm by support vector regression (SVR) firefly (FA). The dataset collected was employed as output prediction, roughness coefficient (JRC), uniaxial c...

in this study, the oil yield, fatty acid (fa) composition and the physicochemical and quality characteristics of salvia macrosiphon crude seed oil were determined. the main fatty acids ranked in the following order of abundance: α- linolenic acid> linoleic acid> oleic acid. the n3 /n6 fa ratio and polyunsaturated fa/ saturated fa ratio were 1.6 and 7.23, respectively. the fa composition reveale...

Chan, Y.-L., Orie, N. N., Singer, M., and Clapp, L. H. (2007). Inflammatory mediators enhance expression of vascular ATP-sensitive potassium channels. Intensive Care Med. 33:S120. Chan, Y.-L., Orie, N. N., Singer, M., and Clapp, L. H. (2008). Enhanced expression of vascular KATP channels in an in vitro model of sepsis. Fundam. Clin. Pharmacol. 22:S34. Chan, Y.-L., Stidwill, R., Taylor, V., Clap...

In this short note, we demonstrate a simple and practical ORAM that enjoys an extremely simple proof of security. Our construction is based on a recent ORAM due to Shi, Chan, Stefanov and Li [SCSL11], but with some crucial modifications, which significantly simply the analysis. ∗Cornell University. {chung,rafael}@cs.cornell.edu Chung is supported in part by NSF Award CCF-1214844 and Pass’ Sloan...

We prove two congruences for the coefficients of power series expansions in t of modular forms where t is a modular function. As a result, we settle two recent conjectures of Chan, Cooper and Sica. Additionally, we provide tables of congruences for numbers which appear in similar power series expansions and in the study of integral solutions of Apéry-like differential equations.

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Please do not quote or cite without authors’ permission. Comments are welcome. Many thanks are due to Yolande Chan of Queen's University for participating in the development of this work. Thanks also to Michelle Brown, V. Sambamurthy and Robert W. Zmud for their comments on our original models. This work has been supported by an operating grant from the Social Sciences and Humanities Research C...