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This expository paper presents known results on distribution functions g(x) of the sequence of blocks where xn is an increasing sequence of positive integers. Also presents results of the set G(Xn) of all distribution functions g(x). Specially: - continuity of g(x); - connectivity of G(Xn); - singleton of G(Xn); - one-step g(x); - uniform distribution of Xn, n = 1, 2, . . . ; - lower and upper bounds of g(x); - applications to bounds of ; - many examples, e.g., , where pn is the nth prime, is uniformly distributed. The present results have been published by 25 papers of several authors between 2001-2013.

In a recent paper, (Math Notes 91(3–4): 508–516, 2012) Zarhin proved that each member of a naturally defined family of linear maps \({\mathbb {C}}^n \rightarrow {\mathbb {C}}^n\) has co-rank one. We present a direct proof of Zarhin’s result about complex polynomials with distinct roots; it is rather similar to that of Appendix by Vik.S. Kulikov to Zarhin’s paper but we give explicit constants. We also discuss the case of a polynomial with multiple roots.

The enormous usage of mobile gadget in this era gives opportunity to use this facility to improve the communication between researchers or students for sharing scientific paper citation data. Users can access easily electronic scientific journal data using their mobile gadget via internet connection. This research proposes to build mobile client-server application based on Android Operating System. Mobile application also equipped with social network feature, where users can share paper citation through Facebook. The integration with social network improves paper dissemination and facilitates collaborative research works between communities or groups on social network.

It is well documented in both the British press and mathematics education literature that many consider A-levels (qualifications for secondary school leavers in England, Wales and Northern Ireland) to be insufficient preparation for undergraduate mathematics study in the UK. A-level Mathematics and Further Mathematics are not solely intended for those wishing to go on to study undergraduate mathematics, though this is often the only mathematics study and preparation available to, and done by, most students. A number of British universities now require applicants to perform well on entrance examinations or ‘extension’ papers in addition to achieving certain grades in A-level Mathematics and, sometimes, Further Mathematics. This article outlines research which used the Mathematical Assessment Task Hierarchy (Smith et al., 1996) and builds upon the work of Darlington (2014) to describe the mathematical skills required to answer the questions in extension papers. These are then contrasted with skills required at A- and undergraduate level. Each of the three extension papers analysed (Advanced Extension Awards, Sixth Term Examination Papers and university admissions tests) were found to differ from each other, as well as from A-level and undergraduate examinations. This suggests that there are benefits for students doing such papers before university mathematics study. The advantages of doing these papers are not only for admissions tutors, who can use them as additional indicators of candidates’aptitudes, but also for the students themselves as they gain insights into the nature of undergraduate mathematics and related further mathematical challenges.

Discoverability enables scholars to locate the content needed to advance their research and other creative activities. Improved discovery experiences require heightened collaboration among: (1) scholarly publishers and their published authors; (2) search engine developers, database providers, abstracting and indexing services, and academic publishers; (3) electronic resource management and integrated library system vendors, and ; (4) librarians who advance institutional discoverability. To further exploratory cross-sector conversations, SAGE commissioned a White Paper, "Improving Discoverability of Scholarly Content in the Twentieth Century: Collaboration Opportunities for Librarians, Publishers, and Vendors," released in January 2012. The research report presents highlights of interviews conducted from July to October 2011 with fourteen value chain experts. The White Paper also summarizes results of peer-reviewed publications and proprietary research studies to further characterize the currently fragmented discovery environment. In conclusions, the authors propose cross-sector conversations among publishers, vendors, and librarians to further visibility and, ultimately, usage of the scholarly corpus on the open Web and within library services.

We develop a theoretical framework for rigid origami, and show how this framework can be used to connect rigid origami and results from cognate areas, such as the rigidity theory, graph theory, linkage folding and computer science. First, we give definitions on important concepts in rigid origami, then focus on how to describe the configuration space of a creased paper. The shape and 0-connectedness of the configuration space are analyzed using algebraic, geometric and numeric methods, where the key results from each method are gathered and reviewed., Comment: 29 pages, 7 figures, submitted to the Proceedings of the Royal Society A

The aim of this paper is to study a new equivalent form of the weak maximum principle for a large class of differential operators on Riemannian manifolds. This new form has been inspired by the work of Berestycki, Hamel and Rossi for trace operators, and allows us to shed new light on it and to introduce a new sufficient bounded Khas’minskii type condition for its validity. We show its effectiveness by applying it to obtain some uniqueness results in a geometric setting.

For any discrete valuation ring R, any R-linear mapping u from an R-module E into an R-module F and any \(y_0\in F\), a necessary and sufficient condition for the solvability of the equation \(u(x)=y_0\) is established, and an application of this result is presented.

Tourism is one of the National Key Economic Area (NKEAs) as initiatives to ensure sustainability of growth in Malaysia. One option to increase the national income is through promoting event tourism. Organizing events are highly resource intensive, and can have negative environmental consequences such as waste of water, energy and materials. Therefore, greening of events is critically important to ensure sustainability development in event management by making responsible decisions during planning, organization and implementation of an event. Sustainable event management is the process used to produce events with particular concern for environmental, economic and social issues. Identification of factors that increase the demand for sustainable events would greatly contribute to the country’s NKEAs to improve business services and generate the economy with event tourism. Thus, creating a competitive domestic economy as stated in the country’s Strategic Reform Initiatives (SRIs), by creating more green events using sustainability issues as the main attraction to increase the rate of attendance. The objective of this study is to identify the demand for green events to promote sustainable tourism.

English Abstract: The Komponisten der Gegenwart ( KdG ) is currently the only ongoing and continuously updated German reference work on music. As of 2016 it comprises over 10,250 pages, a number that periodically increases with the addition of new entries. The lexicon includes both contemporary composers considered part of the musicological canon, and neglected or forgotten figures. The KdG operates on a very small scale with very limited institutional and private economic support. It neither benefits from the framework of a university or research institute nor does it have the financial backing of a foundation, creating serious structural problems affecting production and proper distribution. Therefore, the inclusion of KdG in meta-encyclopedias such as the RILM Music Encyclopedias facilitates the way in the digital future. French Abstract: Komponisten der Gegenwart ( KdG ) est actuellement le seul ouvrage de reference en musique en allemand dont la mise a jour est continuelle. En 2016, ce lexique comprend 10 250 pages, chiffre qui s’accroit regulierement par l’ajout de nouvelles entrees. Il comprend a la fois des compositeurs contemporains reconnus ou des personnalites moins eminentes. KdG fonctionne sur une echelle relativement restreinte avec un soutien financier limite, d’origine institutionnelle et privee. Il n’entre pas dans le cadre de recherches universitaires ou institutionnelles et ne possede pas l’appui d’une fondation, ce qui cree de serieux problemes de structure, de production et de distribution. Par consequent, le rattachement de KdG a des meta-encyclopedies telles que RILM ou Music Encyclopedias facilite sa perennite digitale. German Abstract: Komponisten der Gegenwart ( KdG ) ist derzeit das einzige fortlaufende und fortwahrend aktualisierte deutsche Nachschlagewerk zur Musik. 2016 umfasst es uber 10.250 Seiten und wachst weiter mit der Erganzung neuer Eintrage. KdG umfasst sowohl Nachweise zu zeitgenossischen Komponisten eines allgemein anerkannten musikwissenschaftlichen Kanons als auch zu vernachlassigten und vergessenen Personlichkeiten. Es wird in kleinstem Rahmen mit auserst geringer Unterstutzung durch institutionelle oder privatwirtschaftliche Zuwendungen erarbeitet. Das Projekt kann weder aus der Nahe zu einer Universitat oder anderen Forschunginstitution Vorteil ziehen, noch verfugt es uber den finanziellen Ruckhalt einer Stiftung, woraus ernstzunehmende strukturelle Schwierigkeiten fur Produktion und Vertrieb resultieren. Daher eroffnet die Aufnahme von Komponisten der Gegenwart in Metaenzyklopadien wie die RILM Music Encyclopedias einen Weg in die digitale Zukunft.

Let [Formula: see text] be a projective variety of dimension [Formula: see text] over an algebraically closed field of arbitrary characteristic. We prove a Fujiki–Lieberman type theorem on the structure of the automorphism group of [Formula: see text]. Let [Formula: see text] be a group of zero entropy automorphisms of [Formula: see text] and [Formula: see text] the set of elements in [Formula: see text] which are isotopic to the identity. We show that after replacing [Formula: see text] by a suitable finite-index subgroup, [Formula: see text] is a unipotent group of the derived length at most [Formula: see text]. This result was first proved by Dinh et al. for compact Kähler manifolds.

We complete a gap in the proof that exceptional polynomials are complete orthogonal systems in the associated Hilbert spaces.

We show that the extension of Rock-Paper-Scissors to include Lizard and Spock is the unique such five move fair game up to isomorphism. We also categorize all analogous six move fair games.

The aim of this paper is to discuss the main result in the paper by D.Y. Gao and X. Lu [On the extrema of a nonconvex functional with double-well potential in 1D, Z. Angew. Math. Phys. (2016) 67:62]. More precisely we provide a detailed study of the problem considered in that paper, pointing out the importance of the norm on the space $C^{1}[a,b]$; because no norm (topology) is mentioned on $C^{1}[a,b]$ we look at it as being a subspace of $W^{1,p}(a,b)$ for $p\in [1,\infty]$ endowed with its usual norm. We show that the objective function has not local extrema with the mentioned constraints for $p\in [1,4)$, and has (up to an additive constant) only a local maximizer for $p=\infty$, unlike the conclusion of the main result of the discussed paper where it is mentioned that there are (up to additive constants) two local minimizers and a local maximizer. We also show that the same conclusions are valid for the similar problem treated in the preprint by X. Lu and D.Y. Gao [On the extrema of a nonconvex functional with double-well potential in higher dimensions, arXiv:1607.03995]., 12 pages; in this version we added the forgotten condition $F(x) \ne 0$ for $x\in (a,b)$ on page 3

College algebra fulfills general education requirements at many colleges in the United States. The study reported here investigated differences in mathematics achievement between undergraduates in college algebra classes using one of two homework methods: WeBWorK, an open-source system for web-based homework, or traditional paper-and-pencil homework. We assessed learning for 439 students in 19 college algebra classes at a large public university in the United States. Twelve classes used WeBWorK and seven had traditional paper-and-pencil homework. Analysis of covariance revealed no significant differences in algebra performance or achievement gain by homework group, ethnicity or gender when statistically controlling for previous mathematics achievement. Results support the conjecture that WeBWorK is at least as effective as traditionally graded paper-and-pencil homework for students learning college algebra in moderately sized lecture-based classes.

Objective. To objectively evaluate the quality and effectiveness of teaching and identify the problems in the teaching process, and to carry out the comprehensive analysis and evaluation of the final examination paper of medical record informatics. Method. The final examination paper of medical record informatics is analyzed through the education survey. Result. The average score of the examination paper is 70.6, and the examination results obey normal distribution. The examination paper has the features of moderate difficulty, general discrimination and good reliability. The proportion of easy questions is too large, and the proportion of the relatively difficult questions should be increased. Conclusion. The proportion of the relatively difficult questions on the examination paper should be increased promptly, so that the examination paper with moderate difficulty can objectively reflect the actual level of the students, thereby improving the quality of teaching.

In this paper author was proved the boundedness of the multidimensional Hardy type operator in weighted Lebesgue spaces with a variable exponent. As an application we prove the boundedness of certain sublinear operators on the weighted variable Lebesgue space. Note that the proof of multidimensional Hardy type operator in weighted Lebesgue spaces with a variable exponent don't contained any mistakes. But at the proving of the boundedness of certain sublinear operators on the weighted variable Lebesgue space Georgian colleagues discovered a small but significant error in this paper. This result is assigned as Theorem 5 in noted paper. In other words, sufficient conditions for general weights ensuring the validity of the two-weight strong type inequalities for some sublinear operator was found. In this theorem the inequality (9) isn't true. In this note we give the details of the correct argument. We presume that the reader is familiar with the contents and notation of our original paper. At the heart of our correction is the following Theorem which replaces Theorem 5.

The shift of traditional service perspective to a more transformative service orientation given the rise of customer citizenship behavior thought. This concept considers customers as the citizen instead of a mere service recipient. Derived from organizational citizenship behavior, customer citizenship behavior (CCB) phenomenon led significant research interest among academicians and practitioners in recent years. However, the effect of CCB in relation to online commerce community is yet to be tested. It is obvious that online commerce is spreading day-by-day which became another strong medium of marketing. Existing literature stressed on sharing of knowledge and information among online consumers. However, more importance should be given to understand consumer behavior like CCB. As such, it is utmost necessary to study the behavioral pattern of online commerce community. Furthermore, there is a dearth of study that investigated the elements of social capital (structural, cognitive and relational social capital) in relation to CCB. Such social capital also translates into firm value/profits through congenial customer citizenship behavior. Considering such gaps in the existing literature, the present study aims to propose a conceptual framework highlighting the antecedents and consequence of CCB in the context of online commerce community.

To prove Theorem 2, we use the following two facts about the class F: 1. F is a differential ring [2]. This means that F is closed under addition, multiplication and differentiation. 2. All functions y ∈ F are entire functions of completely regular growth in the sense of Levin–Pfluger [4], with piecewise-trigonometric indicators, the notions which we recall now. Let f be a holomorphic function in an angular sector S = {re : |θ−θ0| 0}. We say that f has completely regular growth with respect to order ρ > 0 if the following finite limit exists

The purpose of the present note is to point out mathematical mistakes in some published papers on boundary value problems to prevent usage of mistaken results and methods by mathematicians. Copyright © 2013 John Wiley & Sons, Ltd.

Directed graphs with an odd number of vertices n, where each vertex has both (n − 1)/2 incoming and outgoing edges, have a rich structure. We were lead to their study by both the Borromean rings and the game rockpaper-scissors. An interesting interplay between groups, graphs, topological links, and matrices reveals the structure of these objects, and for larger values of n, extensive computation produces some surprises. Perhaps most surprising is how few of the larger graphs have any symmetry and those with symmetry possess very little. In the final section, we dramatically sped up the computation by first computing a “profile” for each graph.

We show that a relative entropy condition recently shown by Leger and Vasseur to imply uniqueness and stable $L^2$ dependence on initial data of Lax 1- or $n$-shock solutions of an $n\times n$ system of hyperbolic conservation laws with convex entropy implies Lopatinski stability in the sense of Majda. This means in particular that Leger and Vasseur's relative entropy condition represents a considerable improvement over the standard entropy condition of decreasing shock strength and increasing entropy along forward Hugoniot curves, which, in a recent example exhibited by Barker, Freist\"uhler and Zumbrun, was shown to fail to imply Lopatinski stability, even for systems with convex entropy. This observation bears also on the parallel question of existence, at least for small $BV$ or $H^s$ perturbations, Comment: to appear in Proceedings of the AMS

In order to recognize outstanding papers that have been published in Symmetry, the Editorial Board established an annual “Symmetry Best Paper Award”. We are pleased to announce the first “Symmetry Best Paper Award” for 2015. Nominations were selected by the Editorial Board Office, with all research articles published in 2013 and 2014 eligible for consideration. Following review and voting by the Symmetry Best Paper Award Committee, the following three papers have won Symmetry Best Paper Awards for 2015

This study aims to investigate plane geometry problem-solving strategies of prospective mathematics teachers using dynamic geometry software (DGS) and paper-and-pencil (PPB) environments after receiving an instruction with GeoGebra (GGB). Four plane geometry problems were used in a multiple case study design to understand the solution strategies developed by 2 prospective teachers. The results revealed that although the participants mostly used algebraic solutions in the PPB environment, they preferred geometric solutions in the GGB environment even though algebraic solutions were still possible (the software did not preclude them). Furthermore, different proofing strategies were developed in each environment. This suggests that changing the environment may prompt students to seek for additional solutions, which, in turn, results in a deeper understanding of the problem. As such, using both environments simultaneously in solving the same problems appears to bring about important benefits.